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Journal - Gorman Chat: Maria Angelico \| Gorman Online Fresh and independent, Gorman is Australian fashion designed with the local lifestyle and culture at the forefront. With a strong focus on in-house textile design and artist collaborations, Gorman offers unique, colourful, fun and exclusive prints across a broad range of contemporary and classic shapes. Gorman Chat: Maria Angelico 24 May 2019 10:17:18 am Story by: Lisa Marie Corso Photographer: Amelia Stanwix Maria wears: Eva Blouse (shop) + Gingham Polo Top (shop) + Eva Pant (shop) Maria Angelico Actress, Writer, Creator In show business there are triple threats. These are the people who excel at, you guessed it, three things or more. It's easy to feel intimidated by these folk who emanate talent from their pores but not when they're as nice and down-to-earth as actress, writer and creator Maria Angelico. For this Melbourne-based creative becoming a performer was a no brainer, it's in her DNA. Her parents met in a touring cabaret and Maria has been wooing audiences since she was a youngin'. She loved the thrill of being in character so much she confesses that as a child she "used to sometimes go to sleep wearing a clown nose!" Now an adult, Maria's ditched the clown attire for professional acting roles full-time. She's an onscreen regular, with filming beginning next month on Cate Blanchett's new tv series 'Stateless', having recently played a leading role in Sisters (which is currently streaming on Netflix), and with appearances on Glitch, Mr Black and The Inbestigators airing this year, while developing her own projects. We recently caught up with the actress in her Carlton North home with her Australian Shepherd accomplice Peta, to chat about how to go after the career you want with gusto, telling your own stories and organising hypothetical dream alfresco dinner parties with her favourite celebrity couple, Goldie Hawn and Kurt Russell. Hi Maria, let's go back to the almost beginning! When you were young was there a feeling you'd end up an actor? I knew it from day one! I used to go sometimes go to sleep wearing a clown nose. Both my parents are performers and I was always singing and dancing at home, it came very naturally to me. I recently found one of those old Groovy Chick diaries from when I was little and inside I had written: "When I grow up I will be an actress or a fashion designer." So your family definitely had an influence on your creative career path? Definitely. I was raised by mum but both my parents were performers. They met in a cabaret and toured the world where they lived on a house boat in Amsterdam before I was born. My mum's name was Peaches and she was also very encouraging, almost too encouraging, and was always like "you can do whatever you want", which gave me enormous confidence. I did a lot of school plays and stuff but it wasn't until I started getting my first proper roles that I took acting more seriously. One of your first prominent TV gigs came while you were still at high school, when you starred in the ABC comedy We Can Be Heroes. What did you do in the audition to nab this role as a 16-year-old? It was actually an improvised audition and you could bring a friend, so I brought my best friend then (and now) Adrienne Smith. We were going for the role of two high school girls and in our audition we just flipped through a trashy gossip magazine while making comments and got the job! After school you briefly took a break from acting to pursue fashion before seguing back into acting, this time, full-time. What prompted you to give acting your full attention? I was making jewellery and did a collaboration with a local label, which allowed me to do fun stuff like go to fashion week. It was during this period that I got a small guest role on Rush. I was only on set for two days but just fell in love with it and thought this is what I want to be doing and then got really serious about making my acting career become more viable. My mum had passed away during this time and I think that kind of put things into perspective for me, that you need to go for what you want in life, so I studied acting in Melbourne and New York. Maria wears: Green Fingers Linen Pantsuit (shop) + Gingham Polo Top (shop) + Loretta Loafer (shop) A little while after you wrote and starred in your own web series Movement. How did this come about? After I returned from overseas, I moved out by myself to Elwood and had a lot of reflective time. My friend Rhys Mitchell actually encouraged me to write something but I was unsure if I wanted to pursue something other than acting. It was when he said I couldn't use his pool until I wrote something for myself (he lived around the corner from me) that I started writing. Initially it was more as an exercise but then something clicked in me and I discovered I really loved writing and Movement came from that. We eventually got it made with myself and Rhys starring in it and with our friend Jess Barclay Lawton directing. We ended up taking it to Tribeca Film Festival in New York where I actually wore a Gorman geology print dress to the screening. It was exciting and real whirlwind. How do you feel making your own content opened you up to further opportunities in the industry? I think I already had a good reputation in the industry as an actor but as a result of Movement I think people saw me in a potentially different light and I got a lot more feedback. One of the big things that happened shortly after Movement was that producer Imogen Banks wanted to meet with me and have a chat. I thought she was possibly interviewing me for something but wasn't sure. Six months passed and nothing happened, then one day I got a call saying Imogen had created a show and she had me in mind for one of the lead roles. The show ended up being Sisters! It taught me everything you do has a ripple effect and you just don't know what impact the things you do now might have further down the track. Working as a woman in the film industry what have you noticed about the opportunities for women today compared to 10 years ago? I feel we have a long a way to go particularly in Australia and still find we have to prove ourselves more than men. There's still that idea that if 'she' doesn't do a great job in this, it might be her last chance, which I don't feel is equal to men's experience. On the flipside, I do feel at the moment people are hungrier for female creators and stories, which is exciting. This differs to a few years ago where you'd have to have so many credentials before you could even get your foot in the door. If you could cook dinner for any actor or writer living or dead – who would it be and why? And what would you cook? If I could get a combo deal it would be Goldie Hawn and Kurt Russell. I feel like they'd be a good time, we might play a parlour game and things would get a bit loose. I'd cook something interactive, maybe tacos or a Moroccan multi-dish, and serve it alfresco for sure. Your go-to 3pm pick up snack? I'm a big snacker! Popcorn never fails but I'm currently bringing back nostalgia snacks like sliced apple and cheese for some real little lunch vibes. Any podcasts you've been loving recently? I'm also a big podcaster! I'm currently alternating between Oprah's SuperSoulSunday, Elizabeth Day's How To Fail and for some laughs Seek Treatment with Cat & Pat. How do you think wardrobe can bring a character's personality visually to the screen? I think wardrobe can sometimes unlock a character's personality. For me as an actor I feel wardrobe is super important as it impacts how I carry myself, even subtle things like the pair of shoes a character wears can say a lot. As an audience member I think wardrobe is also super integral, I can really get pulled out of a show if a character is wearing something that doesn't feel like them. What's your daily wardrobe involve? I'm so big on colour I often worry I'm edging on clown territory (which I am okay with). I'm also a mood dresser and express myself with my clothes. I've recently also got into the habit of letting my boyfriend choose my outfits when I'm a bit tired – it's low risk because I bought all of my clothes – but he does choose some interesting combos I never would have thought of that get lots of compliments. I'd definitely recommend letting your partner choose for you! And lastly, how would you describe Gorman to a friend? You know something's Gorman when you see it and wearing makes you feel like you're taking care of yourself without taking yourself too seriously. Instagram: @mariagloriagraceangelico Posted in News By Chevon Oakley Comments are Closed for this post	{ "redpajama_set_name": "RedPajamaCommonCrawl" }	1,783
Table of Contents Title Page Copyright Page Dedication PART ONE - Exile from Eden One Two Three Four Five Six Seven Eight Nine Ten PART TWO - Lilith's Blade Eleven Twelve Thirteen Fourteen Fifteen Sixteen Seventeen Eighteen Nineteen Epilogue Ace Books by Dianne Sylvan PRAISE FOR QUEEN OF SHADOWS "Sylvan's powerful debut is packed with startling action, sensual romance, and delightfully nerdy vampires . . . [Her] compelling take on vampirism, her endearing characters, and a complex, unabashedly feminist plot will have readers hungry for a sequel." — _Publishers Weekly_ (starred review) " _Queen of Shadows_ pulled me in . . . Dianne Sylvan's rich, dark, sexy reimagined Austin is filled with people I want to visit again and again . . . Sylvan's got voice, doesn't miss a beat, and rocks it all the way to the last note. Sit down. Shut up. And enjoy the show. It's intense, dark, sexy, with just the right touch of humor. Looking for a new addiction? Go no further." —Devon Monk, author of _Dead Iron_ "Grabbed me on the first page and didn't let go. Miranda, the heroine, is vulnerable and gutsy, with magical abilities even she doesn't suspect. Vampire David Solomon is as powerful and heroic as he is deliciously seductive. Dianne Sylvan has created an original take on vampires that I thoroughly enjoyed, and I'll be looking for her next book with great anticipation. She's a skilled and talented storyteller who definitively knows how to deliver one hell of a book!" —Angela Knight, _New York Times_ bestselling author of _Master of Shadows_ "Dianne Sylvan is an incredibly talented writer. She draws the reader not only into the story but into the very marrow of someone who is starting to question [her] grip on reality. If you aren't familiar with the Austin area, you will be once you turn that last page . . . _Queen of Shadows_ concludes with a great flourish, leaving the reader euphoric." — _Sacramento Book Review_ "It's not hard for me to pinpoint why _Queen of Shadows_ works so well for me. There [are] three reasons, actually. One, Miranda doesn't just suddenly overcome her fears. Two, David is honest about who he is [and] what he has done, and doesn't expect anything more from Miranda than a safe recovery. And three, the soul mate/destined-for-oneanother principle works here in a believable way." — _Night Owl Reviews_ "Well written . . . The relationship between the empath and the vampire makes for a strong Shadow World thriller that will enthrall the audience with a sense of awe, as supernatural Austin comes across [as] realistic through the filters of the flawed lead protagonists." — _Alternative Worlds_ "My favorite book of 2010 so far . . . Moving, well written, suspenseful, and sensual, this is a novel you won't want to miss." — _Fantasy Literature_ "Miranda's character is a treat as she moves from victim to self-possessed, capable heroine . . . The supporting characters are equally well developed, providing a sense of weight and history to this thoroughly entertaining take on paranormal romance." — _Monsters and Critics_ "Plucked at my heartstrings in a smooth rhythm of fear, mistrust, and love . . . Watching the romance between Miranda and David develop was a treat. Watching Miranda become a true warrior woman was the icing on the cake." — _Bitten by Books_ " _Queen of Shadows_ will make the reader feel. Feel the emotions of the characters and their own emotions . . . a perfect 10. Highly recommended." — _Romance Reviews Today_ _Ace Books by Dianne Sylvan_ QUEEN OF SHADOWS SHADOWFLAME THE BERKLEY PUBLISHING GROUP Published by the Penguin Group Penguin Group (USA) Inc. 375 Hudson Street, New York, New York 10014, USA Penguin Group (Canada), 90 Eglinton Avenue East, Suite 700, Toronto, Ontario M4P 2Y3, Canada (a division of Pearson Penguin Canada Inc.) Penguin Books Ltd., 80 Strand, London WC2R 0RL, England Penguin Group Ireland, 25 St. Stephen's Green, Dublin 2, Ireland (a division of Penguin Books Ltd.) Penguin Group (Australia), 250 Camberwell Road, Camberwell, Victoria 3124, Australia (a division of Pearson Australia Group Pty. Ltd.) Penguin Books India Pvt. Ltd., 11 Community Centre, Panchsheel Park, New Delhi—110 017, India Penguin Group (NZ), 67 Apollo Drive, Rosedale, Auckland 0632, New Zealand (a division of Pearson New Zealand Ltd.) Penguin Books (South Africa) (Pty.) Ltd., 24 Sturdee Avenue, Rosebank, Johannesburg 2196, South Africa Penguin Books Ltd., Registered Offices: 80 Strand, London WC2R 0RL, England This is a work of fiction. Names, characters, places, and incidents either are the product of the author's imagination or are used fictitiously, and any resemblance to actual persons, living or dead, business establishments, events, or locales is entirely coincidental. The publisher does not have any control over and does not assume any responsibility for author or third-party websites or their content. SHADOWFLAME An Ace Book / published by arrangement with the author PRINTING HISTORY Ace mass-market edition / August 2011 Copyright © 2011 by Dianne Sylvan. All rights reserved. No part of this book may be reproduced, scanned, or distributed in any printed or electronic form without permission. Please do not participate in or encourage piracy of copyrighted materials in violation of the author's rights. Purchase only authorized editions. For information, address: The Berkley Publishing Group, a division of Penguin Group (USA) Inc., 375 Hudson Street, New York, New York 10014. ISBN : 978-1-101-52927-0 ACE Ace Books are published by The Berkley Publishing Group, a division of Penguin Group (USA) Inc., 375 Hudson Street, New York, New York 10014. ACE and the "A" design are trademarks of Penguin Group (USA) Inc. <http://us.penguingroup.com> _To Red, who opened the first door, and to Meredith, who opened the second_ PART ONE Exile from Eden One Autumn that year came in like a lion and devoured the last few straggling moments of an endless, scorching summer. Storms swept through central Texas and scoured the world clean of dust and dried grass. The entire city seemed to come alive once the burden of heat was lifted. The nights were already chilly the first week of October when the last known member of the Blackthorn gang sprinted in terror through the streets of Austin, searching for someone, anyone, who would shelter him. Door after door slammed in his face. No one in the Shadow World was stupid enough to take him in . . . not tonight. Bars closed early, windows went dark, and the wind's icy fingers snatched all hope of escape from the city's empty streets. Only a fool would look outside tonight. Only a fool would get involved. The Signet was on the hunt. Desperate, he ran for the heavily populated areas of downtown, hoping to get lost in the mortal crowd, unaware that across the city his low body temperature and preternatural speed were being tracked by a bank of computers that sent out his coordinates every five seconds. There was nowhere he could go now without a target flashing on his every move. "Status report." Faith's voice was fierce even through the digital ether. _"Rabbit is approaching the eastern corner of Fifth and Trinity. Move to intercept?"_ From her perch atop the restaurant across the intersection, the Queen of the Southern United States watched the streets with her eyes narrowed, sweeping the area with her senses. She stood with one foot up on the low wall around the roof's perimeter and held her hair back out of her face with one hand. Her breath came in smoky clouds, slow and calm, as she waited, patient, unhurried. Human traffic was high even for a Thursday. Their quarry had no doubt come this way precisely for that reason, believing that the Elite wouldn't want to cause a scene. "Hold your position," she replied into her com just as a thin shape darted around the corner, weaving his way among the people on the sidewalk, trying not to look like he was on the run. He crossed Trinity against the light, narrowly avoiding a bus, intent on reaching the side nearest her, which was far less busy, darker, and located conveniently near an underground access point. She let him cross and waited. Finally, when he thought he might be safe and slowed his pace, she vaulted over the side of the building. The air rushed past her for two stories, and she twisted in midair to land, her boots striking the pavement solidly. She straightened, tossing her hair back over her shoulders, the wind catching her coat and whipping it back to expose her throat. When the rabbit saw what was around her neck he froze and went ghostly white. He spun around to run back the way he had come, but he was surrounded. Behind him Faith crossed her arms and smiled. He faced Miranda an inch away from panic. "Would you like to beg?" she asked. Mindless survival instinct gripped him and he threw himself at her, snarling. She laughed, stepped to the side, and caught him in the face with a fist. He landed sprawling with an animal cry of fear and pain and scrambled back to his feet, trying to gain some kind of advantage when there was none to gain. He took a swing at her, and she blocked it easily, twisting to punch him in the gut and again in the head. He stumbled but didn't fall; he was no weakling, though it clearly surprised him that she wasn't either. Obviously he hadn't listened to the whispers that had rolled slowly through the Shadow World like an oncoming storm for the past three months . . . or he'd heard the stories and dismissed them, as no mere woman could be so strong. He was learning differently now. She ducked another hit, this one more reckless. His fear was beginning to show. She liked that. She spun around and kicked him in the head, and he went down but immediately forced himself back to his feet despite the blood flowing from his nose and mouth. He was clearly dazed, but desperation drove him to try again and again, only to be beaten back by a laughing Queen who hadn't even broken a sweat. There were humans nearby, approaching from the east. Distractedly she bent her will toward them and gave them a mental nudge to turn left instead of right. By the time they realized they were headed in the wrong direction, there would be nothing to see. She moved closer to the rabbit until she was only a few feet from him, allowing her power to swell around her. He let out a whimper and fell back. "Kneel before your Queen," she hissed. He dropped to his knees, sobbing incoherently in her shadow. "A fine display from a man who killed two of my Elite during the war," she said. "You were a key player in the gang, Jackson. We know who you are and have a list of your crimes. You've eluded capture this long only because you hid like a coward while your friends died in your place. But not anymore." At the sound of her sword being drawn from its sheath, Jackson fell down on his elbows, clapping his hands over the back of his neck. Now he decided to beg; he blamed the others in the gang, especially Ariana and Bethany Blackthorn, for forcing him to kill. He wasn't responsible, they were; he was only following orders. She'd heard it all a dozen times in the last few months, and she knew every time, as she did now, that it was a lie. "You disappoint me," she told him. "Worse? You bore me." She kicked him again, this time in the side, so he instinctively moved his arms down to protect his stomach and left his neck exposed. With a single graceful swing she beheaded him and leapt back in time to avoid the gush of blood that bathed the sidewalk scarlet as his body toppled over. Dark, grim satisfaction warmed her as the body twitched into stillness. The head had landed faceup, its eyes gaping open in shock, mouth slack. She leaned down, seized the edge of Jackson's jacket, and used it to wipe her sword before sheathing the blade. She would need to clean it thoroughly when she got home; Sophie had taught her never to let a blade go to rest still bloodied . . . not to mention that the sword itself had once belonged to Sophie, and Miranda could practically hear the diminutive vampire's acerbic voice every time she was tempted not to treat the weapon with the respect it was due. She looked up at Faith, who was smiling ferally. "Cleanup on aisle three," Miranda said. Faith gestured to the rest of her team. They knew the procedure: Take the body and the head up on the roof of a nearby building where it would be exposed to the sun at dawn but not likely found by any passing mortal. Tap into the hydrant nearby to spray off the blood. Hopefully after tonight it would be the last time they'd have to go through the routine for a while. She stood watching for a moment while they worked, and Faith joined her. "You're getting disturbingly good at this kind of thing," the Second said quietly. "I'm still not used to seeing it." Miranda smiled. "What's even more disturbing is that I'm not disturbed at all." Faith shrugged. "I recall you saying that first night: This is your work now." The Queen thought back to the battle at the Haven and the long night of cleanup and casualties that had followed. Faith had wanted her to go and rest. She had declined and instead stepped into her role without hesitation, organizing the Elite to burn the dead and patch up the wounded, leaving the Prime to restore the network and deal with the damage to the building itself. It had been nearly sunrise before either of them had stood still. "Where is our Lord and Master tonight?" Faith asked. "Shouldn't he have been out here, too?" "No," the Queen replied, eyes on Jackson's headless corpse as two Elite maneuvered it onto a plastic sheet to carry it away. "He had an appointment. It's best if I handle this anyway—I want my presence known." "I think you've succeeded there." Faith nodded toward the scene. "We've got this if you need to go." "Good. I'll see you back at the Haven. Have the night's final report on the server before you code off shift." Faith bowed to her, as did the others. Miranda nodded, then turned and walked off into the darkness. The standoff took place in a back corner booth at Kerbey Lane Café. A woman with a shaved head and multiple facial piercings stared down a blue-eyed man in a long black coat as he drank a Corona with lime and she ate a plate of black bean nachos. Around them the café bustled as always, the patrons blessedly ignorant of what might be unfolding among them. They could have been any two people—albeit an odd couple—on a date getting to know each other over Tex-Mex. "So . . . you're a vampire." He gave her a measured nod. "And you're officially the most badass vampire in Texas." "The Southern United States, yes." Kat stared at him hard, and he couldn't help but be impressed; she wasn't afraid of him, at least not yet. Most humans could feel something of what he was, and it made them uneasy. Either she couldn't feel it, which made her as dumb as a bag of hammers, or she was strong enough to stand her ground. His money was on the latter. He knew he could terrify her if he wanted to. All he had to do was let his shielding slip or will his eyes to silver or his teeth to extend. He could fix her with a certain facial expression—that of a panther watching a deer from a tree overhead—and she would instinctively seek an escape, any escape. He didn't do any of those things. This was too important for such childish play. For the first time in a long time, David Solomon had something to prove besides how frightening he was. "You turned my best friend into a vampire," Kat said, her stare unwavering. "Why should I have anything to do with you?" "Because you care about her," he replied reasonably, "and you know that I'm not going away." "I know this story," she told him. "Hot mysterious guy sweeps in right when she needs someone, isolates her from her life, pulls her into something dangerous. You know how those things end up? In bruises and hotline phone calls. Restraining orders. Best friends with concealed handgun permits showing up at the guy's house and shooting his balls off." He looked down at her messenger bag. "Let me guess . . . a Sig P232?" "Not the point, Count Pretty Boy." Her eyes narrowed. "Although, if I shot your balls off, would they grow back?" David smiled. "I think you and I are going to get along fine, Kat." "Speak for yourself. Tell me what makes you the kind of guy that deserves Miranda." "I don't," he said. "But she and I are bonded and will be so until our death. Nothing can change that now. She's stuck with me . . . and so are you, if you want to keep her friendship, and I sincerely hope you do." "Why?" "Because she's going to need you. In some ways she's as old as I am, but in others still so young . . . she still has ties to the mortal world that she wants to hold on to. Whether that proves possible will depend on the kind of support she gets from that world, namely you." "Then you're saying I'll help keep her human." "No." He sat forward, holding her gaze. "She isn't human, Kat. She never will be again. One day she'll watch you grow old and die, and she'll stay the same, ageless, eternal, until someone murders us both. What she is, is your friend, and the fact that she wants to stay your friend despite the pain inherent in loving a mortal speaks very highly of you. You should be honored." Kat nodded slowly, almost smiling. "So should you." "I am." She nodded again, and then said, "You're buying, right?" "Absolutely." "Then let's talk about dessert." Five minutes before curtain—just as her agent, Denise, was about to have a coronary—Miranda Grey strode into the club with her hair tangled from the wind and her eyes bright with the thrill of the hunt. She could hear the crowd on the far side of the stage, one low murmur of three hundred voices, their collective expectation a living thing crawling up the walls. She took the flight of metal stairs up to the wings with a grin on her face and drank in their emotions on a single deep breath. She gave Denise a thumbs-up. Denise made a foreheadwiping motion of exasperated relief in return. Flipping her hair back and shrugging her coat into the tech's hands, Miranda turned toward the stage manager and nodded. A hush fell as the house lights lowered and the spotlight trained on the mike and the single object behind it: her guitar, on a stand, gleaming black. Applause erupted when they saw it. Miranda smiled and walked out into the light. There were three things that Miranda wanted after every show: blood, chocolate, and a hot shower. Before she could have any of those, however, she had to get backstage and run the press gauntlet, then somehow sneak out the back to either drive herself or wait for Harlan to take her somewhere more private to hunt. There were a great many vehicles at the Signet's disposal, but the one the Prime favored was the Town Car that Harlan piloted through the city streets; if he and the Queen needed to be in separate places or ran on different schedules, as often happened these days, they had to coordinate Harlan's trips or, as she preferred, she had to bring her own car into town. Although David had serious misgivings about her being alone in the city, Miranda loved her car, and she loved taking the winding road that led up to the Haven through the Hill Country. She liked being independent. So most nights after she was finished at her gig and had found herself someone for dinner, she slid behind the wheel of her little silver Toyota and took Loop 360 out of town. She was almost ready to escape the club's heat and noise when Denise knocked on the dressing room door and said, "Hey, do you have a minute?" "Sure," Miranda called, double-checking that the mirror was still covered with a towel. "What's up?" she asked, gathering her sweaty hair back out of her face and securing it with a stretchy band. Denise MacNeil was a strikingly beautiful black woman who radiated competence and confidence, two things that Miranda had discovered were vital for a woman in the music industry. Denise carried herself like a warrior, and in fact she reminded Miranda strongly of Faith, except instead of a sword Denise was armed with a briefcase and BlackBerry and hunted opportunities, not lawbreakers. Miranda would have continued to play the bar circuit without much thought if Denise hadn't come along, but in the short time she'd been the Queen's agent she had already set the wheels in motion for a recording contract and doubled her bookings. It would have been easy for someone so ballsy to be a bitch, but Denise still had a warmth to her that seemed to bring her even greater respect. "There's a woman here from the _Statesman_ who wants an interview for their weekly entertainment supplement," Denise was saying. "Nothing drawn-out, just a few questions. Are you up for it?" Miranda sighed. She had played hard, and worked hard, holding the audience's attention pretty easily, but it was still draining, and she hadn't fed tonight. Her teeth were starting to ache and her insides felt like they were drying out. She took a quick internal inventory and judged she had about half an hour before things got unpleasant. "Sure." "Great. Also, don't forget next week we have a meeting with the guys over at the Bat Cave." "Got it." Denise grinned at her. "And one other thing. They have these weird little devices now that you can talk into so your voice comes out the other end—that way if you're going to show up, say, two minutes before curtain, you can keep your agent from pissing her designer pants." Miranda smiled back. "Not once have I ever been late," she pointed out. "But I'll try not to cut it so close next time." Denise shook her head and left, saying, "I've been in this business fifteen years and I've never adjusted my watch to Musician Standard Time." Miranda closed her guitar into its case, running her hand along the Martin's gleaming neck. "That's Vampire Standard Time," she said quietly to the instrument, "but we won't tell her that." A moment later, there was another knock, and a woman poked her head into the dressing room. "Ms. Grey?" Miranda looked up from her phone, where she was checking to ensure there were no texts waiting from the Haven, and gestured for the human to enter. The reporter was completely average looking, with mousy brown hair in a rather severe cut with bangs and glasses that made her look like a librarian. She was wearing a nondescript suit a year or two out of style and was clearly nervous. "I'm Stacey Burnside with the _Austin American-Statesman_ . Denise said you had a moment for me?" "Come in," Miranda said with a smile. Her Signet had come with a set of new and strange instincts, one of which was to put humans at ease whenever possible; she felt almost maternal toward them, especially the awkward young women so unsure of their place in the world who could barely make eye contact with the glamorous rising star who seemed to have it all. "Have a seat." Stacey almost knocked over the folding chair as she sat down and rummaged for her recorder. Miranda could sense the experience of an educated reporter—and Stacey was no amateur, she could feel that much—warring with awe. Miranda got that a lot . . . at least, from humans. She was trying to get used to it. "I won't keep you long," Stacey said, fiddling with her digital recorder until a red light came on. "We're just doing a piece this week on emerging artists who do their recording here in Austin." "Well, I'm happy to support the local music scene," Miranda told her, taking the other folding chair and crossing one leg over the other. She had her coat on, but her Signet peeked out from her collar, and she caught the young woman staring at it for a moment. That also happened a lot. Most of the time people had the same look on their faces: _Is that thing glowing?_ "Austin has been very good to me since I started performing," the Queen added. "I'm hoping to work with the guys at the Bat Cave on my upcoming CD." Stacey pushed her glasses back on her nose. "That's the studio founded by Grizzly Behr, the father of Mike Behr of Three Tequila Floor, right?" "Yes." "I hear it's impossible to get into the Bat Cave these days." Miranda smiled. "They were as excited about the prospect as I was." The music business was all about influence . . . and Miranda had that in spades. There was no door that was closed to her, no velvet rope to keep her out no matter how exclusive the club. The Signet held sway in every level of government and the Prime a hand in every game in town, legal or otherwise. It wouldn't take much effort to have her first single on the _Billboard_ charts the day it was released. She didn't want that. She had every intention of making it on her talent . . . but she wasn't so naïve as to think the industry cared about talent as much as it cared about power. She was quite willing to kick down the door to success with one of her brand-new knee-high boots. "You recently debuted a new song, 'Bleed,' " Stacey said. "Critics are having trouble categorizing it—what influences gave rise to its sound and lyrics?" Miranda toyed with her com, considering her answer. "It's a deeply personal song," she replied. "The lyrics were some of the first I wrote after a particularly difficult time I had last year. I felt that the shift in tone, from pain to triumph, was something that would resonate with audiences. It definitely has the feel of an early Tori Amos track, but the studio version will have more electronic elements. The vision we have for the album as a whole is a lush, dark sound that still leaves room for the rawness of some of the lyrics." "You tend to play your personal life close to the vest. Recent rumors have you married—is there any truth to that?" She smiled. "Yes, actually." She held up her left hand, showing the platinum band around her finger. "I've been married for about two months." Stacey's eyes lit up—a scoop! "Can you tell me anything about your husband?" "Oh, I could tell you a lot of things, but he's a very private person, as am I. I will say that meeting him absolutely changed my life, and that we make a perfect pair." "Do you live in the Austin area?" "Yes." "In the city itself, or a suburb?" Miranda chuckled. "In the area." She checked her watch, rose, and said, "I'm sorry, but I do need to head home." "One more question, please, if that's all right?" She looked so eager Miranda couldn't help herself. "Fire away," she told the woman as she folded her chair and leaned it back against the wall. She tried to leave things tidy for the band that came in after her, though they rarely saw fit to return the favor. Stacey reached into her bag again and dug around for something. "Um . . . hang on . . ." Miranda refrained from rolling her eyes, but the gnawing feeling in her stomach was starting to become a serious issue. She was still learning to manage her hunger; unlike skipping a meal back when she was mortal, waiting too long to feed could impair her judgment and lead to unfortunate incidents . . . and had, more than once, the first few weeks. If David hadn't insisted on hunting with her for a while, she might have killed someone. She had an emergency pack in her car, kept safely on ice in the trunk, but her car was a block away and there were usually people milling around outside so she couldn't just pop it open and slurp it down. "Okay," Stacey said, straightening. Miranda noticed she had something in her hand, something metal with the flash of wood— "How stupid are you for being caught without a bodyguard?" Stacey asked, and lifted her hand. Miranda's body reacted before her brain could register what was happening; she threw herself backward as the gun went off, twisting sideways a split second before the stake bit hard into her shoulder. The impact threw her backward into the wall, and she snarled, springing forward toward the woman, who had already turned on her heel and bolted from the room. Miranda missed Stacey by mere inches and flung herself after the woman, her vision gone scarlet with rage; Stacey sprinted through the narrow backstage passageway, knocking people over as she ran. Miranda snaked through the crowd, ignoring the pain and the feeling of blood running down her torso. She heard gasps behind her as she closed the space between herself and the would-be assassin, but Stacey reached to the side and hauled a stack of speakers on wheels out behind her to block Miranda's path. The Queen kicked them out of the way and resumed her pursuit, but by the time she burst out the backstage door there was no sign of Stacey, no sign of anyone; the alley was empty. "Goddamn it!" Miranda snapped to the empty air. Immediately, the alert on her com went off. _"Emergency team to Mel's Bar and Grill, code Alpha One!"_ she heard Faith's voice command in broadsend-mode, then, _"Star-two, Star-two, Miranda, are you all right?"_ Miranda took a deep breath. "Star-three, this is Star-two, and I'm fine. I'm injured but not severely. A woman posing as a reporter staked me in the shoulder. She had some kind of spear gun. I lost her but I'm heading out to track her now—" "Like hell you are," came a voice. Miranda turned in time to see the shadows beyond the edge of the building grow dense and coalesce, the substance of the night twisting on itself, resolving into the shape of a man in black with a glowing stone at his throat. The Prime was at her side in seconds, and the look on his face, though extremely attractive to her, would have made a human's blood run cold. "What happened?" he asked, taking hold of her shoulders. When he saw the stake he hissed and his eyes went silver. "It's not bad," she insisted. "If we hurry, we can still—" "You're hurt," he replied tersely. "That takes priority. Now, hold still, and brace yourself . . . take a deep breath in . . . now breathe out slowly . . ." She did as he said, and on the out breath, he took hold of the stake and pulled it. Miranda cried out; she felt the wood sliding through her muscles as if every splinter of the stake were jagged and tore the flesh around it. It was as if the wood left behind something oily and poisonous that seeped into her body and stole her strength away. Her vision swam, and she sagged into the Prime. "Oh, God . . ." "Easy, beloved," he said, considerably more gently. "Easy. Close your eyes . . . breathe." Miranda clamped her eyes shut and dragged her awareness to the feel of his hands on her arms, the sound of him breathing, the rhythm of his pulse that she could feel, always, beating in her own veins. She felt him drawing power up out of himself and feeding it along the connection between them, and her shoulder grew unbearably hot for a moment, then itched horribly before fading into numbness. When she opened her eyes the wound was gone, though there was a gaping hole in her coat. "Shit," she murmured. "I love this coat." With that, she passed out, thankful he was there to catch her. Faith managed, somehow, to keep David from tearing the building apart in search of the attacker, but it wasn't easy. The half-dozen Elite who reported to the scene were obviously frightened by his anger. Who wouldn't be? A black cloud of seething energy surrounded him as he stood cross-armed and watched the team sweep the club for evidence and another team followed the fading traces of the assassin's flight. The few humans who were aware of the situation had no idea what they were really dealing with, but they knew Miranda had been attacked and that her security personnel were handling it. The look on her husband's face was enough to keep everyone, human or otherwise, at a distance. She joined the Prime once the team had things in hand and took her usual place at his side—his left, as the Queen's place was his right. The Queen herself was unconscious in the car. "This is unacceptable," David said darkly. "She is not to go anywhere without a bodyguard. Understood?" "Fine by me, Sire, but you'll have a hard time convincing her of that." "I'll have her followed if I have to." Faith merely nodded. She had already learned not to take sides. "Aside from the stake itself, which we'll bring in for analysis, there's nothing," the Second said. "No one has any recollection of what this woman looked like, except of course for the Queen. Somehow the bitch managed to convince Miranda she was human, and that's . . . disturbing." "Agreed." "Best guess, she was a vampire with a hell of a shield, but there's no way to know for sure." "Here's a better question," David said. "Forget what she was and let's ask ourselves _who_." "Obviously it was a planned hit. She had fake press credentials and even a dummy phone number. I'll put out feelers for anyone buying an ID by that name, but I doubt we'll get anything." Faith nodded to Elite 33, who was carrying Miranda's bag and guitar out of the club to the car, and asked the Prime, "Didn't the network register something was wrong?" David's expression went from dark to hellfire. "Interestingly enough, no. There wasn't even a blip." "How did you know to call us here, then?" "I felt the stake." His eyes were fixed on the car at the end of the alley. "Either the attacker was human and faster on her feet than a Queen, or she was a vampire who somehow doesn't show up on the network. I don't like either of those possibilities, Faith. I'm counting on you to find this person and bring her to me." Faith didn't mention how difficult, if not impossible, that would be. The Elite had expert trackers, but so far the team had come up empty-handed; this woman had vanished into the crowded city without leaving a single footprint or energy trace. Even the strongest psychic they had—Miranda—had lost her, though if she hadn't been injured chances were the Queen could have hunted the woman down in minutes. A planned attack. Specific, focused . . . which led Faith to believe that this Stacey had known exactly who and what she was trying to kill. The Shadow World was aptly named; very few humans knew of its existence, and few vampires would associate with the human world enough to connect Miranda Grey the singer with Miranda the Queen. Even fewer vampires would be stupid enough to go up against the Signet after the example that had been made of the Blackthorn. Someone had known that Miranda would be alone—if she'd had even a standard Elite security detail, the guards would have been right outside the door to block the assassin's escape. Harlan appeared at the Prime's elbow. "Sire, the Queen is asking for you." David nodded to Faith, who followed him to the car, where Miranda was sitting with the door open, looking disheveled and seriously pissed off. The Queen's Signet was glowing brightly and there was dried blood all over her coat and jeans and some in her hair. Her heart-shaped face held a look even scarier than David's had. She looked up at her mate and spoke very deliberately. "Blood. Shower. Chocolate. _Now._ " David actually smiled, bowed, and said, "As you will it, my Lady. Harlan, start the car. Faith, finish up here and have a report on my server ASAP. I'd like you to drive the Queen's car back to the Haven yourself when you're done. I want a full patrol sweep of the city with a description of the suspect—have the description sent to APD as well, just for laughs. Also, inform the owner of this establishment that he will need to double security for all of her shows; money is no object. I want a short list of bodyguard candidates by morning." "Yes, Sire." He met her eyes. "This doesn't happen again, Second." Faith bowed. "You have my assurance, Sire." He gave her a nod, then got into the car with his Queen, and a moment later they were on their way back to the Haven. Miranda wanted to punch someone, but she settled for sinking her teeth into someone's throat. Blood, hot and salty-sweet, flowed into her mouth, filling the sandpaper emptiness in her belly and veins, soothing the need to claw and kill. She drank deeply, her hand wrapped around the woman's neck to hold her still, her power wrapped around the woman's mind to keep her calm. The girl was a jogger, very healthy, her heart rate up so her blood was fully oxygenated. She tasted faintly of coconut, meaning she'd probably had Thai at her most recent meal, and her skin had the warm scent of youth and raspberry body wash. Miranda released her, holding her steady for a moment while her awareness returned but impressing strongly on her mind that nothing out of the ordinary had happened. She'd been out for a jog and tripped. "Are you all right?" Miranda asked her, giving her voice silvery tones of concern. The girl blinked. "Um . . . yeah. I guess I tripped." "You should get home. It's late." "Yeah. Thanks." The girl pushed her earbuds back in place and started her iPod again; Miranda heard the Black Eyed Peas as she ran away. The wound in her neck would close by morning, leaving what looked like twin mosquito bites, and those would be gone a few hours later. The stronger the vampire, the faster the bite healed; it was usually the young and weak who were discovered because they were unable—or too stupid—to cover their tracks. Relief moved through Miranda's body and she sighed, rolling her head to the left and right before turning back to the car where her Prime was waiting for her. She knew that look. He always got it when he watched her hunt. Deliberately, Miranda licked her lips and smiled. Prime and Queen stared at each other for a long moment before she walked back to the car, stepping into his arms and kissing him hard. He made that purring noise she loved and pulled her against him, letting her suck on his tongue and dig her nails into his shoulders, the contact banishing the last of the lingering anger from the attack and replacing it with an entirely different kind of intensity. Still, the events of the night had drained her, and she eventually drew back and laid her head on his chest, eyes closing. "That was stupid," she muttered. He didn't say anything, but of course she knew what he was thinking; he had protested her desire to go anyplace alone for months now, insisting that something like this would happen the second she let down her guard. She felt guilty—it wasn't just her life she was gambling with by traipsing around the city by herself. If that stake had hit true, if her reflexes had been slower, they would both be dead now. And whoever it was, having failed, might very well try again. "Let's go home," he said softly. She nodded and sank back into the car, leaning on him after the door was shut and they were on their way again. "All right," she said. "You win. Bodyguards it is. But they can ride in their own damn car." He put his arm around her and kissed the top of her head. "Deal." "Is this kind of thing going to happen a lot?" "Oh, yes," he replied, not reassuring her in the slightest. "My first year I had at least a dozen assassination attempts. Most of them were lone nutjobs or Auren's old cronies. They waited until the transition was secure, a few months, before trying anything, thinking they'd lured me into complacency." "But you don't travel with bodyguards now." "No . . . but I did for a long time. It takes a while to establish a reputation, Miranda. Right now you're being tested in the eyes of our kind. They want to see how you handle yourself, how tough you are. The longer we stay in power, the fewer fools will try to take us down." She wriggled as close as she could, not caring that she was probably getting his clothes as filthy as hers. "Thank you for not saying 'I told you so.' " He shrugged. "I understand that you value your independence. I don't want you to lose it. But now you see that we have to be careful. The more you're in the public eye, the harder it will be to keep your two lives from colliding. I want you to live the life you want to live for as long as you can, but you have to be realistic. Plus . . ." His voice darkened, and despite the words the sound caused a low current of electricity through her body. "Lone nutjob or not, I intend to find whoever hurt you and tear the skin from her bones with my bare hands." She looked up at him and said wryly, "You're such a ball of sunshine, baby." As she'd hoped, he laughed and kissed her. Miranda settled back against him and closed her eyes, the vibration of the car beneath her and the heartbeat at her ear lulling her as much as the thought of what she had to look forward to: a steamy, hot shower; a Snickers bar; and most important, a long morning spent in the arms of her Prime. Two Midafternoon, while the human world bustled around in its frenetic race, was a time of peace at the Haven. The halls were dark and silent, except for the footsteps of the half-dozen diurnal guards. There were no training sessions in the Elite quarter, no patrols checking in and out, and the sensor network powered down partway to conserve energy. Throughout the complex of buildings and the mansion that made up the Haven, 126 vampires slept. Today, it was 125. David lay on his back with one arm up under his head and the other wrapped securely around his Queen, who slumbered with her head on his chest and her hair spilled out over his bare skin. His hand moved in absent circles on her back, and though she often tossed and turned throughout the afternoon, today she was tranquil. Indeed the radiating heat from the fireplace, the weight of the comforter, and the pull of Miranda's exhaustion should have drawn him along into dreams himself, but his mind simply refused to be still. He'd had many sleepless days during his tenure as Prime. There was always something to worry about, the night-to-night welfare of his territory an endless equation to solve . . . and the last three months had added a new variable. She could have been killed. The memory of seeing her blood running down from the stake wound made him clench his hand into a fist so hard it shook. He had never feared for his own life, and he didn't now, but having Miranda complicated matters—he could no longer discount the ever-present threat of assassination. As he had pointed out to her, more than one life was at stake. If he died, she died. That was reason enough to be more careful. Eventually Miranda grunted and rolled away from him, and he gave up trying to sleep. He got out of bed, pulled on his robe, and sat down at the computer to run a few quick checks. Situation normal. The city was quiet; it was rare to have any sort of vampire activity during daylight, and then it was confined to the indoors and there wasn't a whole lot he could do about it. He knew there were about two dozen vampires living belowground in the sewers and old tunnel systems, but unless they made a nuisance of themselves he saw no reason to bother with them. They were followed on the sensor network like everyone else; in Austin—and eventually every metropolitan area of the South—there was no such thing as privacy for vampires. If they didn't like it, they could leave. The Shadow World's denizens weren't known for their good behavior toward humans, and it was his job both to keep their people safe and to keep his people safe from discovery. So far it was working. The vampire population of the South had actually increased since the network had gone up, and vampire-on-human crime had dropped. Other Primes who opposed his ideas had prophesied a mass exodus of vampires unwilling to be followed around, but they'd been proven wrong . . . and nothing pleased David more than proving the Council wrong. The Haven's various computer systems were all running happily. There was nothing to worry over. Out of curiosity he did a diagnostic of the solar panels that supplied the entire complex with power; there had been a few glitches with the subsystem that charged the cars, but he'd debugged them and so far this week there'd been no additional problems. Yawning, he checked his e-mail, then opened his schedule to have a look at the week's events. There at least something interesting was happening. When a new Prime claimed the Signet or took a Queen, his allies and those wanting to curry favor paid state visits as soon as they could. Pairs from all over the world as well as powerful vampires from his own territory came to offer their congratulations and get to know the new administration. Of the twenty-six other Primes, nineteen had made overtures toward visiting, and four had already come and gone. They arrived in style, stayed a few days, and went home to spread the latest gossip among their Court. Faith had dubbed the whole tradition the Magnificent Bastard Parade. So far things had gone smoothly. The four Primes—and two Queens—had all been friends of his and had taken to Miranda immediately, though Tanaka of Japan had observed to David privately that the others might not be so . . . open-minded, as he put it. Tanaka, an expert diplomat who managed to keep up good relations with all but about three Signets, hardly ever gave bad advice, and though David's first inclination was to insist that Miranda could handle herself . . . he did have a few misgivings. The Signet system was thousands of years old. The youngest living Prime was over two hundred, and Miranda was one of a handful of Queens in history to take a Signet just after coming across. Primes weren't known for their forward thinking or progressive politics. In other words, most of them were sexist pigs, and Miranda . . . well, she wasn't the type of woman to keep her mouth shut when angry. She spoke her mind, was smart and observant, and David knew that the very qualities he loved about her were going to get them in trouble if she didn't learn quickly that these old, hidebound men of privilege were not all going to like the fact that David treated her as an equal. Primes and Queens were meant to function as two halves of a whole. History, however, had not been kind to women, and neither had vampire politics. Queens were powerful, yes, and certainly had a reputation of their own, but they usually took a backseat to their mates. For the most part the Queens were perfectly content with the way things were, as were their husbands, and because they were bound at the soul the Primes tended to give their Queens as much or as little responsibility as they wanted—but some were out-right subservient to their Primes; a mystical relationship didn't always mean a healthy one. David was already considered something of a maverick for his love of technology and got plenty of stern looks and raised eyebrows thanks to his history with Prime Deven. He was used to it, and he knew when to ignore it. Miranda had not yet learned to pick her battles. In the coming week she would have to. They were due a visit from Prime James Hart of the Northeast; his territory included New England as well as the most densely vampire-populated metropolitan area, New York. He had ruled a hundred years with no Queen, and five minutes after meeting him it was obvious why—but his sexual appetite was well-known, and it was rumored he kept a harem of vampire women whom he terrorized into obedience. He was not a friend to David. In fact David had no idea why Hart was so keenly interested in coming to Texas so soon; generally a Prime's allies came first, and it took months for everyone to make the arrangements. Pairs were mostly anchored to their territories, and leaving even for a few days was a major undertaking. Allies made the effort as soon as possible as a show of support. Usually neutral parties or antagonistic ass-kissers waited until the rush was over. David hadn't expected Hart to come at all, and that would have been just fine. Obviously Hart wanted something. That alone was enough to make David uneasy about the visit. The thought of Hart and Miranda in the same room, while wickedly amusing to Faith, set his teeth on edge. As he was closing his schedule—Hart was set to arrive on Tuesday—he looked over at his contact list and noticed that only one other person was online at this ungodly hour. "What are you doing up?" he typed. _"Painting my nails & watching porn,"_ Deven answered promptly. David grinned and replied, "Right. What color/kind?" A pause, then: _"Black/Midget."_ David snorted quietly. "Couldn't sleep?" _"No. You know how it goes."_ David glanced over at the bed, where Miranda was still blessedly asleep. Yes, he knew how it went. At least once a week, sometimes more, she fought her way out of night-mares, and once she'd been so inconsolable that the only thing he could do was mentally knock her unconscious. It bothered her that she wasn't "over it" already. Her life was so different now, last year seeming so far away that she expected herself to have healed and moved on, and she refused to be seen as weak or needy no matter how much it hurt. He had tried again and again to tell her that it wasn't that easy. Old scars persisted into immortality. She wasn't the first person he'd had to watch cope with a traumatic past. "When are you coming to Austin?" he asked. _"Still working on it. Maybe next month?"_ "Just let me know so I can stock the house with good whiskey and dancing boys." David imagined Deven in his private study at the Haven in Sacramento, a cozy room with leather couches and a small part of the Prime's impressive weapons collection on display. Even if he was in nothing but a bathrobe, Deven would have a knife on him somewhere and a sword within easy reach. He even kept a blade hanging on the back wall of his shower. And all of that was after seven hundred years. David thought about telling Miranda that, but he had a feeling she'd find it more depressing than reassuring. _"Have to go,"_ Deven said. _"Meeting."_ David wished he could communicate "quizzical" over the Internet. "At two in the afternoon?" _"Talk to you later. Kisses, sugarblood."_ David chuckled. Dev signed off before he could reply, but that wasn't unusual; the Prime of the West wasn't much for online communication, preferring to size people up face-to-face. David stretched, closed his computer, and stood up, going over to put another log on the fire before he tried sleeping again. Then he returned to the bed and drew the curtains so that only the foot was exposed, allowing and keeping more heat in. He smiled at Miranda, who had in the space of thirty minutes managed to sprawl out so she was taking up the entire bed. One of the pillows seemed to have vanished completely and the comforter was tangled around her legs. But even with her limbs akimbo and in a rather inelegant position, with the firelight casting a golden glow over her skin and catching the jeweled highlights in her hair, she was a breathtaking creature to behold. A moment later she made a noise that might have been a word, then blinked and opened her eyes, their green a bit dull with sleep. She didn't ask why he was up; it was hardly the first time. She simply extended a hand to draw him back into bed. He was quite happy to comply. He took the opportunity to unwind the covers and shuck his robe, then slid in next to her with a sigh. She resumed her former position with her head on his chest, lifting a hand to touch first his Signet, then his lips. "Love you," she murmured, eyes already closed. He kissed her almond-scented curls. "Love you, too." This time he fell asleep. The nine candidates for the Queen's personal guard stood at attention, each impeccably uniformed and waiting expectantly for judgment. They ranged in appearance from a huge tattooed bald guy with enormous holes in his earlobes to a petite blond pixie who according to Faith was actually older than David. Miranda walked along the line slowly, looking each one up and down; only one looked visibly cowed by her gaze, and she crossed him off the list in her head immediately. She didn't need someone following her around who was terrified of her. She had met a few of them before. One was a new recruit since the war and had moved up the ranks quickly. Two had experience as the Prime's guards, and two others had stood guard at their suite door. All had been vetted by Faith for their ability as warriors, their stealth, and their dedication. David had done extensive background checks when they were new to the Elite, of course, but he'd rerun them all. All that remained was for Miranda to choose four; they would work in pairs. "What do you think?" Faith asked. Miranda went to stand beside her, crossing her arms. "I don't know. I mean, we're not going to hang out or anything—they're going to follow me around and make sure I don't get staked. You vouch for their fighting skills, so what else is there?" Faith shrugged. "You have to pick them, my Lady. I've done my part." "All right . . . let's see." She took Faith's clipboard and pen and crossed off the timid man. "Four is scared of me. Six is so tall and gangly he'd stand out in a crowd. Three looks bored. Two more? Hmm . . ." She walked back over to the line and did another slow circuit of the guards, this time extending her empathic energy toward them, not intruding but just testing the waters for anomalies. Two was too ambitious. He was more interested in impressing his superiors and moving up through the ranks than protecting her. That didn't bode well; if the situation was dire he might make some stupid hero move to show off. She crossed him off. She stepped back and addressed the guards. "Raise your hand if you like Nickelback." The guards exchanged glances, and reluctantly the blond pixie raised her hand. Miranda crossed her off the list. "Numbers two, four, six, three, and nine, you may go. One, five, seven, and eight, please remain for your briefing. Thank you all." The four who remained were consummate professionals and kept their happiness to a brightening of the eyes and a relieved sigh. The others departed with varying degrees of grumbling or head shaking. That was all right; if they really were worthy of the post, they'd have another chance. There was always a need for the true Elite and the truly loyal. Miranda handed Faith back her clipboard and addressed the guards. "Welcome to my service," she said. "As you know, I am in need of bodyguards to accompany me into the city for regular performances, meetings, and other appointments. If we're all very lucky, your job will be extremely boring. I'd like you each to introduce yourselves briefly—Elite designation, name, and favorite musical genre or artist." As each one spoke she shook his or her hand, taking a moment to do an extra psychic sweep of each. "Elite Seventy-two, Aaron Sawyer, jazz." "Elite Twenty-six, Jake Verona, Johnny Cash." "Elite Forty-four, Minh-Li Tsai, trip-hop." "Elite Sixteen, Lalita Madhavi, anything with a violin." Satisfied, Miranda nodded to them. "Again, welcome. I'll leave you to Faith for the rest of your briefing. I look forward to working with all of you." With that she looked over at Faith, who bowed; the four guards echoed her motion, and Miranda nodded again, then walked away with a sigh. Bodyguards. She still didn't like the idea . . . but there really wasn't much choice, at least not right now while she was so new to the Signet. David couldn't be with her every minute of every day, and though her combat skills were already excellent—and improving continuously as she kept training—she still wasn't as quick on the draw as the Elite could be. The extra eyes looking for threats would be invaluable the more she got out in public; most humans would have no idea what she was, but any vampire who wanted her dead would have a great many opportunities to come at her while she was onstage or in a crowd. She left the Elite training building and headed toward the left; in her mind she could sense a low-burning spot of energy that she recognized as David, over near the pasture where the horses were kept. She could find him anywhere with a thought, and call him to her side almost instantly, but still, even someone as strong as David couldn't be everywhere at once. If she wanted her own life beyond the Haven and beyond their marriage, she had to get used to the idea of bodyguards. She didn't have to like it. "I know this is hard for you to accept," Faith had noted mildly before bringing out the candidates, "but there are some things your Prime and I know that you don't. Diplomacy, for example . . . and security for another. You have to trust us, Miranda. Not everything is going to be instinctual for you." Sighing again, Miranda left the path and angled toward the long white fence beyond which stood a single structure, the stable. Inside the building smelled of hay and alfalfa and horse, though it was as scrupulously clean as everything else at the Haven. All but two of the stalls were usually empty; David's two prized four-legged friends were housed at opposite ends of the stable. Miranda passed by Isis, the female, but didn't go any closer. Isis pointedly ignored her. The Haven had staff to work in the stable, seeing to the night-to-night care of the horses and keeping the place clean, but David preferred to manage them himself as much as possible and always took care of them after a ride. The two horses deferred to him readily but mostly seemed to think Miranda was beneath their notice or, at least, viewed her the way she imagined a lion would view a hamster: harmless, possibly delicious. The Prime entered the stable leading Osiris; the Prime was sweaty and dusty and so was the horse, though Osiris clopped along with his head high and proud, his tack jingling. They had no doubt taken the long course around the Haven's extensive grounds, which had its own system of programmable lights. Miranda didn't like horses. They were big and dangerous and strange. But she had to admit that David looked astonishingly hot next to one, and even more so on the stallion's back. She'd watched him ride a few times from the safety of the fence and then dragged her Prime into an empty stall to put him through his paces. David knew she was there, but he smiled when he saw her. "Fair warning," he said. "I stink." "I know. I can smell you both from here." The smile became a grin. "Didn't bother you last time." She grinned back. "It's not my fault—it's all the leather and sweat. The boots alone are worth a good shag." He brought the massive beast to a halt and set to removing his tack, a lengthy ritual she'd sat through before; there was a lot involved in the care and feeding of a horse, and Osiris stood placidly and let himself be pampered. The grooming process involved several kinds of combs and brushes, a rag, a hoof examination, feeling along the legs—as far as pets went, cats were so much easier. "You don't have to stand quite so far away," David told her. "He's about as fierce as a puppy." Miranda stayed where she was. "A thousand-pound puppy that could kick my brains in." "Osiris," the Prime said to the horse, "are you going to kick the Queen's brains in?" To Miranda's surprise, the horse snorted and shook his head, his feathery mane flying to either side. He looked for all the world like he understood every word. David rubbed Osiris down with sure strokes. Miranda had learned that grooming his horses, along with debugging code and taking apart complex circuitry, was like yoga for the Prime. She climbed up onto a rail and let her feet swing, trying not to bother him while he was so immersed in what he was doing; instead she took the time to admire how he moved, how his hands followed Osiris's muscles to check for injuries or other problems, how he murmured to the animal as if they shared a secret. She could almost understand the attraction some women had to horses, watching them like this. "You shouldn't be uncomfortable around powerful beings," David said. "You're a powerful being, too, remember?" He led Osiris into his stall. "It's not just that," Miranda replied. "They look at me all sideways like they're trying to decide whether to eat me." "That's because their eyes are on the sides of their head, not the front," he explained. "They have a nearly three-hundred-sixty-degree range of vision. They need to be able to see all around them in the wild, both to keep tabs on herdmates and to watch for predators. That's how they look at everything—don't take it personally." She hadn't really thought much about it. "Oh. Makes sense, I guess." He gestured for her to come closer, and after a moment's hesitation she came to stand next to David, ready to jump back out of the stall, examining the enormous nostril that was entirely too close to her face. The horse's ear flicked toward her, but he made no sign of agitation and turned his attention to the hay hanging in the back of the stall. "It's safe," David said gently. "I promise." Tentatively, sure that Osiris was going to turn and bite her hand off, she reached out and lightly touched the side of his neck, her heart pounding in her throat. Osiris suffered the touch without comment and didn't so much as bat an eye when she tried again, this time laying her hand on his neck and gingerly stroking the hair and the powerful muscle beneath. "Isis and Osiris are Friesians," David told her, no doubt to distract her from the huge wall of animal she was touching. "They're very showy and proud, but usually pretty docile. Osiris's dam—his mother—was a handful, though." "How many generations have you owned?" she asked, running her hand along the horse's side, amazed at how solid and strong he was. "Three, counting him. I had his mother and grandfather." "What about Isis?" He smiled. "She was a bribe. The Prime of Eastern Europe was trying to get on my good side. It worked." Miranda, quite done with her experiments, moved back out of the stall, crossing her arms, grateful to put distance between them again. David gave her a look that held more than a little pride; he knew how much she hated being afraid of anything. The first month she had refused to even go in the stable. He was hoping one day she'd want to try riding, and though she'd snorted openly at the suggestion, it wasn't as if they would run out of time for her to overcome her fears. "I've still got a while here," David said, taking a metal thing—a hoof pick, she remembered—from the wall and gingerly lifting up Osiris's front left foot. "Why don't you go on inside and I'll finish up, shower, and join you?" She nodded. "Sounds good. I'll be in the music room." Another smile. "You're kidding." Miranda stuck her tongue out at him. "I have songs to finish," she said. "I'm in the studio in a few days." "By the way, how did the bodyguard roundup go?" he asked as he inspected the hoof in his hand for rocks and, she guessed, small mammals. "Fine. I guess we'll see tomorrow. After the latest Magnificent Bastard gets here, I've got a show." "Right." David's voice and expression altered very slightly, and she frowned, catching the subtle hardening of his tone. "What's wrong? Are you still worried about Hart?" "I want to know what he's up to, but there have been no rumors or intelligence suggesting why he's coming here. The only thing I can think of is that he wants Kentucky back—there's a full Council in three years and we have to rebid for it, but there's zero chance I'll be outvoted. I've got representatives from Louisville ready to testify that they want my continued leadership, and Hart can barely hold his own territory without constant threat of revolt. So, yes, I'm suspicious. Not even Dev has any idea, and if anyone would know, he would." Miranda had been hearing about Deven for months now, and she was both anxious to meet him and on the verge of rolling her eyes every time she heard his name. According to both David and Faith, Prime Deven knew all, saw all, and had never lost a fight; he was old and smart and powerful and apparently shot unicorns out of his ass. "Don't worry," she told David. "We can handle him, can't we? He'll be on our turf, after all. You have the right to toss him out if he misbehaves." "Not if," David said. "When. And it's not that simple. Hart has allies in the Council who aren't known for their fair-mindedness. They're a minority, yes, but they can still make life very unpleasant for us if they want to. It's in our best interest to maintain good relations on the surface." Now she did roll her eyes. "If you say so. Personally I don't see the point in playing nice. You're David Solomon. Everyone's scared shitless of you." David shook his head. "Not everyone." "Well, they should be." Miranda moved just close enough to kiss him on the cheek—he did smell rather horsey, after all—and said, "I'll see you after you've showered, Lord Prime. Have fun giving your pony a pedicure." The Prime chuckled and swatted her lightly on the ass as she walked away. Faith met her on the steps to the house. "I've got Lalita and Jake scheduled for tomorrow night, if that's all right with you." "Any particular reason you matched them that way?" "I ran them through some scenarios in various pairs, and they seemed to work well together, as do Aaron and Minh. Also Lali and Jake have run patrols on the same team, so they're comfortable with each other. I have them as your primary guards for now, but we can change that if you find you prefer Aaron and Minh." Faith walked beside her down the hall; as they passed, the guards at each station bowed, and Miranda gave them an acknowledging nod. "I'm in for the night," Miranda told the Second. "The Prime will be soon, too—I'm sure he'll want you to check in before you log off." Faith nodded, then slowed down. "My Lady . . ." "Yes?" Miranda turned to her. "I know what you're going to say to this, but . . . I just feel like I need to say it." Miranda sighed. _Here we go again._ "Go on." "I'm just wondering if it's safe for you to continue playing in public." At Miranda's expression, Faith added, "Someone tried to kill you, Miranda. I'm not being paranoid. And having a Prime like Hart in town . . . well, it tends to bring out the crazies. I'm perfectly willing to give you as big or small a security detail as you and the Prime think is best, but I just . . . I just want you to think. Think about how many lives depend on you." Miranda made a face. "Faith, nobody but David depends on me. If we die, there will always be another Prime." "Maybe. But I don't think you get how important you are to all of us. What do you think it was like in this territory before Auren was deposed? Vampires killed at will, and no one even tried to stop them. Hunters were starting to flood the major cities of the South, and the entire Shadow World was almost exposed. Right now the Council majority sides with David that no-kill laws are the safest thing for all of us, but Hart is one of the ones who disagrees. What if he's got some hotshot vampire friend willing to start a war for your Signet?" Miranda crossed her arms and faced the Second. "What do you want me to do, Faith? Give up everything that matters to me? I can't do that. I can't live forever—and moreover, I can't be the person David needs as his partner—if I can't be who I am. I'll take guards, I'll have Harlan drive me, I'll do what I can to put your minds at ease. But I can't give this up. Music is . . . it's who I am, Faith." Miranda hated the note of pleading in her voice, but it had the desired effect, as Faith looked stricken by the intensity of her tone, and her whole demeanor changed from "second in command making battle plans" to "worried friend." Miranda tried hard not to take advantage of Faith's friendship, but it was hard sometimes to know where to draw the line between Faith-her-friend and Faith-her-Second, especially given how much older and wiser Faith was. "We're all on your side, Miranda. But we have to be realistic. You're a vampire now, and not just any vampire. You are Queen. You'll never be like the others. Ever." Miranda stopped outside the music room door. She nodded to Faith—not in agreement, but in acknowledgment that she had been listening to her Second's concerns and wouldn't automatically dismiss them. "I hear you, Faith." "Thank you, my Lady. That's all I ask." Faith was clearly not satisfied with the conversation, but she said only, "I'm logging off for the night, then, after a quick check-in with the Prime. Send out if you need me after that." "Thank you, Faith. Dismissed." Miranda slid inside the music room and shut and locked the door behind her, standing for a moment with her back against the door, eyes closed, trying to breathe. When she opened her eyes, she smiled with relief. The room was her refuge, more important to her than any other place in the Haven. Here she could lay down her responsibilities—which she was already having trouble carrying—and just be Miranda for a while. From the moment she'd first set foot inside the room, she had known it was hers. She was meant to be there. Her hands were meant to touch the keys of the magnificent instrument that took up a third of the space: her Bösendorfer Imperial Grand, a gleaming black empress holding court over the room. There was also space devoted to her other instrument of choice, the Martin guitar she had bought after her old one was destroyed. It had its own stand and its own area for her to practice in. Miranda took off her coat and hung it and her bag on the rack by the door. She approached the piano, as always, as if walking into a church. Then she laid her hands on the piano's lid, exposed the keys, and sat down, leaning her head sideways on the keys for a moment, closing her eyes. With her eyes shut she felt along the keys with one hand and gently touched a few, the barest hint of a melody almost too quiet to be heard. She hummed with the notes, letting her energy sync with the piano's; it wasn't alive by any stretch, but it sort of reminded her of the Signets in the way it responded to her. The stones' light flared or dimmed to match the bearer's emotional state, and it felt like the piano's strength rose up to meet her own, or lay down beneath her sorrows. She couldn't believe she had ever lived without it. On the far wall hung a portrait of the woman who had bought the Bösendorfer and set aside this room for it: the seventh Queen of the South, Elizabeth Jensen, who had been murdered, with her Prime, by Auren in 1914. Bess, as she'd been known, was the first African-American Queen in the South, and had been a slave in her human life. She was known all over the territory as a wildly intelligent woman who spent her immortality becoming as educated as she could, studying music, medicine, history, art, and several languages. And though like most Queens she'd taken a backseat in Signet politics and had been the subject of scorn and derision from several other Pairs, she had been a noble woman, greatly respected by many. Miranda wished she could have met Bess, if for no other reason than to thank her for her devotion to music. Bess was the only Queen so far to whom Miranda felt any kind of real connection, and she wasn't even alive. Gradually Miranda applied more pressure to the keys and more notes to the melody, raising her head until it leaned against the piano's lid. She let her fingers find their own way, channeling the pile of confused emotions in her heart into sound where they could be lifted up and turned into something beautiful. The Prime tended horses and worked equations. She made music. Sometimes she played songs that she already knew, and sometimes she just improvised or combined both—without even thinking, it always ended up dark and complex, the lines of melody doubling back and twisting around themselves like Celtic knotwork. Certain themes repeated on certain days. More than once she'd woken up here with David sitting nearby keeping watch over her as she played in her sleep. Her arms would ache for hours afterward, but it was better than having nightmares. As if the thought had summoned him, she felt a warm presence flood through her mind, and she knew without looking that David was there, taking up his usual seat in the small audience section of the room. She still remembered the first time she'd seen him there, back when she was human, back before either of them had been ready to admit what they had, deep down, already known about the connection they shared. He'd be sitting with his hands folded, elbows on the chair's arms, carelessly regal and infernally attractive. She could feel the comfortable weight of his gaze. She reached along their bond, drawing the gentle surety of its power into the music, creating two streams of melody and twisting them around each other so that the chord was stronger than the sum of its notes. Together they were a natural harmony, and she followed it deeper until the room and the Haven and the world disappeared and there was nothing but one song, breathtakingly beautiful and intense beyond words. She brought the piece to a winding conclusion, and by the time the last chords rang into the air, pain had begun to assert itself in her hands. She lifted her eyes to the clock and realized with some surprise that she'd been playing for almost two hours. When she lowered her eyes, David was beside her, sitting down on the bench and taking her hands in his. "Silly woman," he chided affectionately. "You could burn yourself out doing that." She leaned against his shoulder, all the tension gone from her body. The piano wasn't quite as good as sex, but it came damn close. "Only way to fly," she murmured. He was smiling, and she felt the heat of healing energy pass between them again, soothing the cramps in her fingers. It was a handy thing in some ways, being Paired; they could heal each other of anything short of a mortal wound almost instantly, even faster than a vampire's natural regenerative speed. Either of them could draw from their combined power, and there were supposedly ways they could work together to become even stronger, but David had said that must wait until she wasn't so new. She was dimly aware that he threaded his arms around her and picked her up. She heard the faint clunk of the piano lid closing, followed by the sound of the lights clicking off, and turned her face happily into his chest, inhaling the scent of his shirt. There was something in the way he smelled—some undertone of great age that would never have registered to her mortal senses—that she found deeply comforting, like leaning against a mountain or red-wood or some other nearly eternal thing. Doors opened, doors closed; the guards at the suite door gave their greetings. Inside the suite was warm from the hearth that Esther had stoked before they arrived. David deposited her on the bed and sat down, taking one of her legs and removing her boot, unconsciously running his hand along her shin as he had Osiris's. She chuckled. "I'm not a horse," she said without looking up. "I'm well aware of that," David answered wryly. "Horses are far less stubborn than you." "That's why you love me." She could hear him smiling. "As a matter of fact, it is." He pulled off her other boot and then set to removing the rest of her clothes with deft, practiced hands. "That, and about a thousand other reasons." "Such as?" "You're willful, smart as hell, courageous, and you look good in red," he said, touching a finger to her Signet, then lifting a tendril of her hair from her forehead. "You also have a tremendous heart, and, if I may be so bold, absolutely perfect breasts." Miranda's eyes popped open, and she saw the wicked glint in his. "Flattery will get you seriously laid, Lord Prime," she said. "I was hoping you'd say that." She sat up long enough to put her hand around his neck and pull his mouth to hers, and then she rolled back, hauling him onto her with a growl. He braced himself on his hands to keep from knocking the wind out of her, then tore his lips away and leaned down to kiss a slow line from her throat to her breasts, still bound in black lace. She arched her back to let him unhook the offending garment, then shifted her shoulders from side to side to strip it off and toss it aside. Meanwhile her fingers ventured in between the buttons of his shirt to find the muscle underneath and, with only a little fumbling, managed to push the shirt off. She moved her hands up his back, feeling the slightly raised lines of the hawk etched into his shoulders. She loved the sensation of sliding her hands down into the waistband of his jeans and around to the front to unzip them. His skin was like silk over stone and warmed under her palms and lips. She would never have expected in a thousand years to _want_ so much, to crave both the taste of his blood and the deep aching pleasure of their bodies wrapping around each other and joining. That first second of contact when they could finally touch without barriers of space or fabric was the same every time: a shock to her system, like coming in from freezing rain to the edge of a volcano. Her body was still surprised at how badly it needed his. The first time after the battle had frightened her. She hadn't realized just how much he'd been holding back that night in her apartment. A human body was so easy to break . . . and two vampires without restraint could easily break furniture, her screams practically peeling the paint off the walls. The intensity of it had been almost too much, but the trust between them was so complete, and the joy of being reunited so overwhelming, that her fear had evaporated. He alone could touch her. In all of eternity, all the world, there would never be another. She had no desire to ever look at another man—she didn't even feed on them. Her time in hell had made sure of it, and the amulet around her neck sealed it. He alone . . . he alone. Forever. Three Tuesday evening began with the arrival of a blustery cold front that swept through central Texas leaving frost in its wake . . . followed by the arrival of a black stretch limousine and a black van. Because Faith was Second in Command, it was her job to show the visiting Prime to his rooms, see that he was comfortably installed, then come and let the Pair know when it was time for the formal introduction. Meanwhile David and Miranda waited in David's workroom, where he was taking apart the newest-generation Apple gadget to see how it worked. He had an abiding love for the technical poetry of circuits and chips, and elegant design, whether in a phone or a beehive, was his idea of porn. Miranda knew by how intent he was upon the task that he was, if not nervous, deeply uneasy about the meeting. She sat with her feet up on an empty chair, trying not to let his emotions affect her. That was a consequence of their connection: She could not shield herself completely from him, ever, and the best she could do was learn to gently nudge his presence to the back of her mind, where it wouldn't overtake her own. Most of the time she liked having him there. There were times, however, when the whole thing was a pain in the ass. "It's been over an hour," she said. "This is getting ridiculous." David made an irritated noise. "He's doing it on purpose. Throwing us off schedule asserts his control over the situation." "I'm supposed to be in town in two hours. Why don't we just go meet him now?" He looked up at her and smiled. "Because that's not how we do it, beloved. I know, I know—to hell with custom and rules—but these protocols have been in place a lot longer than you have. These silly little niceties keep order among the Signets. Besides, watching the way someone navigates the system teaches you a lot about him." "If this guy is as big a dick as everyone says, I don't think I want to know more about him," Miranda pointed out, but he did have something when it came to the value of observing others; she had been watching her husband since the onset of the Magnificent Bastard Parade and had learned quite a bit about him that she hadn't been aware of before. There were areas where he was perfectly happy to flout custom and others where he was a stickler; if he felt the Shadow World was better served by following the rules he did so, but if he believed something was hampering their evolution as a society he ignored it, taking the flak from the others without batting an eye. "You mentioned you'd met Hart once before," Miranda said. "What happened then?" David set aside his toy and sat back, crossing his arms. "I dropped a dead deer on his head." She blinked, sure she'd misheard. _"What?"_ A nod. "It was his state visit after Deven and Jonathan Paired. He waited nearly a year to come, then proceeded to abuse the Haven staff, belittle the Elite, and treat the Prime like a cockroach. He didn't say anything to Jonathan because Jonathan would have cheerfully crushed his skull, but I heard him in the hallway calling Deven a degenerate faggot, and lo and behold this hideous old deer head that had been hanging on the wall for seventy years fell down. The antlers almost put his eye out." Miranda laughed so hard she nearly cried. It was widely known that David was powerful; he had almost all of the higher abilities attributed to the most powerful of their kind, including the power to Mist, basically a form of teleportation that could be performed only by a Signet bearer. His telekinesis, however, wasn't common knowledge. It was entirely possible Hart had no idea there was any malicious aforethought in Bambi's suicidal leap. Before she could compose herself completely there came a knock at the door, and Faith joined them, looking more agitated than Miranda had ever seen her. The Queen sobered immediately. "Faith, what happened?" The Second shook her head, her mouth set in a tight line. "Your guest is ready for you," she said. Queen and Prime exchanged a look. "Faith, tell me," David said. "I want to know exactly how that bastard behaves while he's here." Faith's eyes were like two slivers of flint ready to spark off any available tinder. "He brought his women," she replied. "Four of them. They're . . . the rumors are true, Sire." David closed his eyes and sighed. "I was afraid of that." Miranda looked from him to Faith. "What rumors?" "Everyone knows Hart has a harem," Faith told her. "There's been speculation for years over whether the women he keeps are there of their own free will, and over how he treats them. The prevailing thought is that he turns them himself and keeps them weak, nearly starving, so they can't fight him." Miranda felt the first stirrings of molten wrath forming in her stomach. "And it's true?" "Apparently. You should see them . . . they're skin and bone. None of them make eye contact. They just shuffled into their room and one of his Elite shut the door and stood guard." The Prime rarely displayed anger, even to his Queen, but she felt it flare up inside him and saw the subtle change in his expression that few other people would recognize as carefully controlled fury. When he spoke he was deadly calm. "All right. So he brought them into my Haven knowing perfectly well how I would feel about it. I think it's safe to assume his intentions in coming here are not pure." David stood, straightening his shirt and reaching for the suit jacket he had hung over the back of his chair. They always dressed to the nines for these things, and although some Primes reinforced their reputations with old-fashioned wardrobes or stereotypical Goth-esque vampire attire, David opted for impeccable hand tailoring from the finest local shops so that everything fit him perfectly and only added to his allure. Miranda was still working out her own style as far as that went. She had her stage clothes, lots of leather and jewelry, and a variation thereof that she wore into town when her presence was required. So far she'd had the most success with what she called "neo-bitch goddess," and tonight she'd worn black pants and heeled boots, a long coat, and a bloodred lace-trimmed top that perfectly matched the stone of her Signet. It was definitely not casual wear, but still wasn't a frilly cocktail dress or Hillary Clinton pantsuit. She wanted to look impressive but be able to breathe, fight, and slouch when necessary. "Let's go, beloved, and get this over with," David said. He turned to her, arms out slightly in the universal vampire gesture of _I have no idea how I look—what do you think?_ Miranda ran her hand down the front of his jacket, resting her palm over his heart. "Gorgeous as always," she said fondly. "You, too," he replied, leaning in to kiss her on the forehead before taking her arm. Faith looked like she'd rather eat a live scorpion than go anywhere near Hart again, but she was nothing if not a professional; she held the door open for them, but as Miranda passed she heard Faith mutter, "We're going to need another deer head." David was immensely proud of Miranda for not drawing her sword and decapitating Prime Hart five seconds after meeting him. In fact, his fears about her reaction were completely overblown; he realized she had been observing him the last three months, and though she was friendly and somewhat relaxed with the first three Pairs who came to visit, when confronted with a notorious man like Hart she did the same thing David did and slipped on a mask of cordiality coupled with professional disinterest. He loved it when she surprised him. It reminded him that though she was young and a little rash, the Signet never chose wrong. He could only imagine her in twenty or so years when she had stepped fully into her power and authority and was every inch the Queen . . . no one, not even Hart, would dare cross her then. Or, it seemed, today. "Welcome to our Haven, Prime Hart," David said, bowing, extending his hand. "Our home is your own." Hart gave a slight bow. "I bring you greetings from the Northeastern United States," he said smoothly, and reached out to shake David's hand. Hart was a handsome man; he had a polished look and demeanor that would not have been out of place debating on the Senate floor and appeared to have been in his early forties when he came across. He had silver hair and iceblue eyes; the overall effect was that of a man who presumably would have had no trouble landing women . . . willing ones. If David hadn't known about the actions behind the suave façade, he might even have called him charming. David turned to Miranda. "Allow me to introduce Miranda Grey-Solomon, Ninth Queen of the Southern United States." Hart looked Miranda up and down, then bowed a bit less than he had to David. Still, he smiled when he said, "A pleasure. Prime James Hart." Miranda bowed. "Welcome to our Haven, Lord Prime. I hope you enjoy your stay." Hart had already returned his attention to David. "I look forward to the next three days," he said. "I think it's time the Northeast and the South renew their friendship, with a Council meeting coming up soon." Having fulfilled the requirements of Signet formality, David nodded. "Perhaps we could retire to the study to discuss matters of state." Hart nodded curtly, then gave Miranda a faintly dismissive look. "I'm sure your young wife has other matters to attend to and is quite busy with her household duties." David wasn't quite quick enough to change the subject. "I am neither a housewife nor a servant," Miranda said coldly, staring daggers at Hart. "I am Queen of this territory and I don't require a man's permission to stay or go." Before Hart could reply, David interjected, "She does, however, have a performance in town tonight, which I'm sure she would much rather attend." Silently he willed Miranda to let it go this time—he wanted to know what Hart was up to, and if he stormed out now in a fit of pique they might never find out. Miranda shot David a poisonous look but merely turned on her heel and walked away. David gestured down the hall. "This way, please, my Lord Prime." The study David had chosen for their meeting was not in the Signet wing; he wasn't going to let Hart anywhere near their private residence. It was a somewhat neutral venue with a square of identical love seats that put no one more in the spotlight than any other and was tastefully decorated to show off the Haven's wealth without ostentation. There was a map of the U.S. Signet territories on the wall in their current configuration with Kentucky firmly in David's grasp . . . just as a little reminder. As they sat, one of the servants came forward to pour their first glass of whiskey. David hoped they'd brought up a very large bottle. "Ice," Hart said shortly to the servant without looking at her. David felt himself bristle at Hart's officious tone but said nothing. He couldn't let every little thing Hart did aggravate him, or they'd be at war before the hour was up. Hart came from a different world and time than David; the rumor was he'd been a Crusader, son of a noble family somewhere in Europe. He'd been ordering people around his entire life. David had spent his childhood covered in soot at his father's side, and as a vampire he had worked his way up through the ranks of the Western Elite. Plenty of Primes were disdainful and dismissive of their servants. He couldn't let it get further under his skin just because it was Hart. Not to mention it would be hypocritical to lecture Miranda about diplomacy and then start trouble himself. "Why don't we get down to business," David said. Hart actually smiled, though it wasn't a particularly friendly expression. "And what business is that, Lord Prime?" "Cut the crap, Hart. What are you doing here?" Hart regarded him silently for a moment before saying offhandedly, "You're going to have your hands full with that woman." "She has a name." Hart lifted his hands. "All right. Pardon my tone. I'm just saying, you know how the others talk. You have a reputation to protect—my advice would be to rein her in before that shrewish tongue gets you in trouble." David didn't bat an eye. "The only person in this building about to be in trouble is you. And if you think I don't notice that you're dissembling, you're a fool." He took a sip of his whiskey, then asked, "Are you after Kentucky again, James? Because you're not going to get it." The Prime made a noise something like a snort of derision. "I have more important things to worry about than a state full of vampires swilling home brew and fucking their sisters, David." "Then what do you want?" His pale eyes narrowed and he said, "You're telling me you don't know?" "If I did, trust me, you would be on the first plane back to New York." Hart's gaze turned speculative, and for just a moment David saw something in his face—not quite fear, but very close, and equally astonishing. Then, even more surprisingly, Hart was perfectly honest. "You and I aren't friends," Hart said, his tone almost becoming amiable; it wasn't as if how he felt about David—or vice versa—were any big secret. "I've opposed you at every turn, and frankly I think you're a limp-wristed, bleeding-heart child with no business playing at the grownups' table." "And I think you're a relic of an age best left behind," David replied, "and also an arrogant, raping, pretentious swine. Your point being?" "Call off your dogs," Hart said. "Whatever you want from me, name it. I'm done with this game." David felt his eyebrows shoot up. "My dogs?" "The Red Shadow, David. Whatever reason you sent them after me—a vendetta, to prove something, I don't give a damn—name your price. I've lost five of my Elite in the last four months and my Court is scattering to the winds. There's unrest in every state. You know damn well what happens then—some little deviant upstart like you slips in and has my head." "Deviant," David said, rubbing his chin. "I haven't heard that one in a while." "I'm serious. Everyone knows it's the Shadow. You're the only Signet with ties to the Shadow. What little intel we've gathered points toward you or someone here in Austin as the Alpha. Insult my belief in our supremacy, insult my virility, but don't insult my intelligence." David leaned forward, frowning. "I have no idea what you're talking about. I don't know any more about the Shadow than you do. How do I have ties?" "That girl, the one who trained your Queen. My sources say she was one of them. She had to have been working for you." Finally something made at least a little sense. "Sophia Castellano? I didn't even know she knew Miranda until later. She was acquainted with my Second, and she told Faith she had left the Shadow." "No one leaves the Shadow. How do you think they've maintained their secrecy for so long? Either they die on assignment or the Alpha kills them. There's no retirement plan. This Castellano woman was either trying to get inside your Haven for something or lying about ever being an agent." "But I thought they only worked alone," David said. "How could more than one be in your territory causing problems? That doesn't sound like their tactics." "Oh, it's them all right. Elite disappearing, not even a second's static in the line, no witnesses, and their bodies reappear after obvious torture—but there's no evidence whatsoever on the bodies or anywhere else. No mere gang is capable of that kind of ghost operation. Then there's this . . ." Hart reached into his coat pocket and tossed a small object to David, who caught it and held it up to the light. "The hell?" "You're the technomancer. You tell me. I recovered it near the corpse of one of my Elite." David frowned and examined the tiny device in his hand. It was some kind of wireless communication device, obviously, but he'd never seen one quite like it. It was made of silver metal, the same size and shape as an in-ear hearing aid, and completely seamless except for the hole that sound came through. The metal was the same color and sheen as the coms his Elite wore, but it was much harder and there were absolutely no markings on it. "You checked this for fingerprints?" David asked. "Of course," Hart snapped. "You're not the only Prime with resources." David smiled. "Oh? Then you had this sent to a lab and analyzed?" "Why? Obviously it's one of your little inventions." David was itching to crack the thing open, but he feigned indifference as much as he could. "Given that I have my own intelligence network and my own Elite, why would I need an organization like the Shadow at my beck and call? As I understand it, they hire out to humans as assassins and spies, to go where human spies can't go. That's why the Council has never bothered tracking them down—they're no threat to us." He turned the device over in his palm again, considering it, and said, "Besides, they predate me by at least a century. Prime Deven heard about them as early as 1500. He'd heard that the Alpha was an Italian connected with the Medici family." "Surely the organization has changed hands by now." "Not necessarily. It's difficult to maintain that kind of secrecy if you have to hand over control to someone else. From what little I know about them, they sound like the kind of network that was created by one person who trained each agent individually." Hart let out a slow breath and downed his whiskey in one long swallow. "Then you give me your word that you are not involved in this." David stared at him for a moment, then down at the device, then back up. "I will do you one better, Lord Prime. Leave this thing with me. If you give me a chance to tear it apart and analyze it, see what makes it tick, I can learn more about its manufacture and send you all my findings. Knowing how it's made and where it came from might help you track down your killers." For a moment Hart looked dubious, but finally he agreed with a nod. "Done." Then Hart set his glass down and stood. "If you don't mind, then, Lord Prime, I shall retire for the morning. We can meet again after sunset to discuss anything else—there are a few finer points I'd like to go over with you about the upcoming Council, but I think that's best saved for later." David stood as well and bowed. "I bid you good morning, then, and good rest." Hart nodded, still curtly, but with a slightly less dismissive edge than before; David could hardly believe it, but it almost seemed like he'd won some grudging respect from the Prime in the last hour. Hart was escorted back to his suite by one of the door guards, and David sat back down in his chair still holding the earpiece. He was madly curious about it. Was it really Red Shadow technology? Or something else? Whatever it was, it wasn't his. David had considered using earpieces for the coms, but in the end he'd gone with the wristbands because they were harder to lose in battle unless the wearer's hand was severed. He'd never been entirely happy with any of the in-ear models he'd tried, and their reception of outgoing speech was iffy. Plus, he'd created the coms with the DNA sampling system, and that would have been much harder on a piece a tenth the size. For his purposes wrist coms worked just fine. Depending on what he found when he got the earpiece open, however, there might be some new tech inside that he'd want. He didn't much care about Hart's problems, but there were plenty of reasons to want the earpiece in his possession. He hadn't lied to Hart—he knew little of the Shadow because there was little to know. They worked for insanely wealthy humans, not vampires; they were mercenaries with no moral code, and they never worked in groups. It was highly unlikely that they were involved in this . . . but still . . . whoever was clearly had advanced tech, and that could pose a problem. He lifted his com. "Star-three." _"Yes, Sire?"_ "Report to the first-floor study, please." _"Two minutes, Sire."_ Faith joined him, still looking a bit frazzled, and he gestured for her to take Hart's vacated seat and pour herself a drink. "What did you learn?" she asked. David held up the device. "We have work to do." Miranda was angry that night. Kat couldn't help but think back to the night she'd seen her friend onstage months ago, back when the worst thing Kat could imagine was that Miranda was strung out on drugs, and she had walked offstage and fainted. Kat had had no idea what was really going on—the possibility would never have occurred to her in a thousand years. And despite everything she'd seen, Kat still wasn't totally sure she believed it. She'd seen Miranda change . . . seen her teeth . . . seen her bite Drew . . . and she'd felt the change in her friend from some deep place in her gut that knew a predator when it saw one. She'd watched David from across a table, all the tiny alien things about him making a disturbing kind of sense. And yet . . . Vampires? Really? Kat hung out in the wings as she often did during Miranda's shows, leaning sideways against some kind of rigging, one hand steadying her and the other resting on her stomach. Funny how having a vampire Queen in her life made all her own problems seem a bit smaller. That wasn't comforting. Something had Miranda fired up, though, and not in the same way as she had been that night months ago—then she had been emerging from years of slumber and shaking off her old life to find herself powerful. Tonight she was just plain old pissed off. Kat could see it. She didn't have to be an empath to read her best friend. Kat didn't bring it up until after the encore, after Miranda had stalked off the stage to her dressing room and changed, after the house lights were out and the applause was no longer making Kat's ears ring. When, finally, they were sitting in the café—at the same table where Kat had squared off with David, it turned out—Kat stirred sugar into her decaf and said, "Okay, spill it." Miranda was no longer fuming but she was still gravely irate, and she lacked her husband's ability to put on a poker face. "It's nothing." "Oh, bullshit." Miranda smiled. "Yeah, okay." "Come on, Your Majesty." Kat took a drink of her coffee and made a face; without caffeine it just wasn't the same. "This is a no-crap zone, here at this table. I am officially your No-Crap Friend." A sigh. "I told you about all the other Pairs coming to visit, right? The one that's here now is a complete dick. He has slave girls, Kat—what do I do about that?" "Slave girls? For real?" "Yes. They're being kept against their will—at least Faith thinks so. I could offer them asylum, but that could cause a rift between the South and the Northeast, and David says that would come back to haunt us—this bastard has powerful friends. But I can't just sit back and do nothing, can I?" "Wow." Kat sat back, staring at her friend. "Your life is just fucking weird now, you know that?" She grinned. "Yes, I do. And I have this feeling it's just going to keep getting weirder." "I can guarantee that," Kat replied, slowly turning her coffee cup in her hand. "Look, Mira, I've counseled run-away teens and battered wives. I've taught English to Afghani women fleeing the Taliban. But when a vampire Queen comes to me and says some vampire bastard is keeping slaves, I have to be honest: I have no idea what to say." Miranda chuckled and shook her head. "Remember when the worst thing that could happen was getting knocked up at a frat party?" Kat swallowed hard, looking down at her cup, her insides knotting up before she could force her emotions back down again. Damn it, if— Too late. "Hey," Miranda said, staring at her keenly, "what's wrong?" Kat still didn't meet her eyes. "Quit doing that psychic thing on me." "I'm not. I promise. I've just gotten a lot better at reading people. It's . . . part of the job, I guess. You've been weird all night, not just now. It's your turn to spill it." "It's not important," Kat said, surprised at the spark of anger in her own voice. "Just a human problem." Miranda didn't snap back at her or even show that she heard the last statement. Kat remembered what she'd said about being empathic, that words didn't always matter and she could feel the truth underneath them, even without trying. It was what had driven her crazy before. Miranda reached over and grabbed Kat's hand, then sucked in a breath. "Holy shit." Kat snatched her hand back. "I told you not to do that!" "I'm sorry," Miranda said. "I just wanted to be sure. I keep myself shielded and I'm not used to picking things up from mortals, but you're different. You're my friend." Kat did something completely out of character and also completely embarrassing. She burst into tears. She felt Miranda shift from the opposite side of the booth to sit by Kat and offer her shoulder. Kat buried her face in Miranda's neck, and Miranda murmured to her, stroking her back. It was as if she were putting off gentle waves of soothing heat, and if that was part of her mojo, well, Kat wasn't going to argue with it right now. "Does Drew know?" Miranda asked. "Not yet. He's in Beaumont at a conference. Due back in a few days." Kat wiped her eyes on her napkin and sat up, but Miranda stayed where she was, a solid presence that Kat wanted desperately to cling to until she wasn't so scared of drowning. "I don't know what I'm going to do." Miranda didn't say anything at first, and Kat went on, "I have an appointment at the women's clinic Thursday for a consultation. I can go back a week later for the big suck . . . but . . ." "You aren't sure," Miranda said. "Kat . . ." "I mean, I have a house, and I've got money from Dad's estate—not piles of it, but I do okay. And Drew might be a good dad. But I'm . . . God, Mira, how could this happen? I'm on the fucking pill!" Miranda had an odd look on her face, at once gravely attentive and miles away, as if she were listening to two conversations at once. Her fingers were still curled around Kat's arm, and they were suddenly hot as she stared off into space. "Kat . . ." she said softly, "cancel the appointment." "Wait, I'm not just going to—" "I'm not telling you to keep it." Miranda cut her off gently but insistently. "I'm saying wait. Give it two weeks. Talk to Drew. You've got a little time to decide . . . I know what you've always said you'd do, but just wait. Just a little while. I promise it will be okay." Kat gaped at her, her panic momentarily forgotten. "What the hell are you looking at?" Miranda's eyes cleared, and she blinked and took her hand away. She looked, and sounded, as rattled as Kat felt. "I don't know. Nothing like that has ever happened before." She moved back across the booth, and Kat was able to breathe again. "Well, it was creepy." "Yeah." Miranda looked a little dizzy and leaned her forehead in her hands for a minute before looking up at Kat. "But take my advice, Kat. Wait. Nobody's going to force you to do anything you're not a hundred percent sure about . . . but make sure you're a hundred percent sure." Kat swallowed and nodded, grabbing her glass of water and gulping down half of it out of sheer nerves. "Okay." Miranda nodded. "Good." She pushed her hair back from her face, seeming a little nervous about the whole thing, but when she spoke again it was with conviction. "No matter what happens, Katmandu, I'm here for you. We'll figure this out." Kat mustered a smile for her. As weird as Miranda's psychic fade-out had been, there was still something incredibly comforting about having gotten the truth out—just knowing someone else knew was a load off her shoulders. If it had been a year ago, Miranda's reassurance wouldn't have been very reassuring, because she had been batshit insane and teetering on the edge of oblivion, but now . . . Kat might not know much at the moment, but she knew that if Miranda said something would happen, God himself would buy a ticket to watch it go down. She was the Queen of Shadows, after all. A woman's duty was to serve her man. She must be quiet and dutiful, obedient, accommodating. She must defer to him in all things, for he knew best, as was ordained by God Almighty when Adam first bade Eve to lie beneath him in the Garden. Cora stared up at the unfamiliar ceiling of the Haven while Prime Hart grunted and swore above her, her mind in the soft dark corner she had long ago created for it, a place where she was dimly aware of what her Master was doing, but it was only her body that he was invading, and she, Cora, was safe, watching from far away. There was only so far she could go, but every inch of distance was a treasure to her, and there she waited once again while he shuddered and burst hot and cruel into her body. Sated, he rolled off her, and the cool air of the room intruded; she felt it most on her damp thighs and the forever-trembling skin of her fingers. All the girls shook. They shook because they were weak . . . because they were women, and women were weak. Cora imagined Eve trembling as Adam ground his hips into hers, wondered if the first woman had felt the shame of it as she gathered her scattered fig leaves and stumbled to the stream to wash that first fallen seed from her. Did she feel dirty afterward, as the earth was dirty, fallen, made of dung and the sticky leavings of men? There were nine women—girls, he called them, and not ever by name, only as "you" or "girl" or "whore"—in Hart's harem, and they had been gathered as thoughtfully as a collector might gather works of art; each one was chosen for specific attributes, so that when he wanted a buxom blonde, he had one, and when he wanted an exotic African slave girl, he could dress Naomi in silks and make her dance for him. Cora had been chosen for her dark hair and her olive skin, neither of which she really had anymore. She remembered, sometimes, the feel of the Italian sun on her arms, the wind lifting her hair as she ran, laughing, through her father's fields, past the lemon trees, among the twisted olive branches. So long ago. Hart pushed himself up off the bed and walked out of the room without a parting word. He had his own room for sleeping and came into the smaller room of the suite only when he wanted a girl. He had brought four this time, and though the servants at his Haven acted like it was some kind of honor, all the girls who got to stay behind were relieved and grateful for a few days' peace. Cora wasn't certain they all understood what they were. They were so young when he brought them in, and he forced his will upon their memories as he forced himself into their bodies. Few of them remembered where they had come from. All they knew was the stabbing pain of penetration, the burn of knees too long on the floor and a jaw cramping from being held open too long. They knew pulled hair and bruises, bite marks, whips, costumes. Hart was creative in his lusts. He'd dressed her as a nun more than once and defiled her while she recited the Hail Mary to him. She turned onto her side for a moment, eyes closed, listening to the furtive movements of the others where they were all positioned around the room on the floor waiting to join her on the bed they would all share to sleep. There was a routine to this. Hart came into the room and pointed at one of them. He gave his orders. The girl of choice did as she was told for however long he lasted, and when he was done, he would leave them alone. The others made sure she fed first when the bottle came around. They tended to each other, not out of any particular kindness, but because they were glad it wasn't them this time. No one spoke of this. It was possible Cora was the only one who thought of anything more than the gnawing hunger that was as much a part of them as the length and thickness of the Master's shaft. Perhaps they even enjoyed it; she didn't know. They didn't talk about it. They didn't talk much at all. She was making them uncomfortable lying there, not moving. More than once he had killed a girl and they'd had to wrap her body in the soiled sheets and lay her in the hallway for the servants to burn. But this was not their Haven, and the Master would be more discreet. There was something he wanted here. Cora slowly, painfully climbed off the bed and drew herself erect, refusing to lurch and hobble. There was so little dignity for them, she clung to whatever shreds she could catch. There, too, she was strange to the others. She walked to the bathroom, coaxing her legs through the steps it took to get there, and closed herself in silently to wash away any trace of her Master. The new girls usually cried the first few times. Not yet suffering the effects of having too little blood, they still remembered enough about life to know that they were being violated. No one offered them comfort; there was no point. They might as well learn to bear it. It was going to happen again, and again, in a hundred different ways, until they were so used up that they simply lay down and died. Cora had seen it. In fact, she had seen it two days before they left their Haven. The long-limbed redhead, Shannon, had been there longer even than Cora, surviving continual starvation and abuse until one night when the Master had been dissatisfied with her and beat her until she was still. Cora had tried to feed her, but she refused to drink. Even so, it took two days for her to die, and the last day she was moaning, delirious with fever, her body rotting from within. Their kind could not sicken unless they were so incredibly weak that their healing ability shut down. Cora cleaned herself up and brushed her once-abundant hair, which had started falling out this past year. She imagined that she had perhaps another decade before she followed Shannon. She could always stop feeding, but he would notice. The ones who died were permitted to do so because he was tired of them. He had yet to tire of Cora. In fact, sometimes it seemed he reserved a special kind of viciousness for her, as if he had noticed her strangeness and wanted to punish her for it. She left the bathroom and took the garment that had been thoughtfully left for her on the chair by the door. The others had curled up on the bed. The bed here was larger than the one they had at home, with a mattress that was new and soft, comforting to joints that had no layer of fat to protect them. She curled up on her side again, running her hands over her body, cataloging how many ribs she could count, how far her hip bones protruded. There was a knock at the door, and she watched the Master's servant, Jones, pass through the room. He was a eunuch, and mute—whether his silence was the result of a natural disability or the Master had cut out his tongue for some perceived offense, Cora would never know. He opened the suite door and one of the Haven servants, a plump woman in the livery of this territory, smiled generously and said, "Good evening. I've brought the blood you requested . . . are you sure it's enough?" Jones nodded and took the tray from her; on it were a single plastic bag of blood and four glasses. The servant looked perplexed but didn't make an issue of it, and left. Jones was fed on a different schedule, and as a man, he was given more. He set the tray down and poured out their servings, then came around and handed each a glass. The new girls always guzzled, but then they realized there was no more coming, and Cora watched the hunger drive them slowly mad until it simply ceased to matter. It was one way in which the Master brainwashed them; the haze of starvation was a mind killer. Sometimes if they performed well he would give them extra as a treat. The veterans learned to sip tiny bits over the course of an hour or more, savoring it, making it last. Cora dipped her finger in her glass and touched the blood to her lips, then licked. It was human, which was nice. They didn't always get human. If the Master thought they were being too energetic, he switched them to rats for a while. She looked over at Naomi, whose eyes were huge and white in her dark face. Cora remembered Naomi when she was new, before her eyes had sunken. She had been so beautiful. Stunning, even. Cora had stared at her for hours, just loving the way she moved and the liquid brown of her eyes. Twenty years later it was all gone and there was a skeleton left . . . all that remained after the girl had decayed. _Why am I different?_ She'd first started seeing it about five years earlier. She'd begun to have thoughts . . . sinful thoughts, violent thoughts. Once, as the Master shoved his dick into her mouth, she imagined biting down hard enough to sever it. She imagined him screaming in agony, and her stomach clenched with hatred. It had been so long since she had felt anything, she had been sick afterward. She began to question things. She began to think about Adam and Eve. Had Adam beaten his helpmeet? Used her body whenever he'd liked—whether or not she was a willing participant? That first creation of God . . . the truest example of what a man should be like, fundamentally, before culture and history had even come to be . . . had Eve been free to speak? God had commanded her to lie beneath him. But had he commanded her to let him grind her beneath his heel? Cora knew another story. Once, when she was a child, a man came to her father's house—her father had called him a Jew. He had told fanciful, even blasphemous stories to the children when there were no adults in earshot. The land he had come from was rich in stories, overflowing with stories, and she drank them deeply. In his land there was another woman, one before Eve. She was flawed, sinful, proud. She refused to lie beneath her husband. She wanted him to lie beneath her. She left the Garden and became a demon, eating the souls of young boys, causing men to think lustful thoughts. The Jews made signs against her, said prayers. She was evil and to be feared. Cora liked her. She had forgotten that story, and that wicked woman, for a great many years. But something had made her remember . . . only hours ago. Something had brought that story, the story of the Lilith, back to her. No, not something. _Someone._ Cora had seen the Lilith. She had beheld that terrifying beauty, mother of serpents. She had seen her walking the halls of this very place. She walked with purposeful steps, clad in black, and the wild snakes of her hair were the color of blood. She did not lower her eyes to men. She was not obedient or quiet. Men followed her, bowed to her. Here, the Lilith was named Miranda, and she was Queen. Cora had seen her for only a few seconds, but her image was burned into Cora's mind, a study in fire and iron. _Queen._ Every time Cora thought of her, she began to shake inside, sometimes so hard it made her head hurt. That thought made Cora remember those long-ago days in the fields, running, laughing, her muscles pumping hard and her cheeks rosy with health. What would this Queen do if the Master commanded her to lie down? Cora knew she would not obey. But how could that be? How could a woman simply . . . say no? Did her Prime let her feed whenever she wanted? How did she not go wild, then, and lose her soul to the devil? Perhaps she already had. But damnation, Cora realized with a spinning feeling in her mind, would almost certainly be better than this. She would never know what changed. She would never understand how, in that moment, lying there with her finger in her mouth sucking the last traces of blood from beneath her nail, she would suddenly look around the room at the pathetic bones of what had once been sweet young girls and her heart would throw itself around the inside of her chest with so many emotions she couldn't breathe. She would never recall precisely what it was, what wanton thought passed through her mind, that pushed her up off the bed, ignoring the screaming pain in her joints and muscles, and to her feet. The others were staring at her as if seeing her for the first time. In a way that was true. They all so rarely looked at each other; it had taken her a decade to realize that Suzette had blue eyes. But they were looking at her now, frightened that her bizarre behavior would bring the wrath of hell down on them. Cora didn't stumble, nor did she hesitate. She went to the door and opened it. There was a guard outside, a tall man with coloring not dissimilar to her own. He was dressed in the uniform of the Signet warriors of this territory, so different from the see-through wisp of gauze she had worn every day for eighty-one years. "May I help you, Miss?" the guard asked in English. She knew little of the language, but she had picked up enough from the other girls that she could say, haltingly, "Please . . . please help me. I . . . please . . . I must see the Queen." Four When ordinary couples fought, they stood face-to-face in kitchens and living rooms. They started out discussing, then moved on to arguing, then shouting. Even in a reasonably healthy relationship sometimes tempers flared and things got broken: A dish might be slammed thoughtlessly on the counter, a pillow thrown into a vase, or, on rare occasions, a fist put into a wall. When David and Miranda fought, swords were involved. Faith watched the whole scene with a morbid fascination akin to watching Mt. St. Helens erupt on television in 1980. She was standing at a safe distance on the edge of the practice ring, and thankfully there weren't any other Elite hanging around this time. Usually at least a few liked to eavesdrop on the Prime and Queen sparring, to see if they were really as good as rumored to be. They were. Obviously the Prime had at least a hundred years' practice as a warrior over his mate, but the Queen was no slouch and had already doubled her speed and agility since taking the Signet. It was the Queen, in fact, who had decided they should learn to fight as a team, two coordinated halves of a damned scary whole. "So what am I supposed to do, then?" Miranda asked, swinging her blade in a smooth arc toward his head. David parried easily and drove her back. "I told you," he said calmly. "Stay out of it." "I can't stay out of it," she snapped. "He's starving and raping those girls to death." She leapt out of the way of the sword that barely missed her sleeve and spun sideways, bringing her sword up hard and almost knocking his from his hand with a loud ringing strike. "He's been here two days—I can't just look the other way while that's going on under my own roof!" "Unless those girls come out and say that they want to be rescued, we can't assume that they're unhappy," David shot back. "Intervening without an accusation of abuse from one of them would be tantamount to a declaration of war against Hart. No doubt he has them too scared to speak up for themselves. Chances are that's why he brought them in the first place—to try to goad us into acting." "Then why all this 'let's be allies' crap?" David made a disgusted noise and ducked her blade, spinning around to slam his sword back into hers. Sweat was running down Miranda's face, her hair and T-shirt were soaked, and even David had beads appearing on his forehead—a first, Faith thought, since she'd last seen him fight Deven. Miranda's fighting style was similar to David's already, so she knew a lot of his moves, and her only disadvantage other than inexperience was her tendency to let emotions get the better of her. That, too, would take time to overcome. "That's exactly what it is—crap," David said. "As soon as he gets what he wants, he won't need to kiss ass anymore. But I'll have the analysis of that earpiece and he'll have only what information I want to give him. He thinks he used me, I keep the device, everyone wins." "Not everyone." Miranda dropped flat to avoid being cut, then swung her leg around and knocked David backward off his feet; he hit the ground in a roll and was up again in a blur of motion, already driving the Queen toward the edge of the circle. She dove in to counterattack, but all she got was her sword clattering to the ground several feet away, just out of reach. David paused, glanced at her sword, and the blade rose into the air and zipped over to his outstretched hand. "Now what are you going to do, my Lady?" he asked politely, swinging both in circles. "How can you be such a coldhearted bastard when you know what's happening to those women?" she demanded, crossing her arms. "After what happened to me?" He gave her an annoyed look. "Oh, were you turned into a vampire as a teenager against your will and taken to be part of a harem?" "You know what I mean!" The Queen's anger flared and she pushed it outward—Faith could feel it starting to boil in her own blood. The nerve of the Prime, refusing to help . . . what kind of man was he, anyway, to . . . Faith caught herself and bolstered her shields before her thoughts became violent. This was one of Miranda's weapons; it was hard to defend against and most people would have no idea how. Luckily she did. So did David. His power-aura expanded, her wave of wrath bouncing off him harmlessly, and he gave her a stern look. "Remember the rules, Miranda. I don't throw things at you, and you don't try to heart-spank me." "Maybe you deserve it," Miranda said. Even if her anger wasn't affecting them anymore, it was still a palpable force in the room, and Faith knew, from seeing this sort of thing before, that if she didn't ground it out it would make her do something impulsive and foolish— —like throwing herself to the ground, rolling under the Prime's spinning blades, and crashing into his feet, which worked well enough at first, sending both swords into the air and the Prime to the floor on his stomach. Miranda got up first and flung herself sideways in time to catch one of the swords, and David rolled right and caught the other. Then they were back on their feet, Miranda attacking with unrestrained fury, exactly the kind that got rookie Elite killed. For a few minutes there was nothing but the sound of blade and blade hitting each other so hard it was a wonder neither broke. Faith watched, smiling, feeling proud of the Queen for having learned so much so quickly. Sophie had been a good teacher . . . . . . whoever she was. Faith frowned, her attention momentarily sidetracked by the memory of the night she'd met the diminutive warrior. Sophie had been drunk off her ass and boasted she was ex-Shadow, which Faith had scoffed at until Sophie challenged her to a fight out behind the bar and proceeded to kick Faith's ass up and down the alley. Faith had asked her for pointers, and they'd met periodically to spar, just for fun, but she'd never really known anything about Sophie beyond that, and Sophie had never mentioned the Shadow again. Had she really had an ulterior motive? Or was Hart being, as usual, a paranoid shit-stirrer? If someone had hired the Shadow, why would they want to help Miranda become Queen? What other motive could they have, given that Sophie had had plenty of chances to kill Miranda when she was human, but had been, more or less, her friend? Had Sophie gone off mission when Miranda won her over to the Signet cause? There was no way to know now. A search of Sophie's old studio had turned up absolutely no personal effects whatsoever, only a cache of weapons that were clean of any kind of fingerprints, even Miranda's. Faith came back to reality in a rush as a loud clattering sound startled her. She looked up to see that Miranda was once again disarmed and David was standing over her, sword pointed at her throat. To his credit, at least he wasn't stepping on her neck. "Goddamn it!" Miranda snarled. She tried to escape first to one side, then the other, but David was too fast for her and kept her pinned. He was calm as always—Faith was sure it infuriated Miranda, because it infuriated most people. "Eventually you're going to have to learn to listen to me," David told her. "Sometimes life is unfair, beloved. If there were a war between our territories, Hart would hire hunters, send assassins by the dozen, and rally other Signets against us. If you want to do something for those girls, you're going to have to think of a better idea than charging in there to liberate them like some avenging man-smiting angel." They glared at each other for a long moment, and Faith wasn't sure whether they were going to start fighting again or jump each other and have sex on the training room floor. She was pretty sure both had happened at least once. "So you don't care at all what happens to them," Miranda accused. "You'll be fine with him taking them back to New York and using them as toys until they die." Finally an edge of anger crept into David's voice. "I never said I was fine with it. But I have considered the consequences, which apparently you have chosen to ignore. In this case the price of their lives doesn't weigh more than all of those that would be lost in a war. They don't outweigh the thought of Hart having you killed, or worse, in revenge. This is how it is, Miranda. The decisions we make aren't pretty, but we have to consider the Shadow World as a whole, not just individual lives." Miranda slapped his sword away, and he stepped back to allow her to stand. She ignored his proffered hand up. "Individual lives are what make up our world," she said. "If we're not willing to step in and help when someone is suffering, then why are we even here? To maintain some bullshit social order that in the end means nothing without justice and compassion? I tell myself you're not as heartless as you act, but sometimes I wonder if I'm wrong." If anyone else had tried to bait the Prime, Faith would have run for cover. David, however, simply took a deep breath, retrieved both swords, and handed Miranda hers. He took his own and wiped the blade down, then sheathed it. He addressed Faith. "I'll be in my workroom for the remainder of the evening." Without looking at or speaking to Miranda, he walked away. Miranda's anger seemed to deflate once he was gone, and she shook her head and went over to a bench to examine her sword. Faith sat down next to her. Miranda still had no idea that Sophie's motives were in question. As far as she knew, the warrior had been her teacher and friend and had died helping her. Miranda treated Sophie's sword with reverence, even though it wasn't the ideal weapon for her—she needed something balanced a little differently, and a little shorter. They'd tried her out on other blades, including some from Sophie's collection, but so far nothing had been perfect enough to persuade Miranda to give up the one she had. Miranda obviously didn't want to talk, and that was fine, although Faith knew in a few minutes she'd probably change her mind and get angry all over again. Before Faith could offer any sort of conciliatory advice, however, her com chimed. "Star-three here," Faith said. _"This is Elite Sixty-two, door guard at the guest suites. I have a situation here that needs your urgent attention."_ Miranda sat forward, listening keenly, though the guard probably had no idea she was there. "Go ahead, Elite Sixty-two," Faith said. _"I have a woman here from Prime Hart's . . . entourage . . . asking to see the Queen."_ Faith and Miranda exchanged a look of shock, and Faith raised an eyebrow at her; Miranda nodded once. "Request forwarded," Faith replied. "Stand by for further orders." Miranda lifted her wrist and said, "Elite Sixty-two." _"This is Elite Sixty-two, my Lady."_ "Bring the woman to the first-floor audience room. Keep her under heavy guard. I'll be waiting." _"As you will it, my Lady."_ Miranda hit the door running with Faith one step behind her. The audience chamber was one of the most pretentious things in the Haven, but under certain circumstances it was extremely useful. It was about the size of the other meeting rooms and studies where the Pair conducted receptions and business with the visiting Primes, but it was not set up to create comfort and camaraderie; it was a royal chamber whose entire design was meant to intimidate visitors and remind them who was in control. Primes were occasionally called upon to settle disputes among the more powerful vampires of their territory, known as the Court—those who weren't warriors, but who were allies of the Signet, were considered noblemen and assisted the Signet in various ways. In return they were protected from gangs, hunters, and human interference in their affairs; smarter Primes like David kept up good relations with human institutions as well, particularly state and local governments, so if someone from the Court had, say, an issue with zoning laws or trade regulations, the Prime could use his influence—and occasionally his cash—to smooth things over. David had lent Elite to some of the higher-ranking vampires to help train their own personal security forces or run investigations into various forms of unrest, especially in other cities in the South where he couldn't be a constant presence as he was in Austin. Some of the Court were entrepreneurs, and some came from old money. David's Court was made up of a combination of the two, weighted toward the former, as most of his friends were involved somehow in security, technology, or finance. Vampires learned quickly that they could easily outlast their own money, and living in poverty wasn't exactly a fun way to pass the centuries, so those who were remotely intelligent found ways to save and invest. That was part of how David had become so wealthy even before taking the Signet. He knew a good thing when he saw one and had invested in little-known start-up companies like Apple and Intel. He still had a large sum in the market, but most of it was socked away in accounts all over the world, and he could live on the interest alone for another five centuries. Miranda was entitled to half of the Signet account, but she had her own separate account for her musical earnings as well, and with David's shrewd advice it had already grown by leaps and bounds. Miranda and Faith made it to the audience room in less than a minute, and the Queen took her chair, to the right of the Prime's at the far end of the room facing the doors. Aside from those two chairs the only other furniture was long benches lining the sides of the room, so that whoever came before the Pair had to stand. Their seats were elevated, as they would be in any throne room. She really hated the place, but it seemed appropriate for the situation; there was no way to know what this woman wanted, whose side she might be on, or what her true intentions might be. David had said Hart had brought his "girls" here to taunt the Pair, and if he knew they would oppose his perversions, he might have sent her as bait. David might not think much of Miranda's diplomatic abilities, but she wasn't a complete idiot. They waited a few minutes, long enough that Miranda started to wonder if the whole thing was Hart's idea of a joke, but then there was a chime, and Faith had a brief conversation on her com. "They're here," Faith said. "It took a minute because they had to find someone who speaks Italian—the girl's English is rudimentary at best." "Bring them in," Miranda replied. Faith nodded and strode over to the double doors. Miranda took a minute to compose herself—too bad she hadn't had a chance to shower beforehand, so she wouldn't be such a sweaty mess—and sat up straight and tall in her chair, one ankle crossed over the other, her hands folded. Her Signet was plain to see, as was her sword, and she quickly reached up and yanked the elastic from her hair so it fell loose down her back. A ponytail wasn't nearly as impressive. Faith held the door open as Elite 62 and three other guards escorted a pitifully thin figure into the room. She was leaning on Elite 62, who treated her with surprising tenderness, helping her walk the long expanse to the dais, steadying her when she stumbled. The other three guards followed at a respectful distance, as if the woman were an honored guest and not a potential enemy. Miranda saw Faith's mouth set in a grim line at the sight of the woman, and as she got closer, it was clear why. The girl couldn't be more than seventeen physically, perhaps even younger; she was so skeletally thin that it was hard to tell. Her skin, once olive and probably beautiful, was ashen, her eyes sunken in with dark circles beneath them. Her dark hair was waist-length, but lank, dull. She was dressed in a gauzy thing that barely covered her wreck of a body. Miranda saw the shadows of bruises on her breasts and legs, and she had a fading black eye that, on a vampire, should have healed in thirty seconds. Miranda gripped the arms of her chair until her fingers went numb. One of the Elite, 29 if Miranda remembered correctly, stepped forward and offered herself as translator; Miranda nodded to her. Elite 29 went to the woman and touched her shoulder lightly, gesturing for her to speak. The girl's voice was tremulous but held the faintest hint that it might once have been very different. "My name is Cora," she said through Elite 29. "The Master brought me here to your Haven." "Welcome, Cora," Miranda said. "I am Miranda Grey-Solomon, Ninth Queen of the Southern United States. How can I be of service to you?" Cora looked like she was sure Miranda, or possibly one of the Elite, was going to strike her down at any second for what she intended to say. "I . . . I need your help, Lady Queen. I want to leave my Master's house, where he keeps me as a slave to his lusts. If I do not get away from him, I will die like all the others do. I want . . ." She looked around helplessly, waving her pencil-thin arm weakly as if to take in the Elite, the Queen, and everything around her. "I want to be free of him." Miranda took a deep breath. "Come here, child." The Elite helped Cora approach the dais, close enough that Miranda could lean forward and look directly into her eyes. "Are you here of your own free will?" Cora was taken aback by the question. Apparently the thought had never occurred to her, but slowly, she nodded. "Yes." "Be still a moment, please." Miranda extended her empathic power toward Cora, who seemed not to feel the intrusion at all; she wasn't shielded, but as weak as she was she probably had no need for psychic protection. If she had any gifts, they were buried under years of hunger, fear, and shame . . . but something was there, some barely shining potential struggling to be released. Miranda held the girl's mind and heart in her palm, looking her over, trying not to be harsh in her touch. She knew how it felt to have one violation piled on top of a mountain of others. There was no need for that. Miranda clamped down on the immediate reaction of her body, which was to charge into the guest suites and rip Hart's dick off and feed it to him. Right now she had to think of Cora . . . who had risked her life and everything she knew to crawl toward something better. That simple courage sparked something fierce and protective in Miranda. She would not allow Hart to hurt Cora again. If David didn't understand, he would just have to, as Kat would say, put on his big-girl panties and deal with it. "Very well, Cora." Miranda stood and walked down from the dais to stand eye to eye with her. The girl shrank back, but Miranda caught and held her gaze. "If it is your will to leave Prime Hart's . . . employ, then as Queen of this territory, I offer you asylum here at our Haven until such time as you are safe and strong again, after which you may choose your own fate. As a refugee you bear the same concomitant rights and responsibilities under the law as any other vampire under the mantle of our authority. Do you accept?" Cora was shaking hard, tears running down her face, and her relief was like rain coming to the desert. "Yes. I do." Miranda nodded. "Then welcome to our Haven, Cora. Let's see what we can do for you." The Queen looked over at Faith. "I want her in one of the suites nearest our wing, with twenty-four-hour guard as long as she's here. She's not to go anywhere without a bodyguard and is to be restricted to the gardens and common areas for now. Have the Elite medic look her over, then see to it that she has as much blood as she needs, and for God's sake, find her some clothes." Faith bowed. There was satisfaction in her face. "As you will it, my Lady." Cora was still crying, swaying back and forth, but she looked up and met Miranda's eyes. _"La ringrazio,"_ she whispered. _"Grazie mille."_ Miranda smiled. _"Prego."_ Just then, the doors opened and David walked in, his expression grave; when Cora saw his Signet and realized who he was, she all but melted into Miranda's side, trying to hide from him. The other Elite parted to let him pass and he came up to them, silent for a moment as he stared hard at Miranda. She stared right back. "Go ahead," she said. "Look Cora in the face and tell her she has to go back to him." David shook his head in exasperation, but when he turned to Cora, his expression softened, and he spoke in a low voice, in perfect Italian that, Miranda had to admit, made her insides shiver a little. "Welcome to our Haven, young miss," he said—the Elite translator leaned closer to Miranda and told her so. "I am Prime David Solomon, and I would like to assure you that you are safe here for as long as you need sanctuary. Please allow the guards to escort you to your room." She stammered a question, and he smiled. "No, you will not have to share it with anyone. You'll have a bed of your own and your own bath as well. Once you've fed properly, you'll feel much better." He gestured to the guards, and Elite 62 bowed politely to Cora, then took her arm and slowly led her away. Then he faced Miranda. "She asked for asylum?" "Yes," she replied. "Completely of her own volition. I don't know what motivated her to do it, but I looked into her as deeply as I could, and she's clean. Innocent. And broken." David's eyes followed the girl and the guards out the door. "Well, she's safe now." "What about Hart declaring war?" The Prime crossed his arms, giving her an unreadable look. "I told you. Going in and taking the harem would be a declaration. She came to you. That's different. Cora is a refugee. Under the law we can take her in and Hart has no recourse against her or us. Any action he takes against us therefore becomes an act of war and he'll have the full Council to deal with." "What about the other girls?" "Unless they ask for asylum as well, things are exactly as I said before. But depending on how he reacts when he finds out about Cora, he might tip his hand and give us the opportunity to take the rest—we'll just have to see how—" _"Where is she?"_ David's com chimed a second after the voice roared in the hallway, and one of the Elite said, _"Sire . . . incoming."_ Prime James Hart flung open the double doors of the audience room, scattering the Elite who were still in attendance as he shoved his way past them toward the dais. "I demand an explanation for this!" he thundered. His eyes were pure silver, practically glowing, and his teeth pressed downward, though not quite enough to impair his speech as he yelled, "You will return the girl this instant!" Miranda wasn't afraid of Hart, but the sheer strength of his rage almost made her take a step back. She stood her ground at David's side, and the Prime crossed his arms and regarded Hart coolly. One of these days she was going to figure out how to do that. "Be very careful, Lord Prime," David told Hart. "You are not in your home territory and there are now four crossbows pointed at your back." Miranda kept her eyes on Hart, but she heard the creak of wood from the corners of the room, where four Elite had appeared and were now awaiting the order to shoot. "This is an outrage," Hart ground out, towering over David, who merely looked up at him with a completely neutral expression. Hart was a tall man, imposing, used to intimidating people, but he couldn't intimidate David. It simply wasn't possible. "Give her back." "No." "This is an act of—" "Say it, Hart," David hissed, eyes narrowing, their blue going silver at the edges. "Say the word and I'll have you shot before you take another breath. Start a war between us right now and it will be finished right now." Hart snarled, "You had no right to steal what rightfully belongs to me." "I stole nothing. Cora came to my Queen and asked for asylum. She has exposed your cruelty and your participation in illegal slavery—and we'll see what the Council has to say now that we have evidence to back up the rumors." Hart turned on Miranda. "You did this, then. I should have known. You stupid little whore—no woman takes what's mine. I'll teach you—" Hart raised his arm to backhand her, and Miranda felt David start toward them, but finally, Miranda's rage and hatred toward this sick excuse for a man had an outlet, and she let it fly, drawing up her power and _pushing_ — Hart flew backward, thrown hard across the room, and the sound of a body hitting the far wall and the crunch of breaking bones caused the Elite to freeze where they stood, staring with huge eyes at their Queen . . . . . . their Queen, whose palm was outstretched toward where Hart had been standing. She was breathing hard, but her body sang with pleasure and satisfaction, and she knew she was smiling. David crossed the room to stand over Hart, and she heard him say very quietly, "You have exactly one hour to leave my Haven. If you stay one moment longer, you will die. You are to leave the other three women here. Now, go." He turned his back on Hart and returned to where Miranda stood; the armed Elite converged upon Hart and waited while he got to his feet, one arm sticking out at an unnatural angle, and limped away with the four crossbows still trained on him. Miranda lowered her hand, grounding herself, letting the excess power drain out of her. When she looked up at David he was staring at her, and to her amazement, he looked completely dumbfounded. "That was you," he said. She nodded. "Yeah. I know; I shouldn't have lost my temper." "No, Miranda—it was _you_. You threw him." "So?" "With your _brain_." She frowned for a minute before she understood what he was saying. "Oh." "How did you do that?" Miranda's heart was pounding. "I . . . I don't know. Is that . . . not normal?" "No . . . it's beyond not normal. Pairs share power, but they don't share talents. That's not possible. How could you suddenly be telekinetic?" David had all the answers. The thought that there was something that baffled him this much, and obviously worried him, worried her even more. "I don't know. But I didn't know I was prescient, either, until that thing with Kat yesterday." "Every Queen has that talent to some degree. It usually doesn't fully develop until after she takes her Signet." Seeing her distress, and moreover feeling it, David took a deep breath, then came over and put his arms around her. "It's all right, beloved. I'm sorry I overreacted—there must be an explanation. I'll see what I can find out. Maybe it is normal; I've never heard of gift transfer, but I've never had a Queen, either." She leaned into his shoulder, suddenly exhausted by the whole evening, wanting nothing more than to climb into bed with him and shut the world away. "And you're not angry at me over Cora?" "No. You did the right thing. I'm proud of you." "Good," she said. "I was afraid I was going to have to kick your ass." He sighed. "You don't really think I'm a heartless bastard, do you?" She chuckled in spite of herself. "I think you know a lot more than I do about all of this, and we're going to butt heads a lot until I figure it all out. But if you can be patient with me, I'll be patient with you, and it will all work out." "I hope so," he said, holding her tightly. "I hope so." A little over an hour later Faith followed the frantic call of Elite 18 to the guest suites. One of the servants had gone into the rooms that Hart had abandoned to start what would no doubt be an arduous cleanup, and her scream had brought the guards running. Faith stood in the doorway, gripping the frame with one hand, the other on her sword hilt. Hart had destroyed his own room, dumping books from shelves and knocking over furniture. He had thrown anything breakable he could get his hands on onto the wall, and there were bits of broken glass and ceramic all over the wood floor. Nothing appeared to be missing, just smashed and torn. Faith, however, was in the doorway to the smaller bedroom, which reeked of sex and blood. The only thing in the room that had been broken was a single wooden chair. Three of the legs had been snapped off. Each leg now protruded from the chest of a naked woman. Hart had stripped them, murdered them, and then thrown them into a pile, their long bony limbs splayed out on the floor of the bedroom. Faith had seen a great many dead bodies in her life, mostly from violence without warning. So many faces had been marked with horror and fear at the moment of death. Here, on the other hand, she saw girls whose dying expressions had been utter indifference to fate, and one was even smiling. Elite 18 was kneeling by the bodies and pointed to one of their bare stomachs, where it looked like Hart had slashed her with a knife. "Look," he said. Faith came closer and squinted. The slashes weren't random. They were letters. "Clean it off," she said. Elite 18 nodded and grabbed a discarded pillowcase, wiping gently at the dead girl's midsection; a servant brought a cup of water, and they scrubbed at the dried blood until the letters were visible. Faith's chest tightened as she read it. _SOON, BITCH._ "All right," Faith said quietly. "That's enough. Let's take care of these poor girls." She ordered them separated, cleaned, shrouded, and burned, and everything in both rooms stripped and replaced from the handful of bedrooms toward the back of the Haven that hadn't been used in decades. Then she shook her head with heavyhearted resignation and went to call the Pair. Before she could even say "Star-one," however, she heard footsteps behind her and a shakily drawn breath. Faith turned to the Queen. "My Lady—" Miranda darted into the bathroom without speaking, and Faith heard her retching. Several of the sturdier-stomached servants had converged on the bodies and were gently coaxing the girls apart, laying them out on plastic sheeting. Esther, who normally saw to the Pair's wing, had arrived with cleaning supplies and grim determination and was overseeing the whole operation; the little woman had been on staff longer than Faith had been in Texas, and, having worked for Auren, surely she had seen worse. By the time Miranda emerged from the bathroom, her composure regained though she was still pale and a little green, David had arrived, and he drew the Queen into his arms and held her, silently, while the bodies were tended to. "We should never have left him alone with them," Miranda said softly. "We should have had guards on the suite as soon as he walked out . . . why didn't we send guards?" "It's my fault," David said, sounding as disturbed as Faith had ever heard him. "I was so rattled by you throwing him that I didn't think . . . I just didn't think." Faith could see the anger in David's silver eyes, and the shock and guilt in Miranda's, and after a few minutes, Miranda visibly steeled herself and stepped away from him to kneel next to the girls. She gestured to one of the servants, who handed her a wet washcloth, and joined in on the nearest victim, helping to draw the bloody stake from her chest and then swab her cold skin clean. Faith sighed and looked over at David, who through his carefully lidded rage was obviously unsurprised by the violence of Hart's reaction . . . sickened, yes, but not surprised. The Prime took a deep breath, then turned to Elite 18, who couldn't seem to bear looking at the girls but had devoted herself to righting the pieces of furniture that weren't hopelessly damaged. David touched her shoulder and said something to her quietly. Elite 18, clearly relieved, nodded, bowed, and disappeared. David took over for the warrior, examining a chair and then moving it to the side of the room where the usable items were being stacked. Faith nodded to herself and joined the others on the floor, where she lent her hands to help Esther wrap the first girl in a clean white sheet. They all worked in silence until there was motion at the door, and Elite 18 said in a low voice, "I've brought her, Sire." Faith looked at David, who inclined his head toward the door; she rose and followed him into the hallway. Elite 18 had in her company the refugee woman, Cora, who looked positively petrified at being led back to Hart's suite. Seeing her fear, David and Faith both placed themselves between her and the door so she couldn't see inside. David spoke to Cora in Italian, but Faith knew what he was asking. He wanted to know the names of the other women. Cora stammered a little, but answered him. He thanked her, then told her, gently, what had happened. Cora didn't seem to react at first. She looked over Faith's shoulder at the doorway, then down at the floor, and said something; her voice was wooden, but her eyes were full of tears. "Of course," David said in English. Then to Elite 18: "You can take her back to her room now. Make sure she's comfortable and has fed before you leave her. Then see to the pyre, please." "As you will it, Sire." After she left, Faith raised an eyebrow at David. "She didn't seem too upset." He crossed his arms. "The women in the harem don't interact much. The black girl's name is Naomi, the blonde is Marie, and the Chinese girl is Mei. Cora wasn't sure about the last one—Mei was new and no one else spoke her language." "At least we know what to call them now . . . they won't have to be burned without identities, such as they are." "True." They returned to the room, and David joined Faith and the Queen next to the bodies. He lightly touched each of the girls' heads in turn and told everyone their names. Miranda was helping Esther wrap Mei, whose skin had been carved with Hart's scathing, vicious message to her, in the sheet that would be her burial shroud. "I'm sorry, Mei," the Queen whispered as she covered the dead girl's face. "I wish we had helped you sooner. This is the best we can do for you now . . . be at peace." David knew better than to think he'd be able to sleep that morning. After he was sure that Miranda was out, he carefully untangled himself from her arms and legs and put clothes on, then left their suite for his workroom. He was not happy. He was grateful that Hart was gone, but the whole situation had left him fighting mad, and the downside was that Hart wasn't there to punch in the face. Now he was left to figure out what steps to take next in the wake of Hart's dramatic exit. The Council had to be informed, of course. He would notify all his allies that he and Hart had officially severed all relations, and the news would be all over the world inside an hour. Though Hart had friends, nobody really _liked_ him; those who sided with him shared his beliefs but would be more than happy to throw him under the bus if it served their interests. David sank into his chair, leaning forward to put his head in his hands for a moment; he had a mighty headache but he wasn't about to wake Miranda up to heal it. She was going to have trouble sleeping today as it was. Despite the horror of Hart's aftermath, one question kept returning to David's mind: How had Miranda done it? David had felt her drawing on their combined strength, but that happened all the time. That was what their connection was for, to make them more powerful as a whole. But he had never heard of anything like one member of a Pair inheriting the psychic abilities of the other. He hadn't developed empathy . . . not yet, anyway, thank God. It frustrated him how little was known about the history of the Signets, and how little the others seemed to care. He had proposed a research project more than once and been sneered at. As long as they had power and money, it made no difference to them where it came from. It wasn't as if they could do anything with the knowledge anyway. Fools. Old, blind fools with their heads planted firmly up their asses and their hands planted firmly in their pocket-books. Now here David was, with a burning question he had no way to answer. It was possible that Deven might know—he was one of the oldest Primes in the Council and had been all over the world before settling in California to rule over his territory. He'd never shown any interest in Signet lore, but that didn't mean he had no knowledge of it. It was, however, the middle of the day, and a quick look at his computer told David that the Prime was not online. It was the pinnacle of bad manners to wake a Prime during daylight. His questions and vague nameless fears would just have to wait until sunset. To distract himself he decided to try to crack open Hart's little toy. He retrieved it from the locked cabinet where he'd stashed it, as well as a number of tools, a scanning module he'd built, a vise, and a handheld laser-cutting torch. He placed the earpiece in the vise and hooked up the scanner to his computer, then spent a while running preliminary tests to see if he could learn anything from the piece without breaking into it. There wasn't much to learn; it didn't put out any sort of signal, and even if it had, that signal wouldn't have made it past the Haven without being hopelessly scrambled. Whatever network it had been connected to, it was dead now. David paused here and there to type up a few quick notes. _Casing appears to be a similar titanium-aluminum alloy to the fourth-generation wrist coms. Seamless except for a single hole approx. 1 mm in diameter. No obvious signs of manufacturer, not recognizable as belonging to any well-known designers in the communications industry. Possible DOD origin?_ Unlikely. The Defense Department could scarcely make a move without his knowing it. He changed the scanner's setup to tell him more about the internal makeup of the piece so at least he'd know how thick the shell was and could calibrate the cutting laser appropriately. It was unusually thin, barely an eggshell over an interior tightly packed with wiring and what looked like a single tiny chip. Before he tried opening the thing, he had the scanner take surface images and put all the technical scans into a folder, then moved his laptop away from the table in case of any accidents. He turned the vise and raised it slightly, then switched on the laser, a compact handheld model he'd won in a poker game from the head of research and development at one of the other defense contractors. It was a thing of beauty, precise and lightweight, and could cut through anything at any thickness without damaging whatever was inside. He could only imagine the mischief it would cause if the outside world got hold of it, which was why, like all his toys, it was locked in this room. David calibrated the beam and got to work. Given how small the thing was, it didn't take long to neatly bisect the casing. He set the torch aside and pulled on a pair of gloves to make sure he didn't damage the components or get anything toxic on his skin. He unscrewed the vise and transferred the piece to a tray sized to fit under the microscope. With a pair of long tweezers and a probe, he peeled one side back from the other, gingerly exposing the perfect twist of wires within. He slid the probe into the wires and teased it apart, exposing the chip like a pearl inside an oyster. The explosion sent Miranda screaming out of sleep. Five "Mother _fuck_!" Miranda had known David for a little over a year, and she had never heard him curse quite so much. Faith slapped his hand. "Lie still," she said. "Do you want this out or not?" Elite 12, who was known to his peers simply as Mo, was the official medic for the entire Haven; for the most part a vampire's healing abilities made short work of any injuries, but if something was embedded in a limb, something was torn off, or the victim was weakened to the point that his or her abilities were compromised, Mo took care of things, even sewing on a few fingers now and then until a warrior's natural defenses kicked back in. Infection and the presence of foreign substances slowed the process down, too, so in cases of serious wounds, antiseptics and hygiene were as important to vampires as they were to humans. It was even possible to poison a vampire given the right ingredients, though it couldn't kill one, and Mo had been called upon more than once to administer antidotes to painful and debilitating toxins. Mo leaned over the Prime, who was laid out on his worktable with a shard of metal buried in his left eye. "You know, Sire," Mo said, his cheerful Iranian accent unusually stern, "I have said many times that you must wear eye protection when you play with sharp things." "Yes, and I've said many times you can stuff it where Allah don't shine," David said irritably. "Son of a bitch! What are you using, a fucking jackhammer?" Miranda snorted. Mo was unperturbed. "Sire, if you do not stay still, I may do more damage to your eye or perhaps the nerves around it. It would be rather painful and I think perhaps your Queen would kill us both." She had sprinted into the workroom to find David on the floor bleeding from several small wounds where Hart's mystery earpiece had shattered and flown everywhere. Nothing else in the room appeared to be damaged, although David had urgently commanded her to hit the override on the fire alarm so that the smoke—scant though it was—wouldn't trip the system. Mo had already removed shrapnel from David's face, neck, and left arm, all of which had closed and healed as soon as the bits were taken out. If they had been wood splinters, it would have taken twice as long, if not longer. Apparently a titanium-aluminum alloy was no big deal unless it was stuck in your cornea. Miranda couldn't watch. She'd nearly been sick when she saw his blood; the thought of seeing a scalpel in her husband's eye made her queasy. She had already sent up a dozen thank-yous to whatever god watched over vampires who were too pigheaded to wear safety glasses. It amused her that, even three and a half centuries old and so far removed from human notions of masculinity, David was as much a drama queen about pain as every man she'd ever met. "Stop being a baby," Faith admonished the Prime. "You're lucky that thing didn't blow your head off." David grunted but lay still, letting Mo hold his eyelid open so he could dig in and retrieve the shard. Even Faith looked a little nauseated at the sight and pointedly turned her gaze up toward the ceiling. "It wasn't meant to kill anyone," David muttered, trying not to move his jaw too much and disturb Mo's arm. "From what little I saw it was basically just a nanotransmitter." "Could you make something like it?" Faith asked. The Prime made a noise that might have been a sardonic laugh, but it ended up being a pained growl as Mo pulled his hand back, revealing a centimeter-long arrowhead of silver metal held in his tweezers. Unfortunately Miranda looked just in time to see a scarlet tear of blood oozing from the corner of David's eye. She turned away, groaning, nauseated, determined not to be sick a second time in twenty-four hours. "All right, Sire, go ahead," Mo told him. David clamped his eyes shut and in a few seconds opened them again, blinked, and sat up. "Good work, Mo. Thank you." The medic shrugged. "All in a day's—and I do mean day, Sire, it's ten in the morning—work." David looked chagrined as he wiped the blood away. "Sorry to get you out of bed. You're dismissed." Mo smiled, gathered his supplies, and left. "Let me know if you notice any other stray poking things poking you." David blinked a few more times, focusing his gaze on Miranda, and smiled at her. "I'm fine," he insisted. "It wasn't a disaster." She glared at him, unwilling to concede the point. "It could have been. Hart could have easily made that thing as a bomb and conveniently let you have it knowing you couldn't resist taking it apart." "It wasn't a bomb," he said, which wasn't in the least bit reassuring. "It was a pressure-sensitive trigger designed to destroy the tech if someone got it open. It wasn't intended to do any real harm to the person unless they happened to be staring right into it at the time. Hart is a technophobe—and as much of a psychopath as he is, I honestly believe him that this came from somewhere else. And in answer to your question"—he turned to Faith—"of course I could make something like it. What little data I got suggested it's not nearly as complex as the coms. It was a lovely little thing, though. Beautifully crafted. I wish I could have studied it more." "You're hopeless," Miranda said. "I'm going back to bed." She pushed herself out of the chair and left the workroom, pausing to let the guards know everything was all right and commend them on their quick response. They looked as frightened as she had been. It still surprised her how loyal they were to him—and now, her—and how invested they were in the Pair's welfare. It was unsettling to know that her fate governed the lives of so many people . . . Faith had said so to her a dozen times, but it had yet to fully sink in. Miranda knew better than to think she could really sleep until David joined her and she could run her hands over his body to convince herself he was really okay. But she also knew his fastidious nature and knew he would clean up the workroom before coming to bed. There was no point in even trying to rest until then. She picked up her guitar from where she'd left it earlier, leaning next to her chair by the fireplace. Then she sat down cross-legged on the sofa with her guitar and picked at it mindlessly for a few minutes, letting whatever needed to be played arise. Esther had been in, kind soul, and added another log to the fire at some point; the woman was a born nurturer and no doubt had been at a loss as to how to help David after the accident, so she did what she could do: She made the room comfortable. She'd straightened up the room, built up the fire, and hung a bundle of some kind of herb from the mantel, probably one of her Mexican folk charms. Esther knew all kinds of arcane things for protection from the Evil Eye, to bring money, to lure in a lover . . . she had trained with a _curandera_ when she was human and would have been one herself if she hadn't been brought across. Miranda loved everything about her, especially the way she still called Miranda _reinita_ , "little Queen." The Queen closed her eyes and started humming, then let music and voice both evolve into an actual song, one she'd covered onstage a dozen times. _Like you're trying to fight gravity on a planet that insists that love is like falling and falling is like this . . ._ When she finished the song, she looked up at the Prime, who was watching and listening while he leaned against the bedpost, smiling softly as if nothing in the world existed but her. He had taken off his shirt, and the firelight bathed his bare skin in flickering gold. Was it stranger that the Elite cared so much about him or that she did? "Come to bed, beloved," he said. She set her guitar aside and rose, holding his gaze until she was close enough to fold herself gratefully into his embrace. Faith went into the city with David, Miranda, and her bodyguards Thursday night, but they split up as soon as they reached Austin. Miranda, Jake, and Lali disembarked and headed toward the Bat Cave studio, where Miranda would have her first recording session; Faith and David stayed in the car, bound for a high-rise in the heart of downtown Austin, with everyone set to rendezvous in front of the Bat Cave at three A.M. David was understandably tense. Word had gone out about the drama with Hart, and now he was waiting to see how the other Signets reacted. He anticipated that twelve total would side with him without any argument, and seven with Hart; that left six wild cards who could be swayed either way. Some would be easy enough, like Tanaka, who always maintained his neutrality but considered David one of his oldest friends and, given the evidence presented by Cora, would throw in his lot with David. He required only good reasons and good evidence before making a move, which was understandable, given that he was the parliamentary leader of the Council and was expected to stay as fair as possible. In the end, however, Hart would make the next move. If he never spoke of the incident again and never returned to Texas, there might not be a fight. If assassins started showing up in Austin, it would be obvious to whom they belonged. If Hart was smart, and Faith doubted he was, he would let the matter drop and keep his distance from now on. But Hart had been bested by a woman, and that would rankle him to the point of madness. He hated women pathologically, with religious fervor that rivaled the Blackthorn gang's hatred of gays. It was Miranda's act of defiance that would drive any plans he had for revenge. His bloody message left on the corpse of an innocent woman had made the point quite succinctly. David was quiet on the drive. He brooded far less now that Miranda had come into his life, but he was still prone to long periods of stewing, and Faith could guess at least a dozen of the subjects that might be on his mind tonight. "Is it Hart, the Council, the attack on the Queen, her sudden bout of telekinesis, what to do with your new houseguest, your Queen's security tonight, the Red Shadow's involvement with Hart, its involvement with Sophie, or the exploding hearing aid that's got you all knotted up?" she asked. David leaned back in his seat and groaned. "It wasn't any of those things until you brought them up. Thank you, Second." "Then what were you mulling over?" "Signet history. Why we threw away our own past. How much there is out there to learn and what it could do for us. Imagine if there are powers we don't even know we can access—things even more miraculous than Misting. Pairs can combine their power and boost one or the other's abilities, but I've never heard of a case where one took on the other's abilities and used them without any training or prior talent. What if we can all do that?" Faith smiled. "Then Jonathan could borrow Deven's fighting ability and Deven wouldn't constantly bitch about what a horrible warrior he Paired with." "There has to be a way to find out more. Archives somewhere. Journals. Something. I can't believe that nobody in our entire history has agreed with me on this. We can't all have been that stupid." Harlan pulled up to the front entrance of the building, and Faith and David got out; the Prime leaned in to tell Harlan something, probably a reminder of their rendezvous plans, then straightened, adjusting his coat. It was another cold night; since the hard freeze the night of Hart's arrival, the weather had been insanely frigid with the constant threat of ice on bridges. They took the concrete steps up to the glass front of the building, where a security guard met them and asked for ID. David smiled and opened the neck of his coat, revealing the Signet. The guard nodded and unlocked the door. Near the elevators, a gray-haired man in a white lab coat was waiting for them. Their steps echoed in the empty atrium, only a few lights on at this hour. "Sire, Faith," the man said. "A pleasure to see you again." "Doctor Novotny." David shook his hand and the doctor turned to lead them to the elevator. "You said you have made progress." Faith watched the human as they took the elevator up to the twelfth floor; he was reasonably comfortable in their presence, but he still seemed a bit twitchy once the doors slid shut and he was trapped in the small chamber with two vampires. Novotny was hardly psychic, but a human in a coma would have been able to sense something strange about David. Usually it wasn't anything they would be able to pinpoint, but it was instinct for mortals to edge away, to keep one eye on the door. If there had been ten people in the elevator, by the time they got to their floor, it would have been Faith and the Prime in one corner and all ten humans clustered on the other side. Those who knew what they were, or were gifted enough to know what they were sensing, tended to be much more relaxed around them. Novotny's research lab took up the entire twelfth floor and was accessible only by a special elevator code. The company, Hunter Development, was one of several that David worked with when he needed something done he couldn't design, fabricate, or investigate himself. Naturally he owned about 80 percent of it. The doctor led them to a locked room that scanned his retinas, fingerprints, and voice before allowing them access. Inside were two long tables and a variety of machines whose purpose Faith could only guess. "So you say the thing exploded?" Novotny was asking with interest. David smiled. So did Faith, to herself, at the idea that David had associates as geeky as he was. "I've brought you what was left." He retrieved a flat metal case about the size of a pack of cigarettes from his coat and handed it to the doctor. "There's not much, but if you get anything off it, let me know. All of my preliminary findings are on the drive inside." "Excellent, excellent. It sounds like pretty standard stuff, but you never know. Now, over here . . ." Opening a small door in the far wall—also encoded—Novotny retrieved another case, this one larger, and laid it on the steel table in front of them. "We ran it through the full battery of parameters." Novotny opened the case to reveal a sharpened wood cylinder inside a plastic evidence bag, resting in a nest of gray foam. It didn't look much different from when Faith had taken it from the crime scene, except that Miranda's blood had been cleaned off and a few splinters seemed to have been picked out of it for testing. The scientist went on, "It was easy enough to identify it as _Betula pendula_ , silver birch, found widely in Europe. This particular specimen can be traced all the way to the Lapland region of Finland." "Finland," David repeated. "That's different. Can you tell if it was made there, or imported to the States first?" "There are traces of low-grade steel in the grooves left by the carving implement, and that steel is well over a century old—it predates the Bessemer process. Our conclusion, based on contaminant elements in the steel, is that whatever was used to carve the stake was also made in Finland. Based on traces of soil in the grooves, I can say with confidence that the stake was carved there as well." "What about the person who carved it?" "There I'm afraid the data is inconclusive. I can tell you that he or she was right-handed based on the carving strokes, and there was no extractable DNA except that of the Queen. The blood soaked into the wood enough that it caused interference. As you know, we've made considerable progress analyzing vampire blood on its own, but in the presence of so many other variables, it made in-depth analysis impossible." It was a strange quirk of vampire biology that as soon as their blood was exposed to air, it began to break down very quickly. To the naked eye it still looked like blood, but on a microscopic level it essentially died, the cells dissolving as if in an acid. When ultraviolet light touched it, it actually began to smoke. That made it very difficult to study, and Dr. Novotny's people were some of the few who had had any success. Thanks to their work, David had been able to develop the DNA scanners inside the coms, primarily using skin cells. On the bright side it meant that human authorities couldn't positively isolate vampire blood at a crime scene or learn anything about it in a standard forensics lab. On the downside, it meant the stake probably wasn't going to tell them anything useful about the woman who had attacked the Queen. David looked disappointed but not entirely surprised. "So we're possibly dealing with a Finnish woman, although the stake may not have been hers to begin with, and possibly a vampire because it's so old, though we don't know that for sure either." "She moved way too fast to be human," Faith pointed out. "Have you made any progress on the sensor failure?" David asked. Novotny shook his head. "No more than you have, Sire. We have no idea why this assassin didn't register on the network. She was perfectly average in height and weight, based on the Queen's description. Psychic shields wouldn't block the sensors—they read purely physical traits. Somehow she found a way to confuse the signal, like a stealth bomber. I'm guessing some sort of scrambling device." "Which gives her more than passing familiarity with the system," Faith observed uneasily. "How many people outside the Haven know how it works?" "I want another check run on Elite and staff," David said to Faith. "This time concentrate on hires since the war. Look into their prior associations, employers, friends. Find any connection you can to Finland—it's worth a try. Flag anyone who was separated from their patrol unit or otherwise unaccounted for at any time, for any reason. Pull them in for questioning." "I thought you monitored all your staff and Elite," Novotny said. "If one of them is passing on information, when and how would they go about it?" "Last time it was through the mail," Faith responded. "Security is tight," David added, "but no system is perfect. I learned that the hard way." "In reality all someone would have to do is leave a note somewhere that's picked up by someone else," said Faith, discouraged. "We've gotten a lot more detailed in our security screenings on hire, and we track everywhere they go through the coms, but there are always holes." "Frankly I'm more concerned with motive at the moment," David said, crossing his arms. "It's highly unlikely a gang would have organized so quickly in Austin after the war; aside from the sensor network, we have operatives on the streets of every city in the territory listening for unrest or organization. There hasn't been a single group formed since the battle at the Haven. They're still far too nervous, and they're waiting to see just how strong Miranda and I are before they try anything. To me that suggests we're dealing with a vendetta." Faith nodded. "I was thinking the same thing. Also, Sire . . . I've been considering the exact sequence of events, and I had an observation. The assassin posed as a reporter, which means she knew enough about Miranda to worm her way in to see her. Given how young and new to the Signet Miranda is, word of her two careers hasn't had time to spread very far. As a musician she's well-known locally, but not much beyond Texas. Then there are the questions she asked—she fished for information about the Haven's location. If we were looking at someone in cahoots with one of our people, why wouldn't they already know where the Haven is?" David leaned back against the table, chin lowered, a typical listening-and-mulling-over posture for him. "Go on." "One more thing. The woman told Miranda she was stupid, which suggests a certain arrogance on the assassin's part. That's not typical of gang hit men. They generally don't banter, and when dealing with a Signet they don't risk wasting time with insults. Either you take out a Signet on the first shot or you die yourself. Again, I think we've got someone here who has a personal reason to kill Miranda." Novotny considered that as he closed the case and returned the stake to its cabinet in the wall. "Is your Queen the sort of woman who makes enemies?" David laughed. "She's getting better at it." Miranda had already decided to like her new bodyguards, especially Lali, a petite woman originally from India who, underneath her Elite uniform, wore a T-shirt emblazoned with _Om Shanti, Bitches!_ Lali had a biting wit that seemed out of place with her quiet, melodic voice, and by the end of her first shift with the Queen the two were chatting like old friends. Jake was more stoic, more a stickler for professional demeanor, but he exuded calm confidence and competence, and though he looked like a Marine Corps rookie he moved like some kind of exotic jungle cat. He was from Laredo originally, son of an honest-to-God Texas cowboy, which took Miranda forever to get out of him. By the night she went into the studio, Jake seemed to have warmed to her, and even cracked a joke or two. He wordlessly picked up her guitar from the car's trunk and carried it for her, and though she might have protested anyone else doing the same, Jake was simply being courteous, not implying she couldn't handle it herself. Miranda was ready for the recording experience to be a bit grueling, but she was still amazed at how exhausted it left her. Grizzly Behr, the owner and sound engineer, was a cheerful fellow with a big beer gut, a big beard, and a big accent, and he laughed sympathetically at the way she wilted as the hours went on. "It sucks a goat's balls, but it's worth it," he told her from the far side of the glass, where he and the producer were going back over the third take of the song they were working on. It had taken an hour to get everything set up, another for Grizzly and the producer to record some preliminary tracks to adjust the headphones and mikes, and two more to actually record the song, listen to it, go back and fix the second verse where her voice wobbled, listen to it again, record the harmony, listen again . . . Miranda was starting to hate the damn song, though Lali, in the corner of the control room keeping an eye on things, gave her a thumbs-up more than once after hearing what they'd captured. At least they were starting with an acoustic song that didn't require any other instruments. There were eight more songs to go, and they were far more complicated. They were going to have to get a Bösendorfer in the studio for several of them, which Grizzly assured her was going to be child's play. He had a larger studio room where orchestral groups had recorded, and it was big enough for a grand piano. That would be Saturday's session, however. Tonight was simple . . . comparatively speaking. Finally at about two A.M. Grizzly called a halt to things. She wanted to kiss him. "Good job," he said, shaking her hand when she joined them in the control room. "And thank you for not being a bitchy prima donna. We get a lot of those." She grinned. "Funny—I thought I got a little bitchy there for a while." "Nah. Just wait until we do 'Bleed.' That one should be fun." Miranda gave an exaggerated groan. "God have mercy. Have you found a violinist yet?" "Actually I was just talking to your friend here, and she says she plays." Miranda looked at Lali. "You do?" The Elite smiled. "I do indeed, ma'am." "Congratulations," Miranda said. "You're my new favorite person." By the time they were packed up and ready to go, it was twenty till three. Miranda was grateful for the freezing cold air outside; she was sweaty and sleepy and the chill perked her up a little. Harlan was already parked out in front of the studio, along with the second Haven car for Lali and Jake. Jake, who had been on front door duty, stowed her guitar in the Town Car's trunk. While it was open Miranda fetched a bottle of water from the pack that was always there, in a small cooler that typically held an emergency supply of blood as well. She also took a moment to put on her coat and strap her sword in its place on her hip. She'd been reluctant to take the blade inside the studio in case someone noticed it and raised awkward questions. "I'll get you the demo CD for the songs where we need a violin," Miranda told Lali. "If you're on board, I'll pay you whatever the going hourly studio rate is plus a bonus." Lali looked thrilled and was about to reply, but Miranda held up a hand to shush her, lowering her water bottle and staring hard into the night. What had she heard? She concentrated, extending her senses around the parking lot and the intersection adjacent to the studio, sweeping the area for anomalies as she tried to hear the noise again. Her hearing could catch sounds half a mile away, and if she focused her energy on a particular location, she could pick up conversation at more than twice that distance. It came again, this time clear as a bell: a woman screaming. Miranda was off and running before either of the guards could react. Adrenaline surged through her body, and she let her muscles take over for her brain, carrying her faster than even an Olympic sprinter. The streets were nearly empty at this hour, the sounds of traffic distant in this neighborhood tucked away off Lamar Boulevard. She made it to Lamar in seconds, then across, snaking between cars whose drivers could barely see her as she closed in on a spot that burned in her mind with fear and violence. A quarter mile later Miranda skidded to a halt, drawing her sword, her mind and senses both spinning in a circle as they tried to take in the scene before her. A woman in a business suit was on the ground, sobbing, the contents of her purse strewn around her. Her hair had been ripped loose from its clip, and her lip was bleeding where she'd been hit. Her clothes were in disarray and she had lost one of her pumps. The Queen's gaze lifted from the woman, and her heart seemed to thud onto the scene as her feet had moments ago, lumbering to a stop in her chest. In the watery glare of the streetlight a figure stood over the struggling form of a man. The human, a thirty something white male with eyes huge and rolling in panic, scrabbled uselessly at the sidewalk, trying to escape the black leather boot placed squarely on his neck. "Step away from the human," Miranda commanded, letting her powers flare around her. That alone should have warned the standing figure away, and the sight of a woman holding a sword ought to have at least surprised him. He merely looked at her, chin tilted slightly to the left, as if translating her words into a foreign language. Staring back at him, Miranda felt a slow quake of unease in her stomach . . . unease and recognition. He looked like little more than a teenager, but the shadows in his blue-lavender eyes spoke of great age, of a creature older than she could even imagine now that she, too, was immortal. The way he held himself was regal and proud, as one born to the crown. It was something of a contrast with his wardrobe. He wore black leather: a coat down to his knees, pants, and boots nearly as tall as the coat was long, covered in buckles and rivets. Several pounds of silver jewelry adorned his neck, hands, and face; his eyebrow, nose, and ear were all pierced, the eyebrow three times. His fingernails were painted black, and black perfectly outlined his large, long-lashed eyes. Spiky dark hair over a high-cheekboned, ivory face gave him the look of a punk angel, just as likely to be Lucifer as Gabriel. He was absolutely beautiful, both ethereal and sensual . . . and so powerful Miranda had to steel herself not to take a step back. "I am the Queen of this territory," she said, pushing iron into her voice and energy into her aura. Her Signet brightened with her words. "You will do as I say." Vampires and humans both had quailed before that tone of her voice. A few had bolted. Several had cried. He simply looked at her a moment longer, then lifted one hand and opened one side of his coat. The streetlamp caught the gleaming edge of a sword concealed inside, as well as at least three other knives and what might have been a throwing star. That, however, wasn't what sent Miranda's pulse skyrocketing. At his throat, nestled in among the chains and a heavy silver ankh, was an amulet set with a huge emerald. The stone was glowing. Slowly, deliberately, Miranda lowered her sword. Slowly, deliberately, he closed his coat. "All right," she said. "Who the hell are you?" Ignoring the question, he smiled. She noticed the pointed canines. "At last . . . the flame of the South." He had a gentle voice that still carried to her easily. Something about it, and about the smile, offered up a realization that she didn't especially want, and she nodded, the pieces falling into place. "My Lord," she said. He bowed slightly. "My Lady." The Prime of California had arrived. Six "My Lady! Are you all right?" Lali came thundering around the corner, ready to fling herself into peril on her Queen's behalf, and nearly ran smack into Miranda. A few beats behind her, David and Faith appeared, both coming to an abrupt halt on either side of the Queen, both staring at their . . . visitor. "Holy crap," she heard Faith mutter. Completely oblivious to the injured woman or the still-struggling man, David broke out into a grin and walked forward, laughing. "Sire," the Prime said, "it's good to see you again." "It's good to be seen." David held out his hand, but the other Prime reached up, pulled David's head down, and kissed him on the mouth. Miranda felt her mouth drop open as David returned the kiss . . . for several seconds. When they pulled back, smiling at each other far more intimately than she would have believed possible, the visitor said, "There's my boy." David turned back to Miranda, who was gaping at the entire tableau and feeling rather like she'd stepped through the Looking Glass. "It's all right, beloved," he told her. "Allow me to present Prime Deven O'Donnell of the Western United States and its adjacent territories. Lord Prime, this is Miranda Grey-Solomon, Queen of the Southern United States." Prime and Queen bowed to each other, and then Miranda said, a bit tersely, "Would you care to explain what's going on here, my Lord Prime?" Deven looked down at the human under his foot with open disdain and gestured toward the woman. "An attempted robbery, near as I could tell. I found this thing attempting bodily harm toward the young woman, and I intervened." "Lali, see to the human," Miranda ordered. Behind her Lali dove to the woman's side and began reassuring her, checking her for injuries; the human was bawling, confused and still terrified, but didn't look badly hurt. "Faith, call it in. Inform APD that we have a mugger in custody, and—" She glanced back at Deven in time to see him bring his foot down hard, and with a horrible crack, the assailant's neck snapped beneath his boot. The man twitched twice and then lay still, eyes still staring. "For Christ's sake, Dev," David said, wincing. "Was that really necessary?" Deven looked down at the corpse, then back up at them, and asked politely, "Oh, I'm sorry . . . did you need that?" "This is a no-kill territory." Miranda stepped forward. Deven walked over the body and came up to her; they were almost exactly the same height, but he gave off the aura of someone twice as tall and twice as broad. There was a dare in his voice. "Execute me." Then he moved over to David. "Jonathan is waiting at the car a block east," he said. "Shall we follow you?" David looked a tiny bit bewildered by the way his Queen and the Prime were staring daggers at each other, but he said, "Yes, good idea." Deven gave him a genuine smile, bowed, and walked away. Free of the Prime's presence, Miranda felt her stomach unclench, and she took a deep breath. There was a moment of silence before Faith said, "Okay . . . er . . . APD is on its way, with an ambulance for our victim here. Lali has altered her memory to delete us and insert a struggle with the assailant that ended in him breaking his neck as he tried to climb the fire escape nearby. We're good to go—Lali, stay here until the police arrive and make sure she gets to the hospital, then head back with Jake . . . where's Jake?" Everyone looked around. Jake was nowhere to be seen. "He must have stayed with the car," Lali said. Prime, Queen, and Second started back toward the Bat Cave, and David went ahead a bit so he could call the Haven and get a guest suite ready for the Littlest Magnificent Bastard and his Consort. Out of earshot, Miranda said, "So . . . that's Deven." Faith grinned. "That's him." "He's . . . quite a bit to take in." "That is the popular opinion, yes." Faith looked at her keenly. "What's wrong?" "Besides yet another Prime coming into my town and waving his dick around? Nothing." Faith laughed. "I promise, he's nothing like Hart. Underneath the swagger is a very kind soul." "Right." The Second raised an eyebrow. "What else?" "Nothing, just . . . are they always like that? Him and David?" "What do you mean?" Miranda made a helpless gesture. "With the . . . kissing." Faith, perplexed, shrugged. "I suppose so. Why?" "It's just strange seeing David acting affectionately toward anyone besides me. Is he like that with all his friends? He just shook hands with Tanaka." Faith's mouth formed an O of surprise. "You . . . didn't know?" "Know what? Am I missing something?" By now they had arrived at the parking lot where Harlan and both cars were waiting; to Miranda's surprise, Jake was nowhere to be seen. David was talking with Harlan, and as they approached, the Prime came to them, his expression serious. "Harlan says Jake took off after you and Lali. I tried to raise him on the coms and there's nothing." "Oh, shit," Miranda said. "Faith—" "I'm on it," Faith interrupted, already barking out orders into her com to get a search team to the area immediately. There should be a patrol unit nearby that could be diverted; Jake being off mission was one thing, but not answering his com . . . David had just pulled out his phone when it sent up a network alarm. "We've lost his signal," the Prime said. "That's not good." "You're not even getting life signs?" Miranda asked, peering around his arm at the tiny map of their current location. "No," David replied. "He just disappeared. Faith, get the team to Lake Street and Paredes. He dropped off network at the eastern corner. It's about a block that way." He gestured toward the right. "It looks like he started to follow you but then got distracted. He may have seen or heard something, or been ambushed." He turned to Miranda. "We should head back and let Faith handle this." Miranda agreed reluctantly and joined him in the car. Faith came over to shut the door, ducked her head in, and said, "I've got Unit Five coming in to search for him—ETA three minutes. I'm heading to Lake and Paredes now. I'll com you as soon as I have news." Her expression briefly switched from all business to all mischief: "Enjoy your ride home." "Do you think he's okay?" Miranda asked once the door was shut. David merely looked at her, and she shook her head, heart sinking. "I don't think so either." Neither spoke again until they were on the highway, and Miranda wrestled with the other question on her mind for quite a while before she was ready to say it: "So . . . about Deven." David smiled. "He just likes to make an entrance. The exterior's a little spiky, but inside he's really a good friend." "Is that all?" she asked. "What do you mean?" She took a deep breath. "I mean, were you ever more than friends?" David blinked, mouth opening slightly, as though he had expected any question but that one and had no idea how to respond. Then he said hesitantly, "I thought Faith told you." "Told me what?" Now he looked actively sheepish. "That Deven and I were lovers." She knew she must look like a stranded fish, but she couldn't help it. "When?" "When I was in California. We both served in Arrabicci's Elite, as co-Seconds. We got together about ten years before the assassination. Then Deven took the Signet and we stayed together until Jonathan came along." "Ten _years_?" She put her hand on her forehead, unable to think of anything else to do. "And it never occurred to you to bring it up?" "As I said, I thought you knew. I didn't realize it would be such a problem." "It's not, it's . . . God, I don't know." Now he looked amused, and it annoyed her. "Would it be easier to take if he were a woman?" "Honestly, I have no idea. Although since I had no idea you were bi, it does kind of force my perceptions to realign a little, and I wasn't expecting that." "Oh, I wouldn't say bi, exactly. If you add up all the people I've slept with in three hundred fifty years, men account for less than two percent." "Except that you weren't with anyone else for a full decade, were you?" "Well, no." "So you can see why this throws me just a bit?" Miranda's thoughts and emotions were falling over themselves, and she didn't like it. She wasn't going to be some jealous wife who couldn't stand being around her husband's ex when that ex was his best friend; it was a long time ago, and besides, he'd had plenty of women in his time, including a wife. Why was this any different? "I understand that you're upset," he told her, touching her face. "I wish I'd realized you didn't know. We could have talked about it before they got here. I'm sorry to have dropped it on you like this." "It's fine," she insisted. "I mean, it's not fine, as in I'm a little freaked-out, but not because . . . I mean . . . it's just . . . weird. I learn something about you every day, and I love that, but considering how significant this one is, maybe you could have _mentioned_ it at some point?" David was thoughtful for a minute, but then he said, "There are a lot of things you still don't know about my past, beloved. I have about three hundred twenty-five years' worth of history on you." "I know," she said. "I think about that a lot." He met her eyes. "Then ask," he told her gently. "Whatever you want to know, just ask. I don't ever want you to think I'm keeping secrets. There are some things I don't like to talk about, true, but if you want to know, you deserve to. We're going to be with each other a long time, and that means we have to be honest. No hiding." "Thank you." She leaned over and kissed his nose, smiling a little. "I take it since you never talk about that part of your past, and you're not together anymore, it's not an entirely happy story." His eyes flicked away from hers just long enough for her to know she was right. "It didn't end well," he said. "At least, not for me." "Wait . . . you mean he dumped you?" David's smile was touched with regret, and it made her heart hurt, realizing how much pain was underneath the words as he said, "Unceremoniously and resoundingly." "But . . . why?" Even before the question was out, though, she knew. "Because of Jonathan. That's why you left California. It wasn't about getting your doctorate as much as it was about getting away from Deven." "Yes." "Were you in love?" Again, the smile, but it faded quickly. "Very much so. But everyone knows that a Prime is destined only to be with his Consort. Everyone in the Court thought that the Signet would choose me, but it didn't, and within six months, it chose someone else that Deven had known for all of ten minutes. The two of them fell for each other instantly, as if they'd been struck by lightning, and I . . . I ceased to exist." "That little bastard!" He made an indefinite move of his head: half a shake, half a nod. "He was as confused by it as I was, I think. I pretended everything was all right between us and that I understood, but of course I was a wreck. Jonathan was the one who realized I was lying, but by the time Deven grasped how badly he'd hurt me, I had fled California, and I never went back." There was old, old grief in his voice, and she took his hands and kissed them, almost regretting bringing the subject up at all. "I'm so sorry." "It took years to repair our friendship," David went on, staring down at their joined hands, stroking her palm with his thumb. "As soon as Jonathan had the vision that I would take the South, I began to understand why Deven and I had never Paired, and that helped. I had my own path to take and I couldn't do it with him. Not to mention," he said, smiling again, this time without such sadness, "I had you to look forward to." "But it still hurt," Miranda said, moving closer to him. "You still had your heart broken." He put his arms around her and said with a sigh, "Yes. Worse than I think I ever had in my life . . . except for when I thought you were dead." She leaned back enough to look him in the eye. "And I'm supposed to like this guy?" David chuckled. "I hope you do . . . although I imagine it will take the two of you a while to get there. Dev is hard to know at the best of times. I think you'll find Jonathan much easier to get along with. He's more open, friendlier. But please, Miranda . . . give Deven a chance to win you over. For my sake." "I'll try. But I'm going to have a hard time not kicking him in the balls for hurting you." His smile broadened. "If you want to kick him in the balls, you have my blessing. God knows I wanted to for a long time." "Can I ask you one more thing?" "Anything, beloved." "How the hell does he put on all that eyeliner without a mirror?" David laughed, but before he could reply, his com chimed. He sobered, sighed resignedly, and said into it, "Star-one." _"Sire, it's Faith. I have news about Jake."_ Prime and Queen looked at each other. Faith sounded unusually subdued. "Go ahead," he told the Second. _"He's gone, Sire. Someone took him—without his com."_ "How is that possible? They can't come off." _"They can if the hand comes off, too."_ David closed his eyes. "You found his hand." _"Yes. It had been severed at the wrist and left in the middle of the sidewalk. There's a lot of blood. The team had a forensics kit so they were able to determine it was Jake's. But there's no other evidence we can see. We're trying to track them, but so far there's just nothing to go on. No footprints, no fingerprints, nothing on the sensors. No body. He could still be alive."_ "God," Miranda whispered, resting her head on the cool glass of the car's window. "Poor Jake. And poor Lali . . . they were friends." "Keep looking," David said. "I'll run a search and review activity in the area. Return to the Haven before dawn and give me a full report." _"As you will it. Star-three, out."_ "He might be alive," Miranda muttered, holding back tears of both sorrow and anger. "Why would someone kill him and just leave his hand?" "I don't know. If they wanted him for information, it stands to reason they'd remove the com so we couldn't find him . . . but even for a vampire that's a serious wound." "Would he bleed to death?" "It depends." David unconsciously rubbed his own wrist. "It would be easy enough to reattach the hand; almost any vampire could do that in a few minutes, though it would take several hours to get all the feeling back. Without the hand . . . if it were me, I could stop the bleeding and force the wound to close, assuming I was conscious, in about twenty seconds. But if he had other injuries, or had been knocked out, or was hung upside down so gravity was working against him . . ." "That's enough," Miranda said, covering her face with her hands. "I get it." "We don't know for sure," David told her. "Let's not assume the worst until Faith reports back." Even as he said it, though, Miranda knew what he was thinking, and she knew, in her gut, he was right. Jake might have survived the amputation, but they wouldn't find him alive. "Poor Jake," Miranda repeated, wiping at her eyes. "I liked him." David drew her head to his shoulder again and they spent the rest of the trip home in silence . . . but in her heart Miranda knew that whoever was behind this wouldn't stop with one murder . . . This was only the beginning. David was right about one thing: Jonathan was nothing like his Prime. In fact, Miranda adored the Consort the moment they met. "Jonathan Burke," he said, taking Miranda's hand and kissing it gallantly. "I'm so excited to finally meet the woman who got David's head out of his Mac." Miranda smiled. "Once in a while, at least." "Good God, David, you didn't tell us how beautiful she is," Jonathan added as he looked Miranda up and down with obvious appreciation that was neither lecherous nor invasive. "You're not nearly good enough for her." Now Miranda laughed, as did David. "You're absolutely right," David replied. "But I was hoping she wouldn't figure that out for a few decades at least." After the formal introductions they retired to the same study where David had taken Hart, although the Pair were given a suite of rooms closer to the Signet wing, in recognition of their relationship with the South. Miranda walked alongside Jonathan, who was a good six inches taller than David and therefore almost a foot taller than both Miranda and Deven. He was built like a football player, broad-shouldered with formidable muscles, but he carried himself the way all Signet bearers did, with uncanny grace and comfort in his own skin. It would have been easy for him to be a lunkheaded lumbering giant, but he was good-natured and refreshingly open, with a cheerful British accent and sparkling hazel eyes under his unruly blond hair. He wasn't as stereotypically hot as many of the vampires she'd met, either; he was handsome, but in a rugged way, someone you wouldn't want to meet in a dark alley but would want on your side in a bar fight. He was dressed in a suit and tie in a gorgeous dark purple, and Miranda had to return his compliment: "You're pretty damned impressive looking yourself, my Lord." Jonathan paused and did a runway-esque turn in the hallway. "Thank you, my Lady. I'd like to take credit for this, but I have the fashion sense of a blind Amish ditchdigger. Deven dresses me on special occasions; otherwise I'm strictly a jeans-and-tees sort of fellow." Deven glanced back over his shoulder at Jonathan, and the smile he gave his Consort was fond, even gentle. "You're just lazy," he said. "I am, indeed, darling. But I also know when to let an expert take over." They entered the study and took up two love seats, one Pair in each. The servants had already brought a bottle of whiskey, which Deven picked up and read, then smiled at David. "You're learning," Deven said. "Macallan Fine and Rare Collection, forty years old. Not bad at all." David snorted softly. "That's to keep you from complaining about my trailer park taste." "Jack Daniel's is worse than trailer park," Deven said. "It's a date with your sister at the family reunion." "You, my love, are a snob," Jonathan told his Prime with a smile. "I've seen you drunk on just about everything from Château Lafite to bathtub gin." The men all drank whiskey, which Miranda hated; she poured a glass of Cabernet and sipped it, admiring the way the firelight caught the wine's jewel tones and made it look like blood-colored stained glass. "I understand you had something of a row with Hart," Deven said. "Well done." "That was Miranda's doing," David replied, taking her hand. "It's been a long time coming, but Cora, one of Hart's women, was the catalyst and Miranda the spark. After he murdered the other girls, any hope of amity between us was done for. The next Council gathering should be interesting." "You've opened a bloody hornets' nest," Deven said, a bit sternly. "It's not wise to cross someone as unstable as Hart. This will come back to haunt you, I promise." Miranda said coldly, "I'll gladly take that chance if it means saving Cora from that animal." Deven looked at her over the rim of his glass. "That's because you're too young to know any better." Her temper flared. "And would you have let him take her, Lord Prime? Knowing what she was going through and how she was going to die?" Deven was unaffected by the edge in her voice. "In our position we must consider the common good and not go courting wars because of our pet causes." She knew her eyes were going silver, but she didn't care. "Perhaps you should consider the common good and not go courting wars to compensate for a cold heart or a small—" "Miranda," David began, but Miranda held up a hand, and he fell silent. Meanwhile Jonathan was watching the whole exchange with a slight smile, glancing back and forth between the Queen and his Prime as though it were a highly entertaining tennis match. Deven tilted his head again, set down his glass, and said, "Any fight between us, my Lady, will be short and unpleasant." "Just like you," Miranda bit back. Silence. Then Deven laughed. Miranda didn't, but she felt the tension in the air dispel and sat back with her wineglass. "I like her," Deven told David. "She's bright and fearless, just like they say. Give her fifty years and she'll be a force of nature." David gave Deven a look that made Miranda feel a lot better. "She's a force of nature right now, and I think you'd best keep that in mind, as well as the fact that regardless of our past relationship, I don't take kindly to anyone baiting my Queen." Whatever words David had given her in the car, Miranda could sense now that things between him and Deven were far from resolved. There was anger there, steeped in the pain of betrayal. "Jonathan," Miranda said, "how would you like a tour of our Haven while our Primes discuss whatever business they need to discuss? I'd love a chance to show you our home and get to know you better." She pointedly ignored Deven as she spoke. Jonathan grinned. "That would be lovely, my Lady. Shall we?" He offered his arm, and Miranda smiled and took it, leading the Consort out of the study and taking no little delight in closing the door firmly behind them. "London?" Miranda asked. Jonathan grinned, loosening his tie. "Good catch, my Lady. I was born and raised in Southwark, served the Queen for a good many years, then made my way across the Atlantic and, eventually, to the West, like so many settlers before me." "How did you two meet?" Jonathan clearly found that funny and chuckled as he flipped the caps off two of the beers from the six-pack they'd fetched on their way. He handed her a bottle and kept one for himself, and they clinked them together before taking a drink. "It was like something out of a bad romance novel," he said, leaning back against the chimney. "It was 1952—a big group of the Elite, and the Prime, were having an after-hours drink in a bar downtown, and I went to try to get a job with them. I was new in town; I figured I'd be on patrol duty for a few years and work my way up. I met David and Faith, who took me to meet the Prime, and the minute we shook hands, bam! His Signet lit up like Christmas. Five seconds later an assassin tried to take him down with a crossbow. I pushed Dev out of the way, took the hit, and woke up in his bed." "You didn't know each other at all?" "No. I didn't even know his name. But I knew I belonged with him." Jonathan smiled out over the roof at the woods surrounding the Haven. "Strange, really. I'd been with a hundred men over the years and they were all more like me—brawny and a bit on the brash side. Then here was this fragile-looking boy with his tattoos and scars, and I completely lost my mind." "Scars?" The Consort nodded. "Many. Inside and out." "How old is Deven?" "We don't know exactly, because there's no record of his birth, but it was sometime in the early 1300s, in Ireland." "He's seven hundred years old? Jesus!" "One of the oldest living vampires on earth." "And is he a dick to everyone, or am I just special?" Another smile, another swig of his Shiner Bock. "Isn't it obvious, my Lady? He's jealous." "Jealous? Why?" They had gone to one of Miranda's favorite spots in the Haven, or rather, atop the Haven: a rooftop nook near the Signet suite that offered a sheltered place to watch the night go by. When she needed a minute alone she often sneaked off to the roof, and she was aware that David did the same thing, sometimes to this exact spot. It was quiet and the view was spectacular. From here she could see the pasture, where Isis and Osiris were currently grazing in slow circles, and the gardens she and David had walked through when she first came to live at the Haven. Jonathan, whose long legs were dangling from the eaves, said, "They never really got any closure on their relationship," he said. "David ran away—rightly so—and Deven did his best to atone for being such a fool, but until a few months ago they hadn't even been in the same room. They put aside their feelings in order to keep their friendship, but it was never truly finished between them. And as long as David was on his own, things could stay that way. Now, you're here, and like it or not that chapter has closed for them. They're going to have to work it out somehow." "Does that mean they still love each other?" "Oh, undoubtedly." He saw Miranda's face and added quickly, "But you needn't worry." "Are you kidding?" "Listen to me, Miranda, and remember this, because it will save you a lot of heartache as the years go by." Jonathan sat forward, holding her gaze, his usually cheerful expression gone grave. "You are his soul mate. You are bound unto death and possibly longer than that. No one, and I mean this literally, _no one_ can usurp your position in his life or heart. He will love you until the sun burns to dust. But that doesn't mean neither of you will ever love anyone else or want someone else. Forever is a long time, and even mortal relationships evolve—so must ours, if we are to survive." Miranda sighed and picked at the label of her beer. "So you share Deven with other people?" "Dev? Oh, hell no. He's not interested in extracurricular ass. He shares me." "Seriously?" Miranda gave him an incredulous look. "I would think he'd be the one shagging every guy that moves." Jonathan's smile returned, but she could feel something lurking beneath it that was all too familiar. "I won't go into the details of his past—that's for him to reveal. But I will say that when he and David first coupled, it had been over a hundred years since his last lover." "Whoa. Really?" "Yes. And our relationship isn't what you'd call passionate. Every Pair comes together to complete each other, and in our case, what he needed wasn't someone to have sex with, it was someone to love who would place no demands on him, just be a comfort and a companion who would never abandon him. We agreed early on that our sex life would be somewhat sporadic, and that if I felt the need for more, I was free to seek it out. It's a perfect arrangement for us." He laughed again at the look on her face. "As I said, forever is a long time. The 'in love' stage of a relationship is fleeting. What you need are partnership and companionship, a deeper and more abiding love that transcends the physical. Sometimes that's romantic and sexy, sometimes not. But over time you and David will find what works for you." "No offense, Jonathan, but I find that kind of depressing." He grinned. "No offense taken. I realize it sounds strange, especially since you probably spent your whole human life within the bounds of traditional human relationships. But we're not human . . . and the way we love isn't traditional. It can't be, when eternity is a factor. Not to mention, Dev . . . well, as I said, he has scars. And really, if he had it to do over again, he probably would have stayed out of Signet politics entirely and joined one of the Orders." "Orders of . . ." "Vampire monks," Jonathan explained. "Religious orders of immortals. There are several scattered around the world. Deven has connections with one of them, the Order of Eleusis—they're mystical metalworkers connected with the Eleusinian Mysteries of ancient Greece, and it's rumored they first forged the Signets themselves. Get Deven to show you his sword sometime; it was made by the Order, and it has their symbol, a waning crescent moon above the Greek symbol of infinity, worked into the blade's design." Miranda had no idea what to think of that—it sounded so outlandish and unbelievable to think there were actual religions for vampires, although any race that had existed so long was bound to have its true believers. She wondered if David had looked into it, given how wildly curious he was about the origin of the Signet system. She'd have to mention it later. "So, about Deven . . . what do I do when he gives me attitude?" "Give it right back. Show him you've got balls and you're not going to back down, and he'll respect you. As soon as he feels like you're a match for David, he'll back off." She raised an eyebrow at him. "Why are you so free with the advice? Why don't you give me the same grief he does?" Jonathan snorted. "In case you haven't noticed, we're not the same person. I'm a Consort, which means I read people very well, so I knew you were fantastic from the get-go. Deven tends to reserve judgment. But the worst thing you can do is let him intimidate you." "I hate to say this, and I hope it doesn't upset you, but right now I don't really care about his respect so much as I care about my foot planted on his ass." The Consort broke into a loud and contagious laugh that had her laughing, too. "All right," he said. "You kick his ass, Miranda. He's earned it." They clinked their bottles again and leaned back against the bricks to finish their beer as the cold night kept turning overhead. Neither of them spoke for a while, but finally just to break the silence David observed, "You cut your hair off." Deven lowered his glass. "Yes." "How's being a roadie for the Cure working out for you?" Deven shot him the finger, and they grinned at each other. "You're looking well," Deven noted. "Much better than last time I saw you." Crossing one knee over the other, he added, "Of course, now you have your lovely firebrand to keep you warm." David's eyes narrowed. "Are you jealous, Deven?" For once, Deven lowered his gaze first. "The Council is all atwitter about your break with the Northeast. I haven't heard much, but so far the gossip has been in your favor. Considering everyone hates Hart, it's not surprising, but still, the fallout is going to be interesting." David didn't point out the change in subject. Deven had, without saying a word, answered the question. "I'm not going to lose sleep over Hart. Miranda's actions may have been rash, but they were right." Deven smiled. "At long last you have a mate who shares your idealism. I hope that she doesn't become as cynical as I am once she's outlived her humanity." "You're more human than you like to admit." "There's no need to be insulting, David." Dev sipped his drink and added, "She has no reason to be threatened by me." "Oh? After you show up and practically piss on me, when I hadn't even told her about us yet—" "You hadn't _told_ her?" Deven sounded genuinely incredulous, a rarity for him. "We were together ten years, I was your first and only long-term male lover, and you didn't tell her? What the hell have you two been talking about for the last three months, then? Horses and circuit boards?" David had to admit that Deven was right, and saying that he'd expected Faith to have related the story to Miranda wasn't entirely honest . . . he had thought that, true, but knowing Miranda, if she _had_ known, she would have wanted to talk about it with him as soon as she heard the story. "I feel like a bit of an idiot about it," David said a little irritably. "I think part of me wanted to play it off like one of my many disastrous love affairs instead of what it really was." Deven's eyes locked on his. "And what was it, David?" David stared at him . . . God, he'd forgotten how good it felt to fall into those eyes, and how dangerous it was, for they went on forever and there was no way out. "It was a tragedy," David replied softly. "Perhaps the greatest tragedy of my life." "Worse than Elizabeth?" "Yes." "Worse than Anna?" David shut his eyes against the memory, stacking the pain of that loss against the pain of losing Deven . . . "Yes. You put me back together after Anna, but would you care to guess who put me back together after you?" Deven sighed. "No one did. You were alone." "Exactly. All those years on my own, living with your ghost, knowing you were happy with your new Consort and I had suddenly become useless to you, and you really wonder why I didn't want to tell Miranda about it?" Deven looked like he wanted to say something, but paused, then told David, "You don't need to protect her from me. She's a strong, capable woman who can fend for herself." "I know that." "But she is young and needs to learn to pick her battles. She could have found a less combative way to help that girl, and you could have had time to find out what Hart was really doing here." "I did, actually, or at least part of it. He's having a little assassination problem—he claims the Red Shadow is behind the deaths of several of his Elite." Deven's brows knitted in surprise. "Based on what?" "He found something—a silver earpiece. I tried to analyze it but it had a self-destruct mechanism and nearly put my eye out last night. Hart claims it's Shadow technology, but he has only hunches and hearsay to back it up. He also thought I had something to do with it because of my predilection for gadgetry and because Miranda learned to fight from a vampire claiming to have been a former member of the Shadow." Deven looked even more dubious. "They don't have former members, do they? I thought joining the Shadow was a lifelong commitment." "Faith said she met Sophie in a bar, and they hit it off and got drunk together. In the course of the night Sophie told her she was ex-Shadow." "I find that unlikely," said Deven. "The girl may have been a hell of a warrior, but if you were the Alpha, how would you react knowing one of your employees was spilling her guts in public?" "There is that. I'm guessing that the Alpha would have killed her—but Sophie died in the battle here, months after she told Faith who she was." "Not terribly efficient for an organization that's supposed to be untraceable," Deven pointed out. "How much do you know about them, then?" The Prime circled his glass around in his hand, the ice clinking. "I've heard all the usual rumors. All that can really be verified is that they're a network of operatives who hire out to human clients for insane amounts of money. They answer to a single individual called the Alpha. They always work alone, and I've heard none of them even know each other. Code names, that kind of thing, all very cloakand-dagger. I can't imagine why they would start picking off Hart's Elite, unless a human has a grudge against him and hired them, which I admit isn't impossible." "Do you think that an earpiece like that is something they'd use?" "If the stories are true and they're all solo, with whom would they be communicating?" "The Alpha?" "Maybe. But it seems like it would be more efficient to use phones or, perhaps, something like your coms. An earpiece is too easily lost." "That's what I thought. Plus, they're supposed to be the ultra-Elite; one of them just dropping evidence like that is pretty sloppy." "And completely out of line with their MO," Deven added. "As I understand it, most of their work is totally covert, but sometimes people hire them not just to kill someone but to send a message. In that case they always leave something behind, a calling card of sorts." "Which is?" Deven knocked back the rest of his whiskey and reached for the bottle. "The victim's left hand." David dropped his glass. Seven For the first time in her memory, Cora was alone. She sprawled on her back on the huge soft bed that was miraculously all hers—not only did she not have to share it, she could sleep there as much as she wanted, roll around and disrupt the covers, even jump up and down if she liked. It had thick blankets and velvety sheets that kept her warm all day long, and it was about the most wondrous thing she had ever seen. She could sleep all day without the fear that sweaty hands would seize her and drag her across the room. She didn't have to listen to the other girls wheezing and whimpering. There was no screaming, no cursing, only the sound of the fire crackling. Wonders were hardly scarce here, though. She had an entire room to herself! There was a guard outside, but he didn't bother her except to knock on the door and bring her blood. All the blood she wanted! She drank so much the first time, just because she could, that she was sick to her stomach, but after that she took things slowly and carefully and managed to keep down more and more each time she fed. She kept the leftovers in a small refrigerator in the room, and warmed them in the microwave as the servants had shown her, but if she had wanted, she could have requested a brand-new bag every day. Every day! Just for her! Even that next night she felt stronger. Her limbs no longer shook. She wasn't freezing all the time. Her skin felt less stretched over her bones. She spent hours in the large bathtub, just soaking and splashing like a child, or standing under the scalding hot shower spray and scrubbing herself over and over with lavender-scented soap. Then she dressed herself in the nondescript but comfortable clothes the Elite had brought her: black cotton pants and a short-sleeved shirt which were apparently standard issue for sleeping and working out at the Haven. She had never worn pants before, but she loved them. She had plush socks on her feet and a hairbrush all her own. It was an unbelievable amount of luxury for a woman who had spent so many years sharing a room with eight other women. Those few people she had encountered so far seemed taken aback by her naïve appreciation for such commonalities, but for her they weren't common. She had not yet seen the Queen again, which was fine by her; in person, the Queen had been terrifying, though she had swept in like an avenging angel—or goddess—and taken Cora in like her own fledgling. The Prime, too, had been frightening, but he had given her a reassuring smile and spoken to her in her own language, a courtesy she would never have expected for a nothing like her. Cora had been spared a last meeting with the Master, but she knew he was gone, just as she had known there would be consequences even before she found out what had happened to the other girls. He might come back for her, or kill her. He might simply abandon her and find another slave. But for now, at least, she was at peace. Finally she began to get a little bored, or at least a little interested in what lay beyond her door. She didn't want to interact with anyone if she could help it, but she was curious about this huge place that was, for the moment, her home. She poked her head out and saw that her guard had gone; it was shift change, so another would be along in a few minutes. She knew they would be unhappy if she wandered too far afield. But surely it wouldn't hurt just to walk down the hall and back again? She wasn't strong enough to get much farther than that anyway. Cora took the hooded jacket that had been given to her and put it on to keep the late autumn chill off her skinny arms. She had no shoes, but she didn't intend to go outside, and the floors here were so immaculate she could have eaten off them. Certainly the Haven she had lived in was never this clean. Here there was no dust, no underlying reek of unwashed bodies and sex. She smelled furniture polish, fireplace smoke, and candle wax. She still had to move slowly. Years of starvation and abuse had left her weaker than a newborn barn cat, and sometimes her legs simply gave out beneath her and she toppled to the floor, bruised and embarrassed. The hallway turned out not to be terribly interesting. It was lined with closed doors, but she spent some time looking at the artwork and decorative objects as she made her way along the corridor. She peeked into a few open doors, finding a few unused bedrooms, a chamber full of antique weapons, and a study of some sort. Finally she took a left-hand turn down a hallway that had far more light than hers. She realized what it was: windows. Almost giddy with excitement, Cora made her way toward them, and her breath caught when she looked out. She hadn't seen the outside world in so long . . . she had had glimpses when the van carrying her and the other three girls arrived here, but before that, it had been years. There were no windows in the harem room. The Master hated natural light, even from the moon, and didn't want to give them any ideas about escape or suicide, not that they could have if they had been so inclined. She stared out, hand to her mouth. It was so beautiful. The hallway was on the second floor, looking out over a garden labyrinth and beyond it, a forest. The stars were burning in their diamond finery, and by the half-moon's light she could see deer picking at the outermost shrubs. The garden was full of night-blooming flowers, and though she didn't know their names, some were familiar, whispering to her of a long-lost life lived on grassy hillsides, punctuated with youthful laughter and the sound of cows lowing in the distance. Cora stood there staring at the world, her mind whirling, her heart so full it hurt, for a long time. She watched owls swoop down from the trees to snatch small creatures from the grass. She watched a buck with gleaming silver antlers make his regal way along the edge of the wood. She watched the stars turn, and she wept with silent joy. She was so absorbed in witnessing the night that she didn't hear footsteps, but she felt someone move up beside her. She shrank back, turning, ready to run—or try to run, whatever her body would let her do. "Don't be afraid," he said softly. "I won't hurt you." Now, instead of staring at the window, she stared at him. He was a young-looking, slender vampire, stranger than anything she had ever seen at the Master's Haven. He had an angelic face run through in several places with silver rings, and his hair was dark; he wore a short-sleeved shirt that showed tattoos covering both of his arms from wrist to shoulder. On one side was an angel with a sword; on the other, a winged demon holding a dove. She saw the amulet around his neck, this one glowing faintly emerald green, and she swallowed hard around her fear, dropping painfully to her knees. "Forgive me, Sire," she whispered. "For what?" he asked curiously. "I did not avert my eyes." He made a disgusted noise and muttered something about a dickless bastard, then gently lifted her chin with his hand so their eyes met. "Never avert your eyes to anyone, Cora," he told her. He spoke nearly flawless Italian save for the lingering traces of some lilting accent. "Now, get up." She obeyed, wiping her eyes. He joined her at the window, looking out as she had. "This place is magnificent," he said, maintaining his distance but speaking to her casually. "I wish my own Haven had a tenth of its beauty." Cora swallowed again and asked, haltingly, "Where do you live, my Lord?" "California. I think you'd like it; our home reminds me a lot of Italy." "How . . . how did you know my name?" He smiled. "I heard all about you from Prime Solomon and his Queen. Your room is down the hall from ours." "Your Queen is here with you?" "My Consort," he corrected. "His name is Jonathan." "Oh . . ." She suddenly knew who he was; she had heard the Master ranting about him, his deviant ways, his perversions . . . he had made him out to be some kind of twisted monster, not . . . like this. "You are Prime Deven." "I am. It's a pleasure to meet you, Cora." He took her hand and kissed it lightly, and she blushed. It was the most courtesy a man had ever shown her. She had been so afraid of the Prime of the South, but this Deven was different; she knew by instinct that he had no interest in doing the things to her that Hart had done, no interest in touching any woman out of rage or lust. It was comforting. "My Master hates you," she said. Deven chuckled. "I know. It gives me such pride, as does knowing I could tear his limbs off with one hand. He likes to think he's strong, but if he were half as powerful as he claims to be, he would have laid me low long ago. He knows he can't. And, Cora . . . he isn't your master now. You are a free woman, your own master." Cora digested this for a moment, but it left her feeling shaky in her stomach, panicky. "What am I to do?" she whispered. "Nothing, for now," he told her. There was such caring in his eyes, which in the darkness glittered like amethysts. "For now, concentrate on becoming strong and healthy. The Pair will let you stay as long as you want to, no questions asked. You're safe under their care." "Why is everyone here so kind to me?" she blurted, then felt her cheeks growing even more scarlet. "I'm no one. I don't matter to anybody." Deven put his hand on her face, and she felt warmth and strength flowing into her body that helped her stand a little straighter and get her tears under control. Standing there with his palm touching her skin, she felt something . . . something stirred in her, and an image flashed in her mind's eye: She saw a young man with deep violet eyes and auburn hair, standing at the edge of a wood with one hand on the trunk of a tree, smiling at her . . . no, not at her . . . at Deven. The image was gone as soon as it came, and she had no idea how to interpret it, or if it was in any way real. "You matter," he said, startling her out of her mental tumble. "I assure you, you do. As to why . . . well, I can tell you that the Prime and Queen are both good people, very protective of those who cannot protect themselves. At heart that is why the Signets exist, but most of us have forgotten that. And, Cora . . . I don't have the level of sight that my Consort has, but I know one thing: You have work to do in this world. I know it." She was shaken by what she had seen—and all the more by his words—but she had a feeling, deep in her belly, that she shouldn't speak of it. Not yet. "You do?" He smiled again. "Yes, I do. Now . . . will you be able to find your room again, when you're ready to rest? It's just around this corner, five doors down on the right. And if you go another two doors and cross the hall, you'll find us. We'll be here a few days, so if you need anything, you need only come ask." Sniffling, she nodded. "Thank you, Sire." He stepped back and bowed. "Good night, young one." Cora wiped her eyes one last time on the sleeve of her jacket, then turned back to the window, where she stayed until her legs could barely hold her up, then made her slow way back to her room, smiling. "Wait, wait . . . you're telling me David had a boyfriend?" Miranda nodded. "More like a husband, really. And he's a total jackass." "Wow." Kat leaned back in her chair, watching Miranda wriggle into the black vinyl corset top, shaking her head in disbelief. "That's crazy. I mean, yeah, he's a little swishy, but—" "You think David's swishy?" Miranda asked, pausing, a bit out of breath from trying to get the damn thing zipped. "I never noticed that." "It's nothing in particular, just a . . . quality." "Well, I had no idea. The whole thing completely caught me by surprise." Miranda pulled the top into place, then leaned over to wiggle her breasts into it properly. "Is it wrong that I feel weird about it?" Kat made a face. "Mira, of _course_ you feel weird. Think about it: In relationships we form concepts of people based on their behavior and what we know about their histories. Those concepts can be accurate or not, and they can be healthy or not, but regardless, if something shakes them, it shakes us, too. You knew David one way, and it turns out that way wasn't entirely on target, so now you have to adjust. Given how close you are, that makes it even harder." Miranda faced her friend. "Well?" Kat frowned, eyeing the outfit. "I liked the first one better—the red lace brings out your eyes, makes the green more intense." Miranda wished for a moment that she could see herself; instead she was in a dressing room with a curtain pulled over the mirror and Kat there to critique her. She'd never really liked shopping, and she liked shopping for stage clothes even less. Luckily she trusted Kat's judgment. "You're right. Let me try the other one with these pants—if I can get the pants zipped. Jesus, Goth girls are skinny. At least I've got an ass." "And a killer rack," Kat commented. "Especially in that getup." Miranda ran her hands down over her torso to smooth the shirt, which wasn't a real corset; she couldn't wear a real one onstage and sing the way she did. There were also limits to the cleavage she could manage with a guitar hanging over her middle. "I'll bet that there are much more disturbing things in David's past than a jerk boyfriend." Kat returned to the subject, handing her back the first top. "He's three hundred fifty years old, after all. And he probably didn't get where he is by being nice." "No, he didn't." Miranda hadn't told Kat much about David's past, not even how he had gotten his Signet; she wasn't sure if Kat was ready for that. "He's been through a lot and done a lot." "Well, if you can deal with all of that, you can deal with a little swish. It's not like it's a bad thing. Bi is the new hotness, you know." Miranda rolled her eyes. "Only if it's two women in a porno movie for straight guys." "And as for the ex being a jackass—if David still likes him, and his hubby is a great guy like you said and loves him, he must not be all bad. Maybe you should try to find some common ground. Besides David, I mean, because that could get weird." Miranda smiled at her. "How did you get so damn wise?" Kat snorted. "Wise would be if I hadn't gotten knocked up." The Queen sat down on the changing room's bench, abandoning her quest for a moment. She'd been avoiding the subject for most of the evening because she knew Kat was tired of thinking about it every moment of every day, but now that Kat had brought it up, Miranda asked what she'd been wanting to since meeting Kat outside the shop: "What did Drew say?" Kat shrugged. "He's overjoyed. He wants to get married." Miranda could hear the ambivalence, and moreover she could feel it. "And you?" "I don't know. I'm done panicking, so that's progress. And I'm glad I didn't go through with the abortion before Drew got back. But I still don't know what I'm going to do." Miranda didn't say anything, though the desire to make Kat promise to keep the baby was so strong she had to bite her lip against the words. It must be part of her prescient gift, if it could be called a gift. She knew, she just _knew_ , that Kat would have the baby, and that it would be a girl, and somehow . . . somehow that little girl would grow up to be very important to a lot of people. But she wasn't about to put pressure on Kat. "I love kids," Kat went on. "But I've seen so many who were so screwed up, and seen how the world is so hard for them . . . how can I have a kid?" Miranda took a deep breath, stood, and changed into the red-trimmed top, saying as casually as she could, "Maybe you're exactly the kind of person who _should_ have kids, then. Someone who's been there and seen the best and worst of people. Someone educated, with common sense. You could give a kid a great home, with or without Drew." "But am I ready for this?" Miranda leaned over and did the boob shake again, settling into the outfit and testing it out to see if she could breathe. So far so good. "Is anyone?" Kat leaned the chair back on two legs, sighing heavily. "Distract me, okay? Tell me more about your big gay husband." Miranda threw a hair scrunchie at her. Kat laughed, setting the chair back down. "Oh, come on. Is the guy at least hot?" "Disgustingly," Miranda replied. "He's all Goth and leather." "And he's really old and powerful?" "Over seven hundred years old, and yeah. Apparently most regular vampires only live to about five hundred at the outside, so he's like a little fanged Yoda." Kat gave her a playful grin. "Have you had any fantasies yet?" "About what?" "About the two of them getting it on." "God, Kat! No!" Kat laughed. "Which means yes. Admit it, Mira, it's a turn-on! Just picture them in bed—" "Kat!" Miranda groaned, looking for something else to throw. "Who do you think would be on top?" Kat pondered eagerly. "Quit it!" Miranda tried to sound outraged, but she was laughing too hard, and said, "Okay, I'll give you this, seeing them kiss was kind of . . . sexy." "They kissed? Was there tongue?" This time Miranda threw a balled-up shirt at her. "Not that I saw. Now tell me what you think, so I can either buy this thing or get the hell out of here." Kat looked her over again, then flashed her a thumbs-up. "Perfect. I dare anybody to be a jackass to you in that outfit." "Thank God. I've had enough of this shopping crap for one night. Let me put my real clothes back on and we'll go for ice cream." A few minutes later Miranda was mercifully back in her jeans, although she was wearing a lace-up black top with belled sleeves and her favorite big black boots. She'd spent long enough slobbing around in threadbare T-shirts back when she was crazy; comfort still came first, but she knew she looked good in slightly more . . . vampire-appropriate clothing. She took the new outfit up to the counter, where the bored girl with the pierced upper lip and six pounds of white foundation looked up from her copy of _Catcher in the Rye_. "Can I help you?" "Yes," Miranda said. "Do you have the pants in a size ten? These are a little snug." The girl didn't roll her eyes, but Miranda knew she was doing it in her mind. Her tone was both bored and dismissive as she said, "Did you see any on the rack?" Miranda's temper flared, and she looked into the girl's eyes and said, power and immortality both clear in her voice, "Go check in the back, please." The girl went pale under her Urban Decay and stammered for a second before saying, "Yes, of course. Hold on just a sec." Miranda shook her head and glanced at Kat, who was looking at her appraisingly. "You didn't even have to vampmojo her." Miranda smiled. "How do you know?" "I remember that tone of voice from the time I took you to the ER and you almost flattened that nurse. You were standing there in your panties and you might as well have had a crown on your head." The clerk returned with a pair of pants guaranteed to fit the Queen, who handed over her Visa wordlessly. "Aren't you going to check the price?" Kat asked. Miranda shrugged. "I'm not worried about it. I have to wear this in front of an audience, so I don't mind spending more." "Oh, right, I forgot, you're Miss Gotbucks von Rich-Ass now." Miranda signed the charge slip and said, laughing, "That's Queen Gotbucks von Rich-Ass, thank you very much. Now come on—there's a double-scoop Mexican vanilla hot fudge sundae out there with my name on it." David wasn't the kind of man to procrastinate, and he certainly wasn't one to avoid facing his problems—at least, not anymore. Once upon a time he had run as far and fast from Deven as he could, and only when there were several thousand miles between them could he breathe again. He'd thought that all those miles and all those years had done what apologies could not. He'd thought that the past was past, and now that they both had Consorts and were presumably happy and settled in their reigns, it would be just like it had once been, when he had been Deven's student in the training ring and they had been friends outside it. Denial, denial, denial. Now here he was, in his bedroom pondering the sword in his hand—a sword that Deven himself had given David after he took the Southern Signet—growing progressively later and later for their appointment in the training room, and David Solomon, Prime of the Southern United States, was scared out of his mind. It was all coming back now. The flash of Deven's smile, the softness of his mouth, the way he moved like a dancer and an assassin in one . . . the cold fire in his wide eyes that belied the molten passionate core of him, a core that had only ever laid itself open for one man . . . and that man was not Jonathan. For ten years David and Deven had been inseparable. From the night they first fell into David's bed, stripping off each other's Elite uniforms and pressing needy, sharp canines into each other's flesh, they had been bound by blood and sex so tightly that neither of them knew their boundaries anymore. Finally Prime Arrabicci had gotten wind of what was going on in his Elite and called the Second and his lieutenant into the Prime's office. "I've heard some disturbing rumors regarding the two of you," Arrabicci had said tiredly, and David had known exactly who had been in here first, ranting and raving about the perverts in their midst. "Lieutenant Torvald has informed me that the two of you have been conducting some sort of horrible sexual relationship." David and Deven had stood side by side in front of their Prime, and Deven had said, "Sir, Lieutenant Torvald is, as always, mistaken. David and I are not conducting some horrible sexual relationship. We are in fact conducting a fucking fantastic sexual relationship." Arrabicci had groaned and put his head in his hands. "Do you two see the position you've put me in here? Aside from any concerns about the two of you doing . . . whatever you do, the fact is we have rules about senior Elite consorting with their juniors. I could have you both thrown out of here on your asses." "But you won't, Sire," David had pointed out. "You've said yourself we have the best record in the Elite. To toss us out just because we sleep together—off duty, Sire—would be strategically unwise." "Rules are rules, Lieutenant. Therefore I have no choice but to promote you." David had paused, frowned. "I'm sorry, Sire?" "You are hereby promoted to co-captain and will serve at Deven's side. You aren't to be granted any privileges or pay raises before a six-month probationary period, just to make it clear that I'm not rewarding deviant behavior—I want everyone to see you've earned your place at the top, David. And as for your . . . relationship . . ." David had braced himself. But all the Prime had said was, "Obviously it's affecting your fighting abilities in a positive and useful manner. You've both gone from the best damn warriors in my Elite to the best damn warriors I've ever seen. So whatever you two are doing to each other in bed, keep doing it . . . just don't let me hear about it." "As you will it, Sire," they had both said together. Then they had left the office and walked with utmost dignity back to Deven's quarters, where they proceeded to shag each other senseless for the entire rest of the night and the following day. Deven had needed someone to bring him out of his darkness. David had needed someone who wouldn't die on him. At first it had been an ideal friendship, two very different lone wolves in search of a pack . . . but soon . . . a look began to linger; a touch seemed to happen of its own accord; and was there a softness in Deven's eyes when speaking of him? Neither had been looking for a lover, yet they had tripped and fallen headfirst in love like a pair of hormone-ridden teenagers. They had spent ten years fighting gangs and making love. Their desire for each other thrived on combat. A victory in the streets meant they would be half naked and going at it in the car on the ride home. Their blood boiled and they tore into each other rabidly. David's entire world contracted to whichever bed they were in, the exquisite pleasure-pain of who was sucking or stroking whom, the sweetness of Deven's blood on his tongue. And now, when things were so very different, his traitorous heart wanted to travel back in time, back before either of them knew the burden of a Signet, back when he had believed they had a future together. _No. It's over with. You're friends now. Nothing more._ It was understandable that seeing Dev again would cause old feelings, and old hurts, to bubble to the surface. The last time they'd seen each other, David had been lost in his grief for Miranda, so there was no time for any of that, only time for Deven to help bring him out of it, set him back on his feet, and leave him ready to go back to work. This time there were no such emotional distractions. Now, the Pair were here, and he was about to go to sparring practice as they had a thousand times, and either they would start airing some things out or their friendship was ultimately doomed. Logical, yes . . . and about as appealing as a fireplacepoker lobotomy. The bedroom door opened and Miranda walked in laden with several shopping bags and the expression of a woman who had just been victorious in an epic battle. "Thank God that's over," she said breathlessly, dropping her plunder on her chair by the fireplace. "I'm set for a few months provided I don't acquire too much more muscle." She came over and kissed him on the forehead. "Aren't you supposed to be in the training room beating up our houseguest? Whoa . . . what's wrong, baby? You look like you've seen a ghost." She knelt in front of him. He leaned his forehead against hers. "In a way, I have," he managed. "I don't suppose you would come with me?" She looked into his eyes, and he didn't bother trying to hide his feelings. It would be pointless. Miranda laid her hands on the blade he was holding, projecting calm support, though if he were her he would be a bit perturbed at finding his husband in such a twist over an ex. "Tell me what you're afraid of." David tried to find words. "I don't want to upset you." "All the more reason why you should," she said. "If there's something you think you can't tell me, it must be important. No secrets, remember? Although . . . I can guess." "Can you?" "Of course. I'm not blind, David." He rested his head on her shoulder. "What should I do? Force a confrontation? Go on pretending nothing's wrong?" "I don't think that would work," Miranda told him. "It's just going to keep getting in the way—and if you want to stay friends you're going to have to get it all out in the open and just deal with it head-on." "I hope you're not worried that I'll . . ." "I trust you, David. I know you wouldn't do anything to jeopardize our relationship. Besides, I can sense . . . it was really intense between you, but intensity has a way of burning to ash in the real world." "I don't know," he murmured, tracing her upper lip with his thumb. "I think things with you and me get pretty intense sometimes." She smiled, and her tongue flicked out to touch his skin, sending electricity between them. "True, but I have a few distinct advantages over Deven." "What are those, beloved?" "One: I have a vagina, which statistically you prefer. Two: I'm prettier. Three: I'm not a total asshole." She stood, pulling him along with her. "Now, come on. No hiding, remember? You go and cross swords—and I mean that in a martial arts sense, thank you—and try to get some of this angst out of your system. I'm going to take a shower, and then Jonathan has asked to hear me play." "Are you sure you won't come with me?" He tried not to sound plaintive. "I'm sure. You're the Prime of the Southern United States, baby. You strike terror into the souls of lawbreakers and tremors into the thighs of your Queen. There's nothing in your heart that you need to fear." He smiled at her, kissed her, then said, "I am the luckiest bastard on this earth to have found you." Miranda nodded. "I know." Then she handed him his sword and ushered him out the door. Gossip traveled with vampiric speed in the Haven, and by the time David reached the training room a sizable crowd of off-duty Elite, including Faith, had gathered to watch him go up against the Prime of the West. Deven was already there, punctual as always, and David wished that Miranda had come—not because of his dread of the whole thing, but because she would have loved to see Deven out of his rock star apparel. Dev wore the same sort of black workout clothes as anyone else who practiced in the training ring; even without all the leather, though, he was still an impressive sight, as the shirt he wore revealed the full-sleeve tattoos he'd had as long as David had known him. "You're late," Deven observed mildly. "Prime's prerogative," David answered, shucking his coat and shifting his sword from its concealed sheath to one at his belt. Underneath the coat he, too, was dressed to fight. He gestured at Deven's tattoos. "Did you get the angel touched up?" Deven glanced down at his right arm. "The color was fading in places. Ironically the other side hasn't changed at all." David smiled. "I don't find that particularly ironic, Sire." Dev flashed him a blinding grin. "Ready to have your ass whipped?" "Not in front of all these people," David fired back with an arched eyebrow. It was easy, so easy, to slip back into the mildly flirtatious banter that had been a hallmark of their early years. It even felt good—but sex had complicated everything. It always did. "You realize of course that you can't possibly beat me," Deven said, drawing his sword. The blade caught the light perfectly, and Deven raised it, then bowed, something he'd learned during his time in Japan when, legend had it, he'd studied with the samurai. "You may be surprised," David said, echoing the salute. They circled slowly around each other for a moment . . . and then dove in. David had no intention of losing easily, even though Deven was right—the Prime of the West had a number of advantages in this fight, even aside from his age and experience. Deven had two psychic talents, neither of which were terribly common: He had been born with healing ability, which differed from what Pairs shared in that he could use it on anyone, even humans; and he had a strange combination of telepathy and low-grade prescience that, coupled with his strength and agility, enabled him to anticipate an opponent's moves. He had taught the technique to a few people, including David, but without the psychic gift itself there was a limit to how much one could learn. David was not prescient—Miranda was, as Queen, but her talent was still new and undeveloped. If she were ever able to harness it, she might learn to power-dance the way Deven could. David, however, had to make do with his inhuman speed and grace. The sound of sword against sword was sharp and rhythmic, the two Primes spinning around each other like twin stars, the training room's simulated moonlight catching the steel with every slice through the air. With his Elite watching, David refused to embarrass himself; he threw everything into the match, letting his awareness of the room slip . . . then his awareness of himself. Power flowed through him, liquid silver flame like the blade. He drank it in and poured it into his body. He could feel himself starting to tire, but he reached for more energy along the connection to Miranda. Deven was clearly surprised at how much he had improved since they'd last fought, but he didn't miss a strike, moving so fast he would be practically invisible to a human and a blur even to the gathered Elite. David had been his apprentice for years and knew his style as well as anyone could. The room disappeared. David felt something in himself fly open, and he blinked. Suddenly, his vision seemed to double, but the two images were different—in one, Deven was in front of him, and in the other he was a scant inch to the right . . . David realized what he was seeing just in time to counter the move and, when Deven swung his sword around toward David's throat, David was no longer there. The Prime's shock was obvious, but it didn't distract him long. Gradually they fell into a perfect rhythm, each knowing the other's actions a split second in advance, neither able to gain the advantage. It was as if they were fighting with themselves. At exactly the same moment, they both spun away from each other and stopped. Prime and Prime, both wide-eyed and breathing hard, stared at each other. They continued to stare at each other as the crowd burst into applause. Eight The worst part about unplanned pregnancy was that until she made up her mind what to do, Kat couldn't even get wasted and forget about it. She couldn't think about anything else. Sitting at her desk, wrangling funding for the new family shelter, she pictured herself as one of the battered women escaping domestic hell with a baby in tow. Talking to a teenage runaway—a pregnant one, of course—about her options, she was weighing those same options herself. Giving a talk on birth control to inner-city kids, passing out condoms and info sheets on local clinics that provided low-cost contraceptives, she felt like an utter hypocrite. Here she was, with enough money and education to know where babies came from and keep them from happening, and she was no better off than the girls whose eyes were filled with fear of parents, peers, and the wrath of God. Kat glanced up at the clock, then shut down her computer and put her head in her hands. She wasn't being fair. She was way better off than those girls—she had a stable home, a caring boyfriend, and the money to either keep or abort. She wasn't hamstrung by supposedly celibate male clergy claiming to understand a young woman's problems. She was lucky. If she decided to keep the baby, it wouldn't be because of religious guilt or cultural pressure; it would be because she wanted to raise a child, to be a mother. _Mother._ She had thought that _Queen_ was the most intimidating noun she'd ever come up against. Drew could be a great father, and would, if she'd give him the chance . . . but could she be a mother? Drew seemed to think so. He already had stars in his eyes over the idea of them as a little family. Drew played five instruments and painted in his spare time; he was a music teacher and fabulous with kids. They were both bilingual and college educated. Kat had studied child psychology and development during her undergrad. They both had a lot to offer a child . . . even Miranda, who had the maternal instinct of a doorknob, had made noises that she thought having the baby was the right thing to do. Kat's inner rebellious teenager balked at the feeling that it had been decided for her, but she had to admit that bit by bit the idea was scaring her less and less. She ran her hand over her head; it was getting stubbly and needed another pass with the razor. She'd have to do that tonight when she got home. Five o'clock shadow on your head was kind of ridiculous looking. Kat was the last one to leave the office most nights. Sometimes she was stuck doing paperwork, and sometimes the clients who came to see her could make it only after regular office hours. She didn't mind. She'd known when she left college that the reality of social work was gritty and thankless. But today she had helped a fifteen-year-old decide to put her baby up for adoption and move into the shelter while her boyfriend was in jail. They'd lined up classes for her to get her GED and go to trade school after the birth. The girl had cried and hugged her, thanking her in two languages; the hardest thing was always that feeling of drowning, without anyone to help. Kat's job was to throw the rope out and pull kids to the boat. Then she got to watch the best part: the drowning victim, armed with resources and with advocates on her side, saving herself. Gritty, thankless, and worth every minute. She switched off the lights and locked the office, then headed to her car, keys in her hand. East Austin at night could be hazardous for a lone woman, even if that woman was bald and tattooed and carried a gun. Austin was a relatively safe city—it beat the hell out of Houston, Dallas, and El Paso—but bad things still happened. She was up to her eyeballs in the aftermath of those things every day. Unbidden, the thought of Miranda arose. Yes, bad things had happened to Miranda . . . and Kat hadn't even known until months later. She still ached thinking about Miranda dealing with it all by herself, out there in the middle of nowhere surrounded by all those . . . people. It was a miracle she had come through it with any semblance of sanity, which Kat grudgingly admitted was at least partly David's doing. Damn it, she was starting to like him. She really didn't want to. She looked around as she walked, staying alert, but also wondering: Were any vampires nearby? The whole city was teeming with them, apparently, which was part of why Austin was safer than other Texas cities . . . ironic. There were fewer unexplained murders because the vampires here weren't allowed to kill people. The Elite were under orders to intervene in human crime when they saw it, too, and although David had Elite outposts in all the cities and towns of his territory that had vampire populations of a certain density, it was safest to live in a Haven city, both for vampires themselves and for their human prey. Not every Signet was so kindly disposed toward humans, though. Miranda had made that clear talking about that douchebag Hart and David's ex-boyfriend—boyfriend!—Deven. They could be watching her right now. Suddenly nervous, Kat picked up her pace. Her car was a block from the building; parking was at a premium down here, and always an adventure. It was a cold, clear night, and a few brave stars even peeked through the urban haze overhead. The temperature had dropped early this year, which was fine by most people who lived in Austin. Texas was pure hell in the summer and dreary in the winter, but spring and fall were gorgeous, with sunny days and brilliant blue skies . . . . . . blue skies that her best friend could never see again . . . Kat sighed as she walked. Her breath came out in a cloud. She had to stop worrying about Mira; she could take care of herself, obviously. Still, it was such a violent transition into such a violent world. Kat couldn't imagine dealing with it. It was hard enough to deal with one step removed. She snorted to herself. She would much rather think about vampires than being pregnant. Awesome. As she reached her car, she saw a shadow move across the lot and frowned, staring at it hard. It could have been anything, anyone; it was far enough away not to be a threat. Right? Kat unlocked the car and cast an anxious glance around her, her heart suddenly in her throat. Some instinct she couldn't name made her slide her hand into the flap of her purse and close around the grip of her gun. Was something over there? Had she imagined it? The hair on the back of her neck stood up, and she broke out in gooseflesh. She should have worn a hat and scarf, this weather was bad for her scalp . . . Were those footsteps? Kat took a quick look in her backseat, then all but scrambled into the car and locked it, panting. There . . . She stared into the darkness, her eyes picking out the silhouette of a figure in the alley beyond the parking lot. It looked like a woman . . . a woman who was watching her. Kat's stomach churned with acid as she got a feeling . . . barely restrained menace, even hatred, aimed at her, an oily black desire to drain the life from her, leave her bleeding on the street . . . Kat jammed her key in the ignition and started the car, at the same time groping for her cell phone—should she call 911, or Drew, or Miranda? Was it a vampire or a mugger? Could the cops do anything if it was a vampire? But when she looked up, the woman was gone. Relieved, somewhat, Kat threw the car into reverse and pulled out of her spot, not caring one bit that she squealed her tires around the corner as she floored the gas pedal and headed home. Miranda did not react well. "I want her under surveillance twenty-four/seven, and under guard from dusk till dawn. Why the hell isn't the sensor network catching this bitch?" Kat, who was curled up on her couch drinking a cup of chamomile tea, shook her head. "I don't want to be watched all the time, Mira." "Too damn bad," the Queen snapped. "If she's after you, it's because you know me, and I'm not going to get you killed." "Miranda," David said evenly, "Kat's safe for now. That's what matters." Miranda shot him a distinctly uncalm look. "But what about tomorrow night? And after that?" "No surveillance," Kat said firmly. "I'm serious." Kat had to hand it to David; the Prime had listened to Kat's story without interrupting and was considering it from all sides without reacting emotionally. He practically oozed confidence and security, and he neither coddled nor silenced Miranda but tried to calm her down without discounting her fears. He was either a born leader or a master manipulator; the two weren't mutually exclusive. It was weird having him in her house, though. It reminded Kat of the night he had shown up on Miranda's doorstep while Kat and Drew were there and swept into the room like Death popping in for a game of chess. As if summoned by the memory, there was the sound of a key turning in the front door lock, and while Miranda spun toward the entrance with her hand already seeking beneath her coat for a weapon, David reached out and touched his Queen's arm, shaking his head. Drew burst into the house in a flurry of coat and briefcase and clarinet case, all of which he dropped by the door so he could be at Kat's side in a heartbeat. "Are you okay?" Kat smiled and took his hand. "I'm fine, honey, I told you I was." It wasn't until she glanced up at Miranda that Drew seemed to realize they had company. He looked up at the Pair and went just a little pale before taking a breath and saying, "All right, what are we going to do to make sure this doesn't happen again?" David regarded Drew much the same way he had the first time they'd met, as if he were some sort of curious creature in a zoo, but when Drew didn't avert his eyes, the Prime gave a measured nod. "You will do nothing," David said firmly. "There's no need to risk your own life." "Bullshit," Drew countered, and Kat felt a little tug at her heartstrings at the way he refused to be cowed by a being who could quite obviously snap him in half like a twig. David raised an eyebrow, and Drew just glared at him. Kat found herself smiling. "Here's the thing, Drew," David said. "It's entirely likely that whoever was watching Kat was, in fact, one of our kind. If that's the case, there's nothing you can do to protect Kat. Even the weakest vampire could tear you apart before you could draw a gun . . . assuming you're armed, like Kat, and have impeccable aim. Even then, bullets cannot kill a vampire. They only piss us off." "So how do we kill a vampire? Wooden stakes?" Miranda snorted quietly. "Drew . . . you don't. Unless you have specialized weaponry or arm muscles like a wrestler, you wouldn't be able to get a stake through the sternum into the heart. You're not a vampire hunter. Giving you weapons you can't use would be stupid. It's better to concentrate on staying alert and keeping in contact with us until this all blows over. You have to use the resources you have—like your brain. You can watch and listen and remain aware of your surroundings at all times. Leave the killing to us." Drew took a deep breath, weighing his protective instinct with what Kat knew was the truth. David and Miranda were both right; if they were dealing with vampires, vampires were their best shot at staying alive. "Okay. What can _you_ do, then?" David returned his attention to Kat. "During the day you're typically surrounded by people, yes?" Kat nodded. "Even on weekends. The office itself has security and cameras, but the parking lots don't." He said, reasonably, "We can't be absolutely sure yet that we're looking at a vampire, but regardless, it's unlikely you'll be attacked during daylight in a public place, so there's no real need for daytime surveillance. I would like to put a night guard on you, however, until we figure out whom exactly we're dealing with. Just one, at a distance, strictly non-interfering." Kat started to protest that it sounded like surveillance to her, but for some reason she didn't want to disagree with David. He seemed like he'd be hard to argue with. "Okay. But it's only temporary." "Absolutely." David reached into his coat pocket. "May I have a look at your phone, please?" Nonplussed, Kat handed it to him. He had pulled out his own, and he fiddled with the settings on hers for a second before taking a thin cable and connecting it to both phones. "What are you doing?" Kat asked. David ignored her, absorbed in his work. Meanwhile Miranda was pacing up and down the living room, making Kat faintly seasick, and Drew was squeezing her hand so tightly she was starting to lose feeling. She looked at him. "Honey, you're cutting off my circulation." Sheepish, he let go, nervously wiping his hands on his jeans. "Sorry. I just don't like feeling so helpless." "It was probably nothing," Kat ventured, but she didn't believe it and neither did they. "Whoever it was didn't show up on our network," David said without looking up. "That means it was either a human, which is easily dealt with, or the assassin who came after Miranda . . . and that's a much thornier issue. We can't track her and we don't know why, but she's already made an attempt on Miranda's life." "Seriously, though, why me?" Kat asked. "I get that I'm connected to Mira, but if this chick has already been after her, why come after me? I'm not standing between them. I'm not a threat." Now David looked at her. "Do you really want to hear my theory? I doubt it will make you feel better." Kat pursed her lips. "Don't sugarcoat it, Count. Just tell me." "I would guess that this isn't about killing Miranda . . . or, not _just_ about that. There may be a personal feud involved. Someone who wants to hurt Miranda, not just kill her. The best way to do that is to start with her friends, particularly the human ones who are weak and vulnerable." David saw their faces, gave a one-shouldered shrug, and unclipped the cable from the two phones. "As I said, it's just a theory." He handed Kat her phone back. "Your signal is now coded onto our network," he told her. "Keep the phone on you at all times, and we'll be able to find you anywhere in the city at a second's notice. More important: I've set up a panic button. Hit star-one and it will trigger an alarm; a patrol unit will be sent to your location immediately and you'll get a call from me within thirty seconds to check on your safety." "Wow," Drew said, sounding reluctantly impressed. "You did all of that in less than two minutes?" David smiled. "Didn't Miranda tell you? I'm a genius." "You didn't tell her the whole truth," Miranda pointed out as they left Kat's house and walked up the street to where the car was waiting. "She doesn't need to know the whole truth." David looked at her sharply. "She already knows way more than she should about us." "But her life is in danger." "Irrelevant." He put his hands in his coat pockets as he walked, and added, "The whole truth isn't always the best truth." "What about Jake?" she asked. "We still haven't found his body. I find it hard to believe that it's not connected—what are the chances of someone kidnapping my bodyguard right after someone tries to kill me, and then someone else making fang-eyes at my best friend?" "Remote," he admitted. "I'm almost certain the same person or people are behind it . . . and, if what Deven said holds true, it may in fact be connected to the Red Shadow, and possibly even to Hart. But we don't _know_ , Miranda. We have no real evidence to bind it all together yet. And the more Kat and Drew know, the more danger they're in." Just then, his phone rang. Miranda stopped, her first worry that it was Kat's panic button, but David didn't look concerned; he merely said, "Yes?" Miranda could hear the murmur of a male voice. "Chief Brady, it's good to hear from you," David said. "To what do I owe this honor?" She watched his face go from neutral to ever so slightly confused, then angry, then back to neutral again. Her heart sank. "We'll be right there," he said, and hung up. "What is it?" she asked, but David was already speaking into his com. "Star-three." _"Yes, Sire?"_ Faith piped up. "We have an Alpha Seven at 4109 North Grafton, apartment 28. The Queen and I are en route; send a team." _"As you will it, Sire."_ Alpha Seven . . . a human murdered by a vampire. She hadn't heard that code since the war . . . but usually APD contacted Faith for suspected Shadow World crime, and for the chief himself to call . . . it had to be serious. "What's going on?" she demanded. David met her eyes. "Denise." The sun was well up, the Haven was silent, and Miranda was still sitting in her chair staring into the fire. David had tried to ease her guilt and coax her into bed, but she refused; she just needed time to sit with what she was feeling. He had nodded, kissed her cheek, and let her be. Denise MacNeil had been missing for about twenty-four hours; she hadn't shown up at the office, and by midafternoon her secretary was worried. Calls had gone out and Denise's landlady had finally agreed to check on her. The door was locked from the inside. The police had to break it down. Dried blood was splattered all over the immaculate kitchen counters, soaked into the living room carpet and the sofa. Assuming it all came from Denise, it added up to fatal blood loss. There had been a struggle: lamps knocked over, several things broken. The stereo was still playing, the same three CDs repeating over and over. There was a glass of wine undisturbed on the side table and a folder of redlined contracts still lying open on the couch. All that remained of Denise was her left hand. The police had called David because they knew Denise was Miranda's agent and there might be a connection. So far the police had no leads. The Haven had one. The Elite team had taken samples from the scene, and they would be sent to Dr. Novotny for further testing. It was still too soon for the results on Jake, but Miranda hoped fervently there would be something, any clue, no matter how tiny, to link the two to the assassin who had called herself Stacey. That woman was the only possible suspect they had. Miranda sat by the fire until almost nine in the morning, her heart heavy. First Jake, now Denise . . . was Kat next? It looked like she was already staked out as a possible target. Yes, she was under guard, but Miranda had been under Haven guard once, too, and Ariana Blackthorn had killed her in the middle of the city and dumped her body in the lake. Were they going to find Kat's left hand next? And whose after that? Leaving the hand, Deven had said, was the Red Shadow's way of leaving a message. But if it was the Shadow, for whom were they working? Who could possibly hate Miranda enough to go to this much trouble? It could be a remnant of the Blackthorn . . . or it could be Hart . . . but the Shadow didn't work for vampires, and they commanded huge sums for their services. Hart could pull it off, but none of the Blackthorn or their cronies had been very wealthy. Then again, what human would want to hurt her this way? She barely knew any other humans _before_ she had come to the Haven; who would be after her now? It made no sense. Too restless and anxious to sit still anymore, she got up off the chair and left the suite. She glanced over at the bed to see David deep in slumber, and she smiled in spite of herself. He was sleeping in the same position they tended to end up in, except that his arm was stretched over an empty expanse of blankets when it should have been around her body. For the first couple of weeks she'd had trouble sleeping with anyone so close to her, but she had already come to depend on his presence at her back. Emergency tunnels connected the main house to the other buildings, so if she really wanted to, she could go work out; she could also go to the library, or pound her stress into the piano or her guitar strings. None of those options sounded appealing, for once, but there was something that did. There was a study right between their wing and the guest wing, where David and Tanaka had held informal chats; it wasn't her favorite room, being far more masculine in décor than she preferred, but she happened to know it had the most well-stocked liquor cabinet in the Haven as well as a fridge that hopefully still housed some of David's ice cream stash. She nodded to the hallway guard as she passed, then opened the study door. To her dismay she found she wasn't alone. "Oh, it's you," she said. Prime Deven sat with his feet up on a dark leather chair, one hand around a half-empty bottle of whiskey. He looked about as thrilled to see her as she was to see him. He said something in what she guessed was Gaelic. "Come again?" With a slightly lazy smile, he translated, "The flame enters and casts all the world 'round her into shade." "Are you drunk?" He shrugged. "I'm Irish," he said. "I've spent most of the last millennium drunk." "You have an accent when you're drunk," she observed. "I have an accent all the time," he replied. "It hides its head in shame when I'm sober." Miranda had to smile at that, as well as at the marked contrast in his appearance and demeanor to all their other meetings. He was dressed casually in old jeans and a T-shirt advertising the Vatican gift shop; barefoot, his hair damp from a recent washing and therefore not glamorously spiked, without any makeup on, he looked . . . almost normal. She found she was fascinated by the tattoos, though, and tried not to stare as she entered the room, closed the door, and headed over to the cabinet to fetch a bottle of her own, this one of rum. She also grabbed a bottle of Coke and a glass of ice. "Are you religious?" she asked as she set her wares on the coffee table and flopped down on the couch opposite his. Deven rolled his eyes. "I'm far too old to believe in fairy tales." She indicated his arms with the neck of the bottle. "What are those about, then?" He laid one hand on his shoulder and absently ran his fingers along the line of the angel's wing. She noticed, looking more closely, that the feathers had been designed to run parallel to a series of long scars in his upper arm; the scars were almost invisible with the angel carved over them. "It's a giant Catholic yin-yang," Deven replied, closing his eyes blearily. He seemed so tired; was it a function of being seven hundred years old, or something else? What kept one of the world's oldest vampires awake all morning? Miranda poured rum halfway up her glass, then topped it off with a splash of Coke and took a long swallow, making a face at the taste. "And the scars? Are they from a giant Catholic lion attack?" He took another hit off the whiskey but didn't seem affected by the bite of the alcohol. She suspected the bottle had been full when he started. "A whip," he answered. "You should see my back." "Who whipped you?" "The abbot." "Why?" He opened his eyes and fixed her with a stare. "He caught me in bed with one of the other novices." Miranda wasn't sure how to respond to that. "So you were a monk?" "Until the day I died." He drank again, then again, before saying, "I was the fourth son of a farmer in southern Ireland. I was a weak little thing, far too frail to work the fields. So when I was eleven years old my father sent me to my uncle, who ran a monastery. I was basically a tithe to bribe the Almighty for a better harvest." "That must have been hard for you, to leave home so young," she said. "On the contrary, that journey was the first time I ever remember looking forward to anything. I loved God. I was born to be a monk. I had no desire for a wife or family or land of my own. I longed only for silence around me and the light of God within. I spent hours in prayer, on my knees at my bedside. I hated the farm, my rough rowdy brothers, and the drudgery of our lives. I wanted to devote my life to Christ and to the written word—monks back then were some of the only scholars." "But when you got there . . ." "It didn't take long for my uncle to suspect there was something abnormal about me," Deven said. There was strangely little emotion in his words; even for something so long ago she would have expected a little anger, or sorrow, but it almost sounded as though he were telling someone else's story. "I know now that he started the monastery after being driven out of his old one for accusations of pedophilia. He was obsessed with purity and chastity, and to sublimate his own sexual urges he tried to beat mine out of me. He decided it was his mission to make me fit to stand before God. He forced me to pray for twelve to twenty hours at a time, on my knees, even after I had lost my voice; I was only allowed to eat every few days; I had to recite Leviticus while he tore open my back with the whip. Between broken bones, infection, and starvation I came close to dying more times than I can count . . . but I was so afraid of the damnation I faced that I dragged myself back to life every time." "I'm sorry," Miranda said softly. "I don't want your pity, Queen," he snapped. "Don't think that we have some common bond because men treated us both like trash." "I don't think that," Miranda said, her own anger flashing at him. "We're nothing alike. What happened to me didn't turn me into a drunken prick who tries to get in his old boyfriend's pants after fucking him over. Trust me, I don't want to claim any common ground with you." "If I wanted David, I'd take him," Deven informed her venomously. "What the hell is wrong with you?" she demanded. "You have a fantastic Consort who for some reason I can't figure out loves the hell out of you, and you're fixated on a married ex who doesn't want you anymore? Who are you trying to hurt—me? David? Or yourself?" Miranda sat up straight and leveled a look of loathing on the Prime. "You missed your chance, Deven," she snarled. "You blew it. It's over now. You drove him away, now he's with me, and I'm not going anywhere. So get the fuck over it." The ire seemed to drain out of Deven as quickly as it had come. Silence sat awkwardly, and drunkenly, between them while she finished her drink and poured another. The Prime didn't react to her outburst at all for a while. Finally he said, "You can hate me all you want, but I'm not going anywhere either." "Yeah, I know." "I suppose for David's sake we should try to get along." "Probably." Another pause. Then she asked, "What do you think is happening to David and me?" "What makes you think I would know?" Now it was her turn to roll her eyes. "Oh, come on. Even David thinks you know everything. You can't tell me that in all the years you've been around, you've never heard of psychic gifts being contagious." "As a matter of fact, I haven't," he said. "I picked up on his telekinesis, and he picked up on your fighting mojo. How could that happen?" Deven leaned over the arm of the couch and felt around for a moment before coming up with a second bottle of whiskey, this one new. As he opened it, he corrected her. "He didn't get it from me; he got it from you." "But I don't have it." "You've got precog because you're a Queen," he said. "It's still untrained, and so is his. The telekinesis you got from him was already honed and focused—it took him years to learn how to direct it enough to throw a living thing. What I have isn't a single gift, it's a combination of three factors: prescience, telepathy, and technique. I taught him the third, he already had the second, and from you he got the first. His work was still a little sloppy around the edges, but once he got out of his own way, it was genuinely powerful." "Why is it harder to throw living things?" Deven shrugged. "They wiggle?" "Sophie showed me how to do something similar to that," Miranda recalled. "I wonder where she learned it from." "No idea. But the thing to remember is you've had precog y our whole life—it's part of who you are. It just didn't start to actively manifest until you became Queen. It's practically unheard of for someone to just spontaneously develop a psychic talent without at least some latent ability . . . and even less heard of to start manifesting someone else's." "Still, the central question isn't answered. How did it happen?" "I would venture to guess that the answer is somewhere in our history. Legend has it that back in the ancient days, when the Signets were new, we had abilities we can only dream of, abilities we lost somewhere along the way. We are a mere echo of what we once were." Miranda held her glass tightly. "But some of it is still possible." "Most likely all of it is, if you know where to find it. As to that, I'm as clueless as anyone. I didn't become Prime for mystical powers . . . actually I didn't do it on purpose at all, so I was never all that interested in some grand destiny." She crunched a half-melted piece of ice in her teeth. "Did you mean it when you said you don't believe in God anymore?" He crossed his arms and leaned back. "I went to live in the house of God and spent six years tormented by his holy representative. I prayed and prayed for deliverance, and all I got were broken fingers and lye burns, because God didn't care to save a wretched little sodomite like me. I learned I was hellspawn because of the things I could do, and the only atonement was to let my uncle abuse my body in the name of Christ our Lord. After that I lived for seven centuries, Miranda, and spent much of that looking for some sign, anything, to bring back my faith. I tried. I traveled the world searching. And do you know what I saw?" "What?" she asked softly, unsure how to deal with his sudden, complete honesty. "I saw men raping women and children. I saw men killing each other in God's name. I saw greed and poverty and despair and murder of every conceivable kind. I learned that the loving Father I had yearned for wanted me to burn in hell because I fell in love with the wrong kind of person. I saw mass murder, terrorism, genocide, oppression, and repression, and all of it, all of it, was dedicated to a God who seemed neither to notice nor care. So you tell me, Miranda. What should I believe?" Miranda had tears in her eyes. She couldn't help it, thinking of all that had been done to an innocent child, and all that seemed to still be happening to him, in his memory, seven hundred years later. She could feel, even through his words, the pain that it caused him to feel betrayed by the belief system that had been his reason for living, once upon a time. "But you don't have to be Catholic," she said. "You don't have to define God by what his fan clubs do." Deven smiled, and again her heart hurt for him. "It's too late for me, Miranda. Some doors, once closed, can never be opened again." "What . . . what things could you do, that the monks condemned you for?" As if beaten down by the irony of it, Deven's voice was stony and dull. "I'm a healer," he said. "I've cured the plague. I've reattached limbs. I've brought mortals and immortals both back from the very edge of death." "That sounds like the kind of gift God would love," she said. "God, perhaps. At least I like to think so. Man? Never. To men, God is a weapon. A stick to beat the souls of others into submission. A blade to stab and bleed anyone with power of her own. If there is a God, he has abandoned us all to fear and eventual despair. But in the end, what does it matter to us? Nowhere is it written that heaven would open its doors to a vampire." He met Miranda's eyes. "We're alone, Miranda. Our kind have no savior, no paradise to look forward to. Some of us do evil, so perhaps they'll go to hell, but for those of us who don't . . . we're no less damned. But perhaps our damnation is worse, for all I can see ahead is nothingness. No God, no devil, nothing. Just an eternity wandering the outer darkness." "Wow," Miranda said. "I think you may be the most pessimistic person I've ever met." "Thank you." "But you're wrong," she told him. "We're not alone. We have each other. You have Jonathan, and I have David. Maybe the reason we have soul mates is to make the darkness easier to face . . . forever." Deven gave her a slightly patronizing smile. "Oh, don't worry. You won't have to worry about it forever. Now that you have a Signet I give you, say, two hundred years." With that, he pushed himself up off the couch and, taking the half-empty whiskey bottle with him, left her alone in the study with even more unpleasant thoughts than she'd come in with. "I talked to Deven," Miranda said, falling into step beside David. The Prime gave her a once-over. "I don't see any blood, so I assume it went well?" "As well as can be expected." They walked together along the main street of the Shadow District downtown, while all around them the usual hubbub of a Saturday night in the city flashed and bumped and laughed from the open doors of bars and clubs. The vampires of Austin were out in droves tonight, and though most avoided the Pair's gaze and simply bowed as they passed by, a few made eye contact and called greetings. David paused here and there to visit with club owners or other businesspeople in the area and in some cases introduced her to people she hadn't had the chance to meet; even those who looked at her with some suspicion were friendly to her face, and she tried to be as gracious as possible to lure them into thinking her harmless. She preferred the element of surprise. Clearly some of them had heard about Hart and kept their distance from her or spoke very vaguely about their business dealings, in case she should deem them immoral or illegal on a whim. Miranda found that hilarious but held her tongue. Between visits she told David more about her conversation with the Prime. "I still can't say I like him . . . but I understand him a little better now. I just wish he weren't so fatalistic—especially about God." David looked at her and said curiously, "I didn't realize you were religious." "I'm not, really. I never really felt called to that kind of thing except for some experiments in college. But Deven is different. He needs that belief. If he could find it again, he might be able to finally heal—he's spent seven centuries as a miserable bastard because he lost his faith." The Prime nodded. "I agree with you. But I don't think it's totally lost; I just think he's been unable to reconcile what he's seen with what he wants to believe about God. He's been alive a very long time, beloved. His perspective is broad, yes, but it's also deeply flawed." "What did he mean when he said I had two hundred years?" "The longest a Prime has held a Signet was three hundred twenty years—one hundred without a Queen, two hundred twenty with her." "So the truth is, even though we're immortal because we're vampires, we'll still die because we're Signet bearers." "Eventually, yes. An ordinary vampire could stay out of sight, live quietly. We can't do that. We'll always be in the public eye, always a target for someone who wants to take our place." David just shrugged and offered a smile. "But I have every intention of living at least that long, my darling. I hope that's all right with you. I'm determined to see the future of society no matter how it turns out." "Why? What could be so great that you'd wait three centuries to see it?" He looked over at her again, the uncharacteristically youthful earnestness on his face so adorable that she started to giggle. When he replied it was as if the answer should have been perfectly obvious. "Are you kidding? Vampires in space!" Miranda's giggles redoubled, and she had to stop and kiss him. "I love you, you big geek." After the events of the past week David had suggested it was a good time for the two of them to take a walk, making their presence known to the Shadow World, to remind everyone who was in charge. They had arranged to meet Deven and Jonathan at the Black Door, a popular hunting ground and dance club, to end the evening; the Pair would be on their way back to California the next night, their state visit officially concluded and considered a success from a diplomatic standpoint. Personally, though, it didn't seem anything had concluded successfully. So far David and Deven hadn't had any sort of serious talk about their relationship, and Miranda still wanted to punch Deven in the face. She didn't feel at all satisfied with how things had gone, but there was no help for it; a Pair couldn't be away from home for long without chaos breaking out in their territory. But, she reasoned, it wasn't like they were getting any older. At least now David had admitted there were things to resolve instead of pretending it was all fine and dandy between him and Deven. That was a start. "I love this city," David was saying, looking up at the buildings that rose on either side of them. "Its energy, its people . . . I don't even mind the blistering summers. I'm proud of what I've accomplished here." "You should be," she replied. "After what I've learned about the other Primes and what life is like in their territories—for humans and vampires alike—I can see what an amazing leader you are." He smiled and put his arm around her as they walked. "And just think . . . soon the world will speak of you the same way, and our legacy together will be one of peace through strength. They'll see our tenure as the moment when the Shadow World began to evolve past its primitive history and become something greater." "Hopefully my legacy will include a string of platinum albums," Miranda laughed. "If I can ever get this one finished." She grew serious for a minute and said, "You know . . . I've learned a lot the last three months, but I think the most important thing so far is how lucky I am." He lifted her hand and kissed it. "You and I both." Miranda had never been into dance clubs—she preferred the sort of place where there was live music and less techno—but she was quite fond of the Black Door. At first it had bothered her knowing what the place was for. The term "hunting ground" wasn't a euphemism; humans came to dance and drink, and vampires came to feed. Everything about the club drew mortals in: There was no cover charge, and drinks were deliberately priced below the Sixth Street average; the place was clean and spacious and had a huge dance floor surrounded by a second level of tables and booths. It had two bars, one above and one below, and the music was slightly quieter on the second level. It was one of the most popular clubs in Austin, found purely through word of mouth—no advertising, no website. What the humans didn't know was that there was a separate entrance for vampires. A limited number were allowed in at a time, and security kept a close eye both on them and on humans leaving the club. A vampire who made any trouble was permanently barred from entry. If a human displayed any sign of injury beyond the usual fatigue and confusion of being bitten, he or she was immediately given a cab to a nearby clinic, which, of course, was also run by the Signet. Great care was taken to ensure that the mortal patrons had no reason to complain and every reason to tell their friends about the awesome place where they'd danced the night away. It seemed so . . . manipulative and wrong, like a factory farm, and Miranda had refused to have any part of it until David had persuaded her to go one night and she had seen firsthand how it was all managed. In any other territory things might be very different, but this was the South. The Prime would not allow his human charges to be molested. Vampires needed to feed, and the Shadow World had to remain a secret. Austin had a dense vampire population, and somehow all those vampires had to be fed discreetly; if they were unsatisfied for long, they began to get angry at the authority that kept them from killing, and that was how gangs and rebellions were born. They walked to the front of the human line; David used the front entrance so that everyone inside would know the Signet was in attendance. The doorman took one look at them, bowed, and unclipped the velvet rope to let them in. The bass began to pound its way into her body as they crossed the threshold and walked down the short hallway that led into the club. She shot David a grin, and he kissed her hand one last time before releasing her. Miranda squared off her shoulders, drew her power around her like a cloak, bolstered her shields, and strode into the club with her Signet out where every vampire would see it and know her for their Queen. The Black Door was packed. Only months ago the sheer weight of all those minds rubbing against hers would have sent Miranda to the ground screaming, but she was no longer human and no longer afraid. She nodded to the security staff as they passed; sometimes those who didn't make the Elite but still scored high in the tryouts were offered jobs at Signet-owned establishments, and a few made their way to the Haven after proving themselves here. She recognized a few faces. Not far inside, Lali fell into step behind her, along with Aaron, one of the other two bodyguards. Miranda had offered Lali bereavement leave after Jake was declared dead, but Lali wouldn't have it. Jake, she had said, was devoted to his job, and she was going to honor that devotion by doing her own. Miranda had hugged her, thanked her, and let Faith put her back on the rotation. They were going to have to assign another guard so that they'd have even pairs; Faith said she would go back over the candidates who hadn't been picked and submit her recommendation by Monday. As a matter of fact, Faith was here tonight; Miranda let her gaze meander from one end of the Door's vast space to the other, and she caught sight of Faith not far away, sipping a martini and talking with another Elite. Faith looked devastatingly gorgeous: For once she was out of uniform, in a short green dress with her hair out of its braids and pulled up on top of her head. Miranda wished, sometimes, that she could pull off the glamorous look Faith did without any apparent effort. Then, of course, there was Deven. Miranda wasn't looking for him, but she happened to glance over at her Prime and noticed he was staring off at something. She knew without asking what that something was and followed his gaze to the dance floor. Sure enough, the Prime of the West was in the center of the crowd, surrounded by both men and women who seemed unable to take their eyes off him. He was currently pressed up against a petite blond woman . . . and a striking dark-haired boy of perhaps twenty. Deven was back to his usual wardrobe, this time a black jacket over a dark gray shirt, his Signet visible amid the rest of his jewelry, the allure around him as intense as it had been that night in the alley. The look on David's face was unmistakable, and it filled Miranda's heart with shards of ice: _hunger_. In that moment he wanted more than anything in the world to be at Deven's side, or better yet, pinning him to the wall with deep, hard kisses. "I'm going to get someone to drink," she said, not giving David time to protest as she tore herself from his side and made her way to the bar. She intended to get one of the mixed drinks that the Black Door specialized in—the kind with blood in it—but when she saw Jonathan at the bar, she decided she was more interested in getting blind drunk than anything else at the moment. "My Lady," Jonathan said, raising his beer in salute. "Shiner?" "I think I need something a little stronger," she replied, motioning to the bartender, who set aside the row of drinks he was making and came for her order instantly. She asked for a shot of Patrón. Jonathan frowned. "Tequila," he said. "That doesn't bode well. What's wrong?" She gestured out at the dance floor. "Something about my husband dancing with someone else makes me want to rip that someone's little pixie head off. Sorry, Jonathan. I guess I'm just not as evolved as you." "Actually, he's not," Jonathan said, looking out at the floor. "He's looking for you." Miranda turned to see that Deven was still by himself, though now one of the sexy mortals in his bevy of admirers had two tiny holes in his neck that were swiftly closing; meanwhile, David was standing next to Faith, but his deep blue eyes were scanning the crowd, and when his eyes met Miranda's, he broke out into a smile. Her heart climbed back up from where it had sunk into her feet, and she smiled back, knocked back her shot, and left the empty glass on the bar. Jonathan was chuckling to himself and shook his head. "Jealousy doesn't become you, Miranda. Especially when it's totally unfounded." Bristling, Miranda walked away without answering, but if he'd been a telepath her reply would have been crystal clear: _Blindness isn't particularly attractive either._ She might be young and new to her Signet, but she was well aware that she was one of the strongest empaths among her kind, and she knew quite well there was nothing unfounded about her jealousy, becoming or otherwise. But it seemed that a certain amount of denial was just a part of the Pair's relationship, and she wasn't going to disillusion Jonathan. She liked him too much. If he was content to go on pretending it really didn't bother him, well, so be it. But she was still glad the Pair were getting the hell out of her territory. When she came into view David held out his hands, and she took them, stepping up to him and then turning, slightly, to draw him out onto the floor. One of his hands slid down her back to her waist and the other up to her chin, and she put her lips up to his, claiming his mouth fiercely enough to banish, she hoped, all thought of anything . . . or anyone . . . else. She pulled him with her into the song that pounded all around them, her fingernails scratching lightly through his shirt, her teeth tugging gently on his lower lip. Miranda remembered once, in a philosophy class, hearing about Plato's theory that humans once had had four arms, two heads, and four legs, but they had been split in half by the gods, and spent the rest of their lives seeking that sundered half with whom they fit so perfectly. At the time it had been a fanciful sort of story, ancient philosophy as written by Disney. She believed it now. She was exactly tall enough to rest her head on his shoulder, his arms reaching just right around her middle, hip locking into hip as if they had grown that way from the dark soil of some overgrown, night-blooming garden. She'd danced with him a dozen times and not once had there ever been any awkward bumping; he grabbed her hand and spun her away, then back, and she was laughing at the ridiculousness of such a ballroom move in the middle of a floor crowded with youngsters, but when she came back to him she fit just where she had been, and the electrical charge of that contact nearly tore a gasp from her throat. One hand circling her waist, he tilted her back, and she bent almost double, her hair sweeping the floor. There were, of course, people watching; if anyone in this room knew vampires existed, they knew these two, and knew that the connection between them was stronger than the forces that held atoms together and kept the moon spinning around the earth. She wanted desperately to drag him into a corner of the room and wrap herself around him, but as the song came to an end and his mouth found hers again, she barely had time to immerse herself in the delirium of the kiss before a familiar, and unwelcome, sound broke into the moment. "Damn it," David hissed, pulling his lips away to look down at his phone. His gaze jerked up to her. "It's Kat." "Answer it!" Miranda felt cold dread falling as a stone into her belly. As David said "Star-one," another noise shrilled out, this one a network alarm. "Faith!" Miranda all but yelled into her com. "I need you!" "Here," the Second said, appearing beside her almost instantly. "What's happening?" "Coordinates," Miranda said to David, who was trying to call Kat back and getting no answer. He switched the screen to his view of the network sensor grid and drew a line with his finger over the screen, spinning the diagram around to match their location. "Not far from here," David said. "Faith, get a team to East Seventh and Comal immediately." Faith didn't even bother replying; she simply darted away, already issuing orders into her com, her stiletto heels hitting the floor with as much purpose as her usual combat boots. Meanwhile, Miranda had her phone out and was trying to get Kat, but it kept going right to voice mail. Fear rose in her throat. "Kat . . . Kat . . . David, something's wrong, we have to find her . . ." David pulled her off the dance floor, over to a clear space by the bar where Jonathan and Deven were drinking. Both Prime and Consort looked startled at David's grim expression and her rapidly spiraling panic. David was still staring down at his phone. "Her signal dropped off here, but her call came half a block away, so we can assume she's being taken north—" "There's no time for your dicking around," Deven snapped, and for once Miranda wanted to hug him. "You. Me. Mist. Now." David looked up, shocked, but nodded. About two seconds later, the Primes had vanished into thin air. Miranda was still on the verge of a breakdown. "I have to get there . . . I can't run that fast. The car won't be here in time. Jonathan, what do I do? Kat's in trouble, she might be dying, oh, God—" "You haven't learned to Mist?" Jonathan asked, amazed. "Well, then, we'll start right now. Grab my arm and hold tight—there's no time for finesse, so as soon as we land be prepared to skin your knees and vomit." She didn't care about the consequences. All she could think of was getting to Kat. She seized Jonathan's proffered arm and felt a sickening lurch . . . . . . and the club spun away into darkness. Nine True to Jonathan's word, the second Miranda landed, her knees hit the concrete hard enough that she felt one of her kneecaps fracture, and she pitched forward and threw up all over the median grass. Then she forced herself to her feet, fighting the waves of vertigo that kept battering her from all sides as well as the pain in her knee, and tried to make sense of the scene before her. The first thing she saw was blood, and it nearly made her sick again, because she knew whose it was. "Kat!" she cried, pushing herself forward from the street into the alley. "Where is she? Kat!" Footsteps thundered up to Miranda's side, and Faith grabbed her arm and steadied her. "Miranda, listen to me—you can't help her now. Just stand back and everything will be fine." "I can help her! Let me go!" The panic was so overwhelming that Miranda nearly shoved Faith away, but before she could summon the energy, she felt someone else grabbing her other arm—David. "It's all right, beloved," he said. "Just hold on." Miranda, however, was beside herself and couldn't be consoled. "Is she dead? Did they find her hand? I want to see her hand! David, please, I need to see . . ." "Easy," David murmured. "Come with me . . . one step . . . and another . . . it's all right, just take it slow . . ." He led her around the crowd of Elite—the patrol team that had come as soon as Kat's emergency signal went out, and the second team headed by Faith that was arriving as Miranda stumbled toward the scene. The street corner was splattered with blood. A woman's form lay sprawled out on the concrete, blood oozing out around her, her car keys flung several feet away. Kat was trying so hard not to scream. She was panting, half sobbing, every other breath almost a wail. Her bald head was dripping with blood, as was her arm . . . from the cleanly sliced stump where her hand had been severed. Someone had tied a strip of fabric as a tourniquet and it was already soaked. Worst of all, there was a knife protruding obscenely from her abdomen. "Kat, Kat . . ." Miranda was sobbing as Kat was sobbing, and the Queen fell down beside her friend, her best friend she couldn't protect with all the immortal power in the world. "Help is coming, Kat, I promise." She tried to reassure the human, doing anything she could, because it was why she was here . . . for all the good it did anyone. _"Miranda."_ A sharp voice cut through her panic, and she looked over Kat's bleeding, broken body to see a pair of ice-cold lavender eyes fixed on hers. "Pull yourself together, Queen," Deven commanded gently. "She doesn't need to see you like this." Miranda took a deep, shaking breath and threw her energy into grounding, bolstering her shields, and calming herself enough that she could look at the situation realistically. She knelt beside Kat's body, holding Kat's still-attached right hand, while the Elite tried to stop the bleeding from her left arm and the wound to her gut. A few inches from Kat's arm, the severed hand lay on a clean cloth, blood soaking into it. Deven's voice grabbed Miranda again. "Listen to me. You need to tell your people to step back and maintain their distance. The forensic team must start searching for evidence. There should be a trail—we caught the attacker by surprise and I wounded her. Tell them now." Miranda jerked her head up and gave her orders, and the Elite scattered. "Now. You have a connection to this woman, so I will need your help to help her. Do you understand me? Let yourself be open to me, as if I were David calling for your energy. I'll pull from both you and Jonathan. It will work faster this way. Open yourself, and stay grounded." Miranda fell into a cross-legged position that mirrored Deven's, though he was on the side of Kat with the . . . hand . . . "Focus!" The snapped command made her look away from the gruesome sight and back down at Kat's anguished face. Kat was crying, shaking, and so pale . . . Miranda opened her shields as she'd been told, but she also spared a tendril of her power to reach softly around Kat's heart and soothe her fear, let her know that she was loved and taken care of, and now she was safe. She was safe, and loved . . . safe . . . Kat stopped flailing against the hands that held her, and those hands lifted. Miranda watched in rapt fascination as Deven closed his eyes and held his palms out over Kat's body, first over her belly. He reached down and carefully drew the knife out of her flesh, laying the weapon on a sheet of plastic that would be wrapped for evidence. Then he held both palms over the wound and became very still. All around them, sound seemed suddenly muffled, a strange peace descending over the chaotic scene. Everyone came to a standstill and turned to stare as the light in Deven's Signet began to glow brighter and brighter . . . At first it seemed almost like a trick of the streetlamp, but soon it was too bright for that, becoming like an aura, or a halo . . . Miranda felt a gentle tug at her shields, and she opened them wider to him, feeling him reach in and lift tiny sips of power at a time, feeding them into Kat's body as if she were a starving baby bird. Blended with his own energy, and his Consort's through their bond, Miranda's power added strength and love to the mix, and soon she felt the wound begin to close, all the rips and gouges mending themselves, until even the skin that covered the wound began to knit, first an angry red wound, then a dark jagged scar, then softening to pink, then fading to white. Miranda felt her own energy start to wane just a little and reached sideways to her Prime, who opened himself willingly; now, all four of them were part of the web, each feeding power into Deven, which he fused with his own and directed with utmost care to where it was needed, cell by cell repaired to blossoming health. But Deven still hadn't lifted his hands; his eyes were closed but his brow furrowed in concentration. He looked up at Kat and asked softly, "Shall I bring her back, Katerina?" Kat, too, had been overcome with peace and was breathing in tandem with the Prime, who waited for her answer. She smiled and said hoarsely, "Yes." Nodding, Deven closed his eyes again and went back to work; a second later Miranda felt something . . . something inside Kat fluttered, like a tiny hand waving hello. Then he moved his attention up to her left arm, and this time picked up the poor severed hand and placed it against her wrist, holding his own hands over the joining, closing his eyes and breathing . . . in and out . . . in and out . . . for several minutes, while Miranda felt the ebb and flow of power through her, David, and Jonathan, then through Deven, and into Kat's arm. Finally, Deven withdrew both energy and hands, and a gasp went up all around them as the Elite saw that Kat's wrist was whole again, without even a scratch. Deven disengaged himself from the power matrix, and each of them did the same until their bonds were only for each other again. The connection among them was so infused with serenity, Miranda was reluctant to leave it, but she could feel everyone weakening. It was time to let go. Miranda was crying, but she met Deven's eyes. He looked like he was about to lose consciousness. "Thank you," she whispered. The smile he gave her was one she would always remember: It was one of pure peace, even bliss. Whatever his other gifts were, whatever creature he was, Deven had just done what he had been born to do. He was a healer. She would never doubt that again. "David," Deven said, "catch her." Just as Deven passed out and sagged sideways into Jonathan's arms, so did Miranda do the same, falling backward against her Prime, who held her tightly and picked her up to carry her home. "Thank you, Mr. Behr. Let me know when would work for you and your staff to reschedule, and send me a bill for their time tonight as well—I know it's extremely inconvenient for you to have a no-show, especially when you go out of your way to set up for us late at night. Again, I apologize. Have a good evening." David hung up with a sigh and stood at the foot of the bed, watching Miranda sleep; she and Deven had been the worst off, and so far neither had woken in almost twenty hours. Jonathan said that he had seen Dev heal so intensely only two or three times before, and it always wiped him out for a day or two; vampires simply weren't designed to burn energy that way. They were predators, not healers. He wondered: Had Deven been born at a different time, with the abilities he had, would he have been a valued member of his tribe, perhaps a shaman or priest, instead of constantly coming under the scrutiny and abuse of men who thought their God couldn't possibly have shared such astonishing powers with another? Or would he have been burned at the stake the way Lizzie had been? God, it seemed, had a rather caustic sense of humor. David checked his phone again: a text from Elite 43, the guard he'd already assigned to watch over Kat, who was presently with her at the Signet-run clinic, where she slept in recovery. The clinic specialized in vampire-related injuries and had several immortal staff members who could alter memories as well as manage the symptoms of an attack or overzealous feeding. Kat had none of those, but no normal hospital would understand what she had been through. It was best to keep her somewhere that the doctors knew what she knew and wouldn't refer her to the psych ward or try to involve the police. The Prime had also ordered a guest suite at the Haven prepared for Kat. He doubted she would go along quietly, but he wasn't about to let her stay on her own after tonight. Another message, this one from Faith's team on the scene: The blood trail had gotten them nowhere, vanishing midstride in the middle of the street, but they had collected samples that went immediately to Novotny, and hopefully the good doctor could discern something in the blood before it died. The weapon used to stab Kat had also been retrieved; an egregious error on the attacker's part, but then, she had been interrupted. David and Deven had Misted within five feet of Kat's prone body and the vampire kneeling over her with a knife. Dev had been quicker on the draw and slammed a throwing stake into the woman's back; she screamed and bolted, not even looking back. The stake fell out as she ran, and it, too, had been cataloged as evidence and taken in for trace analysis. Surely, _surely_ something would be found. No criminal was brilliant enough to attack four people without leaving a single speck of evidence. She was clumsy enough to leave both the stake in Miranda's shoulder and the knife in Kat's stomach; she had to slip up somewhere. Red Shadow or not, nobody was that good. He sat down beside Miranda and straightened the covers around her gingerly so as not to wake her. He'd never seen anyone twist sheets the way she did. He laid his hand on her forehead, pleased that her body temperature had dropped to normal; when he first put her to bed she'd had a fever. Her body hadn't known what to do with the wild fluctuation in her energy and had reacted as though it were ill until he woke her long enough to coax her into drinking some blood from their emergency store. She had done as he bade her, murmured something about it tasting old, and fallen back to sleep before the sentence was finished. After a moment of watching, he sighed and stretched out alongside his Queen for a while, facing her, the slow rise and fall of her chest more comforting than he would ever have thought possible. He touched her face, brushing his fingers along her lip, loving every inch of her and gripped, for a moment, with fear; someone was after her, and their reasons didn't matter. What mattered was that he would find whoever it was and hurt them until they begged for death . . . but lying there staring at her, he couldn't think of torture and violence . . . he could only think of how strange and wonderful it was to love her, to have her here, every day, to wake beside her when he had come so close to losing her. He was grateful that the Signet bond ensured that, should she die, he would die within minutes. The thought of existing on this planet without her, as he had for so many years, was too horrible to contemplate. There, he knew, was the difference between how he felt about her and how he had felt about Deven. Losing Dev had been heart-crushingly painful, yes, and there had been days he could barely get out of bed beneath the weight of his sorrow, but that night he had stood before the smoldering ruins of Miranda's apartment, desperate for any hope but deep down knowing there was none, had been the worst moment of his life. The thought, though, brought images to his mind that he didn't want, and a longing that spread from his belly outward, that part of him that still yearned, whispering, wondering what it would be like, for just an hour . . . remembering another face on the pillow before him, another mouth catching his in the darkness, another back arching against his hands . . . Suddenly he had to be out of the bed. Thinking about Deven while lying with Miranda was flat-out blasphemous to them both. David got up, feeling imbalanced and uncomfortable in his skin. Thank God she was asleep. He sat down at his desk and for a moment covered his eyes with his hands, wishing to God or any convenient higher power that he could stop feeling this way. He had thought that he loved Miranda with every inch of his heart, and that there couldn't possibly be room for anyone else. Yet some dark corner of his being had held on to what once was, all this time, and was slowly crawling through his veins, leaving behind an old fire and a new fear. He could tell himself it was purely physical, or just nostalgia . . . but he knew a lie when he heard one. He tried checking his e-mail and messages, but there was nothing new. Still, there had to be something he could do in his workroom, and once he was out of the suite he could talk to Faith without waking Miranda. Once in the hallway, though, he found that his feet refused to carry him to the workroom; they seemed to have an agenda all their own, and he was headed down the corridor before he realized where he was going. _Damn it._ He told himself it would be remiss not to check in on them; they were his guests, after all, and he needed to check on when they were planning to leave now that they would have to reschedule their flight. He could stop by, get a status report from Jonathan, and then go find Faith to go over whatever evidence they'd gathered from the scene. He could also put in a call to Novotny to check on the tests they were running on Jake's and Denise's hands. Pathological analysis took time, but there might be some preliminary results by now. He arrived at the guest suite, where two California Elite were standing guard; it was traditional for visiting Pairs to bring a half dozen or so of their own warriors for personal security. The two guards bowed to him, and one opened the door for him. David looked in, expecting to see Jonathan on the couch while Deven slept nearby, but to his surprise he didn't see the Consort anywhere. "Come in," said a tired voice. The guard closed the suite door behind David, who walked slowly into the room, looking around curiously. "Hello?" There was a faint movement and he realized that it was Deven who was on the sofa, curled up against the arm, under a blanket, nursing a glass of blood. The hearth was bright and warm, the rest of the room dark. "Where's Jonathan?" David asked, a bit nervous without the Consort in earshot. "Remember?" Deven said. "He said he asked if he could take Isis out tonight, and you agreed." "Oh, right." He did remember; they'd been having a brief discussion about the attack and healing once everyone was safely back at the Haven, and Jonathan had said that they would probably remain in Austin until Monday just to be sure Deven was up for travel. Jonathan had expressed interest in the Friesians, and David had been more than happy to give him access to the stables whenever he liked. Jonathan was one of the few people David knew who shared his enthusiasm for the animals and one of the few he would trust with them. He was also probably one of the only people whom Isis would allow near her without biting off a finger just for spite. A bit wary of the situation, David lowered himself into the empty chair, asking, "How are you feeling? I thought you'd still be asleep." Deven half shrugged. "You know how it goes." "Nightmares?" The Prime nodded without lifting his head from the blanket. He looked so young and vulnerable like that, it made David's heart ache. "Whenever I do something foolish with my power I have a hard time shielding myself from the dreams. Jonathan can help, but he was wide awake, so I told him I'd just nap here until he came back and not to worry." "Is there anything I can get you?" "No. Nothing." There was a moment's silence, with the fire crackling and Deven breathing slowly and evenly, though he wasn't asleep. His eyes were partway open, staring at the flames. "What you did for Kat was . . . nothing short of miraculous," David said quietly. "Thank you. And I know Miranda will thank you when she can." "She did already." Dev's eyes opened a little wider, and he fixed David with his gaze, eyes nearly as violet as irises in this light. "David . . . there's something you must know about Miranda. Something important." "What? What is it?" The Prime carefully pushed himself more upright. "She's not like the others, David. She's not like Jonathan, nothing like any other Queen. What she's brought to you . . . nothing like your bond has been seen in the Council in over a thousand years. I wish I could explain it to you, but I don't know what it means, or even _how_ it's different . . . but I can feel it. No Pair can expect to lead an ordinary life, but you . . . the two of you have something very important to do together." "I thought Jonathan was the prescient one," David stammered, trying and failing to cover how rattled he was by Deven's words. "You know I have it, too, in smaller measure. I never use it except to fight, but this time . . . trust me, my darling. It's not a matter of seeing the future. I _know_ this. Whatever life you had planned, whatever peace you had hoped to attain, you'll never have it. Accept that now and you'll be much happier." They stared at each other a long moment before Deven relaxed back into the cushions and said, "It makes it hurt less, somehow, knowing that you were meant for such a life." David raised an eyebrow. "You were the one who—" "I know." Deven cut him off, waving a hand. "I've heard it all before." He ran his hand back through his hair. "David . . ." A note of entreaty entered Deven's voice, as well as reluctance, even fear, to say what had to be said. "I've tried my best to make up for how I treated you. For years now I've done everything I could to earn back your trust. I've done things that . . ." He trailed off, eyes returning to the fire. David frowned. "What have you done?" Deven ignored the question. "I can't force you to forgive me. And if you never will . . . how can we remain friends at all? We've been dancing around this since I arrived . . . no, for years. Somehow we have to move on from here." David, restless, got up from the chair and came over to straighten out the blanket around the Prime as he had earlier with Miranda. "To be honest, Deven, I don't know if we can. I thought I was past all of this, but I think I was just far away from it. From you. Maybe that's the best thing, for us to keep our distance." Deven grabbed his arm, forcing him to stop looking for something else to think about. "Is that really what you want?" Again their eyes held. David found he could barely breathe. "No." "I should never have let you go," Deven said softly, lifting one hand and brushing a stray hair from David's eyes. It felt like his spine was melting under the heat of that one light touch. David knelt in front of the couch, putting his head about level with Deven's. "What about Jonathan?" "Jonathan would have understood. He's said so many times." "He would have shared you with me?" "Of course. He's always had his lovers. So could I, within the terms of our relationship." David smiled wryly. "You're basing your regrets on the assumption that I would have been willing to share." The smile was returned, this time ruefully. "We do a lot of insane things for love. I thought I was doing the right thing by breaking it off with you . . . but what kind of life could we have now if you had stayed?" David's smile faded. "You would have all of your soul mate's heart and all of mine, and I would have, perhaps, half of yours. So things would be wonderful for you, which is what matters, isn't it?" "Are you suggesting that I'm selfish, David?" "No, Deven, I'm saying it. You're selfish. You would rather I were warming your bed with only half a soul than finding fulfillment in my own life—and I'm sure you were much happier before I met Miranda. And now you think, what, that you can walk back into my life and claim some piece of me for yourself after you left me in the gutter with a broken heart?" "You're wrong," Deven snapped, anger sparking in his eyes as they went silver around the edges. "You have no idea how wrong you are. How can you think that of me after everything we've been through together? How can you think I don't want to see you happy?" The Prime sat up, pulling away from David, then shoved the blanket aside and forced himself to his feet. "You should go," Deven said, voice going cold. "I need to pack." But Deven wavered where he stood, dizziness catching up to him, and David caught him as his knees buckled, his heart pounding at the sudden feeling of Deven's slender body against his. Dev tried to push him away, but the effort was halfhearted at best and he was still weak. David held on to him, some desperate wild thing in his chest refusing to withdraw, and after a moment Deven gave up and leaned into his arms. "I don't want to feel this way," Deven murmured into David's chest. "I want to forget we were ever in love and be content with friendship. But I don't think I can, David. I can keep my distance and I can honor your commitment, but I can't ever stop loving you." David drew back to look at him. There was such anguish in his face, and David felt it just as keenly himself even if it didn't show. "I know," he said. "Neither can I." Deven shook his head. "You should go. Go, now, before we do something that . . ." He didn't have a chance to finish the sentence. David's mouth had already covered his. Ten Kat woke to a world that had changed, and changed profoundly, without her permission. She didn't want to open her eyes. There were nightmares in the dark, but she had no idea what being awake would prove or disprove about the night gone by, and better the devil she knew than the one she didn't . . . although . . . what was that beeping? Curiosity got the better of her and she slit one eye open to get at least some idea of where she was. Could it be . . . just maybe . . . she was in her own bed, beneath the handmade quilt her grandmother had left unfinished when she died, the blue and purple one Kat had clumsily handstitched the last square onto? Was she in her cozy bedroom in the townhouse she had bought in a bid to feel grounded someplace, finally at home for the first time in her life, the furniture and DVDs testimony to the fact that she had chosen to call Austin her town after years of wandering around the planet? The beep came again just as her eye opened enough to admit light, and her heart sank as confusion set in. No, this wasn't home. Home wasn't stark white and cold, and it certainly didn't have a bank of machines up by the headboard. "Kat?" She pried her eye open the rest of the way, then its partner, and turned her sight on the origin of the voice, a dark-haired young man whose brow was creased with worry. "Hey," she croaked. Drew let out a breath of relief and squeezed her hand almost too hard; she was aware, then, of something poking her, and a second later realized it was an IV. "Am I in the hospital?" she asked, surprised at how weak her voice was. She sounded like she'd had the flu. He made an indefinite gesture with his head. "Sort of. It's the Anna Hausmann Memorial Clinic down on Fifteenth." "Never heard of it." "Yeah, me neither. I got a call last night that you . . . that you were here. I think . . ." Drew looked around as if worried someone would overhear, then said quietly, "I think Miranda's people run it." Kat blinked. Vampires had doctors? Why? She looked around the small, private room, which could have been in any hospital in Austin. It even had a window whose blinds were open, so at least the nurses had to be human. On the wall, there was a dry-erase board that read, _Welcome to the Hausmann Clinic! Your nurse today is ..._ The space had been filled in by a different hand, with _Jackie_. At the top corner where the hospital logo would have been was a symbol like a family crest, with an S in the center. _Solomon._ Kat shut her eyes tightly as flashes of memory began to intrude . . . not visual, but visceral, the memory of pain, of terror . . . She choked back tears. "What happened to me?" she whispered. Drew stood and leaned over her, putting his arms around her. He smelled like he always did: patchouli, books, and the faint musty scent of the music department classrooms at UT. He'd started a program there for underprivileged kids, teaching piano lessons for free after school. That, his regular class schedule, and all his other volunteer work took up so much time, combined with her crazy hours, that they hardly got to see each other these days. Most guys would have bailed on her by now, but he wanted to sign up for the long haul. He might just be as crazy as she was. She sobbed, and he held her close, while the collective horror of the night sank in. "I lost it," she gasped. "I lost the baby. But then I found her again. They saved me. I was so scared . . ." Just like before when she'd been walking to her car. But this time, it wasn't her imagination or a random stranger. This time it was someone who wanted her dead. She'd barely had a second to hit the panic button on her phone before someone slammed into her from behind, knocking her to the ground, wrestling her to her back. She had looked up into an inhuman face, and all she had seen were teeth . . . the flash of a knife . . . and then there was so much pain, her memory simply stopped. Her brain couldn't cope with reality and everything went gray and silent until . . . She had heard a calm male voice beside her and looked up to see an angelic face—maybe it really was an angel; hell, if vampires were real, what else might be?—just before she heard Miranda, panicked, calling her name. Then there was . . . _"Shall I bring her back, Katerina?"_ Then she woke up here. She tried to tell Drew what had happened, or as much of it as she could make sense of. He looked like he wasn't sure whether to hold her or set something on fire. Drew wasn't an angry person; in fact he was one of the kindest, most compassionate people she had ever met. Knowing that she was the source of his anger made her heart shudder with guilt. Not too long after she got herself back together, there was a knock, and the door swung open to reveal a tiny round woman with a clipboard and a digital thermometer. "Hi there," she said, her Texas accent pronounced and comforting. "I'm Jackie." "Kat." "Nice to meet you, sweetie. And you must be Drew." Jackie reached over and shook his hand, somehow without putting down her things, an impressive feat. "I'm just here to take Kat's vitals. Do you have any questions?" "Yeah," Drew said, more forceful than Kat had ever heard him. "What the hell happened to her last night?" Jackie got to work checking Kat's various monitors and making adjustments in things, saying, "The official word is that you were attacked by a vampire—I understand you're under Signet protection? Good, then I can be a little more candid. The woman who attacked you is suspected of several murders and an attack on the Queen." "Several murders?" Drew demanded. "I thought she had just gone after Kat and Miranda. You mean she's been killing other people and they haven't caught her yet?" "Drew," Kat said quietly, "calm down." Jackie didn't look upset by Drew's outburst. She jotted Kat's temperature on her clipboard before replying, "I'm afraid she's still at large, but Prime Deven wounded her, and there was evidence at the scene that's being analyzed right now. Someone will be in shortly to ask you a few questions, Kat, about the attacker." "Police?" Kat asked. "Elite," Jackie answered. "Police aren't much good in this sort of situation." "What kind of place is this?" Jackie smiled. "The Hausmann was established by Prime Solomon to look after human victims of vampire feeding—even with the laws they have in place, sometimes unfortunate things happen. Our staff are trained to recognize and deal with specific conditions resulting from vampire-related injuries, including abortive transformations and various forms of anemia. We're not very big or very busy, but normal medical facilities often don't know how to treat this sort of thing or its emotional toll. We have . . . counselors for that." The nurse spoke so matter-of-factly about her job that Kat felt a creeping sense of surreality all around her. "Is . . . can you tell if the baby's okay?" Jackie paused and looked at her. "It's tough to say, as early as it is. She's still got a good strong heartbeat and there's been no damage we could see in the scans. You'll want to follow up with your OB/GYN as soon as possible, but I would say, cautiously, it looks like she'll be fine." "How do you know it's a she?" Drew asked. Jackie looked thoughtful. "I don't, really," she replied. "It just came out. Would you prefer I not use a gender pronoun? It is, as I said, really early in the pregnancy." "No, that's all right," Kat said. "I know it's a girl, too . . . and . . . I'm going to keep her. So it's okay." She saw the shock on Drew's face but didn't say anything to him just yet. She was still getting used to the idea herself. Just saying it out loud was jarring enough. "All right, then, I'll get out of your hair," Jackie said with a grin. "All your vitals are stable, and I'm pretty sure you'll be able to go home in the morning. I'll have dinner sent up to you within the hour." "Thanks." Kat saw quite plainly the question Drew was about to ask. "Let's . . . not talk about it right now, okay?" She reached up with her non-IV-laden hand and touched his face. "As soon as I get out of here and there's not somebody trying to kill me, we can start making plans." Drew smiled, nodded, and said, "Whatever you want, babe, but you do realize that I'm moving in now even if I have to sleep on the front porch." Kat couldn't help but smile back. "Fine by me," she said. "Saves me the trouble of housebreaking a Rottweiler." They both laughed a little, though Kat still felt more like crying. Jackie stuck her head back in the door. "You have another visitor," she said. "Do you feel up to a few questions now?" Kat shrugged. Why not? Drew started to say something—and Kat had her theories as to what—but the words died on his lips as a woman walked into the room. She was petite, but muscular, and looked Japanese; her hair was a shining fall of ebony braided back from her face. She wore one of the black uniforms that Kat had seen on the Elite, including the silver wristband that they used to communicate. She also had a sword. "My name is Faith," she said, her smooth voice all business. "I am Second in Command of the Southern Elite. You must be Kat." If Jackie's warmth had been reassuring, Faith's coolness was, too; clearly this was not a person to mess with. Where had she been, Kat wondered, when Kat was on her back with a knife in her gut? "I have a few questions about your attacker," Faith said. "I won't keep you long; I know you need your rest." "Fire away," Kat said, trying to sound hearty but mostly coming off as a bit pathetic. "Have a seat." Faith declined, preferring to stand by the bed with her arms crossed, looking incredibly fucking scary. "What can you tell me about her appearance?" Kat closed her eyes and swallowed, trying to concentrate. "She was blond," she said. "Short hair . . . really short, kind of severe. I didn't really focus on her eye color because it was dark and I was being stabbed and all." "Understandable," Faith said. "Just give me whatever you can remember." "She was wearing black like all of you. Her teeth were . . . out. I mean, they were all fangy and pointed. She was skinny . . . I don't know how tall, but she seemed about average height." "Did she speak to you?" Kat shook her head. "She just grunted. No, wait . . ." Kat thought hard, trying to fight her way through the fog around the memories. "There was one thing . . . something startled her, and she jumped up and ran. She made this noise like something hit her, and she said . . . I heard her say something, like the way you'd say 'Holy shit!' or 'Goddamn it.' " "But it wasn't in English," Faith surmised. "What language was it?" "I have no idea. It sounded like a cross between German and something out of Tolkien." Something flickered in Faith's expression, but it was gone as quickly as it came. "One more thing, Kat . . . was she wearing any sort of technological gadget, like a Bluetooth earpiece or one of these?" Faith lifted her arm to show the metal band on her wrist. "No. Not that I saw." Faith nodded. "Thank you." She started to leave, but Kat called her back with, "What happens now?" Faith turned to her. "Meaning?" "Well, obviously having one guard on me wasn't enough." A raised eyebrow. "I was given to understand that you had refused additional guards." "Something about having my hand chopped off made me rethink that." Faith nodded. "I suppose it would. There's a room for you at the Haven, where you'll be under twenty-four-hour watch and safer than any other place on the planet. Your man would be welcome to join you. I would guess, however, that you don't want to give up your job and life for the duration of the investigation, in which case you go home, but we assign you a full Elite detail of bodyguards and digital surveillance. It's up to you, but either way you need to be watched much more closely until the situation has been dealt with." Kat passed her hands over her face. The tube from her IV hit her lightly on the nose. "Can I think about it?" "Of course. The staff wants to keep you until morning; you can notify us of your decision then. There are two guards outside your room." "Thank you." Faith bowed, then departed. They sat without speaking for a minute, Kat fiddling with her IV, Drew pointedly not talking about the baby. Kat found that she was exhausted just from the two short exchanges, and though the last thing she wanted was to spend the night in a hospital bed, she got why they wanted her there. She felt like her entire body had been beaten with a bat. She'd nearly died. Her hand had been cut off and then reattached . . . with magic. She'd been jumped in the dark and stabbed in the abdomen. Whoever had stabbed her might try again . . . and it was all because her best friend was a vampire. She was pregnant. She hurt . . . God, she hurt . . . And she couldn't even have any real painkillers. Somehow she didn't think Tylenol would do much good after all this . . . What she really wanted was a bottle of vodka and a plane ticket to anywhere else in the world but here. Drew didn't ask why she was weeping again. He just held her and let her cry herself to sleep. The spell went unbroken through long, soul-shaking kisses; through clothes and sheets thrown aside with reckless anticipation; through teeth piercing skin, nails clawing shoulders, the soft cry of joining together and the raggedly drawn breaths that rose and fell; through the worldshattering peak and subsequent tumble down, down . . . . . . until, shaking and bruised, David lowered himself onto the mattress, and his heart battered its way through his rib cage, screaming the question into his mind: _My God, what have we done?_ Neither Prime could speak. For a long time the only sound was panting as David tried to slow his breath and still the cyclone of his thoughts, most of which were a single word: _No._ He looked up, meeting eyes that were as dazed as his own. He knew that whatever shame and shock he was feeling, for once Deven felt it just as strongly, if not more so, because he would never, ever have expected David to do . . . this. Deven's hands were still twisted in the pillows, holding on, perhaps, to the last precious seconds before reality drowned them both. David tore his eyes away and sat up, feeling the air in the room cold on his bare, sweaty skin. He wasn't sure what was worse: lying there entwined with his transgressions or pulling himself away. Strong, warm hands touched his shoulders, and he felt Dev lean against him and kiss the back of his neck. "It's all right," Deven whispered. "No, it's not," David said back, barely able to summon words. "It's so very not all right." "I mean . . . this isn't your fault. I accept the blame." Tempting as the idea was, David couldn't let it happen. "No. I started it. I could have stopped at any moment, but . . ." "You didn't, and neither did I." He ran his hands down over David's biceps, and for a moment, just a moment, David let himself forget what existed outside the room and almost relaxed into the embrace. They had shattered the world beyond the door, but if it would just stay closed a few more minutes . . . It was Deven who broke the silence, sounding achingly young and sad when he asked softly, "How are we going to tell them?" "Her," came a voice. Both their heads snapped up at once. Jonathan had entered the room without making a sound and shut the door behind him; he was standing just inside the threshold, watching them. They were both frozen in place, unable to pull away from each other, as if it would have made a difference in what the Consort knew. But Jonathan didn't look shocked or angry; his expression was one of resignation. "You knew this would happen," Deven said. Jonathan smiled with an uncharacteristic edge of bitterness. "Of course I did." "You didn't try to stop us." The Consort tipped his head to one side, making a noise something like a laugh. "Who can stop the earth from quaking?" "We could have," David said, carefully moving away from Deven and pulling the sheet up around himself, acutely ashamed, like Adam in the Garden. "No one forced us to do this—not fate, not anything. Either one of us could have said no." Now Jonathan looked amused; he often did when David tried to argue with his assertions of destiny. "You're not helping your case any here." "I'm not trying to." David couldn't look at Deven, and he couldn't meet Jonathan's eyes, but he spoke as certainly as he could, given the aftershocks in his mind. "I'm not asking for a pardon . . . if you're going to be angry at someone, let it be me. Don't take it out on Deven." "I'm not angry." "How can you not be?" "I told you, I already knew. I knew before we even came here. There was a ghost between you that had to be exorcised." He fixed his Prime with a steady glare. "And you haven't violated the terms of our relationship by any means. What's fair is fair. I'm not really the one you need to worry about." Deven didn't say anything. For the first time since the night they had met, Deven looked utterly lost . . . and David understood that when it came down to it, Deven would do whatever Jonathan asked, would abandon David again, would sever all ties with the South if Jonathan wanted him to . . . because in the end, David wasn't the one he was bound to. They could love each other until the stars burned out, but they weren't, and had never been, mated in soul. They would never live together, nor die together. David closed his eyes against the denial that rose up rebellious in his heart, but it was the truth. This had been a stolen moment. He couldn't have Deven . . . not ever. He'd wanted closure, and in a way he had it . . . but there was no resolving this, not really. And now things were so much worse. "Well now," Jonathan said. "I smell like a barnyard, so I'm going to have a shower. Close the door behind you, please, David, on your way out—oh, and Deven, if it wouldn't be too much of a bother, change the fucking sheets before I come back." The last sentence was hissed, with so much anger in it that both Primes were taken aback, but Jonathan didn't say anything else until he had reached the bathroom door. He looked over at David. His voice was perfectly even again, perfectly factual. "Incidentally, you're not going to have to tell Miranda either. You haven't had time to learn this, but when you have a bond like ours, you can feel when your husband has an orgasm . . . no matter who it's with." The Consort closed and locked the bathroom door. "Oh, God . . ." David put his head in his hands. "Miranda. How am I going to face her?" Deven almost said something sarcastic—David knew the look on his face—but at the last second the spark drained out of him and he said only, "Honestly." "She'll never forgive me. Three months and I broke faith with her . . . there's nothing I can say to make this right." Again, Deven sounded drained . . . no, defeated. All of his arrogance and self-possession were gone. "You made a mistake, David. She will forgive you." David looked at him. "A mistake?" He sighed. "Yes. A beautiful, terrible mistake that can never happen again. Now we'll go home to the West, and you'll go back to your Queen, and we'll all do the best we can to act as though it never happened. And we'll maintain good relations in Council, and talk on the phone when we need to, but we'll probably never be alone together again." "Deven—" "Go, David. Please. Just go." There was nothing else David could say. He gathered his discarded clothes and put them on with numb hands, aware of Deven's eyes on him. He left the room without looking back, afraid that if he did he would fall apart. He avoided the faces of the guards as well; they belonged to California, not him, so what they thought didn't matter, but once down the hall, approaching the nearest Elite post, he found that he couldn't make himself walk past them . . . and so, risking exhaustion to save face, he Misted, holding the image of his suite tightly in his mind and pulling it toward him, passing through space at a thought. He reappeared just inside the door . . . where Miranda was waiting for him. "Is this the part where I storm out and leave you?" she asked very, very calmly. David was staring at her as if he expected her to do far worse than that; keeping an eye on her, he approached the fireplace and took his chair, each movement deliberate, the way he did when one of the horses got spooked and he didn't want to get kicked in the head. "Seriously, you need to tell me," she went on. Her voice was so even she might have been discussing the weather. "I've never been cheated on before. I'm not sure what my job is here. Do I yell? Do I cry? Throw things? Kill you? Oh, wait . . . I can't do that." He still didn't speak. She could feel the guilt, and the shame, radiating off him, poisonous. Worse, she could smell it . . . sweat, and sex, and _him_. "I could kill you," she reasoned. "I'd only live for about two minutes, but they'd be a very satisfying two minutes." Nothing. "I hope it was worth it," she went on. The pitch of her voice rose just a tiny bit. She couldn't stop it. "It felt like it was pretty fantastic. I was lying in bed feeling almost well enough to get up and go to the music room, not thinking about my best friend who almost died because of me, and wham! Suddenly I was so turned on I couldn't stand it . . . but it wasn't me. Was it good, baby?" Her hands gripped the arms of her chair so hard they were white. "You smell like a good hard fuck. Is it better with a guy? You never did tell me. Do my breasts get in the way? I know I'm pretty good, but did you scream louder for him?" He shrank back further into himself with her every word, staring at her, eyes wide and fearful. She was starting to sound slightly hysterical, but again, she couldn't seem to help it, and besides, she didn't care. She had been waiting for him for more than an hour, feeling vicarious waves of pleasure and pain, her own body responding traitorously even though there were no hands touching her, no tongue against her thigh. She tasted blood in her mouth—not David's, and not hers. Bile rose in her throat, and she stood up. "Was it worth it? Tell me, David. _Was it?_ " He couldn't look at her. "No." "Am I supposed to just sit around barefoot like a good little wife, keep the home fires burning, while you're out sucking off your boyfriend?" He looked up at her. "It was a mistake," he said. "I didn't mean for it to happen." "You didn't mean for it to happen? What does that even mean? You lay down on the ground and he tripped and fell on your dick?" "Beloved, please . . ." The quaint term of endearment had always made her smile, but now it brought a thunderous wave of rage through her body, and she hit him. He didn't fall back, but his head snapped around, and when he faced her again blood oozed from the corner of his mouth. Her vision went scarlet. She hit him again. "Get up, you bastard!" she all but screamed. "If it's so fucking easy to hurt me, do it right! Get up!" He stayed where he was, bleeding, and she punched him again, and again, cursing him, each time her voice rising until she lost her hold on the English language and simply wailed, throwing her betrayal at him the only way she knew how. She heard glass shattering; the force of her emotions was seeping into the room and causing things to fall off shelves. She didn't care. All she could do was scream until her voice gave out and she sobbed incoherently, collapsing on the floor, unable to hurt him badly enough, to make him bleed enough, to match the way she was bleeding. He pushed himself off the chair and came to her, folding her into his arms; at first she tried to fight him off, but he wouldn't let her go, and at last they both wept, clinging to each other like children on a battlefield. "I'm sorry," he whispered brokenly, over and over again. "God, I wish I could hate you," she moaned, striking his shoulder with a halfhearted fist. "Why did you bring me into this life and then do this to me?" Shaking, he reached up to his throat and pulled the Signet from it, pressing it into her hands. "Here," he said, face wet with tears. "Break it. Break it, Miranda." She drew a tremulous breath, not comprehending. "Why?" "Kill one of us and we both die. Break one stone and its wearer dies. It's the only way to sever the bond—otherwise you're trapped here with me forever." She stared down at the amulet in her hand. "Just like that?" "It's something everyone knows but no one has ever done. I don't know what would happen to you afterward. You might not survive long, but at least . . . at least you'd be free." She was still crying, but she shook her head. "No." She lifted the stone and fastened it back around his neck. Her voice was barely a whisper. "You don't get off that easy, baby." She left one hand on his Signet and moved the other hand to cover her own. "I'm not going to let you run away at the first test," she went on. "I'll stay with you . . . but you have to stay with me." "Anything," he said. "I would do anything for you." "Okay," she replied, touching her forehead to his. "The first thing you can do is take a shower." "Yes . . ." He wiped his eyes, seeming bewildered by the display of emotion that had escaped his habitual walls, and got to his feet. She felt so hollow inside, and still weak; she hadn't been ready for this. She tried to stand, too, and couldn't. David saw her struggling and reached down to lift her. Miranda stood, hands on his arms. "Let me help you to bed," he said. "Not yet. First, I'm going with you." She fixed a stony, but not angry, stare into his eyes. "I want to do it myself." He didn't fully understand, but didn't argue, and helped her to the bathroom, then stepped back to see what she had been talking about. She took a deep breath. "Turn the water on. Hot." He obeyed. Miranda nodded and came over to him, unbuttoning his shirt without touching his skin; she couldn't touch him, not yet. He let her without protest or comment. Fighting her weariness, she unzipped his jeans, and finished stripping him slowly and clinically, taking each item of clothing and dropping it in the trash. Then she removed her own, her tank top and yoga pants going into a pile on the floor. When they were both naked, she nudged him toward the shower. The steam made her dizzy, but she was too intent on her task to give in to her body's desire to curl up and sleep. She pushed him into the water spray, for once not pausing to enjoy the sight of hot water cascading down over his body; instead, she took washcloth and soap and, with deliberate slowness, washed him from head to foot, scrubbing some places hard enough to leave the skin raw. There had been a few bruises lingering on his flesh, but by the time she was finished they were gone, as was the faint black eye that she had given him. He stood perfectly still, moving only when instructed, until she was satisfied that nothing of Deven remained on his body, and every last inch of him was clean. "Get out and dry off," she told him. "Then go to bed." He had questions but didn't ask them. He only did what he was told. She gave herself the same treatment, only robotically, her body numb to her own touch and the slickness of the soap. It was her favorite scent, but she couldn't smell it. As she washed, tears streamed from her eyes again, another surge of impotent anger and agony hitting her. She sagged back against the shower wall, washcloth still in her hand, and folded up on herself, sinking to her knees with the water hitting her in the head, dragging her hair into her face as she cried, and shook, until the wave had passed. She took her time drying and putting on clean clothes. She returned to the bedroom, where he was waiting in bed, lying on his side facing her without making eye contact. She considered sleeping on the couch, or making him do it, but something inside her started keening at the thought and she was too wrung out from tears to make herself face the morning in an empty bed. Wordlessly, she climbed in on her side, pulling the covers up around her. David waited for her to indicate it was okay to touch her, but she ignored him and rolled over to face the wall. Couch or no couch, she might as well have been across the ocean. Neither of them slept. Only Faith showed up the next night at midnight to officially bid the West farewell. She was surprised, and made deeply uneasy, by the way the Prime had ordered her to see them off, with no explanation; he didn't sound like himself at all, and it wasn't like him to command her without giving her reasons. When she saw Deven and Jonathan, she knew exactly what was going on. Deven emerged from the Haven first, by himself, which was also weird; he nodded to her without smiling and got in the car, not even saying good-bye. He looked normal, for Deven, in leather coat and studs, a bit more casual this time with fingerless gloves against the chill, his nails freshly painted. He was as stoic as always, but something was missing that she couldn't quite put her finger on . . . until Jonathan came outside. He wasn't smiling either. In fact, he glanced in Deven's direction and the almost undetectable flicker in his eyes gave it away, as did the way he looked back at the Haven as if he'd rather be staked and quartered than ever set foot inside again. "Jonathan," Faith said, unable to keep to protocol any longer, "are you all right?" He paused and gave her a smile that was lacking in its usual good humor. "Not particularly, Faith. But don't worry about us. We'll make it, I promise." He lifted his eyes to the Haven again. "Worry about your own house instead." "Oh, no," she said. "You don't mean . . ." "They're going to need you more than ever," he replied. "Promise me, Faith, that you'll do what you can to help them work things out. They could come through this stronger than before . . . and then, perhaps everything won't have gone to waste." "You know I will," she said. "I promise." "Good. Time to go home now . . . I hope we'll see you again someday." With that Jonathan got in the car, and one of their Elite shut the door. She watched the car pull away, unsure what to feel, but pretty sure she wanted to go kick David in the balls, then find Miranda and hug her—to hell with protocol and professionalism. What must the Queen be going through, if what Faith suspected was true? Miranda wasn't as jaded as the rest of them yet. She couldn't have seen it coming like Faith had. Half the Elite had been taking bets, since that evening in the training room when the two Primes had fought each other into a trance, on how long it would take them to wind up in bed together. But Miranda . . . she was so young, and had been a vampire and Queen for only a few months . . . and, from what Faith remembered, she didn't have much of a history with love. Faith had to check on her. She went back into the building, intent on heading for the Pair's wing to see if she could find Miranda without making it too obvious that she was looking, but one of the other Elite caught sight of her and hurried over to her side. "Lali," Faith said. "You're off shift, aren't you? Why are you still in uniform?" Lali was holding a familiar-looking metal case. "I've been waiting for you," she said. "The Prime sent me to town just after sunset to pick something up from Hunter Development. Doctor Novotny, the human researcher, had something for him—I mean, this. He said the results are inside on a thumb drive, and that I must deliver them only to you or the Pair, in person. But no one seems to know where the Prime is tonight, so I came to you." "Thank you, Lali—I'll take it from here." The bodyguard bowed and went her own way, no doubt to get out of uniform and relax with her violin. Faith took the case with her to the Signet wing, but to her consternation neither Prime nor Queen were to be found in their suite, the music room, David's workroom, or any of their other usual haunts. She would have been alerted if they'd gone to town, so it stood to reason they were somewhere around the Haven, and given what was going on, chances were they weren't together. "Star-one," she said into her com. She was one of only a handful of Elite who had direct access to David's com; in some situations he granted temporary permission for one of the others to relay information to him, and of course he could listen in on anyone on the network whenever he wanted, but for the most part everything went through Faith. She, then, was one of the few who recognized the series of tones she heard as a message: The Prime was not talking to anyone, but she could basically leave him a voice mail, and he would listen to it when he felt like it. It was rare for him to use it, but she had heard it before. "Sire," she said, "Elite Sixteen brought in the case that Doctor Novotny sent over. I'm leaving it in your workroom now. Star-three, out." Faith also had clearance for the workroom, so she unlocked it and went inside, half expecting to find David there ignoring her previous knock. He wasn't; the room was dark. She flipped on the lights and set the case down on the table, fully intending to leave it there without snooping; but technically she did have the authority to look inside, and the need to know what the hell was going on in their city overrode the fear of highly unlikely reprisals from the Prime. She flipped the case open and found what she expected: two wooden stakes and a knife, along with a USB drive containing all of Hunter's test results. Faith noted the contrast between the two stakes: They appeared to be made out of a similar sort of wood, which was unremarkable. Certain woods were favored by vampire hunters because they were harder and more durable. The assassin's stake from the attack on Miranda, however, was traditionally carved; the other, Deven's, was an exquisitely crafted piece of weaponry. It was about half the size of the traditional stake and had a steel hilt that was weighted for throwing. From seeing its ilk before, she knew that the wood was fitted onto a steel shaft. The wood could be removed and replaced if it splintered or dulled, and the shaft inside helped it fly straighter and penetrate farther. Deven's weapons collection was a thing of beauty and had been gathered from all over the globe, but he commissioned the throwing stakes from his own design even down to the elaborate carving on the hilt. The knife, on the other hand, was not the centuries-old implement that Novotny said had carved the Finnish woman's stake. It was a fairly nondescript blade, of decent quality but no real artistry. It had been used to stab Kat in the abdomen, and though the blood had been cleaned off, Faith could still imagine it seething with deadly purpose. Whoever this woman was, she knew a lot about Miranda and her friends, even that Kat was pregnant. It was just the sort of thing the Red Shadow was supposed to be paid to know. Faith took the USB drive over to the bank of computers and interactive screens that performed various arcane functions for the Prime and plugged it in. She was no technological wizard, but the files inside were in pretty basic format, and she knew the password to unlock them. Most of what she saw made no sense whatsoever. The lab had tested for a vast array of trace elements and volatile compounds, many of which could have come from anywhere in the city. Luckily, for the sake of those who, unlike David, didn't get their jollies reading chromatograms, there was an overview of the results and a chart that compared the numbers for all three weapons at a glance. It was there, nestled among polysyllabic chemical names and ratios, that she saw it. Faith stared at the data, rereading it, then again; but the facts didn't change. Still staring, she raised her arm and said into her com, "Star-one." When the same tones alerted her to the voice mail, she said, "Security override, authorization Star-three." The override would push her through to the Prime's com no matter where he was or what he was doing, and it would boost her signal to a practically earsplitting level. David had threatened mayhem if she ever used it, but there were times when mayhem was the least of her worries. A recorded female voice informed her that her identity and clearance were being confirmed; please wait. _"Security override granted."_ Faith said, as clearly as possible, "Sire, this is Faith. I'm in the workroom with Novotny's results. You need to come down here right now." She looked over at the box with its trio of deadly weapons. "There's something here you need to see." PART TWO Lilith's Blade Eleven The squatty little man reminded David very strongly of a toad. His eyes were beady and small, his mouth a long line in a broad, flat face; he might hit David's shoulder if they stood back-to-back, but he was about three times as wide. He had long arms and his torso was heavily muscled from wielding hammers and other heavy implements for two hundred years. David stared at him, and he stared right back, indifferent to his surroundings or his interrogator. "So you're Volundr," David said. A grunted affirmative. "I imagine you're wondering why we brought you here." Another grunt. The man's voice was deep and . . . well, croaky. "Got something to do with the stakes." "Yes, it does. I have a few questions for you about these." David gestured to his left, at the table where Faith had placed the stake that had been shot at Miranda and the one that Deven had thrown at the assassin. A third grunt, betraying no surprise. David glanced over at Faith, who stood in front of the door, arms crossed, listening impassively. It had taken three weeks to find this man and get him to Austin—three weeks and the cooperation of the West, who had extradited him from Washington state where he had dwelt in the forest in a dim little house and forge for centuries. David wasn't sure how the Pair had convinced Volundr to surrender quietly; he was clearly not the type to be easily intimidated. David picked up the first stake. "This was fired from a miniaturized speargun at my Queen," he said. "It's been identified as silver birch from Lapland. The second one belonged to Prime Deven of the West. The Prime identifies you as the man who crafted the interior shaft and hilt, then carved the wood tips for him . . . out of silver birch. We've confirmed that these two stakes not only are the same kind of wood, they came from the same exact forest." "Coincidence," Volundr said with a shrug. "Right." David laid the stake back down in its foam casing. "A search of your property turned up about nine different kinds of wood in addition to all the metals you work with—most were just firewood, but two, the birch and a supply of coastal redwood, are known for their use in battleready stakes. Silver birch, however, isn't typical of the Pacific Northwest. Where did you get it?" He shrugged again. "Did a woman from Finland supply you with it when you made stakes for her?" Nothing. "Sir," David said, letting a little hardness enter his voice, "I feel I've been very patient up to this point. We are trying to catch a killer in my territory. I know you're not the killer because you're neither female nor athletic—I don't doubt your strength with the hammer, but you're hardly assassin material. The birch that we found on your property matches these two stakes exactly. You are without a doubt connected to all of this." "What do you want, boy?" Volundr finally asked. "What do I have to tell you so you'll have your little toy soldiers take me home to my work?" "I want a list of your clients." Volundr looked at David in silence for a moment before he laughed out loud; it was a brash, unpleasant sound that nearly made David flinch. "If this girl is such a problem for _you_ , maybe she threatened _me_ and I'm too scared to talk." David raised an eyebrow at him. "Oh, come on." "Or maybe I don't know this girl," Volundr went on. "Maybe I bought the wood from the same dealer as her and you're wasting my time." David exhaled slowly. He'd been expecting about as much. "You do understand that until I get a satisfactory answer you'll be held here." A flicker of reaction. The smith didn't like being away from home; that much was clear. He probably hadn't traveled out of Washington as long as he'd been living there. He wasn't a psychically strong vampire, living as he did in the middle of nowhere away from a steady supply of human blood, but he was physically strong and his skills were in high demand. He was one of three weapons crafters that Deven trusted with his own designs, and Deven had not been at all pleased to bring Volundr in for questioning; he had agreed, however, as something of a peace offering. Yet peace was not to be found . . . not here. David had let Faith arrange everything. David had spoken to Deven exactly twice since the Pair had returned to the West: once, when Faith's realization about the two stakes drove David to call Deven and essentially accuse him of collusion with the assassin; and again, when David called to apologize after Faith—and Miranda, who had maintained a remarkably level head about the whole thing—pointed out that Deven had no motive whatsoever to kill Miranda, as doing so would kill David, too . . . and, the truth was, if Deven wanted Miranda dead, she already would be. Deven's acceptance of his apology had been icy and insincere, but out of hurt, not anger. David now had one more sin to add to the growing list of wrongs against those he professed to love. He stared at the smith for a moment before saying, "All I want are names, Volundr. Give me a list of people who might be the woman I'm after, and you can go back to work." "I have no loyalty to the South." "What about the West? Surely the Prime's money has bought your loyalty over the years." Volundr shook his head. "Little faggot invaded my house and turned me over to you. I don't owe him sh—" The end of the sentence turned into another grunt as the smith flew backward, slammed into the far wall of the interrogation room, and landed on his ass on the stone floor. The Prime waited until he'd struggled to his feet to say, "We can do this the easy way, Volundr, or the fun way. I'll be the first one to tell you I'd find a great deal of satisfaction in dislocating all of your joints one by one, or possibly peeling the skin from your back and pouring acid on your muscle tissue . . . but I respect you as a craftsman and I would hate to see one of the most talented of your trade treated in such an undignified manner." Yet another shrug. "I'll heal. I got nothing to say to you, boy." "I'm older than you," David snapped, losing just a tiny bit of his patience—he'd had precious little of it these past few weeks, and what was left was wearing perilously thin. "And my respect only goes so far. If you want this to hurt, it can hurt. You know very well what I'm capable of, Volundr—you're no stranger to the Signets. Give me what I want or I start with your fingers." "I'm not afraid of that glowing rock round your neck," Volundr said, still disturbingly undisturbed about the prospect of bodily harm. "You think you're the biggest power in the world? You're hardly out of diapers. I know power a hundred times older than you . . . sleeping in the rocks of the earth." David sighed. "You're not going to give me some poetic tripe about stones and steel and the might of your anvil, are you? That's just pathetically phallic." "I'm not talking about my dick, boy. I'm talking about the Firstborn." Whatever threat David had intended to deliver died on his lips, and he blinked in confusion at the smith, who looked smugly satisfied at his reaction. "Firstborn," David repeated. "That's ridiculous. They're a myth." "Oh, are they?" "Volundr," David told him, smiling a little, "you're not going to distract me with fairy tales. I can see that you take me for a fool, but I'm afraid you're wrong . . . and you're wrong in thinking that you have nothing to say to me. An hour from now you're going to have a lot to say." The Prime flicked his hand, and Volundr flew back against the wall again, this time pinned a foot off the ground by the force of David's power. David looked at the man, trying to maintain his dispassion, but beneath it, dreading the next few hours. _Just talk. Don't make me do this._ He moved close enough that he was only a foot away from Volundr and held the smith's eyes. "You are giving me no choice," he said quietly. "I will protect my Queen and my territory at all cost, and I know that you know the name of the assassin. Whatever she's offered you in return for your silence . . . it won't be worth what comes next." Volundr was still calm. "I don't know who it is," he said. "You're lying." "I don't know who it is," he said again, this time with a faint touch of anger. "And I'm not giving up any names. People pay me to build things and keep them secret. No bratty little upstart with a Signet is gonna get me to break two hundred years of silence. I answer to people way more important to you. You won't dare wake them up." David stepped back, nodding. "All right, Volundr. I understand your position. But there's one piece of advice I should probably have given you before we began." Volundr sucked in a pained breath as the first of his fingers snapped backward. David crossed his arms, and each word was punctuated with the dull sound of breaking bone as he said, "Never . . . ever . . . dare me." A few days of unseasonable . . . or seasonable, as it turned out . . . warmth unfolded gently over the Haven, and finally Cora felt strong enough, and brave enough, to go outside and see the world for herself. She had heard the servants talking about this year's cold weather. Winter in Texas was apparently about as mild as that of Italy, but this year there had been ice already and there might even be snow before January at this rate. Mostly the servants seemed upset about the volume of firewood they were burning through. They didn't talk much to Cora directly, but she was gradually picking up more of their language thanks to the computing machine in her room and its language discs. Mostly she listened, rather than speaking; she learned so much more that way . . . and not just about English. Something had gone terribly wrong here in the last month. She knew that even before she caught snatches of conversation here and there that affirmed the tension she could practically taste in the air. She could feel the change even before she asked one of the door guards if Prime Deven was taking visitors, only to be informed that the Prime had departed the night before. The guard's tone suggested she not make further inquiries, but she caught something in the words, some . . . faint embarrassment, almost. She went over the conversation in her mind and decided that the man was not embarrassed about Deven himself, but about something that had happened to cause the Prime's premature exit from the Haven. Cora didn't know what to make of it. So she went outside. She asked the guards if it was all right, but these days they barely seemed to notice her comings and goings, and that was fine with her; she had explored the house pretty thoroughly, but what really interested her were the grounds and gardens, and one night during the warm spell she decided now was the time. She put on her newest discovery—blue jeans—her hooded sweatshirt, and the soft shoes the Elite had lent her, and left her room. The closest exterior door she had found on her wanderings let her out in the back gardens near a wide trail that she guessed was for the horses. A fence ran alongside it, bordering a pasture. She stayed with her back against the wall for a moment, getting used to the broad expanse of the night sky and the sheer openness of the world in front of her. Her heart was pounding with fear—it felt so exposed, so wrong—and she very nearly gave up and fled back to the safety of her room. _No. I have lived my life afraid._ Biting her lip, Cora pushed herself off the wall and took a few halting steps forward, then a few more. Neither the hand of God nor a lightning strike smote her where she stood. A few more steps and she reached the pasture fence, to which she clung for a moment, panting. "Better," she murmured. "Perhaps there's hope for you yet, girl." She heard a muted, thumping sort of noise growing nearer, along with the rustle of grass. When she lifted her head, she yelped and leapt backward. An enormous black horse was standing on the other side of the fence, staring at her with a distinct look of amusement in its round, dark eyes. It had been many years since Cora had seen a horse up close, but she'd been familiar with them once, and as soon as the shock of such a huge animal sneaking up on her wore off, she moved back to the fence, looking the animal over as it looked her over. "You're lovely," she said to the horse with a quick look to discern that it was, in fact, a female. "A lovely lady." The horse seemed to agree with Cora and dipped her head to rip up a mouthful of grass. It was strange that she should be out at night; could horses see in the dark, Cora wondered? There were lights along the trail, and enough were lit that to Cora's eyes it was nearly as bright as day, but she wondered how odd it must be for such animals to live according to a vampire's schedule. Cora reached through the fence with one arm, gesturing for the horse to come to her; black ears flicked in response, and the horse's plate-sized hooves clomped toward the fence. The horse inclined her head and gave Cora's hand an imperious sniff, then allowed Cora to scratch her between the eyes. "It's a miracle," someone said wryly. Cora jumped but managed not to cry out this time, and she twisted around to see the uniformed woman who had come up behind her and was now watching her with surprise in her almond-shaped eyes. "Her name is Isis," Faith said. "She bites." Cora looked back at the horse. "She is very proud." Faith chuckled. "That's putting it mildly. Only a handful of people have ever gotten that close to her, and it's never her idea. She must like you." Isis gave Faith a look of mild disdain and then ignored her, permitting Cora to continue petting her head and neck. "Were you looking for me?" Cora asked Faith. She had to speak slowly to keep the English organized in her head, but Faith didn't appear to have a problem understanding her. "Yes. I know that with everything that's been going on you've gotten a bit lost in the shuffle, so I wanted to check on you and see if you need anything." Cora frowned and decided to take the plunge. "What has happened?" The Second came to lean against the fence. "I'm not at liberty to say," she replied, "but I can assure you that your safety is still guaranteed. You have nothing to worry about." "I am not," Cora said, adding, "but I know everyone else here is worried about something. Is it my Mas . . . I mean, Prime Hart?" Faith shook her head. "Right now he's the least of our problems. Let's just say there is a situation and we're working to contain it as quickly as we can." "Does the situation have to do with Prime Deven?" Faith's eyebrows lifted. "You're more observant than I thought." Cora wasn't sure whether to consider that a compliment or an insult. She said nothing and merely went on stroking Isis. "Have you given any thought to what you want to do next?" Faith asked. "Yes," Cora said. "I have no idea." The Second smiled. "There's no hurry, of course. I was just curious. I know after everything you've been through, the peace and quiet here must be heavenly, but I also know that eventually you're going to get bored." Cora gave her a sad smile in return. "I have no education, no money, no family, and I barely even know how to turn on a computer. I do not think I will have many options." Faith shrugged. "I'm sure if you want to go to school the Pair will be happy to help you. I can arrange a tutor for you if you'd like to speed up your English lessons or start learning other subjects. We can get you an American ID. Really, you just have to decide what you want." Cora withdrew her hand from Isis and leaned back on the fence as Faith had, looking up at the black dome of the sky. "I have never been free to want anything," she said. "I'm not sure I know how." Faith reached over and patted her on the shoulder. "You'll figure it out. There's time." As Faith touched her, for the second time Cora felt the strange shivering she had with Prime Deven, and for a heartbeat's length she saw Faith in her mind's eye, standing at a window somewhere in the Haven, wiping impatiently at her eyes with one hand. Cora's eyes followed Faith's to the scene she was gazing at, but before she could see what had stirred the Second so, her vision cleared, and she heard Faith's voice: "I almost forgot to give you this." Cora looked down at the bracelet Faith was fastening around her wrist, recognizing it as one of the devices the Elite all wore to talk to each other. "This will let us know where you are in the Haven," Faith was saying. "We can already track you on the sensor network, but this way if there's a problem you can call for assistance. It's easy: Just speak into the com and say, 'Star-three,' and I'll answer. It doesn't have to be in English, either; the system recognizes about thirty languages." "Thank you," Cora said. "I have to go—I'm due in the city shortly. Are you sure there's nothing you need?" "A purpose?" Faith grinned. "You could always join the Elite." Cora couldn't stop herself from laughing aloud. "I lack the grace to walk without tripping. I would slice off my own arm if given a sword." Faith laughed, too, and said, "You know, I think I have an idea that might help you with that. I'll come back to see you tomorrow." "Thank you," Cora said again. The Second gave her a slight bow and a brief smile and left her at the fence, where Isis was already nosing up to her for an ear scratching, giving her a commanding snort and tossing her head impatiently. Cora sighed and carefully climbed up on the bottom rung of the fence so she could reach the horse better. For tonight, at least, this was as close to a purpose as she was going to get. _Baby I bleed_ _I bleed without you_ _Kiss me one more time_ _Then twist the knife_ _And walk away . . ._ Everyone in the studio was crying. The rented Bösendorfer took up perhaps half the room, but its sound, and the sound of heartbreak, filled every inch of space, crawling into every nook and cranny like an oak's roots through concrete. Miranda had decided, seemingly out of nowhere, to record a bonus version of the album's title track. The first version was lushly produced and had a string quartet. This one was just her and the piano, stripped down and raw. _You carved your name into my heart_ _You said we were forever_ _But everything falls_ _Everything falls apart . . ._ She didn't know if her empathic influence would translate through digital media, or if it was only something that worked in live performance, but if it did, no one who heard the song would be able to stop their tears; they would pause in whatever they were doing and find themselves reliving the worst possible breakups, betrayals, and disappointments of their histories. Chances were after hearing the track they would skip it every time they played the CD, preferring the first version of the song. She didn't especially care either way. As they wrapped the session, she looked into the control room to see that Kat had arrived and was sitting on the stool that Lali usually occupied. Lali had been recording her part for one of the other tracks, so she was out at the car stowing her violin. Kat looked tired. Pregnancy symptoms had hit her like a truck in the last two weeks, and she spent most of her mornings with her head in the toilet. Under the boyish half inch of hair that had grown since the attack, her face was drawn and looked a little clammy, but at least she seemed glad to be there. Things were still a bit weird. Miranda hadn't pushed; she knew Kat was having a hard time with what had happened. So was Miranda . . . even worse than Kat, thanks to a heavy dose of guilt on her back knowing she was the reason the assassin had targeted her friend. They were reasonably comfortable with each other again . . . as long as Drew wasn't around. Aside from the fact that he tended to stare at Miranda as if she were about to pop Kat's head like the tab on a Coke and slurp her dry, Miranda found it increasingly difficult to put up with how he doted on Kat. Every other word out of his mouth was _honey_ , and he fussed over her like a child when he wasn't gazing at Kat like she'd hung the moon. There might have been a time when Miranda thought that sort of thing was cute, or at least tolerable. Now was not that time. In fact, Miranda wanted to smack the shit out of every couple she saw—the more affectionate they were, the more she wanted to strangle them. _What kind of moron are you?_ she wanted to yell at them. _He's fucking your sister! She only cares about your money! He posted those pictures on the Internet! She's leaving as soon as she gets her birthday present!_ It was possible she was a little bitter. "So," Kat said as they walked out of the studio into the frigid night, "how are . . . things?" "The same. You?" "Basically the same, but with even more barfing." "How long does that last?" Miranda asked, motioning to Lali and Aaron to follow at a distance but stay unobtrusive. "It depends on the person—it's supposed to be a first-trimester thing, but for some people it never stops." "Sounds awesome." "Oh yeah." Kat shifted her bag on her shoulder, and Miranda thought about offering to carry it but knew it would irritate Kat to be treated like an invalid—she already rolled her eyes behind Drew's back when he fluttered around her. "Look at me, I'm a breeder. Bun in the oven. In the family way. Up the duff. The rabbit died." Miranda smiled, her eyes on the grimy sidewalk that was wet with yet another round of late-autumn rain. She was wearing gloves in addition to her coat; she had been taken aback by how deeply the cold affected her, thinking back to when it was weird to her that the Haven burned its fireplaces in August. It also made a lot more sense to her now that the vampire population of Texas was much higher than in, say, Canada, though she'd heard caribou blood was tasty. "I noticed a lot of red eyes when I got there tonight," Kat was saying. "Were you mojo-ing them?" "I guess. I'm curious to see if it comes through on the recording." "I've been meaning to ask you something—what happens if your CD sells like hotcakes and you're famous? Can you tour? Won't people ask a lot of questions?" "Who believes in vampires?" Miranda asked wryly. "I was thinking about it, too, and I figure, people who think anything about my weird behavior will sound like loonies in the press, and if I need to I can address them head on and make them sound even more loony. As for touring, well . . . I can be away from home for a few days at a time. I probably can't do anything international, though." "His Highness can't police things without you?" "It's not that. This thing, this connection between us . . . if we go too long without touching, it starts to make us crazy. Physical contact reinforces the balance of power. Apparently once we learn to manage it we can go a week, but right now I get twitchy after about three days." Kat raised an eyebrow at her sideways. "So you're still touching, even though you're not sleeping in the same room?" "We're spending time together. Just not like before. I just . . . I needed some space, Kat." Kat held up her hands. "I know, sweetie. I'm not being judgmental. I just want to know you're okay." Miranda wanted to stop and kick a rock, but there weren't any around. "I'm not okay. Not by a long shot. But we're doing the best we can. It's just going to take a while. It helps that he's so torn up about it—and that I can feel he's sincere. I'm not as angry knowing how bewildered and confused he is . . . The guilt feels nice, too." Kat chuckled. "Bloodthirsty wench." "Exactly." "What I texted him last week still holds, just so you know." Now Miranda's smile was genuine. "I appreciate that, Kat." "What about . . . the other two? Have you heard anything from Jonathan?" "No." Miranda's voice went flat when she said it, and Kat took the hint and changed the subject. "So what do you want to do tonight? It's pretty early yet. Ice cream?" What Miranda really wanted was blood . . . her thirst had escalated in the last three weeks, compensating for the sheer amount of energy she spent working out, sparring, performing onstage, and stalking the streets of Austin looking for a fight. Somehow, though, she didn't think hunting would be a good girls'-night-out activity. "Movie?" she asked. "We could go to the Alamo Drafthouse, watch stuff blow up, drink Guinness milkshakes." "You can have a Guinness shake," Kat pointed out. "I'm out of commission for the next seven months or so, remember? But a movie sounds good. We'll eat fries with a fuckton of _queso_ and indulge in some testosterone poisoning. I've been wanting to see the new Johnny Depp. He gives me the tickle." Miranda laughed. "Lucky you. I haven't had a tickle in weeks." "Man, that sucks . . . having a guilt-ridden undead stud at your beck and call and not wanting to take advantage of him." "All right," Miranda said, stopping. "I'm going to call Harlan and we'll bring up the movie schedule on the computer in the car. From this point in the evening, I declare a moratorium on relationship talk, baby talk, and vampire talk in general. Tonight we're going to just be two friends looking for some escapism." "Sounds like a plan," Kat said. Smiling, almost believing it would work, they shook on it. The Winchester Bank building was one of the Prime's favorite vantage points from which to watch the city go by. It wasn't the tallest in Austin, or the flashiest, but it suited him sometimes with its stone gargoyles and half-crumbling architecture. There were nights when he felt like a young god, untouchable; on those nights he took to the tallest skyscrapers. On other nights he felt like a fading relic in a world that would be content to go on without him. Those were the nights when he sought refuge atop the Winchester. Time seemed determined to slog ever onward whether he went with it or not. In fact, at the Haven it was as though time had crawled backward to an earlier, more sorrowful era . . . and if only it were a new beginning instead of falling apart. David could feel Miranda on the streets below, walking with Kat; he could sense her but was too far away to hear anything specific unless Miranda wanted him to . . . and she never did, anymore. For weeks she had kept him almost entirely shut out of her mind, her body, and her life. He wanted to howl his loss and shame at the night above, to fling himself off the building if he thought for a moment that it might help him atone, but all he could do was tell himself, over and over, _She's still here. She stayed._ She stayed, and though she avoided him for large parts of the night and slept by herself, she didn't torment them both with her absence longer than necessary; she came in to see him every morning, and they sat in their chairs by the fire and talked about what they'd been up to, had a drink, made a few jokes, and tried . . . just tried to keep going. She spent more time in the city than he did, so she was usually the one who prowled the streets of the Shadow District to keep their presence at the forefront of everyone's minds. They were rarely seen together. Meanwhile he was still enmeshed in the investigation. Coordinating investigations among the West, his Elite, APD, Hunter Development, and the FBI forensics unit took a lot of time and diplomacy. Faith's discovery—that the stakes were carved of the exact same wood, thereby connecting the assassin to the West—had led them to Volundr, and though the smith had finally wheezed out four names in the midst of choking on his own blood, David wasn't confident that any of them would prove a viable lead. Still, the Prime had been true to his word, and as soon as Volundr broke and gave up the names, David turned him over to the Elite, who had cleaned and fed him and were now arranging transport to return him to his home, along with what Faith considered an obscene amount of money . . . blood money, a penance that would do nothing to erase the sound of the smith's screams from David's memory . . . or the feeling that even as desperate as they were to find their killer, the ends may never justify the means. The wind whipped past him, catching the hem of his coat, but he was far enough from the edge that it didn't hit him too hard. The dreary weather suited his mood. His phone rang: a voice call rather than data. That first week he'd received a text from Kat that simply said, _Your balls + my gun, you rat bastard._ He hadn't been able to think of a clever reply. He glanced down to see who it was and took a deep breath. "Hello?" "Are you alone?" Deven asked. His voice had two simultaneous effects on David: His stomach clenched with anxiety, but his heart quivered with something else entirely. It was maddening that as much as he wanted to stay away from Deven, the investigation kept forcing them back together. "I wouldn't have picked up otherwise. What do you need?" His brusque tone apparently surprised the Prime, who said uncertainly, "I wanted you to know I got the list you sent me and I'm bringing them all in for questioning." "You could have told me that over e-mail." "Fine," Deven snapped. "I was checking up on you. Excuse the hell out of me for caring." "Well if you want to know, Deven, I'm lousy," David replied acidly. "I spent the evening torturing an old man. There's a murderer on the loose threatening my Elite and my Queen. She could strike again at any time and I have no idea how to find her or what her endgame is. Not to mention, my wife is barely speaking to me. Your Consort may have instantly forgiven you, but mine isn't so enlightened, or whatever you and Jonathan call your little arrangement." "Don't throw all your shame on me, boy. As I recall, there were two of us in that bed, and moreover, you started it." "I didn't notice you having any qualms." "I'm not saying I did. I'm just saying, don't expect me to shoulder all the guilt here just because Jonathan is older and wiser." "Are you trying to imply that—" "David," Deven said firmly, brooking no refusal, "I'm not going to do this again." David fell silent, as he always had when Deven—whether his friend, his teacher, his lover, his peer, or his employer—used that tone. He sagged back against the wall of the building. "You're right. I can't fight the world and you, too." "You have to give her time, David," Deven said, going from angry to sympathetic with remarkable speed, which told David he hadn't really been angry in the first place, only reacting to David's foolish clinging to emotional drama. A simple fact of life that David had discovered in his three hundred fifty years was that in the end, problems weren't resolved with hysterics and screaming fits. They were solved in the night-by-night work of honesty and the glacially slow rebuilding of trust. Up until now he had lived that as a given; he just wasn't the kind of person who displayed emotion. But this whole thing had knocked him so far off center that he had no idea how to react to anything anymore. The mere idea that he'd considered throwing himself off the Winchester like some kind of grief-stricken Gothic widow made him cringe. "I know . . . I just hate that I've made her so unhappy. She deserves so much better. As a Prime, I can solve problems, put down insurrections, behead lawbreakers . . . as a husband, I'm useless." A note of amusement entered Deven's voice. "Last time you were a husband you were still a teenager, and your wife couldn't even vote or pray aloud in church. Not even you can be instantly good at everything." "What do I do?" David asked, barely able to hear himself over the rush of the wind. "Give her what she needs," he replied. "Space, time, whatever. Let her come to you when she's ready to deal with you . . . but make sure she always knows you're there for her." "There are days I wish she had killed me, Dev. What do I do with that feeling?" A quiet chuckle. "You're not a coward, David. You don't run away from your pain." "I did last time." "This is different," Deven told him. "Last time you didn't do anything wrong . . . and perhaps you ran, but only because I drove you away. This time you can't put two time zones between you. You have to fight for Miranda . . . for her sake, for yours . . . and mine." Dev couldn't see him making a skeptical face, but David was sure it came across in his voice. "What good does it do you if we work things out?" "I have a vested interest in you and your Queen, dear one." "Meaning?" "If you split up, I owe my Second twenty dollars." David rolled his eyes. "You're so full of shit." "I'll let that comment slide right by. I have to go . . . the first of those suspects is here cooling her heels in the Elite training room, and I have to go terrify her into talking." "All right. Let me know what you find out." "I will. I l—" Deven stopped midword and corrected himself with, "I'll talk to you later." David stared at the phone for a minute after he had hung up. The worst thing—well, one of a hundred worst things in this situation—was that the dam had officially broken. He could no longer pretend, to himself or anyone else, that he didn't still have feelings for Deven that were, to his continued amazement, fully requited. And though he had always prided himself on self-control, he honestly didn't think he and Deven would ever be able to be in the same room without a chaperone. Miranda's trust in him had been shattered, yes, but he no longer trusted himself either. Emotions simply didn't jump and claim him this way. He had fought long and hard to master his heart . . . yet from the moment Miranda had come into his life, that wall he had built brick by brick had begun to fracture, overgrown by tenacious flowering vines that, with each bloom, cracked him open more and more, and now he couldn't be certain of anything except that somehow, some way, he had to make things right with her. It was lucky they were immortal. It might very well take eternity at this rate. His com chimed, and Miranda said, _"We're going to a movie—go ahead and head home, I'll get a ride with Faith later."_ Her voice had exactly the same effect Deven's did . . . no, worse. "I'll go back with Faith," he said. "You keep the car. That way Harlan can take Kat home, too. I have some work to do here in town anyway." _"All right."_ "Have fun," he said hopefully, but there was no reply. She was always more terse when she spoke to him in front of Kat; he wondered if the two of them were discussing his sins, Kat tearing him apart with her quick tongue . . . no. Kat wasn't a behind-the-back-bitching kind of woman. She was direct. She would listen to Miranda and commiserate but wouldn't go out of her way to vilify him. He hadn't been kidding when he told Kat he liked her or that he appreciated her friendship with Miranda. Without Kat she had no one to talk to right now. Faith had been making overtures, but Miranda needed someone who wasn't directly involved, who had known her as long as Kat had. He tapped the back of his head against the concrete wall. Enough wallowing for one night. He did have work to do. He pulled his coat tightly around him, drew in his power, and then allowed the edges of his body to blur, forming the picture of where he wanted to go in his mind and _pulling_. He solidified on the ground a block away; he could have Misted right at his destination, but he preferred to limit the distance unless it was an emergency. Misting was useful, kept one's tracks hidden, and tended to impress the hell out of people, but it took a lot of power. Before Miranda had come along he had rarely used it, but now that he had a Queen, he could draw on their combined power to restore himself afterward, so it was much less draining. Short trips were still best. He'd been giving Miranda the basics of the theory behind Misting when they talked in the mornings, and he'd given her a meditation to do to prepare her for it, but it was very dangerous to undertake without a lot of practice and a lot of strength. Her first experience with it had been hard on her, even with Jonathan to guide her. David had heard of Primes accidentally scattering themselves all over the place, which wouldn't kill a vampire any more than a gunshot would, but it took days to drag themselves back together and the burnout factor was astronomical. Prime Al-Bahin was actually missing part of a finger from a botched Mist early in his tenure. Most of the city's sensors were installed on exterior walls about four feet off the ground, but in areas where the vampire population was especially dense, he had added extra surveillance from above and below, and the device in question was at the top corner of a three-story building. He was going to have to stand on a foot-wide ledge to reach the thing. Before he got down to business, however, he spoke into his com: "Star-three." _"Yes, Sire?"_ "Faith, I'm going to need a ride home. Can you meet me at these coordinates when you're off patrol?" _"Absolutely, Sire. I'll see you shortly."_ "Star-one, out." David walked down the street without really paying much heed to the city teeming around him. He'd chosen a time and day when the district wouldn't be very busy, and the building he was headed for didn't house a club or bar. It was two stories of apartments over a set of offices, nothing glamorous enough to attract attention. He didn't relish the idea of having an audience, especially because most of the sensors went unnoticed by vampire passersby and he wanted to keep it that way. He glanced around to make sure no one was watching, then Misted again, reappearing thirty feet aboveground perched nimbly on the ledge, letting his instincts take over to balance him. He was probably going to pay for the energy expenditure with a migraine later, but it was worth keeping his work out of sight. The last thing he needed was people sabotaging the sensors. He reached up to unscrew the sensor from its housing with one hand and reached into his coat with the other, pulling out what amounted to an entirely new computer system for the device. The sensor itself was about the size of a golf ball, convex like a store security mirror, with a hard black plastic casing. He swapped out its insides in a few seconds with deft hands, removing a small screwdriver from his coat and wiring the new unit into place, stowing the old one to strip for parts when he got home. Then he accessed the device from his phone and ran the initial calibration routine. It would have to be fine-tuned from the Haven, but it came online without any glitches, which pleased him. He needed as few problems as possible if he was going to upgrade in a few days. Compared to this system the original sensor network had been a clumsy, buggy mess thrown together out of necessity with little finesse. In July he had switched the entire network to something a bit more sophisticated, and teams in several other cities were installing systems for those areas. Within a year he'd have every major metropolitan area in the South wired and monitored like Austin was. That would make it much easier for the satellite Elite garrisons to keep things under control. Houston, New Orleans, and Atlanta were first. His lieutenant in Louisiana, Elite 249, who simply called herself Laveau, had already dealt with quite a bit of grumbling over it. Vampires in New Orleans liked their city just as it was, mystery and mayhem intact. They were David's most opinionated constituents. As Miranda had said, they could suck it up and deal. He put away his tools, turning around on the ledge to face outward, reflecting that it would be extraordinarily embarrassing to fall off and break his neck on the street in front of half the vampires of Austin, although chances were he could . . . Out of nowhere, he heard a whistle, then felt something thud lightly into his arm. David looked down to see a small wooden projectile sticking out of his coat; the pain registered a second later. He pressed himself back against the wall and swept the block with his senses, staring in the direction the hit had come from—east. He bent his will in that direction, seeking any sign of whoever had shot at him . . . It all happened in a matter of seconds. The pain from the little stake, which was no bigger around than a chopstick, became searing, and he felt something hot snaking out from the dart into his bloodstream, dispersing through veins and capillaries in the space of perhaps two heartbeats. By the time he even understood what was happening, his senses had gone totally haywire and dizziness swept over him. _Poison._ He grabbed the projectile and yanked it out; sure enough, it was a steel dart with a wooden head, and it smelled strongly of chemicals and now, blood. The wound it left was already closing. Poison couldn't kill a vampire; the only reasons to use poison were either to cause pain during torture or to tranquilize the victim and transport him or her somewhere else . . . . . . perhaps after cutting off the victim's left hand . . . David dug his fingers into the bricks so hard his nails split, but he could feel himself swimming sideways; there was nothing he could do. He couldn't even get a thought organized in his mind, let alone coordinate his limbs to stay balanced. He fought hard to remember where he was, why it was so cold . . . Suddenly a voice cut through the fog. _"Emergency rescue team to Block SD-Three, building Nineteen-A—authorization Star-two. Code Alpha One. I repeat: Code Alpha One."_ He had time to register the fear in Miranda's voice, just before the poison worked its way to his brain, and he felt blood vessels inside his head exploding. It was excruciating even through the fog. He groaned and put his hands on his head, trying to block the light from his eyes, but the pain was coming from inside, and it got worse and worse . . . this must be a stroke, blood clots in the brain, they'd heal in minutes as long as . . . "Sire! Holy shit!" The voice was a hundred miles away, which translated to about thirty feet below him. "Can anyone get up there?" _Probably not . . . but I can certainly get down there._ David didn't even consciously choose to roll over; his body just did it, almost thrashing, his whole being too focused on the pain in his skull to care about staying aloft. The freezing wind rushed past him, and he waited to hit the pavement and hopefully break his head open to release the demons tormenting him, but instead four strong arms caught him and lowered him gently to the ground. "Sire! Can you hear me?" He grunted an affirmative, though Faith's voice was fading in and out. His face felt wet; he patted his skin with a shaking hand and looked blearily at his fingers. Blood. He was bleeding from his mouth, nose, and eyes. Everything was burning . . . cracking . . . his insides were scorched. He could feel his strength sapping as his vampiric powers burned themselves to a crisp trying to stay ahead of the damage. More than anything, he wanted unconsciousness . . . oh, God, oblivion . . . anything to make it stop . . . "Get that thing to Novotny—don't touch it with your bare hands! Help me get him into the car. I've got Mo on standby over at the Hausmann. Okay, one, two, three . . . lift . . ." David felt them picking him up off the ground and carrying him over to the street; before his senses completely shut down he heard the car door slamming and Miranda's anxious voice asking from his wrist, _"Are you all right, baby? Come on, talk to me. David!"_ Twelve Miranda could tell that Kat wasn't very happy to be back at the Hausmann. The blonde hovered in the rear of the crowd as the Elite, Faith, and Miranda bore David's unresponsive body into the clinic, where Mo and the entire staff were waiting to care for their Prime. Miranda turned to Kat breathlessly. "You don't have to stay," she said. "Harlan will take you home." "Yeah," Kat said, her eyes wide with remembered fear. "I think that's a good idea." Miranda ushered her back outside, told Harlan to take her wherever she wanted to go, and paused long enough to hug Kat. "Thank you for being here." "Thanks for the night out. And tell the Count thanks for not getting shot until the movie was over." Miranda waved at her quickly as the car pulled away, then ran back up the steps into the clinic, her heart lurching clumsily in her rib cage. ". . . poison," she heard Faith say as she burst back into the clinic. "The dart had something on it. If he hadn't called me for a ride, we wouldn't have been there to catch him, and whoever fired the shot could have dragged him off the street without anyone seeing." Mo didn't normally work at the Hausmann, but this week as luck would have it he had been asked to come train a new mortal intern on vampire medicine and the needs and rights of the fed-on human. That intern was also standing back, looking bewildered and unsure of himself as the doctors moved the Prime onto an exam table and set about stripping off his coat and shirt to see the wound. "All right," Mo said, taking control of the situation, "I need a pint of O negative infused with antitoxin serum. I'll start a line—Nurse, if you would get the monitors hooked up, please, and reset them to vampiric levels." They looked relieved at having someone tell them what to do. Most of the staff were human. They had never had to deal with an injured Prime; probably none of them had ever even seen their employer in real life. Normally the direst situation Mo had to deal with was a severed thumb, but obviously he was well versed in his craft. "I can heal him," Miranda said, her voice cracking. "Let me do it." Mo saw the state she was in and came over to speak to her. "My Lady," he said calmly, "right now if you tried, you would drain yourself for nothing. This is not an injury that requires a bone set or a laceration healed. The only way to deal with poison is to force it through his system faster, and your mutual healing ability cannot do that. Just as with a stake, the invading body must be removed before healing can begin. We use the antitoxin kit for that, but _antitoxin_ is a misnomer; it is more of a toxin accelerator. It changes the toxin's half-life so that it metabolizes much more quickly. Once it is out of his system, then you come in and heal the damage the antitoxins will cause." "Like chemotherapy," she supplied lamely. "Kill the cancer and hope nothing else dies with it." "Essentially. Now, you must prepare yourself, my Lady . . . some of the substances in the kit may make things worse for a short while. It will not kill him, of course, but it will hurt. It might be best if you left the room for this." Miranda shook her head and struggled to her feet. "No," she said stubbornly. "I want to be here. I can't leave him alone." Mo knew better than to contradict a Queen, so he went back to his work. David's vital signs were erratic; a vampire's pulse and blood pressure were low compared to a human's, but his had dropped almost to nothing. The only thing that reassured her that he wasn't dying was that she could still feel him, his warm presence in her mind where it belonged, and though it was weakened it showed no sign of letting go. But he was in pain. His brain was bleeding . . . if they didn't get the poison out of his body soon, the damage might take weeks to heal, and the brain was such a delicate organ, what if . . . she imagined him losing some part of his vast intellect, even temporarily, and helpless tears flooded her eyes. Aside from the horror of it, it would leave the South vulnerable if anyone found out the Prime was mentally compromised. She half stumbled to the bedside and pulled up a chair, sinking into it and reaching for the hand that they hadn't run the IV into. On the other side, Jackie, one of the nurses, was setting up the bag of blood mixed with a half-dozen specially treated virulent substances, both natural and human created. Mo informed Miranda matter-of-factly that it included tetrodotoxin, botulinum, and dioxin, which were all known to affect vampires strongly. Botulinum was the most agonizing; it passed through fairly quickly but caused such excruciating pain that the victim often snapped his spine spasming before he could metabolize it. The other toxins weren't as painful but would take about an hour total to break down. Miranda's eyes, blurred with tears, were locked on her husband's ashen face and the blood that had marred its flawless features. "Give me something to clean the blood off," she said quietly, but she knew everyone heard her. Someone pressed a damp cloth into her hand. At the touch of the fabric, David's eyes fluttered open and she could feel him trying to focus on her. "It's okay," she said. "I'm here . . . and you're going to be all right." He couldn't answer. His eyes rolled back, and he was no longer aware of her presence. She kept at her work, concentrating on wiping the blood away so she wouldn't lose her sanity. She tried to project comforting energy, but she was so scared she had started to go numb. Gentle but strong hands took her shoulders and guided her back into her chair. "Easy," Faith said. "You've got to ground, Miranda, and reinforce your shields. You're freaking out the mortals." Miranda looked up and saw that the human staff members, every one, had huge frightened eyes, and some were shaking from the carryover of her fear. "They can't do their jobs like that," Faith pointed out. "Pull it back in." Miranda nodded. She forced herself to let go of David's hand for a minute and breathe deeply, seeking the place of silence and stillness she had fought so hard to create inside herself. With each breath she intensified her shields until she was so strongly walled off from the others that she could barely feel the air on her skin. The staff's relief was obvious. They sighed, blinked, and did a little deep breathing of their own—chances were they had no idea where their sudden anxiety had come from. On the other side of the bed, Mo hooked up the IV and switched it on. Miranda watched the infused blood traveling through the tube into David's wrist. She could hardly breathe as she waited for it to take effect. When it did, everyone knew. The Prime's body stiffened, and he gasped. He squeezed Miranda's hand so hard it nearly broke her fingers. A soft sound of surprise and pain escaped his lips, and sweat broke out all over his body; then, like magic, it seemed to pass, and he breathed out. She almost believed for a moment that it had been that easy. A minute later, he cried out again, and spasms began to rock through him so powerfully she heard something in his body snap. Wave after wave of seizures hit him, and Miranda could feel the pain, even through her shields: great hands crushing his skull, needles jabbing, claws ripping out his insides. The light in his Signet was fading in and out, as if it had a short in its wires. Miranda heard screaming. She didn't understand at first where it was coming from, as no one else seemed to notice it, but then she knew: It was inside his mind, and inside hers. One of the nurses made a mewling noise, and Miranda's head jerked up in time to see what might be the oddest thing she'd seen so far in her life: Lightweight objects all over the room were floating. A syringe, a pen, several medical tools whose purpose Miranda couldn't divine, and even the intern's necktie were suspended a few inches in midair. "Oxygen mask, please," Mo said, totally calm. Miranda didn't know if he'd seen this before, but if he was worried it didn't show. He fitted the mask onto David's face and flipped a switch in the wall. David's breathing deepened somewhat and it seemed to calm him a little; a few seconds later there was an assortment of clattering noises as all the levitating items fell back down. The screaming in Miranda's head went on and on, silent but deafening, and she clung to his hand, afraid to get any closer. His skin had a sick, yellowish pallor now, and another spasm arched his back. Finally Miranda couldn't take it anymore. She buried her head in her free arm and shut her eyes tight. She heard Mo saying something about liver damage and jaundice. The nurses were talking, too, reading out numbers to each other and asking the intern for various things. But all Miranda really knew was the screaming, with its answering echo in her heart, and it felt like it went on forever. Then, finally, something indefinable began to ease. The spasms became less frequent and less hard. His pulse began to even out. Miranda raised her eyes hesitantly and saw that the color of his skin was returning to something like normal. He was still even paler than a vampire was supposed to be, but the yellow tinge was gone. She could hear him breathing more deeply. "All right," Mo said. "We are on the downhill run. Nurse Jackie, administer a liter of lactated Ringer's solution, please." To Miranda's questioning look, he replied, "To restore the electrolytes. The poison will be out of his system soon, but it's left his body chemistry in a state of chaos. Anything we can do to bring order will help him recover much more quickly and help your energy repair the cellular damage. The less power you use, the more he'll have available." She nodded. When she spoke she sounded as if she'd been screaming for hours, though she hadn't made a sound aloud. "Can I do it now?" Mo checked the monitors, then said, "By all means." Miranda lurched to her feet and put both her hands on David's chest. He was cold . . . much too cold, though his skin was damp with sweat. It barely felt like there was any life left in him. She had never really worked with their Signet-born healing abilities herself; David had used them on her, but she hadn't needed to try them on him. She had thought he was indestructible. She reached into herself and found the bond between them, then started to push as much power into him as she could—but then she remembered the way Deven had healed Kat, slowly and gently, and tried to do the same, controlling the flow of energy so that it moved into the Prime gradually as a stream instead of a roaring tsunami. She allowed her awareness to sync up more with his, pushing aside the barriers she'd kept between them for the last three weeks so she could see if it was working. It was. She could feel damaged organs and tissues regenerating, scarred veins smoothing out, and, most important, the blood that had erupted in his skull being reabsorbed, returning to balance. Mo had been right—doing this before the poison was out would have been futile, because every time she healed him the poison would just undo her efforts until it had run its course. There was no way to know yet how long that would have taken, but she knew it would have been much longer than an hour. When she felt that a tentative equilibrium had been reached, she withdrew, not wanting to overwhelm his system with too much energy. To her relief he looked a hundred times better. Mo removed the oxygen mask. "I would say we have succeeded," the medic said, satisfied. "We have blood samples for basic toxicology—the Hausmann has the equipment for a narrow range of tests, so we can run them before the samples die. I already sent a courier with additional samples to Hunter Development; perhaps they can get something from them if they hurry." "So we don't know what it was," Faith said. She was standing nearby with her arms crossed, her face lined with worry. "Not yet. Once he is awake I will ask him about his symptoms, and that will tell us much about the culprit." "I think the odds are pretty good we're dealing with our assassin," Faith added. "But I don't really understand why suddenly she'd be using poison." Miranda was staring at David's drawn, exhausted face. "To hurt me," she said. "She couldn't just kill him without killing me, too, but she could hurt him." "Going after a Prime is pretty ballsy," Faith observed. "And stupid. She's going to regret it." Miranda gave a choked half laugh. "Not if we never catch her." It was midafternoon when David woke, more exhausted than he could remember feeling in a century but otherwise comfortable. The absence of pain was such a stark contrast to the hour before he had passed out that he was confused for a minute, feeling out along his body without recognizing the sensations of warmth, softness, and relaxation. There was something nearby that gave off a lot of heat and was also making a rhythmic sound, like a drum . . . it was comforting, and he lay there listening to it for a long time before he tried opening his eyes. The first thing he saw was red hair. "Hey," she said softly. She looked about as tired as he felt, and he sensed she hadn't slept at all. She was stretched out beside him in the bed, propped up on one elbow, watching him wake. She was in bed. Their bed. Next to him. His heart did a cartwheel. "Hey," he answered back. His voice was like sandpaper in his throat. "How long was I out?" "It's Tuesday afternoon." He would have expressed shock, but he could barely move. "So, most of a day. You . . . haven't been here the whole time, have you?" Miranda shrugged. "Most of it. I did the patrol meetings and stuff at dawn but then I came back here." She reached over and straightened out the comforter. "Can I get you anything?" "No . . . you're enough." A smile, tentative but genuine. She left her hand on his chest, right over his heart, and said, "You scared the hell out of me." "I'm sorry." "I'm not," she said. "I mean, I'm sorry you were hurt, but I'm not sorry that we're here now." "Does that mean I'm forgiven?" "I don't know. We can't just flip a switch and have everything back the way it was, but . . . I moved my things back in here this morning. I want to be with you, for better or for worse." He started to say something but heard his phone ring, and Miranda twisted backward to pick it up off the nightstand. She saw who it was and paused for a minute before biting her lip and handing it to him. "Go on," she said. "I'm sure he's been worried about you." David shut his eyes, not wanting to deal with this right now when everything felt so good, but he hit talk anyway. "Hello?" The anxiety in Deven's voice made him sound young. "Are you all right?" "I'll live." "God, David, I . . . I'm so sorry. Jonathan knew something was going to happen, but he didn't know when or where. I should have called you anyway, just so you'd be on your guard." David sighed. "It wasn't your fault." Deven took a deep breath. "I can't stay on. I just wanted to hear your voice—Jonathan's been saying you would be fine, but I had to hear it for myself." "Really, Deven, I'm all right. I'm weak, and I feel like I could drink an entire volleyball team, but I'm all right." "Let me know when you figure out what that shit was." "Okay. Good-bye." David didn't wait for a farewell; talking took too much effort. He handed the phone back to Miranda. "Put that thing on silent," he said. She arched an eyebrow at him. "Did you really just say that? Maybe that stuff did eat your brain." "I just want an hour of peace." With a smile, she turned off the ringer and put the phone back on the nightstand, then returned her attention to him. "Let me get you some blood," she said. "I had a fresh batch brought in—you haven't fed since the intern at the clinic. Don't worry," she added, knowing how he'd feel about feeding on his employees, "I asked for volunteers and offered a hefty bonus in return. The boy was happy to help, and it was much easier than going out and finding someone." "Wait," he said as she started to get up. "Stay here for a moment." She met his eyes, then nodded and lay back down, scooting closer and, after a second's hesitation, putting her arm around him. Being free of poison had been nothing compared to the relief of that touch. She burrowed her face into his shoulder, and he inhaled the scent of her hair; they settled in together as they had a hundred times before, and he felt her sigh against his skin. "I deserved this," he said. "That's all I could think while I was lying there . . . for what I did to you, and what I did to that horrible old man . . ." "Oh, David," she sighed. "You can't torture yourself . . . sorry . . . for what you have to do as Prime. I don't like it . . . and I know you don't either . . . but think of what will happen if this assassin succeeds and we die. There will be anarchy in the South and a lot of people will be killed. You told me yourself, a long time ago, that sometimes being Prime means doing what no one else should have to . . . that you can't always afford the moral high road." He looked at her face. "You didn't always feel that way." She smiled sadly. "You didn't always get this upset over these things." She ran her hand back through his hair and added, "I think we've changed each other, you and I." "I know you've changed me." Miranda was silent for a moment, but then said simply, "I missed you." "I missed you, too." "I don't know if . . ." She trailed off, searching for words, but he intuited her meaning. "I understand," he replied. "I've never asked you for anything you weren't ready to give." "I know." She smiled again. "That's one of the things I love about you . . . you philandering bastard." He couldn't help but laugh, and she laughed a little, too, hugging him, and then kissing his neck. It was the first time she'd kissed him in three weeks. "I just wish you hadn't fucked up so badly, so I could go on thinking you were the perfect man," she added, sighing again. He snorted softly. "I could tell you a thousand stories that prove I'm anything but perfect." "Truthfully, I already knew you weren't. You listen to rap." "I listen to everything." He grinned. "Miss 'three songs by Britney Spears on my iPod that I don't think anyone knows about—' " "Hey, no snooping!" "I didn't. That night I came home and you were singing in the shower with the stereo going, I looked at the playlist because I couldn't believe what I was hearing." "If you have such exalted taste, how did you know it was Britney?" They were both laughing, and it felt so incredibly good, but it was tiring, and he quieted out of necessity. "I love you," he said. She took a deep breath. "I love you, too." He could feel that she meant it. He had never been in danger of losing her love, only her faith in him. He couldn't say how or when he would earn it back, but he would. He would find a way. They were a Pair. So much in the world was uncertain . . . but that much, he knew with every bone in his body now, was unbreakable. Somehow he would restore her trust and they would find a way to live with what he'd done . . . for her sake, so she could have the happiness she deserved. "Go to sleep," she whispered to him. He closed his eyes. "Sing to me." He could hear her smiling. "All right." And, as she sang softly into his ear, and he began to drift off into sleep, he couldn't help but think that being poisoned might be the best thing that had ever happened to him. _You're in my blood like holy wine_ _You taste so bitter and so sweet..._ Running the South on her own was exhausting, but there was satisfaction in knowing that she could handle it, at least for a couple of days. In the evening at sunset she met with Faith for a briefing on the night's upcoming patrols, and then just at dawn, when the shutters of the Haven had closed and the teams had all returned from the city, she met with them to go over the night's events. Sometimes David simply took a summary report from Faith, but with the assassin on the loose Miranda wanted to hear everything herself. And though she didn't have anything like David's technological genius, she knew how to monitor the sensor network, routing it through her phone to alert her to problems. He had shown her how to run the routine on the main server that compiled all the night's data into a single report and saved it for later reference. Technically she didn't need to look it over, because the system was programmed to contact the administrator if anything weird happened, but she gave it a once-over anyway. There were always two Elite monitoring it from the office where the property's security cameras were based, but they could only watch, not interpret, and David had them observing the network mostly as a backup in case on some off chance he or the alert system missed something. Tuesday night she had to mediate a dispute between two members of the Court. Both were nightclub owners and one suspected the other of using mind control to steal patrons. The second owner claimed the humans were migrating to her club because she had started serving food—in fact the _Austin Chronicle_ had voted her tapas the best in the city. As petty and ridiculous as the whole thing seemed, if the issue wasn't officially settled it could lead to violence, intimidation, and the risk of exposure. Miranda made both owners submit to a psychic evaluation, looked into their hearts, and found something interesting: The second owner had not been coercing her patrons, but the first one _had_ been, in retaliation for a perceived threat to his business. He'd been sending his employees over to the second club to "advertise" for his own place, meaning to compel a few humans here and there to come back. The Queen was within her rights to shut him down completely, but she knew from watching David deal with similar situations that a popular vampire establishment disappearing would raise a lot of questions, and besides, she wanted people to feel that the South was a solid place to do business. She slapped him with the maximum fine demarcated for the circumstances and ordered him to pay restitution to the other owner, then informed him that there would be Elite watching both establishments for any further misbehavior. Surprisingly, the first owner wasn't terribly angry about the loss of income—he was more satisfied that his rival hadn't been stealing his customers. Both left the Haven feeling that the results were fair, and Miranda was pleased. She'd been half afraid since the incident with Prime Hart that she had no political savvy at all and was going to have to stay out of administrative and judicial affairs, which she hated to do because it was what all the other Queens did. But it gave her a shot of confidence knowing that she _could_ learn and that she just needed experience and patience. She didn't have much of either, but she was working on it. Her empathy gave her an advantage in this kind of mediation, and the more she learned to use it the better she would be at all of this . . . she would never have believed a year ago that she would think of her gift as anything but a curse, but now she found herself wanting to push it further, see where its edges were, experiment . . . She had to laugh at herself. Yes . . . David had influenced her, all right. She persuaded David to take it easy Tuesday night, although he was totally recovered by the time he woke up and fed. She knew he agreed just to make her happy, but she didn't care. She wanted to be sure he was back to 100 percent before hitting the Austin streets again. Seeing him hurt had shaken her badly. His being hit in the eye with earpiece shrapnel had been minor, but it had freaked her out; this was the real thing. The assassin hadn't been trying to kill him, but she had wanted him down, and if Mo hadn't used the antitoxin kit on him he would have been left in a coma. The preliminary analysis on the dart was that it was a synthetic toxin that targeted blood vessels in the brain; nervous system injuries were tricky and delicate to heal, and something that extreme would have taken even a Prime a week or better to recover from. A lesser vampire could have been out of commission for more than a month. It would have killed a human in minutes. Maybe it hadn't been life-or-death, but feeling his pain and knowing that even the most powerful vampire in the Southern United States could be hurt so badly terrified her beyond rational sense. She wanted to lock the doors, tie him to the bed, and do anything she could to protect him, and therefore herself, from going through that again. Part of her was still so angry at him, yet part of her—a bigger, deeper part that she couldn't deny—just wanted her husband back and was willing to throw aside everything just to make sure he was safe. It was so aggravating. She wasn't ready to stop being upset. She had thought she wanted to hurt him for what he had done to her, but then she realized that was the last thing in the world she could stand to see, and now she was left with a pile of conflicting feelings and the nagging knowledge that she was going to forgive him, even though part of her never wanted to. It offended her knowing that something as cliché as having a soul mate could override her perfectly justified outrage. Things with Kat were still awkward. Though Faith had made it clear she was happy to listen, Miranda hated to put the Second in the middle of her and David's relationship troubles. Faith had been David's friend first, and Miranda could sense she felt conflicted about the situation already. Miranda didn't know what else to do . . . so, in a fit of desperation for someone to talk to, she finally called Jonathan, and they were on the phone for more than an hour. "How in hell are you doing it?" she asked. She could tell he was smiling. "For starters, you can't compare your coping skills to mine or anybody else's. Everyone deals with life's steaming shit piles in a different way." "So you're just . . . okay with the fact that he cheated on you?" Jonathan chuckled. "There you go again. You forget: We don't have cheating, because we decided at the beginning that there were going to be other men in our lives. Of course . . ." He paused, then clarified, "I don't deny I was angry. It shocked me how angry I was, because I thought I was all right with the idea of his taking a lover at some point. It was so hypocritical of me, not to mention totally out of character. But then once we were back home, on familiar ground, I was able to think about it rationally, and I realized the problem was that this wasn't just some blowjob at the zoo." "The zoo?" "Don't ask. The point is, I'm not emotionally attached to any of the people I step out with. It's just sex and we both know it. But whether you or I like it or not, David and Deven love each other, and it's not going away. We can either accept that and deal with it, or we can wallow in our misery for all eternity. I'm accepting it for two reasons. One, because I love Deven and don't want to lose what we have. Two, because he's a recovering Catholic and you wouldn't _believe_ the guilty mess he's been, both for damaging y our marriage and for making me upset. He's spent too much of his life hating himself. I can't bear to make it worse . . . which goes back to reason number one. I love him. And one way or another, we're going to work all of this out, as are you." Miranda sighed, picking at a loose thread in the throw she'd draped around herself when she flopped on the couch with her phone. "How old do I have to get before I'm as well adjusted as you?" "It's a matter of priority. I just know that I want to stay with the love of my life . . . above and beyond the fact that I can't leave. Technically we could live separately and only see each other every few days when the need gets overwhelming, but it would be an awful existence." "Yeah. I tried that. It sucked." "My advice is just this: Do what feels right whether it's 'appropriate' or not. Emotions have no manners. They don't care about what people in relationships are 'supposed' to do. You're not Mr. and Mrs. Solomon living in the Austin suburbs, after all." Miranda smiled. "Really, this whole thing is more like a cross between the British monarchy and _Dawson's Creek_." "Perhaps. In fact, definitely. But after sixty years I can say in all honesty that it's worth it. Trust me, Miranda. It's worth it." After they hung up she sat staring at the fireplace for a while, digesting everything he'd said. She felt a lot better just having talked to someone; there had been such a weight on her back, and she hadn't felt comfortable unburdening herself to Kat, or Faith, or anyone. There were some things that only another Consort would understand. A moment later the suite door opened and David returned from an evening spent in the stables. He looked disheveled but content, and smelled like sweat and horse. They smiled at each other. "How are you feeling?" she asked. "Right as rain," he replied. "Except I have some news that might not be entirely welcome." "Oh, God, what now? Did you hear back from the West about those clients of Volundr's? Were they all dead ends?" David shook his head. "Not yet. They're still questioning them. This is something else." "Go on." He put his phone on its charging dock and his wallet on the desk in preparation for taking a shower—he knew she wouldn't let him sit on the couch if he smelled like Osiris. "Another state visit." Miranda let her head fall back on the couch. "You've got to be kidding. Can't we put it off?" "Only if we want the Council to start gossiping. The others will want to know why we're stalling, then they'll speculate on what's going on in our territory . . . they love nothing more than blood in the water. Besides, it would be a breach of protocol." "Fuck protocol." "I feel the same way, to be honest. But we have to present a strong front." "I know, I know. So who is it this time? Someone I'll have to throw at a wall, or someone else you've slept with?" He looked away when she said that, but said, "Neither. It's Eastern Europe—Prime Janousek. He's an ally and a friend, but nothing more." She almost felt bad for needling him . . . almost. "No Queen?" "No. He's been in power for eighty-seven years, so it's a bit unusual that he's still solitary. And a bit sad, because he's a good man and a solid member of the Council. No real enemies, no drama. He's a competent ruler and a decent warrior. I think you'll like him." She nodded. "That doesn't sound too bad. When's he getting here?" "Next Monday. He'll only be here for three days. It should be painless." "Let's not tempt fate by saying that." "Good point." He pulled his sweater off over his head, then the T-shirt underneath. "At any rate, the visits should slow down after he leaves. There are five or six others who will want to come in the next few months, then after that it will probably stop until a full year has gone by." "Good," Miranda said. "I've had enough Magnificent Bastards for a while. That will make seven, right?" David ticked them off on his fingers. "Japan, the Plains region of the U.S., the Middle East, Western Europe, the Northeastern U.S., and the Western U.S., plus Eastern Europe. Seven." "And Kelley will probably show up sometime in the middle, right?" "Most likely. He's not leaving Chicago until he absolutely has to—the gang war there has been going on for years, and his Court is teeming with strife. I don't really hold it against him, although he is a bit of an ass. He's not nearly as bad as Hart, but he's been responsible for a lot of the corruption in that city." "This Janousek's territory includes Finland, doesn't it?" "Yes. That's another reason I didn't try to put him off. There's a chance he may be able to help us." As he spoke he got the rest of his clothes off, and she rested her chin on the back of the couch so she could watch; another downside of sleeping in the mistress suite was not getting to see him naked. Her mind, heart, and body all had differing opinions on how best to proceed with their relationship. He saw her watching and smiled. "Would you like me to flex something for you?" She giggled. "Just turn around and go take a shower." A few weeks ago that would have been her cue to take off her own clothes and either ambush him in the shower or be waiting in the bed when he came out. Now, though . . . she turned back toward the fire, biting her lip, torn once again. Her body was quite adamant that she should make up for those three weeks of sleeping alone, but . . . all she had to do was close her eyes and think about sex, and that feeling came over her again . . . that night, feeling him with Deven across the Haven, the sensations and satisfaction that had been devoted to her suddenly given to someone else. Could she even lie there with him without thinking about it? Was she doomed to share a bed with Deven forever? She imagined herself in Jonathan's shoes, finding most of his sexual enjoyment outside the Haven—perhaps it worked for them, but she couldn't imagine being happy in that kind of arrangement, knowing that David was out shagging who knew who every night . . . or on the other side of it, being bound to someone she loved so much who just . . . didn't want her that way. If she held herself apart from David for now, it wasn't because she didn't want him, it was because she wasn't ready to be that intimate again after such an egregious breach of trust . . . or was she? Was she just punishing herself now? One thing was for sure: Sitting and stewing about it wasn't helping. She tossed the blanket aside and left the couch, going over to turn off the lights so the fireplace was the only source of illumination in the room. It was about half an hour before dawn, and she could smell daybreak in the air. The Haven's shutters had closed thirty minutes earlier—they always closed at least an hour before any trace of sunlight entered the sky. The room was warm and dark with a hint of steam coming from beneath the bathroom door; she could hear the water being switched off as she turned back the comforter and sheets and drew the curtains around the bed so that it was mostly closed off, cavelike, its own little world. Miranda took off the yoga pants and tank top she usually slept in and climbed in beneath the covers, considering for a moment before pushing the comforter down to the foot of the bed and letting the sheet fall over her as she lay on her side, waiting. A few minutes later David pulled back the curtain; he had on his bathrobe and his hair was damp. When he saw her he froze. They stared at each other for a long time; she knew he wanted to ask questions but was afraid to, lest she change her mind about being there. Still, he didn't move from where he was standing until she deliberately reached over and patted the bed. The Prime took a deep breath and nodded, then took off his robe and slid in next to her, the flickering firelight making him look even more uncertain than she knew he was. They held each other's eyes for a long time, neither sure what to do to break the silence. Miranda understood that he was leaving it up to her. Somehow knowing that made up her mind. She leaned forward and kissed him very softly on the lips, a light touch, almost virginal. She could feel how much he wanted to simply seize her body and reclaim the ground he had lost, but he held himself back, letting her do what she was comfortable with. So close to perfect, even with his flaws—there was no way in heaven or hell she could ever have hated him, no matter what he did. She kissed him again, this time more firmly, pausing to run her tongue along his lower lip and then nuzzle the line of his jaw until she reached his ear. She nibbled his earlobe a moment, eliciting a shiver and a sigh, then let her tongue snake out to touch just behind and below his ear, pressing in. He groaned. She took his shoulders and turned him onto his back, then cast the sheet off her body and let him look at her as she rose up on her knees and tossed her hair back out of the way. She stretched out over him, propping herself up on her elbows to look down into his face. He smiled and sighed at the touch of her skin, eyes drifting shut. "These are the first of my terms," she said. "The rest will be communicated to you as I think of them." His eyes flicked open, but he was still smiling. "Go on." "Tonight's is this: If I'm going to sleep in this bed with you, I don't want to have any unpleasant thoughts or nagging fears keeping me awake. Therefore your task is to make sure I sleep soundly." She leaned down and began reacquainting her mouth with his skin; he tasted like clean water, wine, and almond-scented soap. She loved the skin of his throat, especially; she could feel the pulse strong beneath it, harder right now than at rest, and it was sensitive to her nails scratching lightly over it or her teeth finding purchase in the flesh just where neck joined shoulder, leaving a dark purple bruise that faded immediately. He drew a ragged breath and started to speak, but she wasn't finished. She laid her hand over his mouth. "It will be very taxing for you," she informed him, shifting her hips down slightly to circle against his; she felt how painfully he wanted her, and smiled, continuing. "You'll have to work long hours and lose sleep of your own. And there will be mornings that I don't want you to lay a hand on me—somehow you'll have to find ways to tire me out regardless. It will be quite a challenge." She caught and held his eyes. They were glazed with desire, and she knew that at this particular moment articulate speech would not be his strong suit. "Do you accept these terms, my Lord Prime?" she asked, reaching down between them to catch and stroke him until he was panting, tiny sounds of pleasure edged all around with pain escaping him with each breath. He took a deep breath. "I accept, my Lady." "Good. You can start at once." "Thank you," he breathed, and clamped his mouth on hers. She closed her eyes and let her lips part, allowing his tongue to thrust deep into her mouth, and she sucked on it hard, stealing the breath from his lungs. He grabbed her hips and flipped her onto her back without breaking the kiss, his own hand echoing the motion hers had taken on his body moments ago, but this time pressing in, and in, until she moaned and her back arched off the mattress. His fingers did a ballet between her thighs, and she pressed her hips up to his palm, whimpering. Meanwhile he lifted his mouth from hers to take a slow, wandering path down over her breasts and belly, tracing spirals of kisses and bites, keeping it almost maddeningly leisurely considering what he was doing to her with his clever left hand. His right, he used to push himself down the bed as he continued his explorations until he had reoriented himself alongside her and, with one swift swap of positions, replaced his fingers with his tongue. The noises that came from her were strange and unfamiliar, drawn out of her all the way down from her belly, almost animalistic. She writhed above him on the pillows, her hands clawing the sheets to keep herself from twisting into a knot, sweat glistening over her skin. He lifted his head and looked at her, and she managed to catch her breath long enough to ask, "Why did you stop?" He gave her a devilish grin. "I was simply wondering, my Lady, if I would be more likely to put you to sleep with two orgasms or three." Miranda moaned and dropped her head to the pillow. "Three, goddamn it. Three!" "As you will it." He lowered his head again and pressed harder, at the same time slipping fingers back in, faster. Not thirty seconds later her entire body seemed to explode from the inside out, and she wailed like a banshee while her muscles contracted and her limbs shook. Before she had even started to come down, however, he grabbed her hips and turned her over onto her stomach. She knew exactly what he had planned, and so she was ready for him, planting her knees and lifting her hips to let him enter her hard, then drive her forward onto her shoulders, her hands crawling up the mattress, seeking some sort of stability and finding only pillows. He covered her powerfully on all fours, his chest pushing into her back, and he leaned down and bit her throat and sucked, timing each swallow with the rhythm of their bodies so that the pleasure-pain of being drawn from was boosted exponentially, so much joining, contact inside her body, her blood in his mouth, the smell of her on his breath, both of them sliding against each other on sweat-slicked skin. Knowing exactly how it would affect her, he changed the angle of his hips and pressed forward, driving in so hard that she screamed, but not out of pain. She threw her own pelvis back to meet him each time, wanting him deeper, wanting him to disappear inside her so they shared a skin. It didn't seem like too much to ask. Again, the explosion, and again, the earthquake. She bucked underneath him like a wild animal until the wave passed. Then she collapsed gracelessly face first into the sheets. He let her be for a moment, her body going through the tremors and miniature spasms, tears gathering in her eyes that she wiped away with unsteady hands. She turned over on her back, saw the self-satisfied look on his face, reached up and slapped the back of his head lightly. "That's two," she panted. "Or are you tired out already?" She pushed her hair out of her eyes and added, "I know at your age the stamina starts to go." David gave her a narrow-eyed look of feigned irritation. "It would serve you right if I did stop." She raised him a lazy smile. "And then what would you do with _that_?" she asked pointedly. "Hmm . . . touché." He stretched out next to her and, still not in a hurry, kissed her lips, eyelids, and nose. "You are so beautiful," he murmured, running his hand down over her arm, then around to her back to draw her against him. She wrapped one leg around him, gasping as they slid back in together. Miranda opened her mind to him, and through their bond they were able to touch and connect to each other completely, one consciousness melting into the other the same way they wound around each other in the sheets, moving in a slow undulation, mingled breath the only sound in the room besides the crackling fire. _Yes . . . this._ It was so easy to forget what they really were, with flesh and bone and space in the way, but beneath it all, in a place where pain and sorrow could never reach, they were one, a single soul that had chosen, for whatever reason, to spend this incarnation walking the earth in two bodies. Here in this place there was no separation, no names . . . but there was joy in duality sometimes, a beauty in moving from separation into unity then back again, the intensity building from a reverent give-and-take to something wild. This time the tectonic shift hit them both. They clung to each other, breathing in tandem, drenched in each other's sweat, tasting each other's blood. There was no need to say she loved him—right now words would only force a limit on reality when the truth was simply there soaking into every cell. He laid his head on her shoulder, and she threaded her fingers through his damp hair, her other hand tracing the lines of ink on his back she had already memorized. Finally, knowing that she wouldn't be comfortable with him asleep on top of her, he shifted off, landing with a grunt to her right. She looked over at him, grinned, and said, "Three." Thirteen "What do you know about the Firstborn?" Faith peered quizzically down at David. "It's an old vampire legend," she said, handing him the wrench he indicated with his free hand. She had to speak a little loudly to be heard over the bump of the garage's stereo bass. "Everybody's sire tells it—if you go back far enough in our history, you find references to the vampires who weren't sired, but born. Usually people say they're spawn of Lucifer or Hades or some other dark god. They're like the bogeyman. Behave, or the Firstborn will get you. But it's a myth, like you told Volundr . . . right?" "As far as I know," David replied, sliding back under the car. "I just thought it was odd that he brought it up, of all the things he could have said." "He was playing on the fact that vampire history is your pet cause," Faith reasoned. "I'm sure he'd heard that you've poked around for information over the years. A man like him hears everything, even living in the armpit of nowhere." "I suppose." Faith heard clunking noises, and a moment later the Prime emerged again, handing her the wrench. "Hand me the seven-sixteenths ratchet wrench, please." "Only if you'll turn the stereo down." David sighed. "Philistine." "Sire . . . I hate to tell you this, but you're awfully white to be listening to Tupac." David rolled his eyes, then made a twisting motion with his hand, and the volume of the music dropped to a more reasonable level. "Unless all you listen to are bamboo flutes, Second, you can fuck right off." Faith stared down at the row of shiny tools on the cart. "Which one's a ratchet again?" "The one that—never mind." Faith watched as one of the tools rose off the cart and flew over to the Prime's outstretched hand. She had long ago lost the ability to be shocked or mystified by his talent; now she merely said, "Why didn't you just do that to begin with?" He shrugged. "You were standing right there." "And why aren't you having a mechanic do this?" David made a dismissive noise. "These cars are loaded with proprietary technology, Faith. I'm not letting anyone get their grubby hands on it unless they're vetted by security. Right now there's nobody in the Elite qualified to do it—let's put that on the list for the next batch of recruits, come to think of it. Someone with automotive repair experience as well as computer programming skills who I can train to do routine maintenance. Familiarity with solar power systems would be a plus." "Yes, that's a combination you often find in warriors," Faith remarked wryly. "Which is exactly why I'm doing this myself. Now, did you have an update for me?" "Yes and no. Two of the four names on Volundr's list have alibis for all four attacks. One, Deven is still trying to track down for questioning." "And the fourth?" "Dead," Faith told him. "Cut down in a gang skirmish in Seattle two years ago." "Damn," David muttered; he started to push himself back under the car but paused and said, "We're really screwing the pooch on this one, aren't we?" Faith laughed loudly enough to startle one of the servants, who, nearby, was waxing one of the other cars. "Where on earth did you hear that phrase?" she asked. "From Miranda. Where else?" Faith wanted to ask how things were with the Queen, but she had learned to tread lightly there in the past month. She accompanied the Prime on his various forays into the city and on whatever mission he gave her, and tried to be as useful as possible, remembering what Jonathan had said. But neither of the Pair seemed inclined to open up to her. David simply wasn't the sharing type, but Miranda had become strangely quiet lately, which wasn't like her. Faith knew she'd talked to Jonathan a few times but wasn't spending as much time with Kat as before, and she seemed . . . a bit lost. The Pair were sleeping together again and working hard to put what had happened behind them, but still . . . there was something new and sad in the Queen's eyes, as if the first veil of illusion had been lifted and she found herself a tiny bit further from her mortal life than before. Faith didn't envy her the next few years. That was the hardest part about becoming a vampire; in a lot of ways it just seemed like a new and different lifestyle, but if you had any ties left to humanity they were eventually severed one by one, either by time's incessant decay or by the hard reality that though the human world and the Shadow World might exist within the same cities, in truth they were a thousand miles apart. Speak of the devil: The side door of the garage opened and Miranda's red head poked in. "David?" The Prime responded to the sound of her voice like Pavlov's dog, and Faith heard him drop his wrench on the concrete as he rolled out from under the car and sat up. Miranda gave him an appreciative look; he was dirty and sweaty, had engine grease smeared on his face, and wore a snug, ratty T-shirt bearing the slogan _Han Shot First_. Even Faith, who tried very hard not to look at her boss that way, had to admire the sight. The biceps alone were worth staring at. He smiled at Miranda. "Yes, my Lady?" She smiled back. For a second it almost seemed to Faith as if nothing had ever gone wrong. "We got a call from Signet Air," the Queen said. "Janousek's flight landed in Newark thirty minutes ago. He's staying there for the morning. He'll arrive in Austin tomorrow evening at five fifty and be here at the Haven by eight." "Good, thank you," the Prime replied. He looked up at Faith. "Is everything ready?" "Yes, Sire. I've got the usual detail to meet the plane, and his suite is prepared. We're not anticipating any problems with this one." "That's exactly why we need to be ready for problems. The last thing we need is this assassin going after Janousek on his way from the airport." David returned his gaze to Miranda. "What do you have planned for the rest of the evening? Are you going into town?" "Not tonight. Grizzly and the producers are mixing this week—they're going to call me when they have something for me to listen to. I've got a gig Wednesday but until then I kept things clear for Janousek's visit. Tonight I've got yoga." "When did you take up yoga?" the Prime asked. "Tonight, possibly. Lali has been giving Cora classes, and she asked if I wanted to join in." Miranda raised an eyebrow and smiled. "I'm sure you wouldn't object to my being more flexible." "And on that note," Faith said, "I'm leaving." "Are you on duty all night?" Miranda asked, stopping the Second. "You could come along—Lali says that it's a perfect complementary practice to all our fight training." "No, thank you," Faith replied with a grin. "I tried it once and ended up with my legs stuck behind my head. Lali actually had to come undo me. How about you, Sire?" David was laughing, probably at the mental image Faith had given him. "That's quite all right. I have two more cars to work on and then a conference call with Lieutenants Craig, Laveau, and Nguyen at eleven. After that it's back into the network upgrade. Oh—and I owe Novotny a call. He wants to run some additional tests on the hands." "What kind of tests?" Miranda wanted to know. "He finally got a full analysis back on the poison and wants to see if the assassin also used it on Jake and Denise." "Do you think she did?" Faith asked. "Yes and no," David said, reaching under the car for his discarded wrench and returning it to the cart. "If she'd poisoned Denise, there wouldn't have been nearly so much blood at the crime scene—Denise put up a hell of a fight for a human, and that toxin would have killed her before she could even struggle. But she might have poisoned Jake to bring him down before cutting off his hand. That's Novotny's theory, anyway. But he wanted to run the list of parameters by me first." Miranda leaned her hip against the car, one hand trailing over its glossy finish. "I hate that we're stuck waiting for this bitch to make the next move, David. Something has to give." "I know, beloved. I'm hoping that decreasing the network's cycle time from five seconds to three will give us something." "What about the raw sensor data?" she asked. "How far back does it go?" "Ninety days," he replied. "Why?" "What if you compared the readings at the time of each attack and looked for blips?" "You said there were no blips," Faith pointed out. David nodded. "There weren't on the network itself. But when something moves past a sensor, it records an array of information. The network is calibrated to collect more than two dozen parameters, but only the important ones—height, weight, temperature, and speed—are analyzed, and then the system displays only combinations of readings that indicate a vampire's presence. If something corresponds to, say, a toddler or a German shepherd, it doesn't show up on the grid. But all the raw data is dumped every ten minutes into the backup server. There's a vast amount of data, so it overwrites every ninety days, otherwise we wouldn't have nearly enough drive space to store it all. Most of it is just noise." Faith nodded. "Based on observations from you, Prime Deven, and Kat, our killer is totally average for a vampire, although she is damned fast." Miranda said, "Something about her keeps her from showing on the grid. But the sensors might have picked up something else, something nonvampiric." "Maybe she's a werewolf," Faith said, grinning at the dirty looks they both shot her. "Kidding." "I did a search on the raw data right after Jake went missing and got nothing," David mused, "but once I get the upgrade done, the enhanced sensitivity and processing speed may produce something. I'll try it again. It certainly can't hurt at this point." "I can't believe that with all the technology we have and all the brain power working on the problem, we can't find a single damn thing," said Faith irritably. "Who the hell is this woman? What could she have that makes her harder to find than the Blackthorn?" "It could be magic," Miranda said. David laughed. "Of course. She's a magical werewolf. Why didn't I see it before?" "Don't laugh," Miranda admonished him. "You don't know how everything in this world works." "Beloved, there's no such thing as magic." She gave him a look that Faith almost laughed at. Few people ever seemed to think that David was capable of saying something stupid. Miranda pointed wordlessly at her Signet. The Prime considered that for a second. "I don't think it's magic. I think there's some technology to it that we simply don't understand yet. That's what magic is, in the end." Again, Miranda gave him that look. "So you think that a glowing ruby that has the power to pick out your soul mate has a tiny little hamster on a wheel inside it? What about our psychic abilities, or Misting, or the fact that if one half of a Pair dies, the other does, too? What is that if it's not magic?" He shrugged. "Physics is a mysterious thing, but it's not mystical." Miranda shot Faith an amused glance, then said to her husband, "Whatever you say, dear." She leaned down and kissed the top of his head, earning a sweet smile. "I'm off to learn the Badass-asana." After she had gone, David asked Faith, "Was she mocking me just now?" Faith grinned. "I think it was more a case of humoring you than mocking you." The Prime didn't seem bothered by that; in fact, quite the opposite. He looked relieved. "That's a good sign . . . isn't it?" Faith stood out of the way while he rolled the tool cart and the flat thing he'd been lying on—a creeper, she thought it was called—over to the next car on the row. There were eight vehicles in the garage right now as a nasty autumn storm was supposed to move in sometime after two that morning. Faith's little red hybrid was at the far end, parked next to Miranda's Prius. There were two vans present of the three that shuttled patrol teams to and from the city; those, she guessed, were the ones David needed to work on next. The Town Car that Harlan drove was the Prime's ride of choice, but there was also a limo, a Rolls, and a Bentley, the three of which were rarely used as David hadn't converted them to solar yet. The two vans were gas/electric hybrids. It had never really occurred to Faith before coming to serve the South that vampires should have an interest in the environment, but David had wisely decided that immortality would be far less pleasant on a burned-out husk of a planet, so one of the first things he had done upon taking the Signet was to put the entire Haven complex on solar power. Aside from the ecological impact, it helped keep the Haven concealed; they were completely off the city power grid, a self-contained village of vampires out in the Hill Country. If they could have grown their own blood, David would probably have the place running like the world's weirdest hippie commune. "I think so," Faith responded, not sure what Miranda's comment was a sign of, exactly, but wanting to be supportive. David moved on to the first of the two black vans, settling himself on the creeper again. Faith did as Miranda had done, leaning on the side of the van watching wrenches float from the cart to the Prime, who dragged a plastic tub underneath the van and set to unscrewing something—the oil filter? Faith cheerfully admitted she didn't know a thing about cars. "You shouldn't be so hard on yourself," Faith heard herself say before she could stop. He rolled back out and looked at her. "Yes, I should. What I did was indefensible." "But you didn't hide it from her; you stepped up and accepted the consequences. Believe me, a lot of men wouldn't. You could have blamed it on Deven—there'd be no love lost there. But you took responsibility and you're doing everything you can to make it right. There's only so much good that hair shirt is going to do you, Sire, before you just have to stop castigating yourself and move on." He frowned. "Are you saying that it's . . . no big deal?" "No. You fucked up big-time." "Good. As long as we're on the same page." "I'm just saying that if the woman you love doesn't hate you for what you did, then you shouldn't either." He half smiled. "I'll take that under advisement, Second." Faith rolled her eyes and started to leave the garage, but David said, "Thank you, Faith," and she turned back to him one more time. "I appreciate that you've stood by me," he went on. "By both of us. I'm sure you were angry at me for a while, too, but it didn't interfere with our working relationship, and for that I'm grateful." Faith nodded, bowed. "Just don't do it again," she told the Prime, "or I'll have to castrate you with a seven-sixteenths ratchet wrench." The Prime looked at the tool in his hand and laughed, arching an eyebrow. "Seven-sixteenths wouldn't be nearly big enough." Faith snorted. "Too much information, Sire. I'll take my leave now unless you need anything else." "Nothing further. Dismissed." He disappeared back underneath the van, and Faith left him to it, heading out to an advanced combat training session with several of the newer Elite. Outside, she looked up at the lowering black sky where thick storm clouds hung amid the expectant, electric feel of an oncoming torrent. The wind had kicked up and was whirling leaves all over the gardens. Faith could smell the rain and the lightning and hoped the servants had all the windows shut; they'd been opening some of the groundfloor panes at night to let the fresh, crisp air in between cold fronts, to keep the Haven from feeling stuffy with so many fireplaces going. A chill crawled over her skin. The weather had been building toward this storm for days . . . and as the first few drops began to fall, she hurried from the garage to the training building, hoping to avoid the worst of the rain. Cora was more than one hundred years old and had spent all but eighteen of them trying very hard to divorce herself from her body, teaching herself to run away inside her mind so that she was distant, safe from Hart's perversions. The thought that she might one day want to reclaim her violated flesh and learn to live in it, or perhaps even enjoy physical sensation or, God forbid, sensuality had always been depressingly laughable. Yet here she was, spending hours with her secondhand Elite workout clothes soaked in sweat, learning to twist and bend her body into dozens of unaccustomed shapes, pushing herself until her muscles shook and she was so exhausted she could barely stand while a tiny brown woman with a musical accent guided her from one pose into another. Lalita called it Hatha yoga. It was an ancient art that helped to train the body and the mind together, and Faith had prescribed it for Cora to help strengthen her muscles and bring health back into her pitiful body. Cora was too weak and clumsy for more conventional workouts, and too frightened to learn fighting skills, but Faith assured her there was nothing violent about yoga and that Lalita was a gentle and compassionate teacher. Lalita's voice danced through the syllables of the sacred language of her homeland—the names of the poses and the words of chants far older than anything in the Haven. Cora liked the sound of it, and of Lalita's accented English. Cora might not be an intelligent woman, but she learned the yoga poses quickly. Her body seemed to have its own memory, and a very good one. Only a few sessions in she could fumble her way through a Sun Salutation without prompting. It was strange to be good at something that allowed her to keep her clothes on. Cora usually arrived first, as Lalita had a full duty roster and had to come to the studio once her bodyguard shift was done. They had their sessions in a small room in one of the outbuildings, and Lalita had turned the utilitarian space into a soothing, quiet studio that smelled faintly of incense. Cora didn't mind being alone there; there was only one door, so she felt as safe there as she did in her bedroom. She usually spent those first few minutes in seated meditation as Lalita had taught her. She had fought Lalita tooth and nail over meditation, claiming she didn't want to know the inner workings of her own mind, because there was nothing there except the grimy leavings of Hart's lusts. But she had seen a glimmer . . . just a glimmer . . . of something beyond that, something about her that was not broken, and could not ever be broken. She didn't know what to call it, but she wanted to learn more about it. Once she had slept in a dirty nest of pillows, but now she sat on them with her spine straight, seeking the silence within herself. Lalita, who had arrived silently and let her continue her meditations uninterrupted, sat down before her, mirroring her posture, and said, "Perhaps you are starting to see that there is much more to you than you thought." One day, Cora hoped to be as graceful as Lalita. For now she would settle for being able to support her own body weight on her bird-thin legs. "We have another student joining us tonight," Lalita said. Cora tried to hide her dismay. "Oh?" "Yes—but don't worry, she's a beginner like you were a few weeks ago." Cora nodded. It wouldn't have occurred to her to object. These people, kind though they were, were still in control here, and if Lalita wanted more students she would have them. Besides, she had mentioned that she was pushing Faith to assign more of the Elite to her classes, claiming that they would be better warriors if they could find a calm center from which to fight. The new student might even be Faith herself, come to see what all the fuss was about. At least it was a woman. Cora didn't think she could bear sharing this with a man. She knew from what Lalita had told her about India that yoga was invented mostly by men of the early Hindu traditions, and that every school of yoga and every teacher had his own style. Lalita's was peaceful and flowing, feminine, emphasizing balance and flexibility rather than brutal technical perfection. She had learned in two schools, Hatha and Kripalu, and combined the two to form something that she felt was appropriate for vampires, drawing on their enhanced sensory perception and the inherent strength of their bodies. Strength training wasn't usually an issue for Elite warriors, so Lalita focused on yoga's other benefits, especially on harmonizing body and mind. It was an utterly alien philosophy for Cora, who had been taught—and had clung to the idea—that the body was meaningless and would fall to dust. That had made it easier to let Hart do what he liked with her. But Lalita had created her own spiritual tradition, combining the movements of yoga, meditation, and chanting, with devotion to a goddess named Green Tara who apparently came from the Tibetan Buddhist mythos. There was a statue of that deity in the corner of the studio, sitting on a low table with the incense burner and candles. Cora found herself staring at the Tara often, thinking that she reminded Cora of the Virgin, a gentle mother who was still willing to step down from her throne to right the wrongs of the world. After that Cora threw her fears to the wind and did whatever Lalita suggested. The most amazing thing about the teacher was that if Cora had reasons why something made her uncomfortable, Lalita would listen to her, suggest alternatives, and they would talk about it. There was no yelling, no force, no demands that she obey. Cora didn't know how to assert herself, so her tendency was to let things slide, but finally Lalita called her on it: "You were strong enough to leave the Prime," Lalita reminded her as she went to the bench to remove her onduty gear. "Don't forget that, Cora. You were taught that you were weak and undeserving, but you know that's not true. You, and you alone, walked out of that room to find something better. You had that strength. You still have it. All you need to do is believe in it and learn to draw on it." The Elite had an array of items they carried: Each had a standard-issue sword, a wooden stake, a knife in one boot, a belt pouch whose contents Cora didn't know, and a device that she wasn't sure about. Cora pulled her knees up to her chin and watched Lalita prepare for their session; curious, she asked, "Is that a telephone?" Lalita looked down at the device and laughed. "Among other things. Our intra-Elite communication goes through the wrist coms, but this phone also shows us maps of the city, and some of us get to see parts of the sensor network. I can check the duty roster for the coming week and know when others are on or off shift, as well as accessing weather reports and other information." "All of that in that tiny box?" She grinned and nodded. "Remarkable, isn't it? When I was a young girl, no one could have dreamed of this sort of thing. Even radio was a fantasy back then. To get a message to someone took days of travel and now it takes seconds." She handed Cora the phone, and Cora examined it gingerly, afraid to touch anything. The computer in her room was larger and looked less fragile, but it still confounded her for the most part. When she touched the phone's screen, it lit up, displaying a photograph of several cats playing on a rug; one was biting the other on the neck. Cora smiled. Just then there was a knock at the studio door. Cora handed the phone back to Lalita, who took it and rose gracefully, unfolding herself like Green Tara from her lotus position. "Come in, my Lady," she called. Cora's heart clenched at the words . . . and did so again when the door opened and Queen Miranda entered the studio. "Hello, Cora," the Queen said, smiling. "I hope you don't mind my joining you." Cora swallowed. She tried to speak, but nothing would come out of her mouth. It was the first time she had seen the Queen since she had been granted asylum, and in the intervening days she had forgotten how frightening the woman was . . . she seemed to fill the entire studio with her presence and power, and even dressed in similar clothes to Cora with her abundant hair pulled back, being anywhere near her made Cora's pulse fly into chaos, fear destroying her meditative calm. The Queen came over and knelt in front of her, concerned. "Are you all right?" She laid her hand on Cora's forehead, and her eyebrows shot up. "Good Lord, Cora . . . you have to learn to shield." Lalita looked chagrined. "It never occurred to me that she would need to," she admitted. "Most of us have some telepathic ability, but hardly anyone here needs more than basic grounding and centering." "What . . . what do I have?" Cora asked haltingly. Miranda was staring at her hard, her hand still on Cora's forehead. "I'm not sure," the Queen replied. "Identifying gifts isn't something I'm good at, and it seems like most of your talent is still . . . asleep. Here . . . this will help you for now." Cora felt . . . something . . . move through her, and it was as if someone had pulled a curtain down between her and the Queen; one second Cora was on the verge of panic, and the next she was simply sitting cross-legged in front of a woman with a messy red ponytail. "I've put a shield around you," the Queen explained. "It's temporary, but it will keep me from freaking you out while we're here. I'll talk to Faith about having someone teach you to do it yourself. I would, but I'm not really experienced enough at it to show you the technique, and I have a feeling that you'd do better with a female teacher than with David." The idea of having the Prime—even as kind as he seemed to be—so close to her, touching her energy, was so awful that she couldn't hide her reaction. Miranda smiled. "I thought as much. But we'll find someone. It's something you absolutely must learn before you leave the Haven—our gifted Elite shield themselves, so you're safe here, but you've got enough ability just from what I can see that going out in the world without protection would drive you mad. Trust me, I know." "I should add," Lalita said, "that the practices we are learning here in yoga can make such things worse for the gifted—if you have any abilities, meddling about with your chakras can intensify them, which is probably why Cora reacted so strongly. Fair warning, my Lady. I know you are very strongly shielded, but for your own sake, be careful." Cora was surprised that Miranda deferred immediately to Lalita on the subject; she wouldn't have expected a Queen to listen to anyone. "I'll try to stay mindful," Miranda said. "Excellent. Let's begin, shall we?" Lalita moved to the front of the studio, where her mat was already unfurled on the ground. Cora had brought her own mat; there were several standing in the corner that anyone could use, but Lalita had given her one outright so that she could practice in her room if she wanted. Cora liked the slightly sticky purple foam, which had a paisley pattern in pink outlined along one end. She and the Queen stood up, and Cora rolled her mat out while Miranda sought one of the extras and did the same. Cora hated to admit it, but she felt a tiny bit of satisfaction as the session got underway, because while she was strong and agile, the Queen was no yoga prodigy; her alignment was dreadful, and even with her considerable physical prowess she lost her balance at one point and actually toppled over, giggling. "Why don't you try that one again?" Lalita suggested. Miranda sobered and stood back up, and Lalita led her back into the pose; the Queen concentrated on her work, which was a relief, as Cora had feared she wouldn't take what they were doing seriously, especially not the first time. But Miranda was completely respectful of Lalita's knowledge and even paused to watch Cora during the Sun Salutation to get a different view of the flow of postures. Cora tried not to acknowledge her stare, but found herself blushing anyway. "I'm sorry," the Queen said. "I don't mean to make you uncomfortable. But you really are a natural at this, Cora. You look like you were born to it." Cora blushed even more fiercely. "Thank you, my Lady." Lalita was smiling warmly at her. "I've taught yoga off and on for twenty years, and Cora is the quickest learner I've had so far. Just in the last few weeks she's gained so much poise and grace—I'm very proud of her." Seeing how uncomfortable Cora was at being stared at, Lalita changed the subject. "All right, then, let us continue." After they moved through the entire series of asanas and spent several minutes lying in Corpse Pose, Lalita began a guided meditation for chakra clearing; in her tradition the body had seven primary energy centers, each corresponding to a different aspect of a person's being, and those centers needed to stay healthy in order for the whole person to thrive. She led them through the meditation slowly, in deference to the Queen, and Cora visualized her energy moving up through her body, starting in the root chakra at the base of the spine and ending in the crown of the head. The energy opened each chakra, cleaned out any psychic debris, and left that aspect of the self running more smoothly. Cora wasn't sure how much of Lalita's spirituality she believed in, but when she did the meditation she could certainly feel something, and when it was done she always felt different, better. When they reached the third-eye chakra, which was supposed to govern one's inner sight, Cora heard a gasp. She opened one eye partway and saw that something odd was happening to the Queen. Miranda was white as a sheet, and her breathing was shallow. She sat cross-legged as Cora and Lalita did, but her hands were clenched on her knees and her forehead was creased in what looked like pain. "My Lady?" Cora asked in a whisper. Lalita's eyes popped open and she, too, looked worried. "Are you . . ." Before she could finish the question, the Queen's hands flew up to her forehead, covering her already-closed eyes. She moaned and doubled over. "No . . ." Suddenly things all over the room began to shake. Lalita put her hands on the Queen's shoulders and tried to rouse her, but the Queen didn't seem to hear; she was lost somewhere, and to Cora's dismay the shield she was holding up around Cora began to tremble and dissolve and Cora could feel the Queen's power again, this time surging dangerously. Hot, thick fear seized Cora's heart, and she pushed herself away, all but crawling backward to put as much space between herself and the Queen as she could. Things began to topple over. Mats fell, the fabric hangings Lalita had draped around the room sagged and then slipped from the walls . . . the very ground felt like it was shaking. Lalita cried out in alarm, and Cora followed her wide eyes to see that the ceiling fan overhead was coming loose from its wiring. The Queen screamed. The fan tore from the ceiling and fell. Cora flung herself forward, trying to push Lalita out of the way, and the two women tumbled backward in the chaos— —which stopped as quickly as it had started. Cora, sprawled out over Lalita on the floor, craned her head back to see what had happened, and it was her turn to gasp. Standing in the center of the room, one hand held up toward the fan that had frozen in midair, the other touching Miranda's forehead, was the Prime. The Queen's eyes rolled back in her head and she fell sideways onto her mat, unconscious. The Prime's eyes and hand followed the ceiling fan and it floated over to the corner, where it landed in a heap. He turned, looking around the room, and in seconds everything had righted itself, the scattered pieces of Lalita's altar returning to their places, the tapestries back on the walls. He didn't ask if Cora and Lalita were all right, but she supposed it was unnecessary. Aside from shock they were both fine, not even a scratch on either. He bent and lifted the Queen into his arms, then gave them a quick nod of acknowledgment and strode out of the studio. Cora and Lalita were left staring at each other. _Blood . . . so much blood . . ._ _Someone was dying. She could hear Kat screaming—not in pain, but in panic, in horror, her heart—not her body—rent into tatters. Miranda tried to help her . . . she couldn't move . . . she was an outsider here, trapped behind a glass wall where all she could do was listen and watch, pounding her fists on an invisible barrier. She tried to scream but her voice died on the wind. She could only watch scattered images of the nightmare unfolding before her, powerless._ _So much blood . . ._ _"I'm done for, Miranda. You have to save yourself."_ _Who was speaking? She strained to identify the voice but she couldn't reach it, couldn't . . ._ _She could hear something dripping . . . dripping . . . water, onto a bare floor . . . dripping . . . blood, dripping . . . dripping . . ._ _Bars. Her hands closed around cold steel bars._ _"Please tell me this was all a nightmare, Miranda."_ _"Hello, darling." A man's voice, scornful._ _She heard something shatter, saw shards of crystal catching moonlight as they fell . . ._ _"Miranda, NO!"_ _She could hear the screaming, she could smell the blood and taste it rusty and hot in the back of her throat, but she couldn't stop any of it._ _"Please . . . you have to save him . . . you have to . . . promise me . . . you're the only one strong enough to do it. Promise me . . ."_ _"How dare you come into our house—"_ _Red light . . . red light . . . red . . . four, five, six . . . seven . . . eight . . . glowing red in a circle, one by one flashing, their light falling into sync . . ._ _"Hello, darling." A woman's voice, scornful._ _Agony . . . searing, her soul being ripped in half, her screams tearing the silence of the night as she fell . . . and watched herself fall . . . only it wasn't her . . ._ _Warmth intruded. She felt herself being pulled back from the glass wall, gentle hands drawing her down, out, back into her body._ _She strained to hear the last few words as she began to wake . . . it was almost as if someone were whispering into her ear._ _Firstborn . . ._ _Eleusis . . ._ _Alpha . . ._ _Lydia . . ._ _Trinity . . ._ "Miranda." That last voice, she recognized. She reached toward it, yearning for solid ground, for the waking world, and felt hands taking hers and drawing her down, down . . . She was sobbing as she woke, relief and fear overcoming her, and she fled into David's arms, shaking. "It's all right, beloved. I'm here. I've got you. You're safe now." She was absolutely incoherent for a while but gradually got a toehold of control back, dragging herself toward calm one lurching inch at a time. She could feel a shield around her, probably as much to protect the rest of the Haven from her as to protect her from it. But the feeling—of being contained and held, safe, surrounded by such warm and loving energy—was grounding, and it helped her wrestle her powers back into her own grasp. Once she was calm David lowered the shield around her, though she could still feel him around her, physically and otherwise. She breathed in the warmth of his body and let out a long, shaky breath. "What did you see?" he asked her softly. Miranda shut her eyes tightly and buried her face in his shoulder. "Death," she whispered. "I saw death." "Whose?" "I don't know," she said, barely holding back more tears. "It was all jumbled together—there were words, and sounds, and images, and smells . . . it was like I was watching five TV shows at once. It didn't make any sense." He stroked her hair and murmured to her while she shook, but despite the possibility of dire circumstances rolling toward them he sounded concerned about her, but not about the future. "That's how it started for Jonathan," he said. "Dreams, mostly, so twisted around themselves that he couldn't interpret anything. It took time for him to learn how to see one thing at a time. You should talk to him—he can probably help you." "You're not worried about what I saw?" He shrugged. "Not really. Remember how it was with your empathy? All you could hear were the pain and suffering because they were the loudest. Now that you know how to control it, you feel things differently. It's the same with precognition. Death and misery are the most vivid because they play into your own fears. But that doesn't mean everything in the future is full of peril." She shook her head, marveling at how calm he was about it. If he had seen . . . if he had heard . . . the screams, the blood . . . She shuddered and returned her head to his shoulder, covering her eyes. "It was awful." "Do you want to tell me about it?" "No . . . not yet. But . . . I do have one question, maybe you know . . . who's Lydia?" David went very still. "Lydia?" "Yes . . . there were words, like someone was whispering to me at the end. The only actual name in it was Lydia." She looked at him. His eyes were wide. "You know a Lydia?" Miranda asked. David took a deep breath. "I've known one." "Who was she?" His grip on her arms tightened as if she were a teddy bear and he were afraid of the storm outside. "She was my sire." Fourteen "There's really not much to tell," David said, handing Miranda the Coke he'd climbed out of bed to fetch her from the bar fridge. She was sitting up wrapped in the sheets, listening to him keenly, but practically inhaled the soda—that was another thing David remembered Deven remarking upon when Jonathan was new to the gift; after he had a vision he guzzled caffeine, and it kept him from getting a nasty third-eye migraine. Sitting cross-legged on the bed in front of her, he went on, "When the Witchfinder came to our town, it didn't take long for Lizzie and me to be hauled in front of the court. She was a strong woman who spoke her mind, and I . . . well, there had been rumors about me since I was a child. You don't just start making things float without people noticing. My mother knew if I was ever found out I'd be hanged as a Witch, so she made me keep it secret, but there was still gossip." Miranda stared at him over the Coke can. "So they threw you both in jail." "Yes." "Why did the Witchfinder come to town in the first place?" "There were unexplained deaths all over the county. Bodies were found drained of blood in the woods and the fields." Her eyebrows shot up. "Oh shit." "Oh shit is right. Half a dozen people were killed—and then the burnings started." "Wait . . . I thought you said Witches were hanged in that era." "The most common method was hanging followed by a public burning of the corpse. It was nearly unheard of for someone to be burned alive in England. The panic that swept through places like Germany didn't grip our country; for the most part the judicial system kept things civilized, requiring evidence, a trial. But this Witchfinder preferred a more . . . flamboyant, if you'll forgive the pun, method of execution. He wanted the whole village to turn on each other out of fear. He was paid by the head, after all. The more Witches he found, the richer he became." "Nobody suspected his motives? Not anyone?" "Of course they did. But to speak up would have been an instant confession of collusion with the devil. I remember . . ." He flipped the tab on his own can, this one a Dr Pepper; he'd lived in the South for years before discovering an affection for the regional beverage of choice. "Lizzie was afraid—she knew that what had happened in other places would in ours. She'd heard about the burnings in Germany. She wanted to take Thomas and move away. But back then you couldn't just pick up and leave your home like that. My entire livelihood was there, and it wasn't terribly portable." She grinned. "One of these days I want to see you bang a hammer on an anvil. It's got to be sexy as hell." He smiled back. "It was the closest thing to engineering they had back then." "So, you were put in jail . . ." Her smile disappeared. "Were you tortured?" Now shame gripped him at the memory, and he lowered his eyes. "No. We were threatened with it, and a couple of victims who refused to confess were tortured, but again, it was the Witchfinder's method, not the town's. Still . . . hearing the screams . . . I was terrified. I confessed." She looked genuinely surprised. "What about Lizzie?" He had to smile at that. "She went to the stake raging, shrieking like a banshee that God would judge the town for its crimes and that her conscience was clear. I'm thankful she never knew that I took the coward's way out or she might never have forgiven me. But they didn't torture the women; they simply executed them, five in all over the course of a week. I begged the judge to leave me alive until Lizzie's brother arrived to take Thomas away and I knew he was safe. The judge was an old friend of my father's, so he managed to put the Witchfinder off for a day—because I had confessed I was promised a hanging before my burning. But then that night . . . a woman came to the jail." "Lydia?" "Lydia. I had never seen her before, but she knew my name and knew everything about me. She killed the guard, opened the cell, and attacked me." He closed his eyes, trying to concentrate on the details. It had been so long ago, and the transformation had a way of scattering memories on the wind; that night and the week that followed were a blur of pain and fear and blood, faded by time. "She was pale," he said. "Her hair was golden, her eyes blue . . . exotic for our drab part of the country. So was the fact that she was fastidiously clean. I knew she had to be wealthy by her clothes and the way she moved. And just being near her . . . she was so powerful. She felt to me the way I imagine I feel to mortals now. She drained me near to death, and I woke in the forest just in time for her to force her blood into my mouth." "Did she tell you who she was? What she wanted?" "No. Only her name, and that I had to stay out of the sun. Then she vanished." Miranda was staring at him, mouth open. "She just left you alone in the woods, not even knowing what you were?" "I woke just before dawn and dragged myself to a cave I remembered from my childhood. I spent the next few days . . . well, you know." Miranda nodded slowly, remembering. "God." "When it was over I had to figure things out on my own. I nearly roasted in the sun and spent days recovering. I ate just about every small animal in the county trying to assuage my thirst, but in the end . . . there was only one thing to do." He had slipped through the forest that night, lithe and deadly even in his fledgling power, only two things on his mind: blood and vengeance. He started with the Witchfinder. "By the time I left the town I had killed every man who had a hand in Lizzie's death. I stole their money and clothes, and I broke back into our house long enough to gather a few things. Then I stole a horse and put the town at my back. I made my way to London, where I could disappear into the city. After several months I finally found others of our kind." "I don't understand," Miranda said. "Why would she bring you across and then disappear like that? I'm assuming she had been in the area long enough to kill those six people and find out all about you. And why you?" "I have no idea, beloved. I tried to find her, for a while, but no one had ever heard of her. It was probably a fake name, after all. But for some reason, out of all the crappy little villages in England, she chose ours, and out of all the psychic smiths in the world, she chose me." A blast of thunder rattled the windows, but with the shutters locked down there was no corresponding flash. A thought seemed to occur to Miranda, and she actually grinned. "Your original surname was Smith, wasn't it?" He smiled at her. "Did you see anything else that involved Lydia?" "I don't know. I don't think so. It was just a name. It doesn't feel connected to anything else. I wonder if that means she's going to appear at some point. I hope not. I think we have all the drama we need." "From your lips to God's ears," David said, and they clinked their cans together. But even as he said the words, David thought about what Deven had said . . . that there was something about Miranda, and their bond, that would ensure that their life together was never peaceful . . . and even if he had been unconvinced of Deven's sincerity, he knew, beyond a shadow of a doubt, that _drama_ was the understatement of the century for whatever they had ahead of them. After the theatrics of Prime Hart's visit and the angst of Prime Deven's, Miranda braced herself for some kind of bullshit surrounding Janousek's arrival. She was ready for him to be an ass, or a sexist pig, or at the very least coldhearted and arrogant. She wasn't ready for him to be . . . nice. "Prime Jacob Janousek, at your service," he said, bowing. Her first thought was that he looked like a young hippie Jesus. He had brown hair falling down past his shoulders, and a neatly trimmed beard; his eyes were a warm brown, intelligent and kind, and held hers without the slightest bit of artifice or disdain. He looked to have been in his midtwenties when he came across; David had mentioned that he was actually in his mid-220s. Aside from his Signet, which was set with amber, he wore a plain gold cross on a chain, but no other jewelry that Miranda could see. Another thing he didn't have, which surprised her, was a noticeable accent. When she mentioned it, he laughed and said, "I'm no more Eastern European than your Prime is Southern American, my Lady. My ancestors are from the area now known as Slovakia, but in fact I was born in France and lived most of my life here in America. I moved to Prague because of my friendship with the former Prime, and when he died the Signet chose me. Rest assured, however, I've been there long enough that all of my other languages are accentless as well." "How many do you speak?" she asked as they all settled in the study for the usual drill of drinks and conversation. "Seventeen fluently," he replied. "I can fumble my way through another half dozen and find beer and a lavatory in another three." Miranda looked over at David. "That's more than you speak." David smiled. "I've lived in the U.S. for a long time. The only two languages I've found necessary to get by here in Texas are American English and Spanish. The rest are just for fun." The conversation was friendly and tension-free. Miranda didn't even know how to react to a Prime who was simply himself and had no hidden agenda for visiting; he had come because he liked David and wanted to further solidify their alliance, and that was it. "How is Isis?" Janousek asked. Miranda had forgotten until that moment that the Friesian had been a gift from the Prime of Eastern Europe; a bribe, David had said. Judging from the enthusiasm with which the two Primes talked about the horses, Miranda thought _bribe_ was the wrong word, though it might have been accurate at the time. ". . . just foaled," Janousek was saying. "An absolutely gorgeous male—I'm hoping he'll be as bright as his sire, just like Isis was . . . but perhaps a bit less willful." "Why don't we go out to the stables," David said. "We're due another round of storms tomorrow, so this might be the only chance while you're here to take her out, if you like. Miranda has business in the city tonight anyway." Seeing the glint in the men's eyes, she chuckled. "You two go ahead," she told David as all three of them rose simultaneously. "It was lovely to meet you, Lord Prime. I'm quite pleased to have you as our ally." Janousek bowed to her again. "Likewise, my Lady. I congratulate you both on winning the Pair lottery." Miranda left the meeting feeling completely different than she had at any of the previous Magnificent Bastard arrivals; even Tanaka, who had been perfectly well mannered and given no hint that he disliked Miranda, hadn't put her at ease, perhaps because he was so much older and more traditional than Janousek; and his Queen Mameha, though a fascinating person and blindingly intelligent, had been, Miranda freely admitted, intimidating as hell. She met Lali and Aaron outside by the car. "How did it go?" Lali asked. "Amazingly smoothly," she replied, slipping into the car with her bodyguards and motioning to Harlan to drive on. "I think I may finally have met a Prime I don't want to punch in the head." "It was bound to happen sooner or later," Lali said, her ringing laugh filling the car. "Try not to be too disappointed." "I wish I could be of more help," Jacob said regretfully. "As soon as you asked, I did what digging I could, but you didn't give me much to go on as far as your suspect goes." "I know." David led the way back to the stables, the two Primes leading the Friesians on a slow walk after their outing; Isis and Osiris were in high spirits, which was more than David could say for himself. He'd known that asking Janousek for information about the assassin was a long shot, but still, he'd held out some hope. "You're right, of course. It's not as if you know every vampire who ever came from Finland." "There aren't a lot," Jacob admitted. "Finland's population is pretty sparse. My territory, as you know, isn't the hotbed of vampire activity that yours is. There are practically no vampires north of Latvia, and aside from Prague, Krakow, and Riga, I just don't have that much density. And you know how contentious my borders are." "I do. I suppose you should be glad that Demetriou has Romania—you don't have to deal with all the Dracula wannabes." Janousek's territory was small compared to Western Europe's or the Black Sea's; historically the East had been dealt a lot of in-between countries, and the Prime of the Black Sea, who had ruled for longer than almost any other Prime and was known for his insatiable—and somewhat archaic—greed for land, was a constant threat at Janousek's borders. Janousek had managed to bring a tentative peace, but at the last Council Demetriou had made yet another play for Croatia and Hungary. Janousek's good reputation in the Council had helped him keep his hold. Janousek's western border at Austria/the Czech Republic/Poland had been peaceful his entire tenure, but the eastern border was another story entirely. David knew that part of the reason Jacob was anxious to keep him as an ally was that David's influence in the Council would help him hold his territory together; David didn't hold it against him. If he were Janousek, he'd want David's friendship, too. And if Jacob had been less than a good man with the interests of his people at heart, David would have been happy to leave him to Demetriou's wolves . . . well, that wasn't entirely true. Janousek would have to have been a cock on the order of Prime Hart to make David side with Demetriou. Jacob chuckled. "Demetriou would go after Russia if it weren't for the fact that Dzhamgerchinov scares the devil out of him. Frankly he scares the devil out of me, too." "I think I'm more frightened by how easily you pronounce his name." Another laugh. "Nonsense. Everyone knows you're not afraid of anything or anyone." They took the horses into the stable and got them groomed and fed for the night, letting the topic of conversation steer itself back to horses; finally, with the night waning, they headed back to the Haven itself. "I understand you had a row with Hart," Janousek said as they walked. "Congratulations." "What did you hear?" He shrugged. "Just that you rescued one of his harem girls, he slaughtered three more in your Haven, your Queen threw him into a wall, and he slunk home with his tail between his legs. He's bitching to anyone who will listen, which isn't anyone really, so I would imagine he's got a good case of festering anger up there in New York—if I were you, I wouldn't let him out of my sight." "I don't intend to. I would like to know who's been killing his Elite, though, if for no other reason than to send them a thank-you card." "I heard it was the Red Shadow." "Not unless they've changed their tactics pretty radically in the last few months. I am afraid they're behind what's going on here, though. I don't suppose you know any more about them than the rest of us do?" Jacob gave him a sidelong look, pausing, before he said, "There is one thing. I doubt it will be of much help to you." "I'm desperate, Jacob. Give me whatever you have." He nodded. "I was Prime Horak's Second, as you know. I'm almost a hundred percent certain that back in the 1920s he was acquainted with the Alpha." "How?" "Horak never came out and said anything, but Elite are paid to be observant, after all. One night a messenger brought a note to Horak, and the next night one of Horak's human enemies turned up missing except for his left hand. All Horak would tell me was that a friend owed him a 'recruiting bonus.' " "Recruiting bonus . . . so Horak found someone for the Alpha to hire as an agent, and the Alpha had someone killed for Horak as a reward," David surmised. "Do you remember anything about the note?" "Horak threw it into the fireplace, but I was mad with curiosity, so I fished out what was left." David stared at him. "What did it say?" Janousek smiled and reached into his coat pocket. "You'll have to figure that out for yourself," he said, and handed David a small plastic bag. "I have no idea why I kept it all this time—Prime's instinct, I suppose. That and I admit I'm a bit of a pack rat. I had forgotten all about it until you asked for my help when we spoke last week. I had it stashed away in the archives with everything else from Horak's tenure. It took me hours to find it." David took the scorched scrap of yellowed paper, so old it was crumbling. "My God." He turned it over, trying to discern what was written on it. On one side all he could see was a number, 4.19, and the faded remains of a single word; on the other, it looked like there had been some kind of symbol. "It's probably meaningless. But you're the mad scientist of the Council, so if anyone can make something of it, you can." "Jacob, I could kiss you," David said. A grin. "I appreciate the gesture, Lord Prime, but you're really not my type." "This may be the first solid link we've had to the Alpha, or to the Shadow at all. I'll have it analyzed immediately. Thank you, Jacob." "I hope it helps." They had reached the main building, and the guards opened the doors for them. "Now then," Janousek said, "I was wondering, Lord Prime—does your Haven have a chapel?" David was too distracted by the paper in his hand to be surprised by the question. "Yes—it's in the South Wing. I can take you there now if you like." "I would appreciate that." David led the way down the hall. "I doubt ours is as nice as yours," he told Janousek. "Nice is relative," Jacob replied. "But it's not stained glass and stone that matter, it's what's inside—what you can't see—that counts." "This way." David showed him down a long corridor in the South Wing to a pair of double doors with a stained-glass inset flickering with candlelight. David knew that some of the Elite used the chapel for weekly services; he'd been in the room only once or twice, but he remembered it being a fairly simple space with a peaceful atmosphere, pretty but not pretentious. It had been built without any specific iconography, like a military chapel, so that practitioners of multiple faiths could use it. The far end of the room was oriented east, so even the four or five Muslim Elite he employed found it useful. He didn't expect anyone to be inside now, but an Elite stood at the door; he recognized her as Elite 29, who had been assigned as Cora's main bodyguard because she was fluent in Italian. Cora had no idea how closely she was being watched; David had instructed the guards to keep their distance and let her come and go mostly as she pleased, but he had learned the hard way when Miranda had first come to the Haven that even with a com on her wrist, she could be vulnerable. "Sire," the Elite said with a bow. "I hope this isn't a problem—there were no scheduled services and Miss Cora likes to come here." "No problem at all," David told her. "Prime Janousek wanted to pay a visit." He turned to the Prime. "The woman we offered asylum from Hart, Cora, is in there now; she's a bit shy of strangers, especially men." Janousek nodded, understanding. "I'll wait out here, then, until she's done. I would hate to frighten her in the middle of her prayers." "If you don't mind, then, I'll take my leave for the morning—I need to meet Faith and get this to my lab." "I don't mind at all. I plan to spend an hour with God and then retire for the day. We'll speak again at sunset, of course." "Thank you, Jacob." David started to walk away, but the chapel door opened and Cora emerged. She saw them and made a faint yelping sound, moving to duck back into the chapel. "It's all right, Cora," David said quickly in Italian. "I was just leaving, and our guest wanted to use the chapel when you were finished. There's no hurry." Cora swallowed hard and nodded. He noticed she looked a hundred times better than when she'd come to the Haven; he'd barely looked at her when he had raced into the yoga studio to answer the call of Miranda's distress, but she did look healthier, and even as frightened as she obviously was, she made eye contact with him. Or at least, she did for a second. Her attention was pulled from him to Prime Janousek, who David realized was staring at her, wide-eyed. She stared right back. Suddenly David remembered where he had seen that thunderstruck expression before. Sure enough, as Janousek opened his mouth to attempt to speak, the amber stone of his Signet flared once, twice . . . and began to flash. Cora didn't understand why this man was looking at her as if she were some kind of ghost, but she knew one thing: As soon as she saw him, she was irresistibly drawn to him . . . and the only thing she could think to do was run. The two men didn't chase her, not that it mattered; this was the Prime's house, and she had no right to run away, even if there was anyplace she could go that he couldn't follow. But still, she ran, as hard and fast as she could, until she had gained the safety of her room, flung herself backward against the door, and burst into tears. Her mind and heart were spinning so fast she could barely breathe. The man's kind eyes were burned into her skull, inviting . . . something . . . some part of her that she hadn't even known existed rising up and reaching out . . . She panicked, her breath coming in hoarse gasps, her only identifiable desire to hide. She ended up curled in a ball on the far side of the bed, wishing she could shrink into nothing. What was happening? Who was he? What did he want with her? And why did she want to . . . what did she want? She had been praying, feeling peaceful and at rest, almost . . . dared she say it . . . happy. Her guard had shown her the chapel a few days ago, and she had loved its simplicity: stone walls, a few stained-glass panels with electric lights behind them that cast a soft glow over the movable pews. The panels were images of the countryside where the Haven stood, night time images in blue and purple. A cabinet on one wall contained the trappings of several religions, and her guard had shown her where to find a painted resin statue of the Virgin to place on the altar, along with a cloth and some candles. The only rule was that she had to put things away when she was done. Now her peace was shattered, and she prayed again, mumbling into her crossed arms, asking God to help her . . . whatever this was . . . _please, make it go away. Make him go away._ God didn't seem to be listening, however. There was a soft knock at the door. She couldn't speak, not even when a voice called, "Cora?" She buried her head in her arms, hoping he would leave, but a moment later she heard the door open and footsteps approaching her. "Cora," he said gently in her language, "you don't have to be afraid." She lifted her head. "Who are you?" He had settled cross-legged a few feet away from her, leaving plenty of room but close enough that he didn't have to raise his voice to be heard. "My name is Jacob," he said. "I am the Prime of Eastern Europe." She stared at the Signet around his neck. It was still flashing, but not as brightly, now that it had their attention. "I don't understand what this means." He nodded. "I had a feeling you didn't." They looked at each other in silence for a moment, and she was struck by the overwhelming feeling that she knew him, though she had never seen him before tonight. Her fear, as habitual a response as it was, was fighting with a strange, new curiosity, wondering how she recognized the way his nose crinkled when he smiled. "Do you know what Signets are for?" he asked her. She knew a little, but she couldn't make herself speak, and she shook her head mutely. "They are a badge of office to show the world who the strongest vampires are, but they choose their bearers themselves. It's magic as old as the world—there are even some vague references from biblical times. When a Signet finds its Prime, it flashes and continues to glow . . . and then when that Prime finds his Queen, it flashes again." She hadn't thought it possible to be any more stunned than she already was, but now the shock was so complete she could barely breathe. Her vision swam, and she felt herself sagging sideways. The Prime reached out for her and caught her with a light touch, reaching up with one hand to grab a pillow from the bed and ease it under her head while he lowered her the rest of the way to the floor and sat down beside her. It didn't occur to her for several seconds that she should have shrunk away from him; but as soon as she was lying down, he retreated again, still keeping his distance. Tears spilled from her eyes, and she asked tremulously, "Does this mean I have to . . . lie with you?" He looked positively aghast at the notion. "No," he said. "Absolutely not. I would never force you to do anything you didn't want to do, Cora. Someday, I hope, but not until you desire me in return. Especially not after everything you've been through." "But I have to go with you," she said. He sighed, pulling his knees to his chest and resting his chin on them. "I don't fully understand what intelligence guides these things, but I do know it's never been wrong." Cora thought of Miranda. "I don't think I can be a Queen," she said, wiping her eyes. "I'm not that strong." "You don't have to be like Queen Miranda. Not every Queen has an active role in government. And you are strong, Cora . . . I can feel it. You don't even realize how strong you are. You have the potential to be very powerful, and that's what seems to matter to the Signets—not where you begin, but who you can become." He reached into the pocket of his coat and took out a small velvet drawstring bag. She watched, entranced, as he opened it and withdrew another amulet like his, this one slightly smaller . . . and its stone was flashing, too. "I've been carrying this with me for eighty-seven years," Jacob said quietly. "And every night without fail I've prayed to God that I would find the Queen I was destined for. I was starting to lose hope . . . I've been alone so long . . . but I think we can add this to the list of 'mysterious ways.' " He held the Signet out to her. "Take it," he said. "It's yours. If you want time to think, I'll leave you alone until my state visit is over in two days." She knew that giving her time was pointless. The Signet had spoken; all illusion of choice in the matter was just that. But still . . . he had offered her time, as if it were really something she had to decide, and she couldn't help but be touched at such a sign of respect. And she believed him when he said he wouldn't force her into his bed, or into anything . . . she believed him. "I . . . I don't know if I can love you," she whispered. "That's all right, Cora. We have time. We can get to know each other at whatever pace you need. Whatever you want, if I can find a way to give it to you, I promise you I will . . . but you don't owe me anything. All I ask is that you give me a chance." Tentatively, she smiled through her tears and lifted her hand, letting her trembling fingers close around the Signet he held out to her. Electricity crackled through her. She could feel warmth spreading up through her hand, along her arm and shoulder, into her entire body—suddenly it was as if something new had taken up residence in her skin, and she could feel the low murmur of a presence in her mind. _Oh . . . oh my._ She found she didn't want to withdraw her hand, and once again they stared at each other . . . but this time they were both smiling. Fifteen "And just like that, she's a Queen? Just like you?" "No, not just like me. Cora's going to need time to heal and figure herself out before she decides what kind of Queen she wants to be. She might be the type who stays out of the spotlight and just stands by her man." "Yuck," Kat said. Miranda shrugged. "I guess it's meant to be. Cora's okay with it, which is what matters. I wouldn't have let her leave if I thought he was going to treat her badly. But if I were going to pick a man for Cora, I think Janousek is exactly the type I'd choose—he's gentle, quiet, and clearly smitten. It's the damnedest thing I've ever seen." "It still gets me that you guys just accept the idea that those things know what they're talking about. I think I'd trust a Magic 8 Ball first." Miranda wanted to say that there was no way Kat could understand—she had no frame of reference whatsoever for how it felt to be bound the way Pairs were. But she knew that there were things going on in Kat's life that Miranda couldn't understand, either, and there was no way to really convey any of it to each other. There seemed to be a slowly growing list of things that would always hold them apart now . . . and they were still essentially the same age. How much worse would it be when Kat was forty and Miranda still twenty-seven? She forced herself to put the thought out of her mind as the waitress brought their drinks: hibiscus mint tea for Kat, a Shiner for Miranda. Right now, at least, things were fine . . . sort of. Kat was still under guard, there was still a killer on the loose . . . but she wanted to enjoy the simplicity of just hanging out with someone . . . while she could. She tried to focus on Kat, to memorize all the things she loved about her best friend: her fuzzy head, her nose ring, the way she gestured when she was excited, the way her eyes lit up when she was talking about her job and the satisfaction it brought her to help people . . . how brave she was, not just for keeping the baby, but for staying friends with Miranda even after nearly dying because of her. "Earth to Mira," Kat said. "You're zoning out again. And staring at me." "Sorry," Miranda replied. "I'm . . ." She trailed off, not sure what to say, but as usual, Kat knew what was on her mind. "You're feeling overwhelmed?" "Yeah." Kat smiled tiredly. "I can relate." She stirred a packet of raw sugar into her iced tea, looking thoughtful, then asked, "Have you found out anything new about that Finnish bitch?" Miranda spun the cap from her bottle around on the table with her finger. "Maybe. David's going to the lab tonight—Novotny did some scans for him and wanted him to come see the results. David seems to think it'll be great news, but I'm not sure how." "Maybe you should try using bait," Kat mused. "You could put me out somewhere and try to get her to come out—" "Are you crazy?" Miranda interrupted. "No way." "Come on, Miranda, I'm tired of waiting around to be stabbed," Kat said angrily. "I can't keep living like this." "I'm not putting you at risk, Kat. If anything happened to you . . . no. Absolutely not." Wisely, or perhaps because she was too tired to argue, Kat let the matter drop. Meanwhile their order arrived, and Kat dug into her black bean nachos. Miranda had ordered a brownie à la mode, and she picked at it, not really tasting it. They didn't talk much while they ate—Kat was clearly starving and barely paused to take a breath until her entire platter of nachos was gone, and Miranda had a thousand things on her mind—but they'd known each other long enough that the occasional silence wasn't a huge deal. Miranda's mind wandered as she scooped up tiny spoonfuls of ice cream. Janousek and Cora had left at sunset; Cora was still bewildered by the whole thing but was going along easily enough with the sudden change in her status. She also didn't seem afraid of Jacob, who was solicitous of her well-being but gave her plenty of space. Miranda could sense that he was eager to get Cora to Prague and show her her new home. The Eastern Haven was smaller than the Southern United States Haven, and Jacob had fewer constituents, so they would have a comparatively quiet life, at least until their own Magnificent Bastard Parade got underway. Cora wasn't exactly eager to fly across the ocean with a man she barely knew, but she wasn't afraid. Considering the life she had escaped from, that was a very good sign. Miranda could sense something in Cora that had been hidden before by her weakness and fear. She wasn't sure what to call it besides _potential_ , but Miranda's worry that Cora would never recover from what had happened faded somewhat once she had felt it. Cora had said herself, when Miranda spoke to her briefly before they left, that she was ready to look for a place for herself, and she had always known that place was not Austin. In Austin she could have a good, safe home, but not the life that she knew she was meant for. God, she had said, had led her to Miranda, and now to Jacob, and she was determined to follow. At the very least, David would be able to count Janousek as an ally pretty much for the rest of his tenure. Janousek had given him what might turn out to be vital evidence, and David had, more or less, introduced Janousek to his Queen. Jacob had been all smiles when they departed, with David and Miranda's assurances that the South would be one of the first territories to pay a state visit as soon as Jacob declared the Haven open for the parade to begin. "Are you going to finish that?" Kat asked. Miranda looked down at her swiftly melting mound of ice cream and brownie. "I don't think so. Go ahead." She slid the bowl over to Kat, who grinned and picked up the spoon. "So, I know this is a weird question, but, do you still pee?" Miranda snorted, almost inhaling her beer, which caused Kat to laugh, too. "Yes," Miranda answered. "Much more if I drink other things besides the usual." "Same deal if you eat real food?" Miranda nodded. "Our digestive systems aren't really built for solids, but in small quantities it's okay. Stuff like ice cream that melts into a liquid is a lot easier." "So no more breakfast tacos," Kat said, sounding a little sad. "That would suck." "Not really. I don't want food anymore, for the most part. A lot of us have a sweet tooth, but I don't remember the biological reason for it—something to do with our body chemistry and glucose. Other things, though, I just don't really miss. The main reason any of us eat regular food is to pass as human." Kat paused with the spoon partway to her mouth and said, "You know . . . I know that a lot of people would envy you for the whole immortality thing, but I don't think I do. I'm not sure I would want to outlive . . . everything." "I haven't had much time to think about it, to be honest. Faith said that the reality of it doesn't really hit home until you've outlived a typical human life span." "Speaking of life spans, doesn't it bother you that he's got three-hundred-something years on you and you don't know all that much about him—who he loved, where he lived, how he spent all of those years?" "Sometimes. But really, do you know that much about Drew? You've only been together about as long as David and I have. You probably don't know every detail of his past yet—imagine if he had ten times more stories to tell." Kat thought about it, then nodded. "Fair point." It was rare for Kat to show any interest in the details of life as a vampire. Miranda didn't volunteer anything she didn't ask about; she knew that Kat was trying hard not to think of Miranda as some kind of monster who drank blood, and Miranda was grateful for that. As much as she'd objected to David's neglecting to tell Kat everything that was going on, the Queen was finally starting to agree that Kat already had enough to deal with, and there were some things she just didn't need to know. A lot of things. A few bites later Kat set down the spoon, suddenly looking a little green around the gills. "Ugh." "You okay?" Miranda asked. "Do you need something fizzy?" "No, I just . . . excuse me." Kat darted away from the table, headed for the restrooms, and Miranda kept an eye on her until she'd rounded the corner, then nodded to Lali, who was stationed at a booth nearby, to watch the door and make sure no one approached Kat while she was down the hall alone. Miranda caught the waitress's eye and asked for the check; she had a feeling that Kat wouldn't be up for much else after dinner. Sure enough, when Kat returned she looked pasty and nauseated. "Sorry," Kat said. "I don't know where that came from. I've been doing a lot better this week, but apparently the baby doesn't like nachos." "Would you like me to take you home?" Miranda asked. Kat looked torn. They'd both been excited about the new local band they were going to see, but clearly Kat wasn't feeling up to standing for two hours in a crowded bar surrounded by drunk people. "It's okay," Miranda told her. "Really, Kat—Nice Marmot will have another gig. Maybe we can find somewhere to see them that has actual chairs." Finally, Kat nodded. Her eyes were bright with tears. "If you're sure you don't mind . . . I think I need to lie down." "Come on, then, Harlan will get us there." Miranda kept a steadying hand on Kat's shoulder as they left the café; Lali, who had been able to hear their conversation, was already out front, and the car pulled around as soon as they'd gotten to the curb. "I don't think I'd like the vamp thing, but the service sure rocks," Kat said. Miranda grinned and waited until Kat was in the car to go around and get in herself. "Rank hath its privileges." Sitting beside Kat as the car eased out onto South Lamar, Miranda watched her friend lean back with her eyes closed, her hands resting protectively on her belly, something Kat had taken to doing in the last couple of weeks that Miranda doubted she was even aware of. "Let me know if we need to pull over." Kat opened one eye. "Don't worry, I'm not going to puke in your Lincoln." "I'm worried about you, not the car." She shook her head. "I think I'm okay, I just . . . I have this sick feeling, like I'm scared to death of something, but I don't know why." Miranda frowned. "It's coming from your belly?" "Yeah. It's like somebody spooked the little critter." Before Kat even had the sentence out, dread seized Miranda's heart. She said into her com, "Elite One Nineteen." _"Yes, my Lady?"_ "I'd like a security status update from your position." _"Everything's quiet, my Lady. No one's gone near the house since you left."_ "Thank you. Star-two, out." Kat was looking at her, eyes narrowed with concern. "What's wrong?" "Do me a favor and call Drew, would you?" "Why?" Miranda couldn't explain it, except that if Kat's baby was giving her bad vibes, something was giving Miranda a full-blown anxiety attack that she was hiding by sheer force of will. Her heart had begun to pound, and she felt adrenaline beginning to surge through her veins. _Shit. Something's wrong. Something's wrong._ "Please, Kat, just call him." Kat shrugged and took out her phone. "It's ringing." "Where's he at tonight?" "The school," Kat said, still listening to the phone ring. "Weird . . . he always picks up by the third ring." Miranda called to Harlan, "Take us to 228 East Chicon, as fast as you can." Then she said into her com, "All available patrol teams to 228 East Chicon." "Miranda, what the hell is going on?" Kat demanded. "So he didn't answer, so what? He might not have his phone on him." "Okay, Kat," Miranda told her, keeping her voice very calm despite the alarms going off in her head and her heart, "I'm going to go first and make sure everything's okay. You stay in the car until I come get you." "Um . . . okay . . . but—" Miranda didn't wait for her to ask. "Harlan, pull over." As the car rolled to a stop, the Queen shut her eyes and concentrated, forming the image of the school where Drew worked as firmly in her mind as she could. She'd never done this on her own before, but there was no time to lose . . . she knew it was in her power, if she could just . . . She pulled hard on the image, doing as David had shown her and relaxing her hold on her body in a certain way that made everything feel blurry and strange. She heard Kat gasp . . . . . . and next thing she knew she was tumbling onto the sidewalk outside the school, forcing herself not to be sick as she scrambled to her feet and drew her sword. David and Faith both sat in front of the screen while Novotny pulled up the scanned images of the scrap of paper Janousek had left. "I apologize for the delay in getting this finished," the doctor said. "We had a hell of a time with it. The paper's so damaged by age and improper preservation it's a miracle there was any ink left at all." David nodded. "I understand. I wasn't even sure you'd be able to do it." Novotny chuckled. "Of course we could. It just required some creativity on our part. But that's why you pay us so well, Sire." "True." "Now, then." He tapped his touch pad and the image of the paper appeared, exactly as it had been when David brought it in, but laid over a grid of red light. "Here you see both sides in their original state. Upon first glance there are three things visible: the number 4.19, part of a word, and on the other side, a symbol of some kind. We broke the image down into individual pixels, as you see here, and then had the computer match areas of equal pigmentation, rendering each in its own shade." The first side of the paper, with the number on it, was magnified as Novotny spoke, demonstrating what he was talking about. "We concentrated on the darkest areas and ran them through several filters to sharpen the image." Rows of pixels changed color, moving from the top of the image to the bottom, and the writing became clearer. It was handwritten, and the number 4.19 was much clearer; beneath it, David could just barely make out a word. "Scarlet," he said. "Yes. We ran the number 4.19 through our database trying to match it to known organizations, codes, and significant dates, but got nothing. I would assume that _scarlet_ refers to the Red Shadow." "What about the other side?" "That was a lot harder, but we did the same to it, and came up with this." Novotny spun the image around and flipped it, showing what amounted to half of a symbol on the screen. David sat forward, his mouth falling open. Beside him, Faith asked, "Is that what I think it is?" "Show me the other side again," David commanded. Novotny shrugged and complied. "Oh, God." Faith stared at the Prime. "What?" David put his hand over his mouth, his heart frozen in his chest. It was a moment before he could speak. "I know that handwriting." Just then, his phone tolled out a network alarm, as both his and Faith's coms burst to life and her phone began to ring. Miranda let her instincts guide her around the side of the building to an unlit entrance that had obviously been jimmied open. Her mind still swimming from the Mist, she slid in the door, all her senses going into predator mode. Her vision morphed into blues and purples in the darkness, showing her details no mortal could see from tiny cracks in the plaster to the footprints of mice on the tile. It was ten o'clock at night, and the building should have been empty. It was a small charter school that specialized in fine arts and languages, and Drew taught music both during the day and for free in the evenings to underprivileged kids. There were only three classrooms and a few offices. She'd been there twice before when she was still human. She listened intently, extending her energy along the hallway to look for life signs. She might be wrong . . . Drew might already have left . . . She heard a scream. Miranda broke into a run, following the tortured sound to the last classroom branching off the hallway. There was faint light coming from the door; she remembered that the classrooms had windows along one wall. She burst into the room snarling. Desks had been shoved in all directions; in the center of the chaos a figure crouched over another, and the smell of blood hit Miranda's nostrils with the force of a gale wind. The figure turned and rose, and Miranda heard the sound of a sword being drawn. "You," Miranda hissed. The assassin smiled nastily but didn't speak. It was, without doubt, the same woman who had shot Miranda—even without her wig or the librarian glasses, Miranda knew her face. Behind the woman, a phone began to ring—Miranda's eyes darted to the cell phone on the floor, then to Drew's outstretched hand, and the blood flowing from the wrist that the woman had only partially managed to slice before being interrupted. From the amount of blood he had to have other wounds, and Miranda could tell he'd been beaten—he had tried to put up a fight, but against a vampire with a sword, there was no chance. She saw Drew's agonized face, felt him about to scream again. Miranda spared a thread of power to take hold of Drew's mind and calm him, to let him know it would be all right, that help was coming—but she didn't have time to speak before the assassin took advantage of her distraction and dove in for the attack. The Queen threw herself into the fight, dodging the woman's sword by a scant half inch and spinning around to counter the stroke. Miranda knew from the beginning that she was outmatched, but she didn't care. All she had to do was keep the woman here until the others arrived, and the building would be surrounded with Elite. David would be there any moment, too, and although Miranda might not be able to take the woman down, he sure as hell could. They fought from one end of the classroom to the other, the assassin shoving desks at her, Miranda jumping over them and meeting her sword slash for slash. She could feel Drew weakening. She urged him to take his jacket off and press the fabric against his wrist—he was too far in shock to think of it on his own, but under her influence he did as she commanded, holding the jacket with a shaking hand. Miranda could hear someone speaking . . . the phone? Yes, it was Kat's voice—Drew must have answered it. The woman made for the door, and Miranda flung herself toward it, reaching out with her mind to try to grab the nearest desk and pull it in the way; she saw it scoot a few inches, but that was all the concentration she could manage in the middle of a fight, and she ran for the doorway on the woman's heels. The shadows inside the door frame seemed to shift and coalesce. The Prime walked into the room, sword already drawn, and the woman changed course at the last second to avoid slamming into him; she skidded on the concrete floor and nearly lost her footing but got control back in time to parry the Prime's attack and double back toward Miranda. For a few seconds the woman was caught between Prime and Queen, but Faith's voice erupted from the coms: _"Incoming!"_ David grabbed Miranda's arm and hauled her to the floor. They both dropped flat just in time with the sounds of shattering glass from the wall of windows, the click and whistle of a half-dozen crossbows, and the singing of wood through the air. Miranda craned her neck to see two of the stakes hit the woman—one in her shoulder, one in her chest to the left of her heart. She flew backward, her sword clattering to the ground, the light catching off something shiny at her neck that also fell as she stumbled. Miranda was sure she would fall, but by some twisted miracle, the woman stayed on her feet, blood streaming down her torso. She looked over and met Miranda's eyes. "Give my regards to the Alpha," she hissed. Then she ran forward, throwing herself into the glass wall and tackling one of the Elite who had fired at her. The two hit the ground hard, but the woman used the Elite's body as a springboard and sprinted past the others, who were immediately after her. _"Tracking!"_ Faith said. _"We've got her on the network, Sire! Four units in pursuit."_ Miranda pushed herself up to her hands and knees and got across the floor to Drew. She was about to com out for an ambulance, but she could already hear sirens in the distance; Faith, or David, must have called already. "Drew," Miranda said. "Drew, can you hear me?" She knelt next to him, tears already coming to her eyes. There was so much blood. Miranda quickly cataloged the visible injuries: hand severed, stab wounds in his stomach and shoulder . . . there was at least one penetrating wound to his lower back, maybe his kidney, but she didn't want to risk turning him over. David joined her. His face had that blank expressionless look that Miranda recognized, and her heart sank. "Keep pressure on the wound," he said quietly. Their eyes met over Drew's battered body. Miranda knew what he was thinking. There was too much blood, and they had no healer. He'd been lying there bleeding for nearly ten minutes and it would take an ambulance another two to reach them. "Miranda . . ." Drew whispered raggedly. "Give . . . give me the phone . . . please." Miranda grabbed the cell and said into it, "Kat? Kat, honey, are you still there?" Kat practically screamed, _"What's happening? Miranda, where is he?"_ "Here." Miranda choked on a sob, lowering the phone to Drew's face. "Hey, baby," he said, coughing. His breath came in shallow gasps. Miranda could hear Kat talking to him, could hear her crying. "It's okay," Drew said. "Kat . . . just listen to me." Miranda could hear the paramedics coming down the hall. "I love you," Drew told Kat. "Very much. The baby, too. I think . . . you're going to make a great mom. I love you." Softly, Miranda heard Kat say the same to him. "Thanks," Drew managed weakly, looking up at Miranda. "Take care of her, okay?" Miranda nodded. "I promise." "Good . . . that's good . . ." His fingers barely returned the pressure of Miranda's, then slowly relaxed . . . . . . and it was over. The paramedics and two additional units of Elite entered the classroom to find the Queen weeping into the Prime's arms, as both knelt in a broad pool of blood, and a woman sobbed quietly over the phone that lay on the floor. Miranda stared dumbly at the printout David had given her, trying to understand what she was seeing. Her wornout, bewildered mind simply refused to accept it. "What do we do?" she asked. "I don't know," the Prime replied. He looked as exhausted and heartsick as she felt. "I honestly don't know." Outside the car windows' heavy tint, the countryside scrolled by. Miranda wanted nothing more than to fall asleep and not wake up until the world made sense again. She was completely drained, both from the fight with the assassin and from her first real Mist—it was remarkable she hadn't ended up scattered across Austin. Between that and the weight of sorrow and guilt from Drew's death, she was perilously close to losing it. It was only an hour before sunrise, and Harlan was breaking several traffic laws to get them home before it began to get light out. Dealing with the police had taken a lot longer than Miranda expected—the first responders had not been the people the Haven normally dealt with, and they wanted to take a lot of pictures and ask a lot of questions that were unnecessary and tedious. Finally David had simply called the chief of police and cut through all the red tape. Kat had been taken to the Hausmann for observation in case the trauma had affected the baby, but so far all she'd done was sit and stare off into space, barely rousing enough to answer when the paramedics asked her for details that she hadn't been able to give. She had, as Miranda had asked, stayed in the car until the Queen came to her and led her over to the gurney to provide a positive ID on Drew's body. She had nodded at the police and then gone essentially unresponsive. Miranda had directed the Elite to make sure Kat was brought to the Haven as soon as the doctors deemed her fit, probably the next evening. Finally, the Pair had headed home. They had changed into the spare set of clothes that they kept in the trunk, so at least Miranda didn't have to spend the whole drive back to the Haven soaked in Drew's blood, but she could still smell it, though she'd washed her hands and face and everything she could in the school's restroom. "This is how it goes, isn't it?" Miranda said softly, staring out the car window. "One by one we lose everyone we knew." David looked at her, and she could tell he wanted to be reassuring but couldn't lie to her. "That's what we are, beloved. We stand outside time and watch it slowly consume everything. My son died, his children died, their children died . . . the line continues, spread throughout the gene pool, but everything that made me human has long since faded." She half smiled. "You're still more human than most of the men I've ever known." "Thank you." "I don't know if I can do this," she said. "You can. You are Queen, Miranda. The strength you need is part of who you are." "Sophie told me once that this life was a gift, and that I had to think long and hard about whether I was worthy, because there was no giving it back." She looked down at the sword that lay across her lap, and the one lying on the floorboard wrapped in fabric—the assassin's blade. "I wasn't fast enough to kill her," Miranda lamented. "I wish I could have. I wish I had seen her bleed to death instead of Drew." "So do I." "What did Faith say?" David sighed. "They lost her trail. She dropped off the network again about two miles into the pursuit, then detoured and disappeared into the city. After that it was so close to dawn I had to call them back. By dusk whatever trail is left will be cold." "But she showed up on the sensors for a few minutes . . . why?" "I think this has something to do with it." He held up the thing that had fallen from the woman's neck: a silver disk on a chain with some kind of script carved into it. "Whatever it is, I think it disrupts the network signal. After she dropped it, we could track her, but somehow she got her hands on another one, or had a spare she activated. I sent images of it to Novotny, and I'm going to run the symbols through my database before I hand it over to him." "Why bother?" she asked. "We already know who's behind it, David." He met her eyes. "We might be wrong." The car slowed, then stopped, and a moment later the door opened. Lali stood by while they disembarked, then shut the doors and went ahead of them into the Haven with Aaron to clock off duty for the night. "I thought you said you were sure," Miranda said, falling into step beside David as they walked down the hall to their suite. David's face and voice both were bleak. "I'm sure. God help us, but I'm sure. The symbol, the handwriting . . . I've seen both a thousand times." As David nodded to their door guards and opened the door into their suite, Miranda looked down at the page still in her hand, an image of the back side of Janousek's scrap of paper, which had been digitally restored by Novotny's people. She had never seen the symbol before, but she had heard of it: A waning crescent moon and the Greek symbol of infinity. David froze midstride and made a feline hissing noise. "Son of a bitch." Miranda nearly ran into him but stopped in time to look over his shoulder into their suite. There, sitting calmly in one of the chairs by the fire, sipping a glass of whiskey, was the Alpha. "Hello, darling," Deven said. Sixteen Miranda stayed behind David as he edged slowly into the room, his eyes riveted on Deven, his hand on the hilt of his sword. "I see by your faces you've found me out," Deven said calmly over the rim of his glass. "May I ask how?" Wordlessly Miranda held up the scan. Deven made an exasperated noise. "Goddamn Horak. If I'd known that woman was going to cause all of this, I never would have taken his recommendation." He gestured at the other chairs. "Care to sit?" "You bastard," Miranda said. "How dare you come into our house—" Deven rolled his eyes. "Yes, yes, I know. How dare I, murdering monster I am, traitor, et cetera, et cetera. Now, both of you sit down." Neither of the Pair budged. "I should kill you right here and now," David told him. Deven sighed, looking down into his glass, and when he looked up there was something dark and menacing in his eyes that Miranda had never seen before. "Try," he replied. "But then you'll never have the answers you want, will you?" "He came alone," Miranda observed. "No Elite, no Jonathan." "Jonathan isn't a part of this," Deven said. "Well, he is, because I am, but I didn't want him involved. So if you kill me, you'll be killing him, too, and he's as close to innocent as any of us are. I doubt you want that on your conscience. So, sit." "I don't want to hear anything you have to say," David told him coldly. "Our alliance is terminated—consider yourself at—" "Don't say it," Deven interrupted, eyes flashing. "Don't even think it. You don't want to declare war on me, David. You couldn't win. Don't give me that look, either; you have your technological toys and your psychic parlor tricks, but I have my own ace up my sleeve . . . dozens of aces, all over the world, ready to kill at my command—anyone, anywhere, any time." "It was you all along," David said, and Miranda could feel the sickness in his heart. "You were the Alpha. You set the assassin on Miranda." Deven's eyes were unyielding, like steel. "I am the Alpha. I have always been the Alpha. Each and every Shadow was trained by my own hand. I recruited them from every Elite, every mercenary guild, every class of warriors in six hundred years of history. And I would have done the same with you, darling, except I learned a long time ago not to sleep with my agents." "What about Sophie?" Miranda asked, stepping forward. "Was she really one of yours?" His eyes flicked toward her. "Sophia Castellano worked for me for almost one hundred years. She was one of my most talented agents, one of only four to earn the rank of Scarlet." "Then why did she teach me if all you wanted was to kill me?" the Queen demanded. "Why would I want to kill you, Miranda? What purpose would that serve?" "Then what do you want?" Deven took a long, slow breath, and said, "Marja Ovaska." "Who?" David asked. "Marja Ovaska is the woman who is after Miranda. She, and she alone, wants you dead, my Lady. I didn't set her on you. She has been out of the Shadow for two years." "But no one leaves the Shadow," David said. "You said so yourself." "No one ever had. I've trained hundreds of agents, and in all that time there has only been one way out—the sword. They die on mission or they die by my blade, but they never leave. It's a lifetime contract. Or it always was." He set his glass down and crossed his arms, looking toward the fireplace; David and Miranda both kept their eyes on him, though he didn't seem at all concerned about it. And why should he be? He had gotten into the Haven, into their suite, completely undetected by the Elite, the servants, and the surveillance network. "I have in the Shadow's entire history released exactly two agents alive," Deven said, his voice tempered with something Miranda realized was regret. "One was Marja Ovaska. The other was her lover . . . Sophia Castellano." "So Sophie wasn't working for you?" "Yes, she was." "But you said—" "Let him talk," David said quietly. "Agents of the Shadow do not mingle," Deven went on. "They never see each other's faces. If they speak, it's over the phone. They all have code names. But once in a while a client needs more than one agent to get the job done. Agents 3.17 Scarlet and 4.19 Scarlet—Sophie and Marja—met on assignment, by accident, and as often happens in such tragedies they fell in love, in direct defiance of protocol and knowing that I would kill them both when I found out. I had them brought to me for execution." Miranda knew what he was going to say next; she could feel it. "You couldn't do it." "No, damn it. I should have. But for once in my life I allowed their sad little story to get to me. I had let myself grow attached to Sophie, fool that I am, and so I gave them a choice. They could die right then at my feet or they could each fulfill one last mission and then disappear. If I ever heard from either of them again, in any context, both of their lives were forfeit. They were to go underground and stay gone forever." "And you believed they would?" Miranda asked. "Of course I did. My agents are trained to go into certain death without hesitation. There's only one thing they are taught to fear: me." "But Sophie didn't," David concluded. "She broke her end of the deal by telling Faith she was ex-Shadow." Again, Deven rolled his eyes. "Please. Sophie was no fool. And she was no drunk. She was stone cold sober when she met Faith." "Then why . . ." "Why do you think?" Deven snapped. "Put it together, Prime. My Consort has the strongest precognitive gift in the Council. He knew you were going to take the South. Don't you think he knew you would eventually find a Queen?" "I don't understand," David said. But Miranda did. "You assigned her to me," she said softly. "Sophie's last work for you was to train me. War was coming . . . Jonathan saw it. And he knew that I had to be ready. If it weren't for Sophie—for you—I wouldn't be here." Deven met her eyes, and his gaze finally seemed to lose some of its hardness. "Her job was to make sure you were strong enough and had the skills you needed to help put you in the right place at the right time to become Queen. As soon as that happened she could vanish." "But she died in the battle . . ." "She should never have been there. She was under orders not to go anywhere near the Haven itself, but to train you, then show you the way home and get the hell out." The Prime held her eyes. "She believed in you enough to go off mission . . . and then she died before she and Marja could be free." "What was Marja's last mission?" Miranda asked, holding back tears. "Irrelevant. But if Sophie had done as I told her and left you to fight your own way into the Haven that night, Ovaska would never have been heard from again." Finally, Miranda sat down, head in her hands. "Sophie died . . . and now Marja wants me dead . . . to avenge her lover." David asked, "How long have you known?" Miranda looked up to see Deven shrug. "Not as long as I should have. I suspected Marja might be involved as soon as you mentioned a connection to Finland, but I wasn't sure until I hauled in Volundr, interrogated him myself, and then sent him to you." "You let me torture Volundr even though you knew who we were looking for?" Deven made an impatient noise. "I didn't think you'd have to torture the old toad. I paid him a ridiculous sum to tell you the truth—both Ovaska's identity and what he knew about her location—but apparently his loyalties have shifted. Your people took him back to California and he vanished—along with an entire order of blades I had already paid for, incidentally. You've cost me a fuckton of money." Miranda was shaking her head, not sure whether to laugh at the absurdity of it all or scream herself sick. "All those people . . . Jake, Denise, Drew . . . they all died . . . Kat almost died . . . because I got Sophie killed." "You did nothing of the kind," Deven contradicted her, though his tone wasn't attempting anything like comfort. "Sophie died in battle the way warriors have throughout history, and by her own choice. Ovaska wants someone to blame. She knows she can't kill me, but you are still vulnerable because you're young and rash and have human friends who are easily killed. She sized up your defenses in that first attack and planned out how to destroy you piece by piece. My agents are dangerous sociopaths who will do anything, kill anyone, torture or maim anybody if it means reaching the objective. Even Sophie was willing to paint a giant target on her head by telling Faith who she had worked for—she knew it was the only way Faith would believe that she had the skills necessary for your training." "Oh, God," Miranda said, her memory suddenly intruding. She looked up at David helplessly. "The night of the battle, when we were watching you fight, she said she'd only ever seen one other vampire with your combat style. She was talking about Deven." "That's right," Deven said. "The one who trained both David and Sophie." David sat down beside Miranda, seeking her hand, but spoke to Deven. "What I don't understand here is _why_ , Deven. Why would you intervene in Miranda's future? Why give Sophie that assignment?" Deven sighed. "Miranda, if you wouldn't mind?" Miranda wiped her eyes and said, "Because he loves you, David. And the only way to pay you back for how badly he treated you years ago was to make sure you found your own Consort . . . to make sure you were happy." "You were never supposed to have any idea I was involved. I had hoped to hunt down Marja and have her eliminated before anything else happened," Deven said, and for a wonder he sounded sincere. "I am sorry for the loss of your friends." "How exactly were you going to track her down from California?" David demanded coldly. "You don't have that kind of technology." Deven smiled. "What do you think we did before computers? Good old-fashioned detective work. I happen to have many highly trained detectives at my disposal." "You have an agent here in Austin?" The smile turned wicked. "I have an agent in your house." David blinked. "Bullshit." Deven removed his cell phone from his coat pocket, giving Miranda a glimpse of the array of weaponry he wore. He touched the phone's screen several times, saying, "Before you ask—Hart's troubles have nothing to do with me. My people don't use earpieces; like I said, they're impractical. I would like to know who's harassing him, though. It tickles me." A moment later there was a knock at the door. "Come in," David called without his eyes leaving Deven's face. Miranda could feel the tumble of anger, shock, and pain from her Prime, making her own confusion that much worse. She wanted to put her arms around him, but she was frozen in place, waiting for the other shoe to drop. And drop it did. Deven spoke again. "Allow me to introduce 5.23 Claret," he said. The door opened. "Oh my God," Miranda said. "Lali?" The bodyguard bowed to the Pair, then again to Deven. "Don't be angry at her," Deven said, gesturing for Lali to come stand beside his chair. "Everything about her, as your bodyguard, is true. She would die to defend you. She is in fact very fond of you. You seem to inspire that kind of devotion, my Lady." "You've been working for me for ten years," David said to the Elite, completely thunderstruck by the revelation. Lalita nodded. "Yes, Sire. But I have been working for the Alpha for two hundred. My loyalty to you is superseded only by my loyalty to him." "There's no way you could have known," Deven told David. "Her history, her qualifications, all of it was authentic . . . just incomplete." "How in hell do you communicate?" Lali smiled. "Mostly via encoded pictures of cute animals." "Now, then," Deven said, "enough chatter. Let's get to why I'm here." "Not to tell us the truth?" David asked. "Of course not. If I had been successful in taking out Ovaska myself, I would never have let on I was involved. In six centuries exactly three people besides the agents themselves have known who I was—Jonathan, and now you two." "I could expose you," David said in a low voice, the anger making its way out past his defenses. Deven sat forward, hands clasped, and glared into David's eyes. "Again . . . try it." Miranda looked from one Prime to the other, took a deep breath, and asked, "How is Ovaska getting past our sensor network?" Deven didn't avert his eyes from David's until David lowered his. "Magic," he replied. "Volundr made something for her. He wouldn't tell me how it worked, but he said he'd given her a set of seven amulets that would shield her from any form of detection except plain sight. The spell had a limited life span; each disc would last only a few days once activated." David and Miranda exchanged a look. "She's used up most of them already," Miranda said, "unless she has another supplier." "That is ridiculous," David responded. "Amulets, spells—there's no such thing." Deven chuckled. "Darling, sometimes I think it's a good thing you're so pretty." David looked like he was about to leap up and throttle Deven, but he didn't. "Tell us what you came to tell us, then, and get the hell out of my house." Deven sat back, retrieving his whiskey. "You're angry." "Damn right I am! I've known you almost a hundred years, and you never told me you were running the most notorious network of assassins in the world. You had a spy in my Haven all this time, and you've had your dirty little hands in every aspect of our lives. For all I know everything you're telling me now is a lie. You even broke into this house and got past my guards—" "I Misted," Deven said simply. "This isn't exactly Hogwarts, you know. You might want to adjust your sensors in some way to account for the abilities of a Prime, although I doubt you have to worry about anyone else sneaking in here solo." Then he rose, taking out his phone. "As to why I'm here . . . I brought you this." He held up the phone so the Pair could see the screen: a map with a single red dot in its center. "This is where you'll find Marja Ovaska," Deven told them. "Thanks to Volundr's information and Lalita's excellent investigative work, I finally managed to pin down her location yesterday. I didn't want to trust this information to e-mail, so as soon as I could, I flew in. I want to be there when you find her. At sunset I'll take you there, and assuming she isn't on to us, you can kill her yourself." "Why should we trust you?" David wanted to know. "Trust me, don't trust me, whatever suits you. But if you don't act on this information, more people will die, up to and including both of you. Help me to help you, David. I made this mess. Help me clean it up." "You're giving yourself too much credit," Miranda muttered. "Marja made her own choices." "So did Sophie," Deven replied, "but you still feel guilty for her death." Miranda nodded slowly, then said to David, "He's telling the truth." David looked at her. "You're sure." "I can feel it, David. Besides . . . he came here alone, and it's dawn. He knew he couldn't escape—there's nowhere to go until sunset. He put himself into our hands willingly." Deven asked politely, "Would it make you feel better to cuff me and throw me in a cell?" "I'd like to throw you out into the sunlight," David snapped. "But I trust Miranda's instincts. If she says you're telling the truth, I believe her." Miranda listened silently, feeling numb from the mind outward, as David called in their door guards to escort Deven and Lali to a nearby guest suite and station as many warriors as they could spare at the entrance. "Your weapons," David said flatly. Deven looked at him for a long minute, then reached into his coat and began removing blades, handing them to the Elite who had come in to essentially arrest him. First his sword, then another shorter one, four knives of various lengths, two hilted throwing stakes, and a talon-shaped blade he wore in a slit near his heart that Miranda recognized—Sophie had had one just like it. Lalita had only her Elite sword, a stake on her belt, and a single standard-issue folding knife. David let her keep her com for the time being, but Miranda knew he would put a network lock on it so her access would be limited. "Is that all?" David asked. Deven, completely unfazed at being disarmed, said, "Care to frisk me?" Miranda knew better, and she assumed so did David, than to think that they had all of Deven's weapons, but David didn't push; in reality if Deven wanted to get out of the room he didn't need a sword. Even without Misting, he was still stronger and faster than any of them; he had spent the last seven centuries making himself into a weapon. Surrendering his toys to David was purely symbolic. One of the Elite started to step toward Deven, but Deven fixed him with a look, and the guard fell back. Deven nodded to the guard to lead the way. "Look to your Queen," Deven said to David as they left. "Get her some caffeine and blood before she passes out." David pulled his eyes from the Prime to Miranda, who started to protest that she was fine, but she found she was simply too tired to speak. She shook her head silently, not sure what she was denying, exactly; but between one breath and the next David was pressing a bottle of Coke into her hand and calling Esther to bring her blood. It seemed like days ago she'd fed last . . . had it really been only a few hours since she and Kat had been at Kerbey Lane? Everything had changed so fast. Almost as soon as Deven and Lali were led away, Faith came in, looking utterly confounded by the whole situation. "What in the world is going on, Sire?" she asked. "I got an e-mail from Lali resigning her post, and now Deven's here in some kind of custody?" David had his head in his hands, Deven's sword lying across his lap. "Sit down, Second," he said hollowly. "I have one hell of a briefing for you." Just before sunset, the Prime and Queen dressed silently, each strapping on as many weapons as they could comfortably wear. Miranda pulled her hair back from her face in a tight ponytail and wore the same kind of clothing she had the night she and Sophie had joined in the battle at the Haven. Miranda paused with her hands on her sword . . . Sophie's sword. It was the only blade she'd ever felt comfortable wearing, and it had been on her hip every time she went into the city since that first battle. She had used it to take the heads of the last few Blackthorn and had fought the assassin—Marja—with it. Miranda stared down at the shining steel, thinking back, wondering if there had been a moment when she might have detected an ulterior motive in Sophie's actions . . . but Sophie's act, however much of it had been an act, had been flawless. David put his hand on hers. "She chose to fight with you when she could have run back to her lover and disappeared. In the end she cared enough about you to put her own life on the line. That means something, beloved." Miranda looked him in the eyes. "So does what Deven did," she told him. "I know you're angry, but if you let this end your friendship you'll regret it forever." David turned away, buckling his belt. "I'll think about that after we deal with Ovaska." Miranda went to the mantel and lifted Deven's sword down from where David had left all of the Prime's confiscated weapons. She held it up to the firelight—Jonathan had been right, she could see the insignia of the Order of Eleusis, the same symbol that was on the note Deven had given Prime Horak, worked into the ornate carving that covered the blade. It was a beautiful sword, about the same size and weight as Sophie's, but a little shorter and built for a smaller hand. There was, she noticed, some kind of writing on the other side near the hilt, but she was fairly certain it was in Gaelic. "Do you know what this means?" she asked. David glanced at the script. "Probably its name. Deven names all of his swords." "You don't read Gaelic?" "No. I speak it, but I don't read it." She offered it to him. "We need to give them their weapons back. We don't know what we're walking into tonight." He pondered the blade, saying almost to himself, "I've never seen this one before . . . it must be new. His last one's name was Ghostlight." He turned back to Miranda and said, "We should make them both stay here. For all we know, this is all a plan he set up in collusion with Ovaska." Miranda smiled slightly. "You do remember my saying that he was telling us the truth, right?" "Someone as old as Deven could fool even your gift, Miranda." "Not likely, baby. You're the one who told me that empathy is rare enough that it's hard to protect against and even harder to outwit. Besides, like I said when you first figured out those stakes came from the West, Deven has no motive to kill us. Even if you take his feelings for you out of the equation, you're his strongest ally in the Council, and without you the entire balance of power falls apart. I knew in my gut there was a reason that him being the Alpha didn't make sense to me—turns out it wasn't because he was the Alpha, but because the Alpha is not our enemy." "I don't suppose your gut has anything to say about what we're doing tonight." Miranda drew her awareness into her own mind for a moment to see if her fledgling precognitive gift was offering up any warnings, but mostly she just felt a vague sense of unease, probably the same thing she'd feel any time she was walking into a completely unknown situation to confront someone who wanted her dead. "No." "We could send the Elite by themselves to check it out first," David reasoned. "Do you really want to risk her getting away again? She was trained by a Prime—and not just any Prime. She could take down any of our Elite, even Faith. We don't know how long that amulet of hers is going to keep working, so we might not be able to track her if she escapes. I think we should stick to the plan." David nodded; she knew he agreed with her, he was just reluctant, and understandably so, to risk more lives in the pursuit of Marja Ovaska just on Deven's word. Miranda wanted to be angry with Deven, too, but for some reason she couldn't. She understood that David was having a hard time separating the truth from his perception of his former . . . sometimes . . . lover, but perhaps because she didn't claim to know Deven that well, or like him all that much, she was able to step back and see that as old as Deven was, it was naïve to think he _didn't_ have secrets. Up until now there had been no reason for Deven's two worlds to collide, and she knew that he hadn't decided to reveal himself to them lightly. He didn't strike her as the kind of person who would overshare when there might be lives at stake. She got the feeling that, cold as he might act, he took responsibility for his agents' lives and counted their deaths against his own soul. That didn't mean she didn't have the urge to slap the smug right off his face, but she might give him a pass if his information did bring an end to all of this. "Ready?" David asked. Miranda took a deep breath. "I think so." "Are you sure you're up to this? I know last night wore you out—" "I slept like the dead," she assured him gently, kissing his cheek. "And we'll feed when we get to town. I'll be fine." He slid his arms around her, and they held on to each other for a while, her head resting on his shoulder precisely where it was meant to. "I just want this over with," he said. Miranda sighed . . . a knot of knowledge was forming in her stomach, and she didn't want it, but she voiced it anyway. "It will be. One way or another this will be resolved by the time you and I come home." David shut the weapons cabinet, and hand in hand they left the suite. Faith fell into step behind them as they took the hallway out of their wing. The Second didn't say anything—she, too, was troubled, though whether by the thought of going after Ovaska or the realization that Deven had a secret identity, Miranda couldn't say. Four guards stood in a semicircle around the room where Deven and Lali were; it was the same room that Ariana Blackthorn had stayed in, but now it had a range of new security measures built into it, including a separate sensor system and audio surveillance. It was designed to house people who didn't know they were being watched. So far nothing out of the ordinary had happened; Lali had apparently slept most of the day, and Deven had called Jonathan on his cell phone, but that was it. David had recorded the conversation and said that Deven had let Jonathan know what they planned to do, reassured the Consort he was safe, and that was about it. David nodded to the guards, and they moved aside, one of them unlocking the door and swinging it open. Deven stepped out with Lali at his back. "Good evening, Lord Prime, my Lady," he said with measured deference. "Shall we?" David looked at Miranda, who inclined her head toward Deven encouragingly. David held out Deven's sword with both hands. Deven met his eyes, then took it. As he buckled it on, David motioned for Faith and Aaron to bring forward the rest of Deven and Lali's weapons. "Let's go," David said, and led the way out to where Harlan was waiting to take them into the city. Warmth and pleasure sang through Miranda's veins as she climbed back into the car with David sliding in beside her. She licked her lips reflexively, seeking any lingering trace of blood, and spared her husband a smile. His eyes were a ring of silver around dark pupil, still dilated from the hunt, and he leaned over and kissed her lightly. Miranda resisted the urge to stick her tongue in David's mouth just to spite Deven . . . barely. Now wasn't the time to indulge in her passive-aggressive impulses, and truthfully she didn't want to make the tension between him and David any worse . . . but the idea was still appealing. Instead she took David's hand and squeezed it reassuringly. Once they were moving again, Deven leaned forward so they could all see the screen of his phone. "Right here," he said. "It's an apartment in a small complex off Manor Road. The place looks appropriately seedy. It should be fairly easy to surround. I'd recommend a detail on the roof as well." "Already on their way," David told him, switching to all-business mode. "I've got Faith in the van with two units set to rendezvous with us when we reach the block, and a third coming in armed for roof duty." "Good. The layout is typical of cheap second-floor apartments. Stairs up to a concrete landing. One door with an adjacent window, two windows on the side, no other exits. Lalita's recon showed that half the building is empty, and this unit here on the first floor is a crack house. We probably don't have to worry about human interference." David pulled up the sensor grid on his own phone. "There are no other vampires in the building and no signals of any kind coming in or out except for satellite television in the crack house. I'm still not picking her up, if she's there." "She may not be," Deven admitted. "I know that's her home base, but there's no way to confirm she's actually there without a direct sighting. At the very least we should find some fun souvenirs." "Are you sure she doesn't have anything else from Volundr?" Miranda asked. "Other magical weapons like the amulets?" "Not to my knowledge. Volundr was pretty forthcoming about the amulets, but he could easily have left something out. The way he talked about it, though, it sounded like crafting the amulets was a huge achievement for him. That kind of thing isn't easy to make, and it usually involves blood sacrifice at the very least. I doubt he was in the habit of selling that kind of favor—he just didn't have the psychic strength for that much magic. Either she paid him an outrageous sum for his help, or she was far more persuasive about her cause than I was about mine." "Maybe he bought a shipment of fairy dust from Finland, too," David suggested. Deven gave him a withering look. "If you don't have anything useful to share with the class, put your head down on your desk." "How about you go to—" "Boys," Miranda said tiredly, "can we save the cockfight for later, please?" "At any rate," Deven went on, glaring at David, "I don't believe she has anything else like that in her possession, but we can't rule anything out, so we have to proceed with caution." "Two Primes, a Queen, a Second, a dozen Elite . . . surely we don't have anything to fear," Miranda pointed out. "She may be your prodigy, Lord Prime, but she's still only one woman." "Oh, she's far more than one woman," Deven said with a grim smile. "I made sure of that. But between us I think we can take her—the worst that could happen is that she'll get away." The car slowed to a halt, and Harlan said, "Sire, we're at the rendezvous location." The night was bitterly cold, but at least it wasn't raining; Miranda felt the temperature distractedly, her body still running hot from feeding. She got out of the car and immediately swept the block with her senses, but all she could detect were Faith and the other Elite arriving on the scene and dispersing to await their orders. The three Signets and Faith made their way toward the apartment building in silence, David in the lead, with Miranda at his right hand and Deven at his left. David scrutinized his phone as they walked, then motioned for them to stop just before they came into view of the building. "Still no sign," David said quietly. "The Elite have the place surrounded and the rooftop team is in position. Faith, I want you on the side of the building to block any escape through the windows." "Yes, Sire," Faith said, and melted into the shadows. At the base of the stairs Deven held up his hand for them to wait. "I'll go in first," he said. "Wait for my signal." "Why?" Miranda asked. "I'm more likely to escape in one piece if it's a trap." David shook his head. "If she's got any tech in there, it's not showing up." Deven smiled grimly. "There are plenty of ways to booby-trap a place like this, and I know for a fact Ovaska knows most of them. I know what to look and listen for. Just stay back until I'm sure." Miranda watched, heart pounding, as he took the stairs quickly without making so much as a footfall's sound. He pressed his back into the exterior wall beside the door, listening into the darkened apartment. As he'd said, the place was a dump. It didn't look like anyone had lived there for years. There were lights on in the first-floor unit, but the target unit looked uninhabited; Miranda saw that one of the windows was boarded over, and the other had an air conditioner hanging out of it with a ribbon of torn duct tape fluttering in the air. A pile of old newspapers was stacked in front of the door, and one of the apartment numbers was hanging by a single nail. Deven reached sideways to close his hand around the doorknob and gave it an experimental turn. He frowned; Miranda heard the knob turning freely. The door was unlocked. With his other hand, Deven drew one of his stakes, clearly not trusting the situation any more than Miranda did. Slowly, a tiny bit at a time, he opened the door, exposing a darkened entryway. Miranda listened hard, but she couldn't hear any movement inside. She glanced at David, who was watching Deven intently, the sensor grid up on his phone showing the positions of all the Elite. In a motion almost too rapid for Miranda to see, Deven darted into the apartment. Miranda stared at the doorway for a long minute with her heart in her throat, waiting for the sounds of a struggle or at least conversation. Finally Deven reappeared in the doorway and shook his head. "Shit," David muttered. "She's not there." He addressed his com: "Suspect is not present. Hold your positions; I repeat, do not approach the building until it's cleared. Faith, give me a visual inspection of the building exterior." The light in his phone blinked as Faith beamed in images from her camera; Miranda leaned over and looked, but there was nothing to see, just stills of the apartment's windows and the alley from different angles. Miranda looked back up at the door, where Deven had again gone inside. "I'm going in," she said. "Are you coming?" "Yes," David replied, standing still, eyes on the screen. "I'm right behind you. Let's have a look. Maybe we'll get something out of this wild-goose chase." The stairs were rickety wood, and Miranda had no idea how Deven had managed to scale them without making any noise; she kept her steps light and still elicited a few creaks. She peered carefully into the apartment. It smelled musty and damp . . . but not as if anyone lived there, human or otherwise. "Deven?" "Hold on . . ." Miranda watched the Prime move slowly around the room, looking for signs of something she couldn't see; he ran his hands along the windowsills, rapped carefully in several places on the drywall with his knuckles, then paused. "Well," he said, "I think we've found the right place." The Queen also looked around for any sign of habitation, but all her senses were telling her nobody had dwelled there in a long time. Even a vampire would leave behind some sense of her presence, and if Ovaska had stayed here for long, Miranda should have felt the echoes of her emotions, a vague sensory impression from buildup over time. Miranda picked her way across the refuse-scattered floor and joined the Prime where he stood at a coffee table in front of a couch that had spewed half its stuffing all around. "Whoa." The table was covered in papers: photographs of various locations around the Shadow District; images of Kat leaving work, taken from a distance; a map with the location of Drew's school highlighted in neon yellow as well as Mel's Bar, Denise's office building, and the Black Door. "We should get the rest of the Elite in here to tear the place apart for more evidence," Miranda said, lifting her wrist. "Star-three—" "Wait," Deven said shortly, grabbing her arm and pulling her com away from her mouth. "What's wrong?" Deven's head snapped up, and he looked around, something dawning on his face that left a burning chasm of fear in Miranda's stomach. "We have to get out of here." "What—" Deven's voice was urgent. "No agent of mine would leave evidence lying out in plain sight unless she knew we would see it. She knew we were coming. Go!" He pushed her toward the door, just as David all but shouted from her wrist: _"Get out of there! A signal was just sent from the—"_ Miranda ran for the exit, and no sooner had her face hit the cold air than she was jerked back into something hard—Deven seized her by the shoulders and shoved them both forward, over the railing, twisting in midair to pull her against his chest. The force of the explosion behind them threw them both through the air and into the street below. Miranda felt her shoulder hit the ground and crack beneath her, a dull but fierce pain engulfing her as Deven landed on top of her, shielding her body from flying debris. The noise was deafening—Miranda was sure she screamed, but she could hear nothing but the thunder of the apartment's walls fragmenting and flying outward at lightning speed. She felt pain throughout her body, both from her own wounds and from David's. Her shoulder was in agony, and something was stabbing her in the leg—no, David's leg. "Fuck," she heard Deven grumble near her ear. "That was so stupid." "David," she moaned. " _David!_ He's hurt—get off me!" "Calm down," Deven commanded harshly, not budging. "He's fine. You're still alive, aren't you? Hold still—we're pinned underneath something." He shifted on top of her, and she became aware of a weight pressing down on her that wasn't him; he was, she realized, lighter than she had expected, probably lighter than her. She smelled scorched wood, so they were probably wedged under part of a wall. Beyond Deven's body she could hear chaos—Elite yelling, sirens wailing in the distance, Faith's voice giving orders. The odor of electrical fire and melted plastic and metal were thick in the air. _"Miranda!"_ David said from her com. _"Are you all right?"_ "I'm okay," she panted around the pain in her shoulder. "We're stuck under something. Where are you?" David sounded breathless but otherwise okay, the panic leaving his voice once he heard hers. _"Near the stairs. I was halfway up when I saw the signal—I made it to the lee of the building and everything blew out over me, including you. I'm surrounded by debris and have a piece of rebar in my leg—stay where you are. Whatever you do, don't try to Mist if you're hurt. You won't be able to focus and you might scatter yourself."_ She could feel his fear, for her and for Deven, and she probably would have been afraid, too, but she was so relieved that he was all right that there was no room for any other emotion. "Can you move your legs apart?" Deven asked through gritted teeth. Miranda obliged slowly and painfully. "Probably the first time you've ever asked a woman that," she said. Deven snorted, then made a strained sound and pushed upward, one of his knees between hers using the ground as leverage. She felt the weight on them lifting, slowly at first, then angled hard off to the side. Deven fell down next to her, breathing hard. "Stupid," he said again. "Should have known better . . . but I was sure we had her. The intel was good . . . 5.23 has never been wrong." He forced himself up onto his knees, and Miranda saw that he was bloody and disheveled. As she started to push herself up, too, it felt like something in her shoulder tore, and she cried out. Deven put his hands on her and nudged her back down. "Lie still," he said. "I'll fix your shoulder, but you have to give me a minute to catch my breath." She nodded, trying to stay grounded and keep her breathing steady while Deven looked around them at the demolished scene. "We're all the way across the street," he commented, sounding impressed. "Whatever she used to blow the building had no smell, no vibration . . . I'd love to know what it was. It looks like the whole building went up . . . be glad you can't see it yet. There are . . . a lot of bodies. Humans . . . from the crack house. I don't see any Elite among them." "Faith's okay," Miranda managed. "Have you . . ." _"Sire . . ."_ The voice coming from Miranda's com was hoarse and faint, but she knew it. "Lali?" she asked. "Lali, where are you?" A cough. _"Sire . . . my Lord Alpha . . . I'm sorry. I failed you."_ Deven leaned over toward Miranda, who held up her wrist. "No, Lalita." _"I was sure of the intel . . . must have missed something . . . I failed you . . ."_ Miranda was astonished to see something shining in Deven's eyes. He replied to Lali in a language Miranda didn't understand, and Lali said something almost too quiet to hear. Then silence. "David?" Miranda asked urgently. "Do you have Lali's signal?" She heard him take a deep breath. _"She's gone, beloved."_ Miranda fought back tears as she asked Deven, "What did you tell her?" The Prime looked away. "I told her I was proud of her." "And she said good-bye," Miranda concluded, wiping her eyes with the hand of her uninjured arm. Deven started to speak, then clapped one hand against the side of his neck. "What the hell . . ." Miranda felt something small and hard hit her injured shoulder, and she whimpered, groping with her other hand and finding a thin cylinder of wood jutting out from her coat. She looked up, alarmed, and saw Deven pull an identical object from his neck. Then he gasped and fell forward, catching himself on his hands with a choked groan. She watched in horror as blood began to drip from his mouth and nose . . . he sucked in a hoarse breath, eyes clamping shut, raising both hands to his head. It was only when the pain gripped Miranda's skull that the realization came to her . . . and by then it was too late . . . She was already losing consciousness, the pain engulfing her so completely that she couldn't even scream. Seventeen _"Miranda!"_ David fought his way back to consciousness gasping, choking around the pain that racked his entire body as the antitoxin kit had its way with him. "Sire, please . . . you must hold still." Blinding light sent new flashes of agony through his head, but he opened his eyes anyway, struggling against the arms that held him down until he recognized the tense, pale faces hovering over his. _Faith. Mo. Jackie._ _Clinic._ _Poison._ _Miranda._ "Where is she?" he demanded, his voice thin and raspy as if he'd been screaming—which, given the aftershocks still rolling through his body, was a distinct possibility. "Damn it, what happened?" He tried to sit up again, and again they held him down. "Sire . . ." Faith's eyes were worried, but her voice was steady. "Tell me your name." He shook his head. "Let me up." "Not until I know you don't have brain damage. Name." Rolling his eyes—which hurt like hell—he said, "David Solomon, Prime of the Southern United States. You're Faith, my Second in Command. This is the Anna Hausmann Memorial Clinic. Now tell me what the fuck happened!" "We don't know," Faith replied as Mo moved over and fussed with a monitor. "We got you out of the debris and pulled you off the rebar, and you were in the middle of giving orders when someone darted you—Ovaska, I assume. You went down bleeding. She must have gotten all three of you within seconds of each other." "All three . . . oh, God." David sought inside himself, trying to sense Miranda through the energy that linked them, but though he sensed she was alive, he had no sense of _where_ she was or if she was hurt. He could always find her—he could be at her side in seconds, anywhere—but now something was blocking that knowledge, something that felt almost like . . . "A shield," he murmured. "She's under some kind of shield . . . a powerful one. If she were at full strength, she might be able to break it, but if she was poisoned, too, she's weak." "You can't find her," Faith said quietly, realizing what he meant. "Not psychically." The fear was so thick in his mind he could barely think. "Did any of you see anything?" Anguished, Faith shook her head. "I had just sent Aaron and two others to find them and bring them back when you were hit—by the time we realized you weren't the only one, they were gone." "They . . . she got Deven, too?" Faith nodded. "No trace of either of them at the scene. She moves fast." Now David sat up slowly, and the others allowed him. He leaned his head in his hands, trying to force himself into some kind of mental clarity around the lingering pain from the poison, the antitoxins, and the underlying terror of being so far from his Queen, unable to sense her the way he should. In four months he had already grown to depend on their bond; it was a constant low hum in his mind and heart, like the white noise of a nearby but unseen ocean. That tide of energy sustained them both . . . with it blocked, and the two of them separated, it would be only a matter of days before they both went insane . . . if they even had that long. "Faith," David said softly. "Yes, Sire?" He looked up into her eyes. "I don't know what to do." A flash of fear—as uncharacteristic as his helplessness—crossed her face. Before she could speak again, one of the Elite standing guard at the door said, "Sire, you have a visitor." Not really caring, David waved a hand, and the clinic door swung open. A tall, broad figure ducked through the doorway, his dark gray trench coat swirling rather theatrically as a blast of cold wind accompanied him in from the streets. The light caught the glowing emerald at his throat. Jonathan strode up to the gurney where David had been treated and crossed his arms, regarding the Prime gravely. "Now would be a really good time for one of your brilliant ideas," the Consort said. "Thank God you're here," Faith told him, squeezing his arm. "We need all hands on deck." Jonathan gave her a smile that was both genuine and distracted by his own worries. "They've been shielded from us," the Consort confirmed. "I can feel Deven . . . somewhere, but I can't tell where, or what shape he's in. Except . . . I know he's in pain. I felt it the minute he was poisoned." Jonathan moved to the side to let Mo come in to remove David's IV. "What will happen to them without the antitoxins?" It was Mo who answered. "They will recover, but they will suffer first," he said. "Probably for much longer than the Prime has . . . although, Sire, I suspect this killer has adjusted her dosage, because it affected you for only about twenty minutes once we got the kit into your IV. Last time it took over an hour. I would venture to guess that they'll have two full hours of pain before the poison runs its course." "That gives us two hours to find them," Jonathan said. "She won't kill them until then—otherwise she would have already. She wants them alert, so they'll know it's her." "That first attack on me was a trial run," David realized. "I thought it was a self-contained attempt to knock me down so she could get to Miranda through me, and I was wrong. The first time she shot me was to see how the compound would affect a Signet—she just wanted to test it on me before the big show." "All right," Jonathan said. "We need a plan. List the pertinents, please, Faith." Faith glanced at David, who merely nodded; Jonathan could take charge if he felt up to it. David certainly didn't, not while he was still so foggy from the drugs. Jonathan and Deven had been Paired much longer than David and Miranda, and so they knew how to manage the separation better; Jonathan certainly seemed calm and rational for the moment. "Last night we acted on Deven's intel and invaded the suspect's lair. Said lair was in fact wired to explode via a remote signal, which Prime David detected on the network just before it went off, giving him time to duck and cover. Queen Miranda and Prime Deven were thrown across the street underneath a segment of wall. We freed David from his entanglement and started to find the others, but Ovaska shot all three with toxin-loaded darts—seeing the Prime go down distracted the rest of us enough that she was able to make off with Miranda and Deven unseen." "How did you get to Texas so fast?" David asked Jonathan. The Consort gave him a _You really aren't that stupid, are you?_ look. "I was here the whole time," he replied. "I checked into the Driskill while Deven came to the Haven to see you. I also brought twelve of my Elite—they're outside ready to assist." "How many casualties were there from the explosion?" David asked Faith. "Two Elite dead, five wounded; the wounded are all here at the Hausmann and have already healed, except Elite Seventy-three, who lost an arm." "And the dead?" Faith took a deep breath. "Aaron and Lali." David looked over at Jonathan, who was clearly stricken by the news. "So you know all the agents, too?" Jonathan shot David a warning look. "Mind how loudly you speak," he snapped. "And no, I don't know them all, but I did know Lalita." "I'll talk about whatever I damn well please in my own territory," David returned coldly. "If it weren't for your Prime's lies and secrecy, we wouldn't be in this mess." "That's beside the point—lives depend on our secrecy. Whatever regard you lack for us, have a care for them, and for Lalita, who died in the service of your Queen." "And if both of you don't shut up and put this aside for now, Miranda and Deven are going to die," Faith interjected with surprising anger, given her usual reserve. David and Jonathan both looked at her, then each other, and nodded. "You're right," Jonathan said. "Let's concentrate on finding them. David . . . David?" The Prime blinked and refocused his gaze on Jonathan. "Sorry." Jonathan nodded grimly. "You're already losing it. We don't have much time. If Miranda and Deven are shielded, we have to find a way to track Ovaska down." David, hands on his temples, returned the nod and dragged himself mentally back into the room. "Faith, bring my laptop from the car. While I'm working, get all the Elite you can back to the scene and comb it for even a hair's worth of evidence. Put all available patrol units on the search for the Queen and Prime, but have them ready to divert at a moment's notice when we find them." "As you will it, Sire," Faith said, and vanished. David managed to wait until Mo had unclipped and unplugged the various machines and monitors from his body before climbing off the gurney and buttoning his shirt. "I need someplace quiet," he said. Jackie, the head nurse, showed him to the administrative office, where Faith quickly brought his computer. He sat down at the desk and logged on to the sensor network and the Haven servers, though it took him a moment to remember his passwords, as there were twelve involved in just this part, each one different with at least twenty characters apiece. He had to pause once and shut his eyes, fighting against the panic of not knowing where she was, or how badly she might be hurt . . . she might be calling for him . . . she could be bleeding to death, or being tortured, her hand sliced off . . . "David!" Jonathan's voice brought him back to reality, and he clapped his eyes back on the screen, where the master sensor grid was up and waiting for his commands. He brought up the Haven com network as well and overlaid the two. "All right," David muttered. "Here we go. I'm going back through the data to analyze exactly what happened at the scene just before, during, and after the explosion. Here, look—the red dots are Elite, the blue dots are Miranda and I, and the white dot is Deven. There are no other vampires in the area. Deven and Miranda enter the apartment . . . and seventy-two seconds later a signal is sent from an outside location to the building." The explosion showed on the network as a sudden relocation of every glowing dot—the Elite had either fallen, been blown forward, run, or died. Two of the dots flickered as their life signs faltered, then turned into Xs to indicate that the signal of the person wearing the com had ceased. He clicked on each X, bringing up the designation of each. "That one's Lali," he said, pointing to the dot nearest Deven and the Queen. "She was running to help." Deven and Miranda's signals were across the street from the apartment building; he watched, helpless, as the red dots all converged on his own, indicating that he'd just been shot with the poison dart. Seconds later, the other blue dot, and the white, disappeared, probably dragged by Marja, who still wasn't showing up. Her amulet must have still been working. "Where did they go?" Jonathan asked. "Did she shield them, too?" "She must have," David replied tersely. "Even if she loaded them into a car, they'd still show up on the network unless she had shields around them already. So whatever that amulet does, it must work on anyone she's touching as well as herself . . . and they conceal her from all indirect forms of detection, so it blocks the com signal, too. Faith, get a team to those coordinates, and see if there's a blood trail or any indication of where they went or how she transported them." While Faith gave the order, he rewound the data again and scrutinized it a second time, then a third. "The answer isn't here," David said to himself. "We can't track her based just on what happened tonight. There has to be something . . ." "Can you trace the signal that set off the bomb?" David gave a frustrated sigh. "It was bounced from location to location and most likely originated from a prepaid cell phone that was destroyed immediately afterward. I can narrow it down to within a one-block radius right now, but that doesn't tell us anything—we already know she was within a block of the explosion." He put his head in his hands again, trying to think. "Miranda said we should go back through the raw sensor data. We can't track Ovaska herself—what if we could track the amulet?" "There were seven of them," Jonathan pointed out. "Yes, but they all have to work the same way. Before, when I tried to find anomalies in the network, I didn't know she had an amulet shielding her. I thought she might have some kind of scrambling device that would operate within known technological parameters and give off an electromagnetic field. This is something different." "It's magic," said Jonathan. "How are you going to track magic?" "Everything that people perceive as magic is just science in a party dress. Whatever energy they're sending out to block the sensors . . . it's still energy. It had to have affected the environment somehow, and those effects are traceable. If I can pinpoint those effects, I can recalibrate the network to search for them." "That could take days," Jonathan said, dismayed. "They don't have days." "Days," David said. "Right. Who am I, again? Give me twenty minutes." His fingers flew over the keyboard, and he spared a second to dig in the laptop case and pull out the wireless mouse. He accessed the long-term data storage at the Haven and pulled up the readings for the night that Ovaska had killed Drew. That night had been an anomaly in the attack history; she had momentarily lost her shield, then dropped off the network as soon as she activated another amulet. Somewhere, in that moment, was the answer. Whatever those amulets did, they had to disturb the energetic field of the city somehow. Everything gave off an energy signature, including humans and vampires. He dumped all of the raw data into a single file and ran search strings for commonalities between that night and tonight. He compared the readings—air temperature, atmospheric pressure, even humidity, everything the sensors gathered, no matter how insignificant it seemed. The damn things had to be emitting some kind of signal or putting out some kind of field . . . even just a split-second blip each time . . . "There," David said, pointing again. "At the exact moment that Ovaska activated the amulet outside the school, there was a temperature drop of one tenth of one degree and a twenty-pascal change in the atmospheric pressure where she was standing. If I compare the data from the night she attacked Miranda after her show . . . bringing up the temp and pressure of the entire room indexed in single square-foot sections, you can see a similar reading there . . . and watch it move . . . that's it. There's not an energy spike, there's an _absence_ , like a single dead pixel on a screen. I just have to find the spot at tonight's scene where the temp and pressure are lower than the air surrounding it but she doesn't already show up as a vampire . . . then we can track her like a very localized weather front." "She could have been anywhere—" "No, not anywhere. She was within range to shoot all three of us within four seconds of each other, meaning she had to be somewhere _here_." He highlighted an area on the grid. "Given that the nearest building has no windows facing the street . . . she was either to one side of it or on the roof. With this type of dart, the gun she had to have used has a range of thirty feet, maximum. That building is three stories, but if she shot downward, the darts had to hit each of us at an angle, which they didn't. Mine was sticking straight out of my neck when I pulled it out. That means she was on the ground." He focused the search on the area of the street where she could have reasonably been, given the wind's direction and speed and the locations of the three Signets at the time they were all shot. A spot on the screen lit up and flashed with the temperature: 43.8 degrees, where at least the next five feet in every direction read 43.9. The air pressure showed a corresponding change. He locked the search on those readings and ran a trace that would follow that same anomaly as it moved over the grid, allowing for a slight variation in temperature as Ovaska's body temp rose because of her physical exertion. A few pixels at a time, agonizingly slowly, the computer began to draw a line across the screen, starting at the point where Ovaska must have been standing out of sight to fire the dart gun, closing on Miranda and Deven's location, then moving along the street as she dragged them both away from the scene. He suspected that if he were to go back and run the data right next to Ovaska, he'd find corresponding tracks for Deven and Miranda, but there was no time for that . . . and he had what he needed. The computer churned through immense amounts of data to provide the readings, and it was slow going, but the green line continued to snake its way through the streets of Austin . . . until it dead-ended deep in the warehouse district. David looked up at Jonathan and Faith and gave them a feral smile. "Got her." She woke shivering, her body wrung out and exhausted by pain, the smell of blood still filling her nostrils and a nauseating metallic taste in the back of her throat. Her head still ached dully, but the writhing agony had faded so that instead of wailing she wanted to curl up and whimper. She could barely feel her fingers as she tried to move her hands, touching the ground beneath her, trying to learn anything she could about where she was. Grimy concrete floor. Damp. Slowly, she extended her arm and kept feeling around until her hand hit something hard. Bars. She pried one eye open, groaning softly as light intruded and sent sparks through her head. Everything was blurry at first, but she blinked until her vision started to clear. The only light came from a single incandescent bulb, leaving everything an otherworldly orange. She could make out the bars to her side, and turning her head a little she got a sense of the size of her prison: It was a cell about as big as a walk-in apartment closet. She heard metal clank and tensed all over, waiting for a door to open or something to change, but nothing did. A moment later she heard a faint indrawn breath that hitched as if around a sudden stabbing pain. She lifted her head. "Deven?" Pale eyes still glazed with the aftereffects of the toxin met hers. "Aye." "What are you doing up there?" The Prime almost smiled. He had been chained by his wrists about a foot off the ground up against the back wall of a cell adjacent to hers. "You . . . don't remember?" he asked, panting slightly. "No." "You fought her," he replied, sounding about as well as she felt. "She was going to chain us both, but you woke up and started struggling like a wildcat. She couldn't hold you still enough, so she just dumped you on the floor and locked the cell. She was bleeding when she left." Miranda heaved herself onto her side, wincing—her shoulder was still killing her and it felt like she'd been kicked in the kidneys. "Sounds pretty badass." Deven chuckled weakly. "It was." She ran her hands down over her body, patting herself for other injuries. "She took our weapons and phones . . . but I still have my hand, so I still have my com. Why?" "Don't know. I didn't get a dramatic villain monologue out of her." Miranda shut her eyes again, trying to concentrate. If she could summon enough strength, she could call for help—surely David would be able to sense her, even if they were really far away. She reached out with her senses . . . . . . and found them blocked. She couldn't feel anything beyond the cell. That meant that David couldn't feel her either. "Oh, God," she said. "I can't project. We're cut off." "I know that." "There's a room like this at the Haven . . . it's where I learned to shield myself. No matter what goes on inside, it can't get outside. Psychic signals, even cell phones and the coms . . . they won't be able to find us." "It takes an incredible amount of power to create a shielded chamber," Deven noted, eyes wandering around the room. "Either she's got resources beyond a few amulets from Volundr or this place existed before she got here." "What do we do?" she asked, starting to panic. "What do we do?" "First . . . calm down. They might not be able to find us via the Signet bond, but there are other ways. You're married to a genius, remember?" "He hasn't been able to find Ovaska so far. What if—" "Things are different now. By kidnapping us, she changed her MO. That throws in more variables. They'll find us, Miranda. We just have to survive until they do." "Can you Mist?" Deven shook his head. "I'm way too scattered already." "Why hasn't she killed us yet?" Deven snorted quietly. "Clearly you've never been vengeful. Killing someone who can't see your face isn't nearly as satisfying . . . and killing us while we were in pain would have been merciful." "So she could be here any minute to finish us off," Miranda concluded. "We have to be ready for her—I just need to get up—" She didn't have a chance to finish the thought, much less formulate a plan. There was the sound of a metal bolt shooting home, and a door across from the cells swung open. Marja Ovaska walked into the room, giving them both a nasty, self-satisfied smile. She was wearing a metal disc on a chain identical to the one she'd lost at Drew's school . . . and she was holding a hand-carved stake. She stood in front of the cell doors for a minute, not speaking, just watching Miranda. She was, Miranda noticed, a strikingly beautiful woman with cropped blond hair and large blue eyes; Miranda pictured her standing next to Sophie's dark pixie looks, and the image made a wistful sort of sense. It also helped explain why Deven had developed a soft spot for the couple; physically they reminded Miranda of the Pair, with one small and dark, the other tall and blond. Miranda started to speak, but Ovaska cut her off. "Don't bother," she said, and yes, she had an accent now that Miranda hadn't heard the night of Drew's death. "I don't care if you're sorry." "Well, good," Deven said caustically. "Miranda may have sympathy for your sob story—poor you, your lover died, now you have to strike back. Cue the violins. I couldn't care less." Ovaska looked at him with loathing . . . but also, Miranda sensed, with the slightest undercurrent of fear. Deven had been right . . . even though she had the power here, and even though she was no longer part of the Shadow, an agent was always an agent, and even chained to the wall at her mercy, the Alpha was still the Alpha. "We both know this isn't about Miranda getting Sophie killed," Deven went on. "Sophie made her own choices—that's what's eating you alive. Because when it came down to it, she chose Miranda, and the Signets, over you." "Shut up," Ovaska said softly. "If you're going to kill us, kill us," the Prime told her. "If you stall, you'll be caught. I taught you better than that . . . unless . . ." "Deven," Miranda interrupted, "don't taunt the crazy person with the stake!" But Deven was staring at Ovaska hard, eyes narrowed. "She's not crazy. Are you, Marja? Did you really bring us here to kill us? This whole setup . . . the bomb, the cells, the poison . . . it's more than simple vengeance. I know you." Now Ovaska smiled. "Do you think so?" "You're not this sentimental. Sophie was the one who begged me not to kill you both. Even in love, even facing execution at my hands, you didn't betray a scrap of emotion. If all you wanted was revenge, you would have found a way to kill Miranda by now . . . you wouldn't have missed the first time." "You said she was sizing me up," Miranda said. "And that killing the others was to hurt me." Deven shook his head. "That may be true, but it's not the whole story. The more complicated this whole thing became, the less sense it made. It's cliché, Marja. Scorned woman out for blood—bullshit. Volundr introduced you to someone, didn't he? Someone with a lot of money and a very particular purpose." Still smiling, Ovaska took a key from her pocket and opened Deven's cell door. She walked up to him so that they were inches apart and said to him very calmly, "Now you're the one who's stalling." She rested the point of the stake against Deven's cheek, then drew it slowly down his neck, over his chest. "What do you suppose would happen to the Red Shadow if I killed the Alpha?" she asked. "Well," Deven replied, "given that I issued a kill order on you, even if you walk out of this building alive, you'll find out pretty quickly." "I fooled you once," Marja told him. "You walked right into the trap I set for you. I evaded the Southern Elite for weeks. If I can do that, I can outfox your agents." "Why did you set a trap, again?" Deven asked. "Why are we here?" Miranda focused her will on her limbs, and slowly, very slowly, she got her hands underneath her to try and push herself up. She didn't know what she was going to do, but she wasn't going to lie there on the floor and wait for Ovaska to make a move. One way or another she was going to go down fighting. Ovaska's head jerked toward her. "Don't try it," she snapped. "There's nowhere for you to go." Deven seized her lapsed attention, pulled his knees up to his chest, and kicked Ovaska hard in the midsection. She staggered backward, hitting the bars with a loud clank, and flailed sideways to grab the bars and stay upright. The stake, knocked out of her hand, clattered to the floor inches from the wall of bars between the cells. Miranda shoved herself up and dove for it, sticking her arm through the bars and getting her hand around the stake. As she jerked backward Ovaska regained her footing, and pain exploded through Miranda's hand as Ovaska stomped on her fingers. Miranda cried out and dropped the stake, which Ovaska bent and retrieved. Miranda pulled her arm back just in time to avoid another stomp. Miranda held her arm against her chest, the pain of her broken fingers nearly making her sick. Ovaska glared down at her. "Bitch," she snarled. She returned her attention to Deven, who didn't look particularly disappointed that the gamble hadn't worked. "Worth a try," he said. Ovaska straightened her clothes, rotating her neck as if to work out a kink, then considered the stake in her hand and the Prime bound before her. "You're right," she said finally. "Yes, I wanted revenge. Killing all her little friends did make me feel better . . . although if one of them had talked, told me how to find the Haven, that would have made things much easier for me. Your people are nothing if not loyal. It's annoying. But it turns out there are greater powers out there than the Signets . . . and bigger paychecks than the Shadow." Deven met her eyes. "Who are you working for, Marja?" She smiled. "Not you." She glanced over at Miranda. "The contract stipulates: one live Signet, physically intact, to be delivered tonight. As they say, I can kill two birds with one stone. I can destroy the woman who destroyed my life, and I can make myself obscenely rich and finally get out of the game. This is what I learned from you, Sire. Cold, calculating efficiency. This woman is important to my client, and to my desire for justice . . . and you . . ." She ran her fingers down the shaft of the stake, pondering a moment longer, before she finished, "You, Sire, are expendable." She smiled. Then she drove the stake into Deven's stomach. Eighteen Deven held back his scream, just barely, but his head fell back and hit the wall, eliciting a strangled sound of pain that Miranda herself could feel throughout her body. Blood erupted from the wound, running in coppery dark rivers down over his legs, pooling on the floor. Marja stepped back to avoid the blood and said, "There, now. That's the first problem dealt with. Now I just have to keep you quiet until my client arrives in an hour." She turned to Miranda. "Either you can stay where you are and not make trouble, and watch your friend bleed to death, or I can give you another shot of poison, and you can scream and writhe on the floor in your own blood while he bleeds to death. Up to you." Miranda glared at her, wanting nothing more than to fling herself at the bars and tear them down to get her hands around Ovaska's throat, but she was still too injured and unfocused to Mist, and not strong enough to tear down walls. Ovaska watched all those thoughts cross Miranda's face, her own expression deeply satisfied with Miranda's impotence. "Enjoy your last few moments together," Ovaska said to Miranda. "I'll be back soon." She slammed the outer door shut and locked it. Miranda's hand was still in agony, but she forced energy into it to at least partially mend the broken fingers, and got up on her knees. "Deven!" His head was hanging down, eyes closed, but she could hear him breathing, a shallow rattling in his chest. The blood was still flowing from his abdomen. Miranda dragged herself to her feet and held on to the bars. "Can you heal it?" she asked. Deven could barely focus on her enough to reply, but he said, "Can't . . . stake's still . . . in there. Can't pull it." Miranda tried reaching through the bars, but he was chained at least two feet beyond her reach. Her heart was thundering around her rib cage as she tried to assess the situation for a solution: Deven's cell was still open, but hers was locked. Miranda pushed herself over to the door of her cell and pulled on it as hard as she could, shaking it, trying to make it budge. If she could get it open, she could get into Deven's cell and pull the stake, and he could heal the wound before he bled to death . . . but she had to get the door open . . . "Miranda . . ." She stopped midshake and turned to Deven. "Just hold on," she said. "Just stop the bleeding as much as you can. I'll get that thing out of you, I just have to—" "Miranda . . . I'm done for. Unless I can draw power from Jonathan, even if the stake comes out, I won't last long." He closed his eyes and leaned his head back against the wall. "You have to save yourself. Whatever that woman wants with you, it can't be good." "Let me think," Miranda said. "I'll get us out of this." "Miranda . . ." "I'll think of something!" she said, and she turned to him, tears in her eyes. "I'm not going to let you die." Deven smiled. "Why not?" Miranda shook her head around her tears. "I'm not going to be the one who has to tell David you're dead. It would kill him to lose you. Jonathan, too. Literally." Their eyes met, and to her astonishment Deven's were shining, too. "I'm sorry," Deven said softly. "I'm sorry about David." Miranda hung her head against the bars. "I forgive you," she whispered. "Thank you . . . for Sophie. She was . . ." "She was a good friend," Deven finished, his own voice fading. "That's all you need to remember about her. She was your friend." "I don't want you to die," she said, crying through the words. "Tell me what to do to save you." "You're too weak from the poison to Mist," Deven said. "There's nothing else you can do." Miranda watched Deven's blood falling, drop by drop, onto the cold floor, drop by drop his life draining out of his body, the light in his Signet beginning to dim. "Jonathan," Deven whispered, his eyes slowly closing. "Oh, love . . . don't keep me waiting long . . ." "No," Miranda whispered. "No . . ." She took a deep breath, planting her feet solidly on the ground and holding on to the bars hard. She lifted her eyes from the blood trail to the stake jutting out of Deven's body, right through his solar plexus, making his breath labored, his healing ability unable to stay on top of the damage as it tore through his flesh over and over again each time he inhaled. If she could just get her arm far enough through the bars, she could get her hand . . . around it . . . Miranda gasped. She slid her hand through the bars again, extending her palm toward the stake, and drew up all the energy she could, trying to remember how she'd done it before . . . with Hart . . . she had acted without thinking, acted from emotion, from anger . . . and one thing Miranda knew how to do was manipulate emotion. She reached down into herself and dragged out all the anger she could find: anger at Marja Ovaska for killing Drew, for attacking Kat, for poisoning David, for killing Jake and Denise . . . for bringing fear and violence to the streets of her city . . . Miranda pushed that anger out along her arm, then focused her mind on the stake as if she were mentally wrapping her fingers around its hilt, feeling the wood grain against her fingers, the slickness of Deven's blood around the wood, as she grasped it, and with the force of her anger, _pulled_. Deven cried out in pain as the stake flew out of his body, yanked so hard that it was flung back into Miranda's cell and hit the wall. Breathing hard, barely able to stay conscious from the effort, Miranda held on to the bars. "Deven!" He was icy white and not moving; she couldn't even hear him breathe. He hung limp in his chains . . . but the blood had stopped flowing. "Deven? Are you still there?" she asked. Several interminable seconds later, she heard, "Nice . . . work . . ." Miranda slid down the bars onto her knees. She couldn't keep herself up anymore. "How long can you hold out?" "Maybe . . . half an hour." "Okay. That's a start." She turned and crawled over to the stake where it had landed on the floor. The point had been blunted when it hit the wall, but with enough force it could go through flesh. So they had a weapon; that was step one. If she could get Ovaska into her cell, she could attack, and with the door open she could get out and call for help, find the keys to the shackles, and get them out of here. The only thing she could think to do was feign unconsciousness. "How can we get her in here?" Deven sighed. "Make a lot of noise." Miranda nodded, leaning against the bars to rest for a moment. Exhaustion was dragging her down and she just wanted to sleep . . . no, she wanted to go home and fall asleep in her own bed with David beside her . . . the longing to have him with her was suddenly overwhelming. She just wanted to hear his voice, feel the reassuring strength of his presence, anything . . . "Your husband is really amazing in bed," Deven said suddenly. "I love that thing he does with his tongue—" "Shut up!" Miranda snapped, her attention whipping back to center, and with it, the realization that she was on the verge of cracking. Now was no time to pine herself to death—she had to act. "You're such a bastard," she said, though she was almost grinning as she spoke. Deven managed a smile. "Better. Now get up . . . or I'll give you the play-by-play of the night with the handcuffs—" "Like you're really into bondage," she muttered halfheartedly, focusing her energy on moving back to the corner of her cell. The farther she could get Ovaska in, the more room she'd have to take her down. Miranda fought hard to ignore the pain in her hand and shoulder, the slow creeping madness of being cut off from David, the burning in veins that needed blood, badly, to help her recover from her injuries and the poison . . . soon she'd have time to rest, and she could feed and sleep. But now she had to focus. "Okay," she said. "Try to look dead." "No . . . problem . . ." Miranda tucked the stake out of sight under her arm, took a deep breath . . . and screamed at the top of her lungs. "This way!" Faith held her phone out in front of her, gesturing with her free arm for the rest of the team to follow her around the corner and up the street. The green line that marked Ovaska's trail glowed in the moonless night, leading them miles from where they had originally thought Ovaska was hiding, back to the industrial warehouse neighborhood where Sophie had once lived. Fifteen Southern Elite and twelve from the West converged on the trail's end, Faith in the lead, all of them out for blood and under orders to take Ovaska down by any means necessary. Jonathan and David were right behind them, but David was still woozy from the aftereffects of the poison, and he had sent the Elite ahead instead of making them waste precious minutes waiting for their Prime. "Here!" Faith announced, looking up from her phone. They were in the middle of the street. "Goddamn it!" Faith exclaimed. "What went wrong?" _"Something is degrading the trail,"_ David said over the coms. _"Fan out and search every building on the intersection from sub-basement to roof."_ "You have your orders, Elite!" Faith called. "Go!" Faith turned in a circle, watching the Elite disperse in teams to kick down doors, her heart sinking—there had to be a dozen buildings surrounding the intersection, some of them huge. They didn't have time to canvass the whole neighborhood. The Queen and Prime might have only minutes to live. David and Jonathan appeared by her side. "Whatever she's using to shield them must be interfering with the readings," David told her, panting just a little from exertion. "I don't think I can narrow it down any further without taking more time than we have." "You said this was Sophie's old neighborhood?" Jonathan asked. "Which building was she in?" Faith shook her head. "I don't remember—hang on—" She accessed her e-mail and searched for the message Sophie had sent her with her address, months and months ago when Faith had asked her to train Miranda. She doublechecked the street names again. "That one over there, the red one on the corner. But Ovaska wouldn't use her building, would she? That would be too obvious." "Yes," Jonathan agreed, "and that's exactly why she'd use it. It would be the last place you'd look, especially if you'd already searched it before." David turned to Jonathan. "Do you know if Ovaska was strongly gifted?" "No," Jonathan replied. "She wasn't—she had some telepathy, but nothing outstanding." David nodded once and took off for Sophie's building. Faith ran to catch up with him. "What is it?" "She has to be keeping Miranda and Deven in a shielded room like the one where I taught Miranda to use her empathy. Proximity to a room like the one at the Haven could disrupt the readings that led us here—that would explain why the trail ended. It takes time and power to create a room like that. Ovaska had neither—but Sophie might have, and Ovaska would have known about it." "What if she's got some other kind of magic, or more amulets, and not a shielded room?" David reached the building and angled left, looking for an entrance. "Then Ovaska just happened to choose another building in the exact same block as Sophie's. Which do you think is more likely?" Faith nodded and lifted her wrist. "Report!" _"No luck so far,"_ one of the team leaders answered. _"We've only been through three buildings. They could be anywhere."_ "No they couldn't," Faith said. "I need all Elite to 2421 Buckland." "I can't Mist inside," David told Jonathan. "I'm still too scattered. Can you?" Jonathan closed his eyes briefly, then shook his head and opened them. "Whatever's interfering with the signal is making it impossible to Mist—it's like I can't see clearly enough to get a lock on the destination. We're going to need a good old-fashioned door like normal people." Faith stepped back to look at the building's walls, trying to figure out where the entrance was. "I'll call Mitchell with the city planning office and get a schematic. It'll take two minutes—" No sooner were the words out of her mouth than she heard David say, "Oh, God . . ." The Prime had gone pale, and a second later Faith knew why; faintly, somewhere inside the building, a woman was screaming. Miranda heard the door opening, heard Ovaska demand, "What in hell is going on in here?" She kept screaming, doubled over in the cell corner, until she heard the jingle of keys and the clank of the cell door opening. "Shut up!" Ovaska yelled. "Shut up or I'll dose you again!" Miranda let her get one foot closer, gathering all the strength she could into her body, then clamped her mouth shut and twisted around toward Ovaska, ramming the stake as hard as she could into the woman's thigh. Now it was Ovaska's turn to scream. Miranda threw herself at the assassin, knocking her into the side of the cell, but Ovaska was hardly amateur enough to let a stake wound stop her. She grabbed Miranda's arms and flung her aside, firing off a string of curses at the Queen. Miranda wasn't an amateur either. Adrenaline surged through her, hot and bloody. She caught herself and used the back wall as leverage, flying into Ovaska and tackling her, and they rolled across the floor, both snarling like animals, trying to pin each other, too well matched in strength to do so. Miranda reached down and pushed on the stake that was still in Ovaska's leg, driving it deeper and eliciting a cry of pain. Unyielding, Ovaska shoved her and struggled to her feet, running for the cell door, no doubt intending to lock her in again. This time Miranda was fast enough; she wedged her body in the doorway as Ovaska tried to slam it shut, knocking the breath out of Miranda but not trapping her. Ovaska ran for the outer door, and Miranda ignored the pain in her chest and followed. The cells were in a basement room—the outer door led to a stairwell. Miranda sprinted up after Ovaska's retreating form. Miranda threw the door at the head of the stairs open and dove out, aiming low, anticipating that Ovaska would have doubled back to ambush her as she came out. She barely avoided the sword that whistled through the air inches from her neck, and then she hit the ground rolling, coming up onto her feet in time to leap back from another swipe. She didn't have time to look around, but she knew immediately where they were. She knew this room, had fought in it a hundred times; she remembered where all the weapons had once hung on the walls. The Elite had taken Sophie's arsenal, so the walls should have been bare, but two swords and several other blades were hanging up—hers, Miranda realized, and Deven's. Miranda raced for the wall, and just as she got her hand around one of the swords she felt the sting of Ovaska's blade slicing into her left arm. Miranda forced herself to ignore the pain and the blood and spun around, bringing the sword up to meet Ovaska's. They stared at each other for a few seconds. Ovaska was bleeding profusely from her thigh, and her face was disfigured with bruises from their struggle on the floor. The stake was still in her leg. "Who are you working for?" the Queen demanded. Ovaska laughed. "Your death," she said simply, and attacked. Distantly Miranda heard something pounding on the wall, but neither she nor Ovaska allowed herself to be distracted. This time, with both of them injured, it was a more evenly matched fight. They fought across the broad expanse of Sophie's studio, Miranda backflipping out of her reach then diving back in again, Ovaska spinning in midair to add more momentum to her arm. Miranda felt the sword almost alive in her hand, as if her entire body were a weapon, and she let herself slip into the space that Sophie had shown her, between present and future, drawing on a strength beyond herself until she almost knew what Ovaska would do next— Miranda dropped low, swiping out with her foot, knocking Ovaska off balance as Miranda struck her injured leg. Ovaska tumbled backward, wheeling her arms to regain her equilibrium, but she lost her guard just long enough for Miranda to kick her again, this time in the stomach, sending her to the ground. The Queen sprang back up and went in for the kill. Ovaska scooted back, and instead of beheading her, Miranda's blade opened her chest, blood gushing out in its wake. Ovaska pushed herself backward again, and as Miranda brought the blade down a second time Ovaska reached down and pulled the stake from her leg, using all her remaining will to thrust it upward. Miranda felt the wood penetrate her rib cage, but she, too, had one last burst of strength to give, and as Ovaska fell down onto the ground again, Miranda's sword flashed, and Ovaska's neck parted, her body striking the concrete floor . . . followed by her head. Ovaska's arm fell outstretched, her sword landing beside her with a loud clang. For just a second Miranda heard nothing but the hoarse sound of her own breath, and the world was held suspended, the Queen's eyes on the fallen body of Marja Ovaska, the floor stained with their mingled blood. Miranda heard another thunderous pounding, and it shook her enough to make her remember . . . she wasn't finished yet. She bent over Ovaska's body and stuck her hand in the assassin's pants pocket, retrieving the ring with the keys to the basement room and cell doors. Miranda stumbled back the way she had come, her entire body begging her to fall, her strength finally failing her, in so much pain she couldn't think—but she didn't need to think. She just had to walk. She held on to the rail as she half fell down the stairs, her vision swimming black and gray, her breath nothing but wheezes; the stake had collapsed her lung. She absently reached up and pulled it, but she didn't even feel the wood leaving her body. She had to keep going. In just a minute . . . in just a minute she could lie down . . . The Queen fell against the cell door, swinging with it into the cell itself. Her fingers were numb around the keys, but she used the bars to support herself and put one foot in front of the other, forcing herself to keep going. "Sweet Jesus," she heard someone whisper. "Miranda, sit down . . . you're going to kill yourself . . ." Stubbornly she shook her head and sagged into the back wall, trying to focus her gaze on the keys enough to figure out which one went to the shackles. "Miranda—stop." She could barely move, but she lifted her head and met Deven's eyes. "Put your hand on my shoulder," he said softly. She started to protest, but he held her eyes. She could see how tired he was . . . so tired . . . she understood . . . she just wanted to sleep . . . "Put your hand on my shoulder, Miranda," he repeated. Shaking too violently to speak, she obeyed. "It's all right," she heard him say. "I'm ready." Miranda felt power, more than she would have believed he still had, lifted into her, a gentle current of energy that stemmed the flow of blood from her wounds, eased her pain, and helped her slide slowly to the floor instead of falling. The keys fell out of her left hand, the sword out of her right. "There," he whispered. "We can both rest now." Miranda smiled, nodded, and closed her eyes. Before the Elite even had the door open all the way, David and Jonathan both raced inside the building, into a scene of blood and death, Ovaska's headless body sprawled on the ground, her lifeless face caught in a moment of eternal shock. David had been able to feel Miranda for a few minutes, but she was gone again—back into the shielded room, he knew. She was hurt . . . badly hurt . . . dying . . . So was Deven. Jonathan faltered, gasping, his hand flying up to his Signet. "Dev . . . no, baby, don't . . ." "Over here!" Faith was pointing at an open door in the corner. David grabbed Jonathan's arm and hauled him along into the stairwell. Prime and Consort burst into the room, and David made it to Miranda's side in a heartbeat, falling to his knees beside her and pulling her into his arms, knocking Deven's sword out of her lap. David was already weakened, but he didn't care; he opened himself to her fully, letting the energy between them return to balance, giving her everything he could spare to heal her at least enough to make it home safely . . . but to his surprise she wasn't as bad off as he had felt she was even a moment ago, and her wounds had already stopped bleeding. He looked up in time to see Jonathan lowering Deven's body from the wall where he had been chained, the two of them sinking to the floor together. It didn't look like Deven was breathing . . . but Jonathan was still alive. There had to be some hope . . . He felt the same tide of power between the Pair that had passed between him and Miranda. Jonathan held Deven close, breathing hard, his eyes full of anguish, waiting . . . but Deven hadn't just given all his energy to Miranda, he'd given her everything, even his life force, the base energy that held the body and soul together . . . and Jonathan simply wasn't strong enough to replenish that. Desperate, David extended the connection between himself and Miranda to Jonathan. He wasn't sure if the Consort would know what to do with it the way Deven would, but Jonathan seemed to have learned a few things from his lover; he "caught" the line of energy and drew from it, his gratitude echoing along the line to David. Then, with the four of them joined as they had been that night to heal Kat, Jonathan poured the energy into Deven as gingerly as he could . . . and again they waited, afraid to even breathe, afraid to disturb the fragile equilibrium they'd managed to cobble together for the Prime. Finally, finally, David saw the Prime's lip tremble. Deven's eyes fluttered open, pupils dilating until they focused on his Consort. Jonathan smiled, so relieved he half sobbed, and kissed Deven everywhere he could that wasn't covered in bruises or blood. Deven returned the smile weakly and murmured something in Gaelic too low for David to interpret, but that made Jonathan laugh; then, with a sigh, Deven turned his face into his Consort's chest and passed out. David withdrew from the connection, shielding himself and Miranda off again. He felt Miranda stir in his arms and looked down into her face. Blood had run down her forehead from a cut and was drying on her cheek, but her skin was unmarred, and her eyes were exhausted but full of life as she blinked up at him. She started to cry. She could barely speak, but she was determined to be heard as she whispered raggedly, "David . . . Deven . . . he's . . ." "Shh . . ." He laid a finger on her lips. "He's alive, beloved. He's alive." Miranda was still crying, but she broke out into a smile and nodded with relief. Then she said, "Blood. Shower. Chocolate. You. Now." He laughed quietly, kissed her, and replied, "As you will it, my Lady." Nineteen Texas didn't have much of a winter, but what it had was wet and bitter, and autumn was already headed that way, a line of storms from the north driving freezing rain into the Hill Country with a vengeance. Esther had built a roaring fire for the Queen, clucking over her still-pale cheeks like a mother hen before leaving the suite warm and cozy and smelling faintly of herbs and candle wax. Miranda leaned her chin on her guitar and stared into the flames, absently plucking a string here and there. Despite Esther's worries, she was feeling better tonight, just shaky and tired; for the past three days she'd slept more than she'd been awake, and she hadn't left the Haven even though she was due back at the Bat Cave for a follow-up session to rerecord a couple of problematic tracks. She had told Grizzly she had the flu. Because it was going around in this nasty weather, he had no reason to doubt her. She paused and reached up to touch her Signet. Part of her wanted to cancel the entire project and give up on the idea of performing. So many people had been hurt . . . but in the end, she couldn't be anyone but who she was, and as she had told Faith, music was a part of her she wouldn't surrender unless there was no other choice. She'd find a way to make it work . . . tomorrow. Tonight, she just wanted to be warm and safe and comfortable, with the rain falling outside and the firelight soothing her inside. But her heart still ached, and her body still ached, and it was hard to feel comforted knowing how many of her friends had suffered at the hands of Marja Ovaska. It was hard not to feel guilty—for not stopping Marja sooner, for letting Sophie get killed, for a hundred things Miranda couldn't have anticipated and couldn't change even if she had. There were still questions that needed answering—chief among them, who was Ovaska working for? What did that client want with a Signet? Miranda was afraid to even contemplate that. There was a knock at the door. "Come in," she called. When she looked up, she was surprised, and said, "Deven." The Prime closed the door quietly behind him. He, too, was still drawn and tired looking, moving a little more slowly than usual. He hadn't even regained consciousness until last night. Even Jonathan's power combined with David's and Miranda's almost hadn't been enough to save him—Jonathan wasn't a healer and didn't have Deven's skill to direct the raw power as a healer could. He could only push the energy into Deven and hope it kept him alive. It was something of a miracle Deven had survived at all. It would take a while to fully recover from that, even as strong as he had been. David had apologized to Miranda a half-dozen times for taking the liberty of offering their energy . . . before she reminded him that Deven had given his own life to save her and had been the one to shield her from the explosion before that. She had no regrets about having to sleep an extra day or two if it meant that Deven was still alive . . . and that was something she'd never expected to hear herself say. Deven came to the couch where she was sitting and held something out to her. Miranda frowned. "What is this?" He smiled. "It's a sword, Miranda." "I know that. But why are you giving it to me?" "Because she's yours." Miranda set aside her guitar and took the blade he offered; it was the one he had worn here, the one David had said was new. Her fingers wrapped around the hilt, and she felt a stab of recognition—she had fought Ovaska with it, not with Sophie's sword. This one felt natural in her grip and was perfectly balanced, as if it had been created for her arm. "I had her made for you," Deven explained. "Not by Volundr, though, don't worry. Call her a wedding gift, or perhaps a peace offering." She drew the blade partway from the sheath, admiring the carving along the steel. "It's . . . she's beautiful . . . thank you." He nodded and took a step back, intending to leave, but she said, "I've been thinking." "About?" Miranda went on. "I was thinking that . . . maybe you and David should see each other again." He didn't bother—or perhaps didn't have the energy—to hide his surprise. "What?" "I don't want to be the reason that David is unhappy," she said. "He loves you. So maybe you could meet sometimes, like a weekend every couple of months, no questions asked. We could make some kind of arrangement that would work for all four of us." Deven stared at her for a long moment. Then he smiled and shook his head. "No." "Wait . . . _you're_ saying no?" "That's right." "But . . . why?" Again, the smile; a touch rueful, a touch enigmatic, a touch wry. "Because I don't want to be the reason you're unhappy." "But . . ." He reached over and touched her head as if in benediction. She felt a light energetic pulse, as if he had stroked her hair, though his hand didn't move, and it made her feel warm and safe . . . the way she had craved to feel for days. "It's time for him to be with you, Miranda. You have the right to grow together as a Pair without me interfering. Life is going to be hard enough for you already in the next few years. Perhaps one day later on we can talk about it. But for now . . . Jonathan and I are going home, where we belong." This time he did walk away, but as he opened the door, she glanced down at the sword in her hands, then looked back up and called, "Deven." He paused in the doorway without looking at her. "Yes?" She held up the blade. "David said you name your swords, and that's what this carving is." "It is indeed." "Well . . . who is she? What do I call her?" Deven smiled at her over his shoulder. "Shadowflame." The stables were heated, of course, but David still fretted over the horses' comfort in such ghastly weather, so he visited them every night for at least a few minutes. As far as he could tell, neither one was at all perturbed at being cooped up inside—the forecast called for a few days' clearing before the next front, so he hoped he could take them both out tomorrow night, but in the meantime both seemed content to be coddled. He ran his hand down Osiris's nose. The Friesian flicked his ears toward David and whuffled his hair affectionately. "Here you go," David said to the stallion, offering him a cookie from his pocket. Osiris munched contentedly on the cookie and nosed David for more, but David shook his head and chuckled, admonishing the horse. "Don't be greedy." "He can't help it," came a voice. "You're irresistible." David turned toward the sound; he hadn't felt anyone approaching, but it wasn't that surprising given who it was. "You should be in bed . . . and certainly not walking through the cold to get here." Deven shrugged. He was bundled up in his coat, with a scarf and gloves; he looked a hundred times better than he had even the night before, but still weary, even with his usual wardrobe, jewelry, and eyeliner perfectly in place. For once Deven looked older than a teenager, and it made David want to drag him into the house and tuck him back into bed whether Dev liked it or not. "Our steward called," Deven said. "The jet's been cleared to leave tonight. There's a car on the way to pick us up." "You're . . . you're leaving? Now?" "We've been away too long." When he saw the uncertainty in David's expression, he added, "I'm fine to travel, dear one. I need a few days' rest yet, but I'll sleep much more soundly in my own bed." "With your own Consort," David said—almost blurted—before he could stop himself. Deven gave him a searching look. "So that's why you were angry at me," he mused. "It wasn't just for keeping the Red Shadow secret from you . . . it was for keeping it from you but telling Jonathan." David started to make the expected denial but couldn't. He also couldn't meet Deven's eyes. "You're right." "He's my Consort, David. I don't say that to rub it in your face . . . it's just the way things are. He knows me, and loves me, in a way you can't . . . and vice versa. Each of you is a part of me, and that will never change." David noted the careful distance Deven was keeping—but that might be as much about Osiris as about David. Deven had never been comfortable around horses. Experimentally, David moved away from the stall, toward the Prime, who stood his ground. They faced each other, eyes holding for a while, before Deven said, "I suppose I'll see you at Council." "Right . . . I suppose." Another pause. "Any luck figuring out how those amulets worked?" David didn't remark on the change of subject. "Novotny's analyzing the one we found on the body as well as looking for other evidence. We didn't find anything else in the building—nothing at all, not even personal effects." "So Sophie's warehouse wasn't where Ovaska was living. It was just a holding pen for us. She might have other artifacts at her real home base." "It looks that way. We're working on finding her hideout. There's not much to go on so far, but . . . Novotny's people are smarter than the FBI and have better equipment. They'll find something." "What about her client?" "There were no other vampires in the area that night, at least none that showed up on the sensors. I had Elite canvass the neighborhood. Witnesses we questioned that night saw a limo traveling down Buckland, but it didn't stop at the building. Either her client has a shielding device of his or her own, or her client is a human." Deven nodded. "I'd wager it's a human." "Why do you say that?" "Because the Shadow only hires out to humans. Her leaving her victims' left hands behind indicates she was still following standard Shadow protocol, so it stands to reason she was working for a human." "She didn't cut off Miranda's hand." "Her client wanted Miranda alive and unspoiled." "But we can't know for sure the client is human." "Perhaps you can't. But I know my agents." David asked what had been on his mind for days. "Did you mean it when you said you didn't try to recruit me because we were sleeping together?" Deven sighed, looking down at the hay-scattered ground, then back up at David. "As I said . . . Sophie was the only agent I was ever attached to. I knew better, even as I let her keep working for me. Caring about them compromises my ability to send them into certain death. There was no way I could have done it to you." "Do you enjoy being the Alpha? Killing people for money?" The Prime gave him a mischievous grin. "I don't kill people for money, David. I pay other people to kill people for money. I'm a murder pimp." David laughed. "That's one way to put it." "And to answer your question . . . I enjoy training warriors. I enjoy the satisfaction of knowing that they're the best in the world. And it's not all about vengeance and greed. More than half of our contracts are for governments that need something done that the human military can't accomplish. Many of my people have stopped wars before they started, brought down dictators, taken out spies. I'm not ashamed of what I do . . . or of what I've done." They met each other's eyes again, and David understood what he was saying. Despite the consequences, despite almost dying, Deven would do it all again if it meant bringing Miranda to David . . . and not only had Sophie taught David's Queen, she had fought in the battle of the Haven and had a hand in ending the Blackthorn war. Deven had no regrets about that . . . and, in the end, neither did David. Finally, Deven nodded. "It's time for me to go," he said. "Take care of yourself . . . and take care of each other." "You, too." Deven reached out and took David's hand, lifting it to his lips, squeezing it, and then letting go. "Good-bye, David." David didn't expect to feel his heart breaking as Deven walked away, and yet . . . there it was. No matter what, no matter how much time or distance came between them, some part of him would always be at Deven's side, and part of Deven would always reside in David's heart. David crossed the stable to catch up to Deven, laying a hand on his shoulder. Deven stopped and turned toward him, and David saw the pain in his eyes, pain he had intended to keep hidden until he was safely twenty-five thousand feet above Texas and long gone from here. David slid his hand up to Deven's face, tipping the Prime's chin and kissing him softly. He felt Deven's arms move around him, and they held on to each other for a moment, eyes closed, memorizing the smell and taste of each other, the sound of each other's breathing. "I love you," David said into Deven's ear. Holding on to his hands, Deven stepped back, his smile remarkably like the one that David had seen on his face after he had healed Kat that night in the city: a smile of peace and happiness, untouched by the sorrow that he wore habitually beneath his coat. "I love you, too," Deven replied. Then he released David's hands and walked away. Once again, a car was waiting to take Deven and Jonathan to the airport; and once again, Faith was waiting, but this time she was standing inside the Haven's enormous front doors. Protocol be damned—it was cold outside. The Pair emerged from the hallway with their honor guard. The rest of their Elite were already on the way back to California, but their bodyguards would travel on the jet with them. David and Miranda had said their good-byes to the Pair in private. They were trying to keep as much of the story under wraps as possible to avoid causing gossip about Ovaska's intentions or origins, so they had all agreed not to make a dramatic production of the farewell; but this time no one was slinking away, just observing tradition in truth instead of hiding behind it. This time there were no furtive glances, and Deven and Jonathan were side by side. Faith was just glad to have a chance to hug them both. She smiled to herself. Jonathan gave his Prime a kiss on the forehead, and Deven looked up at him with an indulgent sparkle in his eyes. Yes, this time things were different. Thank God for that. "I'm sorry about Lalita," Deven told her. Faith nodded. "So am I . . . you lost her, too." "Thank you for not being pissed off about that," Jonathan added. "Like Dev said . . . her commitment to her post was genuine." "I know." Faith raised an eyebrow at Deven and said, "But we'll be changing our employee screening methods from here on out." The Prime smiled. "Don't worry, Faith. She was the only agent I had here." Now she gave him a look. "Please, Sire. Surely you know that nothing you say is ever going to go without question again." The smile widened. "Good." Jonathan winked at her. "Take care, Faith. And keep an eye on those two." "As always." Their guards started to open the door, but Faith asked, "Can I ask you something, Sire?" Deven turned back to her, lifting his chin inquisitively. Faith moved close enough that her voice wouldn't carry through the hall. "Why didn't you ever try to recruit me for the Shadow? Was I not a good enough warrior? Not trustworthy enough?" Deven regarded her silently for a moment, considering her question. "You are an excellent warrior, Faith. You would have made a superlative agent." "Then why . . ." Deven's gaze traveled up the stairs, to where Faith realized David was standing at the balcony rail. He smiled and gave Deven a little wave before walking on toward his workroom. When Faith looked back down, Deven was watching her face carefully, and he said with equal care, "Because I demand absolute loyalty from my agents, Faith . . . and I knew that you were already devoted to someone else." Faith frowned. "What does that—" Deven shook his head, smiling. "Don't insult your own intelligence, Faith, or mine. We both know why you're really here." She started to stammer a rebuttal, but he gave her a knowing look that silenced her; then he turned back toward the door, took Jonathan's arm, and left Faith standing in the doorway with her face turning scarlet and her heart in her throat. "It's over." Kat looked up from the box of books she was taping, unsurprised to see Miranda standing in the doorway, resplendent in her long black coat. "Good." Miranda didn't ask what Kat was doing; she didn't protest or try to change Kat's mind. She offered no apologies. She simply sat down on the arm of the couch, silent, and watched Kat pack. "I'm going to stay with my mom until the baby's born," Kat said. "I don't know exactly what I'll do after that. I might do private counseling. Or teach." No reply. Kat wrote _BOOKS_ on the box with a fat Sharpie, then capped the marker and looked at Miranda. "I can't do this anymore." Miranda nodded. "I understand." Kat looked down at the pile of books that had to go in the next box. The one on top was an old Robert Jordan hardcover. It had been Drew's. She rested her hand on the dust jacket for a moment, then said, "Tell me this is all a nightmare, Miranda. Tell me I'm going to wake up a year ago, before any of this happened." She raised her eyes to Miranda, whose expression was strange: not disdainful, exactly, but distant, perhaps detached . . . no, that wasn't it. There was plenty of emotion in Miranda's face, but there was something else as well . . . and it wasn't human. The woman sitting on her couch wasn't human. She might look like one to most people. She might pass for one onstage. She might drink a beer or eat an ice cream sundae. But everything about her, from the tumble of her dark red hair to the almost predatory grace in her posture, was carved out of something ancient and alien . . . something that, Kat had finally realized, was going to kill everything mortal she touched. Something in Miranda had changed, and it would continue to change long after Kat had died of old age. Slowly, the darkness within her was unfolding, its tendrils curling around Miranda's soul, giving her strength, but also stealing her away, the way children in fairy tales had been stolen by elves in the night, leaving a changeling in the cradle. This was a woman with work to do, and that work had no room in it for pregnant best friends, or anything that would bind her to the world she had left behind. She had killed people, had beheaded a woman, would probably kill more, in the name of law and order and justice in a world so far beyond Kat's grasp it might as well be the gilded halls of the gods themselves. Suddenly Kat couldn't look at her. She stared, instead, at the door to the guest bathroom . . . where Miranda had turned into a vampire. "Aren't you going to say anything?" A sigh. "I said I understand." "And that's it?" Miranda's fingers absently touched the stone of her Signet. "You have to do what you think is best for you and your daughter. I don't blame you for being afraid, or tired, or wanting to run. You've lost so much because of me . . . and the truth is, you will probably lose more if you stay." Kat took a deep breath. "Are there any vampires in West Oak?" Miranda smiled slightly. "Not that we know of." Kat nodded, swallowing. She wanted to say she'd e-mail or call. But she knew—they both knew—it wasn't true. Still, Miranda made the effort. "If you or the baby need anything, ever . . ." "Yeah. I'll call." Silence stretched out between them, but finally Miranda said in a soft, sad voice, "Thank you for being my friend, Kat." Kat felt tears burn her eyes, and she started to say something, looking up at Miranda . . . . . . but the Queen was already gone. Miranda closed the front door of Kat's house behind her. She leaned back against the door for a moment, eyes shut tightly, and took a deep breath. It was raining, slow and steady, a quiet rain that seemed to blur everything, make it softer and gentler, even emotions that were hard and jagged and felt like teeth ripping through her heart. She tried to breathe in the softness, to release the pain. When she opened her eyes again David was standing by the curb, hands in his coat pockets, watching her silently. She reached up and wiped impatiently at her eyes. David sighed and opened his arms. Miranda walked down the steps and into his embrace, and they held on to each other for a long time, her face buried in his shoulder, his hand stroking her hair. When she drew back, she didn't speak, and he didn't expect her to. He simply took her hand and walked with her down the street away from Kat's house, into a cold and rainy night at the receding edge of autumn, one year turning slowly into the next, one season at its end, another just beginning. Click here for more books by this author Epilogue She watched from the roof as the dark red-haired figure ran down the street, her leather coat flying out behind her, her boots striking the pavement with deadly purpose. Behind the Queen a cadre of black-clad warriors followed at speed. They chased the man almost to the end of the block before the Queen drew up short, her hand shooting out in a quick flicking gesture, and a trash can flew from the side of the building onto the sidewalk, right into the path of her prey. The man hit the trash can hard and fell over it, landing in a sprawl. He tried to get to his feet and run again, but by the time he got up he was surrounded. Rough hands grabbed his shoulders and hauled him to the red-haired woman, whose green eyes were those of a serpent, coiled, hungry. The Queen removed something from her coat. "Do you know why we came for you, Mr. Shikai?" The man stammered something. His eyes were huge and he was drenched in cold sweat. "Weeks ago we showed you this sketch, Mr. Shikai, and asked if you had ever seen this woman before. You said no." "Don't know her," he panted. "I swear, I don't." The Queen tilted her head to one side, considering the man before her dispassionately. "Trace evidence found on her corpse links her to your building, Mr. Shikai. We know she lived there. We searched the building and found nothing, so I have to ask you: What did you do with her belongings?" "Nothing! She didn't leave anything!" "Ah, but we know you're lying," she replied, stepping closer. "We tracked a particular artifact to that building—an amulet that gave off a very distinct energy signature. It was there yesterday, long after she was dead. It was gone tonight. What did you do with her things, Mr. Shikai?" "Nothing! I swear, I—" "Do you remember the night your wife died a hundred years ago?" the Queen cut in coldly, moving so close she was inches from his ashen face. "Do you remember the pain you felt holding her lifeless body in your arms?" "How did you know—" "I can make you relive that night over and over again," she said, lowering her voice until the moment felt almost intimate. "I can trap your mind in a loop of grief and agony that never ends. I can go through your memories and find every hurt you've ever caused, every one you've ever felt, and you'll spend the rest of your immortality there." He was shaking, staring at her, her power gradually amplifying the fear he already felt until he was so petrified he could think of nothing but escape—and the only way to escape was to give the Queen what she wanted. "I moved them," he said in a hoarse whisper. "Storage unit. Number eighty-five. Victory Storage on Burnet." She stared at him a moment longer, ascertaining whether he was telling the truth, and then took a step back. The man's relief was immense, and his knees seemed to give out. He knelt on the sidewalk panting. The Queen gestured for the others to move back out of the man's way, saying, "Next time my Elite question you, Mr. Shikai, I suggest you simply tell the truth. Ovaska may have terrified you into keeping her secrets, but I was the one who took her head . . . and if you lie to me again, I'll take yours." He said something that was either gratitude or an apology, then lurched to his feet, staggering away as fast as he could. The Queen spoke quietly into the band on her wrist, and her warriors began to melt back into the night that had created them. Then, as if she'd sensed something, perhaps some movement on the roof above, or perhaps someone watching her, the redhead looked up at the building's roof, eyes narrowed, her gaze penetrating. All she saw were shadows. Lydia smiled from the darkness. Let her wonder . . . The Queen would know her soon enough. _Ace Books by Dianne Sylvan_ QUEEN OF SHADOWS SHADOWFLAME	{ "redpajama_set_name": "RedPajamaBook" }	6,878
\section{Introduction } The problem of finding the number of spanning trees of a finite graph is a relevant and long standing question. It has been considered in different areas of mathematics~\cite{OxYa11}, physics~\cite{LiWuZhCh11}, and computer science~\cite{NiPaPa14}, since its introduction by Kirchhoff in 1847~\cite{Ki1847}. This graph invariant is a parameter that characterizes the reliability of a network~\cite{Bo86,Co87,PeBoSu98} and is related to its optimal synchronization~\cite{TaMo06} and the study of random walks~\cite{Al90}. It is also of interest in theoretical chemistry, see for example~\cite{BrMaPoRo96}. The number of spanning trees of a graph can be computed, as shown in many basic texts on graph theory~\cite{GoRo01}, from Kirchhoff's matrix-tree theorem~\cite{ChKl78} and it is given by the product of all nonzero eigenvalues of the Laplacian matrix of the graph. Although this result can be applied to any graph, the calculation of the number of spanning trees from the matrix theorem is analytically and computationally demanding, in particular for large networks. Not surprisingly, recent work has been devoted to finding alternative methods to produce closed-form expressions for the number of spanning trees for particular graphs such as grid graphs~\cite{NiPa04}, lattices~\cite{Wu77,ShWu00,ZhLiWuZo11,ZhWu15}, the small-world Farey graph~\cite{ZhCo11,ZhWuLi12,YiZhLiCh15}, the Sierpi\'nski gasket~\cite{TeWa06,ChChYa07}, self-similar lattices~\cite{TeWa11,TeWa11JSP}, etc. Most of the previous work focused on counting spanning trees on various graphs~\cite{OxYa11}. However, the number of spanning trees is an integrated, coarse characteristic of a graph. Once the number of spanning trees is determined, the next step is to explore and understand the geometrical structure of spanning trees. In this context, it is of great interest to compute the probability distribution of different coordination numbers at a given vertex among all the spanning trees~\cite{Al91}, which encodes useful information about the role the vertex plays in the whole network. Due to the computational complexity of the calculation, this geometrical feature of spanning trees has been studied only for very few graphs, such as the $\mathbb{Z}^d$ lattice~\cite{BuPe93}, the square lattice~\cite{MaDhMa92}, and the Sierpi\'nski graph~\cite{ChCh10}. It is non-trivial to study this geometrical structure for other graphs. In this paper, we study the number and structure of spanning trees of the Hanoi graph. This graph, which is also known as the Tower of Hanoi graph~\cite{HiKlMiPeSt13}, comes from the well known Tower of Hanoi puzzle, as the graph is associated to the allowed moves in this puzzle. There exist an abundant literature on the properties of the Hanoi graph, which includes the study of shortest paths, average distance, planarity, Hamiltonian walks, group of symmetries, average eccentricity, to name a few, see~\cite{HiKlMiPeSt13} and references therein. In~\cite{TeWa11JSP}, Teufl and Wagner obtained the number of spanning trees of different self-similar lattices, including the Hanoi graph. {Here, based on the self-similarity of the Hanoi graph, we enumerate its spanning trees and compute for each vertex of the graph its degree distribution among all spanning trees.} \section{The Hanoi graph} The Hanoi graph is derived from the Tower of Hanoi puzzle with $n$ discs~\cite{HiKlMiPeSt13}. We can consider each legal distribution of the $n$ discs on the three peg, a state, as a vertex of the Hanoi graph, and an edge is defined if one state can be transformed into another by moving one disc. If we label the three pegs 0, 1 and 2, any legal distribution of the $n$ discs can be written as the vector/sequence $\alpha_1\alpha_2\ldots\alpha_n$ where $\alpha_i$ ($1\leq i \leq n$) gives the location of the $(n+1-i)$th largest disc. We will denote as $H_n$ the Hanoi graph of $n$ discs. Fig.~\ref{han} shows $H_1$, $H_2$ and $H_3$. \begin{figure}[htb] \begin{center} \includegraphics[width=0.5\textwidth,angle=90,trim=40 60 100 40]{HanoiWeb01} \end{center} \caption{Hanoi graphs $H_1$, $H_2$ and $H_3$.}\label{han} \end{figure} Note that $H_{n+1} (n\ge 1)$ can be obtained from three copies of $H_{n}$ joined by three edges, each one connecting a pair of vertices from two different replicas of $H_{n}$, as shown in Fig.~\ref{str}. From the construction rule, we find that the number of vertices or order of $H_n$ is $3^n$ while the number of edges is $\frac{3}{2}(3^n-1)$. \begin{figure}[htb] \begin{center} \includegraphics[width=0.6\textwidth]{IterativeConFC} \end{center} \caption{Construction rules for the Hanoi graph. $H_{n+1}$ is obtained by connecting three graphs $H_{n}$ labeled here by $H^1_{n}$, $H^2_{n}$ and $H^3_{n}$.}\label{str} \end{figure} In the next section will make use of this recursive construction to find the number of spanning trees of $H_n$ at any iteration step $n$. \section{The number of spanning trees in $H_n$} If we denote by $V_n$ and $E_n$ the number of vertices and edges of $H_n$, then a spanning subgraph of $H_n$ is a graph with the same vertex set as $H_n$ and a number of edges $E_n^\prime$ such that $E_n^\prime < E_n$. A spanning tree of $H_n$ is a spanning subgraph that is a tree and thus $E_n^\prime = V_n-1$. In this section we calculate the number of spanning trees of the Hanoi graph $H_n$. We adapt the decimation method described in~\cite{Dh77,DhDh97,KnVa86}, which has also been successfully used to find the number of spanning trees of the Sierpi\'nski gasket~\cite{ChChYa07}, the Apollonian network~\cite{ZhWuCo14}, and some fractal lattices~\cite{ZhLiWuZo11}. This decimation method is in fact the standard renormalization group a pproach~\cite{Wi1975} in statistical physics, which applies to many enumeration problems on self-similar graphs~\cite{TeWa07}. We make use of the particular structure of the Hanoi graph to obtain a set of recursive equations for the number of spanning trees and spanning subgraphs, which then can be solved by induction. {Let ${\rm S}_n$ denote the set of spanning trees of $H_n$. Let ${\rm P}_n$ (${\rm R}_n$, ${\rm T}_n $) denote the set of spanning subgraphs of $H_n$, each of which consists of two trees with the outmost vertex $22\ldots 2$ ($00\ldots 0$, $11\ldots 1$) belonging to one tree while the other two outmost vertices being in the second tree. And let ${\rm L}_n$ denote the set of spanning subgraphs of $H_n$, each of which contains three trees with every outmost vertex in a different tree. These five types of spanning subgraphs are illustrated schematically in Fig.~\ref{sub}, where we use only the three outmost vertices to represent the graph because the edges joining the subgraphs to which they belong provide all the information needed to obtain the Hanoi graph at the next iteration. Let $s_n$, $p_n$, $r_n$, $t_n$, and $l_n$ denote the cardinality of sets ${\rm S}_n$, ${\rm P}_n$, ${\rm R}_n$, ${\rm T}_n$, and ${\rm L}_n$, respectively.} \begin{figure}[ht] \begin{center} \includegraphics[width=0.25\textwidth,trim=170 480 180 550,angle=90]{SubGraph03} \end{center} \caption{Illustration for the five types of spanning subgraphs derived from $H_n$. Two outmost vertices joined by a solid line are in one tree while two outmost vertices belong to different trees if they are connected by a dashed line.}\label{sub} \end{figure} \begin{lemma} \label{th:sub} The five classes of subgraphs ${\rm S}_n$, ${\rm P}_n$, ${\rm R}_n$, ${\rm T}_n $ and ${\rm L}_n$ form a complete set because each one can be constructed iteratively from the classes of subgraphs ${\rm S}_{n-1}$, ${\rm P}_{n-1}$, ${\rm R}_{n-1}$, ${\rm T}_{n-1}$ and ${\rm L}_{n-1}$. \end{lemma} We do not prove this Lemma here, since we will enumerate each case. However the proof follows from the fact that $H_{n}$ can be constructed from three $H_{n-1}$ by joining their outmost vertices and each of the five subgraphs are associated with different ways to produce the spanning trees. Next we will establish a recursive relationship among the five parameters $s_n$, $p_n$, $r_n$, $t_n$ and $l_n$. We notice that the equation $p_n = r_n = t_n$ holds as a result of symmetry, thus, in some places of the following text, we will use $p_n$ instead of $r_n$ and $t_n$. \begin{lemma} \label{th:fn} For the Hanoi graph $H_n$ with $n \geq 1$, \begin{equation}\label{eq:sna} s_{n+1} = 3s^3_{n}+6s^2_n p_n\,, \end{equation} \begin{equation}\label{eq:snb} p_{n+1} = s^3_n+7s^2_np_n+7s_np^2_n+s^2_nl_n \,, \end{equation} \begin{equation} \label{eq:snc} l_{n+1} = s^3_n+12s^2_n p_n+3s^2_n l_n+36s_n p^2_n+12s_n p_n l_n+14 l^3_n\,. \end{equation} \end{lemma} \begin{proof} This lemma can be proved graphically. Fig.~\ref{fn} shows a graphical representation of Eq.~\eqref{eq:sna}. Fig.~\ref{pn} provides a case enumeration for $p_{n+1}$. Fig.~\ref{ln} and Fig.~\ref{lnplus} give the enumeration detail of all configurations that contribute to $l_{n+1}$. \end{proof} \begin{figure}[ht] \begin{center} \includegraphics[width=0.30\textwidth,trim=120 380 150 350,angle=90]{Sn04} \end{center} \caption{Illustration of the configurations needed to find $s_{n+1}$.} \label{fn} \end{figure} \begin{figure}[htb] \begin{center} \includegraphics[width=0.7\textwidth,trim=30 130 30 80,angle=90]{Pn05} \end{center} \caption{{Illustration of the configurations needed to find $p_{n+1}$.}} \label{pn} \end{figure} \begin{figure}[htb] \begin{center} \includegraphics[width=0.6\textwidth,angle=90,trim=30 0 0 0]{Hn06} \end{center} \caption{Spanning subgraphs of $H_{n+1}$ that contribute to the term $s^3_{n}+12s^2_np_n+3s^2_nl_n+12s_np_nl_n+14p^3_n$ of $l_{n+1}$.} \label{ln} \end{figure} \begin{figure}[ht] \begin{center} \includegraphics[width=0.6\textwidth,angle=90,trim=20 100 0 0]{Hn07} \end{center} \caption{Spanning subgraphs of $H_{n+1}$ that contribute to the term $36s^2_{n}p_{n}$ of $l_{n+1}$.} \label{lnplus} \end{figure} \begin{lemma} \label{th:fnpnln} For the Hanoi graph $H_n$ with $n \geq 1$, $s_n l_n=3p_n^2$. \end{lemma} \begin{proof} By induction. For $n=1$, using the initial conditions $s_1=3$, $p_1=1$ and $l_1=1$, the result is true. Let us assume that for $n=k$, the lemma is true. For $n=k+1$, using Lemma~\ref{th:fn}, we have that \begin{align} s_{k+1}l_{k+1}-3p_{k+1}^2&= (3s_k^3+6s_k^2p_k)(s_k^3+12s_k^2p_k+3s_k^2l_k+36s_kp_k^2+12s_kp_kl_k\\ &\quad +14p_k^3)-3(s_k^3+7s_k^2p_k+7s_kp_k^2+s_k^2l_k)^2\\ &= 3s_k^2(s_k^2+4s_kp_k+7p_k^2-s_kl_k)(s_kl_k-3p_k^2)\,. \end{align} By induction hypothesis $s_{k}l_{k}-3p_{k}^2=0$, we obtain the result. \end{proof} \begin{lemma} \label{th:fnfn} For the Hanoi graph $H_n$ with $n \geq 1$, $\frac{s_{n+1}}{s_n^3}=\frac{5^n}{3^{n-1}}$. \end{lemma} \begin{proof} From Eq.~\eqref{eq:sna}, we have \begin{equation} \frac{s_{n+1}}{s_n^3}=\frac{3s_n^3+6s_n^2p_n}{s_n^3}=3+6\frac{p_n}{s_n}, \end{equation} which can be rewritten as \begin{equation} \frac{p_n}{s_n}=\frac{1}{6}\left(\frac{s_{n+1}}{s_n^3}-3\right). \end{equation} Using Eq.~\eqref{eq:snb} and Lemma~\ref{th:fnpnln}, we obtain \begin{align} \frac{p_{n+1}}{s_n^3}&= 1+7\frac{p_n}{s_n}+10\left(\frac{p_n}{s_n}\right)^2 \\ &= 1+7\left[\frac{1}{6}\left(\frac{s_{n+1}}{s_n^3}-3\right)\right]+10\left[\frac{1}{6}\left(\frac{s_{n+1}}{s_n^3}-3\right)\right]^2\\ &= -\frac{s_{n+1}}{2s_n^3}+\frac{5s_{n+1}^2}{18s_n^6}, \end{align} which leads to \begin{equation} \frac{p_{n+1}}{s_{n+1}}=\frac{p_{n+1}}{s_n^3}\frac{s_n^3}{s_{n+1}}=\left(-\frac{s_{n+1}}{2s_n^3}+\frac{5s_{n+1}^2}{18s_n^6}\right)\frac{s_n^3}{s_{n+1}}=-\frac{1}{2}+\frac{5s_{n+1}}{18s_n^3}. \end{equation} According to Eq.~\eqref{eq:sna}, we have $s_{n+2}=3s^3_{n+1}+6s^2_{n+1} p_{n+1}$ and \begin{equation} \frac{s_{n+2}}{s_{n+1}^3}=3+6\frac{p_{n+1}}{s_{n+1}}=3+6\left(-\frac{1}{2}+\frac{5s_{n+1}}{18s_n^3}\right)=\frac{5s_{n+1}}{3s_n^3}, \end{equation} which, together with the initial condition $\frac{s_2}{s_1^3}=5$ yields \begin{equation} \frac{s_{n+1}}{s_n^3}=\frac{5^n}{3^{n-1}}\,. \end{equation} \end{proof} We now give one of the main results of this paper. { \begin{theorem}\label{th:solve} For the Hanoi graph $H_n$, with $n\geq 1$, the number of spanning trees $s_n$ and spanning subgraphs $p_n$ and $l_n$ is \begin{equation}\label{so:sna} s_n=3^{\frac{1}{4}3^n+\frac{1}{2}n-\frac{1}{4}}\cdot 5^{\frac{1}{4}3^n-\frac{1}{2}n-\frac{1}{4}}, \end{equation} \begin{equation}\label{so:snb} p_n=\frac{1}{6}\cdot\frac{5^n-3^n}{5^n}\cdot3^{\frac{1}{4}3^n-\frac{1}{2}n+\frac{3}{4}}\cdot5^{\frac{1}{4}3^n+\frac{1}{2}n-\frac{1}{4}}, \end{equation} \begin{equation}\label{so:snc} l_n=\frac{1}{4}\cdot\left( {3^n-5^n}\right)^2\cdot 3^{\frac{1}{4}3^n-\frac{3}{2}n+\frac{3}{4}}\cdot5^{\frac{1}{4}3^n-\frac{1}{2}n-\frac{1}{4}}\,. \end{equation} \end{theorem}} \begin{proof} From Lemma \ref{th:fnfn}, we have $s_{n+1}=\frac{5^n}{3^{n-1}}s_n^3$, which with initial condition $s_1=3$ gives Eq.~\eqref{so:sna}. From the proof of Lemma~\ref{th:fnfn} we know that $p_n=\frac{s_{n+1}-3s_n^3}{6s_n^2}$. Inserting the expressions for $s_{n+1}$ and $s_n$ in Eq.~\eqref{so:sna} into this formula leads to $p_n$. Lemma~\ref{th:fnpnln} gives $l_n=\frac{3p_n^2}{s_n}$. Using the obtained results for $s_n$ and $p_n$, we arrive at $l_n$. \end{proof} Note that Eq.~\eqref{so:sna} was previously obtained~\cite{TeWa11} by using a different method. After finding an explicit expression for the number of spanning trees of $H_n$, we now calculate its spanning tree entropy which is defined as: \begin{equation} \label{eq:en} h=\lim_{V_n \to \infty}\frac{s_n}{V_n} \end{equation} where $V_n$ denotes the number of vertices, see~\cite{Ly05}. Thus, for the Hanoi graph we obtain $h=\frac{1}{4}(\ln3+\ln5)\simeq 0.677$. We can compare this asymptotic value of the entropy of the spanning trees of $H_n$ with those of other graphs with the same average degree. For example, the value for the honeycomb lattice is 0.807~\cite{Wu77} and the 4-8-8 (bathroom tile) and 3-12-12 lattices have entropy values 0.787 and 0.721, respectively~\cite{ShWu00}. Thus, the asymptotic value for the Hanoi graph is the lowest reported for graphs with average degree 3. This reflects the fact that the number of spanning trees in $H_n$, although growing exponentially, does so at a lower rate than lattices with the same average degree. \section{The degree distribution for a vertex of the spanning trees} In this section, we compute the probabilities of different coordination numbers at a given vertex on a random spanning tree on the Hanoi graph $H_n$. We note that, by using similar techniques, it has been possible to obtain more results for the closely related Siperpi\'nski graphs~\cite{ChCh10,ShTeWa14}. In the previous calculation, each vertex of $H_n$ corresponds to a state/configuration of all $n$ disks and thus is labeled by an $n$-tuple $\bm{\alpha}=\alpha_1\alpha_2\cdots\alpha_n$. In what follows for the convenience of description, we provide an alternative way of labeling vertices in $H_n$, by assigning to each vertex a sequence $\bm{\alpha}=\alpha_1\alpha_2\cdots\alpha_e$, where $1\leq e \leq n$ and $\alpha_i\in\{0,1,2\}$. The new labeling method is as follows, see Fig.~\ref{hanchan}. For $n=1$, $H_1$ is a triangle, we label the three vertices by $0$, $1$ and $2$. When $n=2$, $H_2$ contains three replicas of $H_1$, denoted by $H_1^{1}$, $H_1^{2}$, and $H_1^{3}$. On the topmost copy $H_1^{1}$, we put a prefix $0$ on the label of each node in $H_1$. Similarly, we add a prefix $1$ (or $2$) to the labeling of vertices on the leftmost (or rightmost) copy $H_1^{2}$ (or $H_1^{3}$). If a vertex's label ends with several identical digits, we just keep it once. For example, we use $010$ to replace $0100$. For $n\geq 3$, we label the vertices in $H_{n}$ by adding prefixes to three replicas of $H_{n-1}$ in the same way, and delete repetitive suffix. \begin{figure}[htb] \begin{center} \includegraphics[width=0.6\textwidth,angle=0,trim=80 60 160 20]{Fig08} \end{center} \caption{An illustration for a new labeling of vertices in $H_3$.}\label{hanchan} \end{figure} In this way, all vertices in $H_{n}$ are labeled by sequences of three digits 0, 1, and 2, with different length ranging from 1 to $n$, and each vertex has a unique labeling. For example, for all $n$, the three outmost vertices of $H_{n}$ have labels of 0, 1, and 2, while the other six outmost vertices of $H_{n-1}^{1}$, $H_{n-1}^{2}$, and $H_{n-1}^{3}$ forming $H_{n}$, each has a label consisting of two digits, which are called connecting vertices hereafter. After labeling the vertices in $H_{n}$, we are now in a position to study the probability distribution of degree for a vertex on all spanning trees. For this purpose, we introduce some quantities. \begin{definition} Consider a vertex $\bm{\alpha}$ in $H_n$. We define $s_{n,i}(\bm{\alpha})$ as the number of spanning trees in which the degree of the node $\bm{\alpha}$ is $i$. Then the probability that among all spanning tree the degree of vertex $\bm{\alpha}$ is $i$ is defined by $S_{n,i}(\bm{\alpha})=s_{n,i}(\bm{\alpha})/s_n$. {Similarly, we define $r_{n,i}(\bm{\alpha})$ $(t_{n,i}(\bm{\alpha})$, $p_{n,i}(\bm{\alpha}))$ as the number of spanning subgraphs consisting of two trees such that one outmost vertex $0$ $(1$, $2)$ is in one tree while the other two outmost vertices $1$ and $2$ $(0$ and $2$, $0$ and $1)$ are in the other tree, and the degree of $\bm{\alpha}$ is $i$. Define the probabilities $R_{n,i}(\bm{\alpha})=r_{n,i}(\bm{\alpha})/r_n$, $T_{n,i}(\bm{\alpha})=t_{n,i}(\bm{\alpha})/t_n$ $P_{n,i}(\bm{\alpha})=p_{n,i}(\bm{\alpha})/p_n$.} Finally, we define $l_{n,i}(\bm{\alpha})$ as the number of spanning subgraphs containing three trees such that the three outmost vertices $0$, $1$ and $2$ belongs to a different tree, and the degree of $\bm{\alpha}$ is $i$. Define the probability $L_{n,i}(\bm{\alpha})=l_{n,i}(\bm{\alpha})/l_n$. \end{definition} In the following text, we will first determine $S_{n,i}(\bm{\alpha})$ for the three outmost vertices in in $H_n$, then we will compute $S_{n,i}(\bm{\alpha})$ for the six connecting vertices, and finally we will calculate $S_{n,i}(\bm{\alpha})$ for an arbitrary vertex $\bm{\alpha}$. For the three outmost vertices 0, 1, and 2, each has a degree of 2, and thus $s_{n,3}(0)=p_{n,3}(0)=l_{n,3}(0)=0$. In addition, by symmetry we have $s_{n,i}(0)=s_{n,i}(1)=s_{n,i}(2)$, $p_{n,i}(0)=p_{n,i}(1)$ for $i=1,2$, and $l_{n,i}(0)=l_{n,i}(1)=l_{n,i}(2)$ for $i=0,1,2$. Hence, for the outmost vertices, we only need to find $S_{n,i}(0)$ for $i=1,2$. \subsection{Determination of $S_{n,i}(0)$ with $i=1,2$} For the graph $H_n$, associated with the Tower of Hanoi puzzle with $n$ disc, we have the following result. {\begin{theorem}\label{ther1} For the Hanoi graph $H_n$ with $n\ge1$, \begin{equation} \label{sn120a} S_{n,1}(0) = \frac{5}{7}-\frac{5}{7}\left(\frac{1}{15}\right)^n\,, \end{equation} \begin{equation} \label{sn120b} S_{n,2}(0)=\frac{2}{7}+\frac{5}{7}\left(\frac{1}{15}\right)^n\,. \end{equation} \begin{equation} \label{pn120a} P_{n,1}(0) = \frac{5}{7}+\frac{9\cdot 5^n+5\cdot 3^n}{7\cdot15^n\cdot(5^n-3^n)}\,, \end{equation} \begin{equation} \label{pn120b} P_{n,2}(0)=\frac{2}{7}-\frac{9\cdot 5^n+5\cdot 3^n}{7\cdot15^n\cdot(5^n-3^n)}\,, \end{equation} \begin{equation} \label{Pn0n12a} P_{n,0}(2)=\frac{5\cdot(15^n-1)}{7\cdot5^n\cdot(5^n-3^n)} \,, \end{equation} \begin{equation} \label{Pn0n12b} P_{n,1}(2)=\frac{5}{7}-\frac{12}{7}\left(\frac{1}{15}\right)^n-\frac{3\cdot(15^n-1)}{7\cdot5^n\cdot(5^n-3^n)}\,, \end{equation} \begin{equation} \label{Pn0n12c} P_{n,2}(2)=\frac{2}{7}+\frac{12}{7}\left(\frac{1}{15}\right)^n-\frac{2\cdot(15^n-1)}{7\cdot5^n\cdot(5^n-3^n)}\,, \end{equation} \begin{equation} \label{Hn0n1n20a} L_{n,0}(0)=\frac{10\cdot3^n}{21\cdot(5^n-3^n)}+\frac{18\cdot5^n+10\cdot3^n}{21\cdot5^n\cdot(5^n-3^n)^2}\,, \end{equation} \begin{equation} \label{Hn0n1n20b} L_{n,1}(0)=\frac{5}{7}+\frac{9}{7}\left(\frac{1}{15}\right)^n-\frac{2\cdot(15^n-1)}{7\cdot5^n\cdot(5^n-3^n)}-\frac{8\cdot3^n}{3\cdot5^n\cdot(5^n-3^n)^2}\,, \end{equation} \begin{equation} \label{Hn0n1n20c} L_{n,2}(0)=\frac{2}{7}-\frac{9}{7}\left(\frac{1}{15}\right)^n-\frac{4\cdot(15^n+6)}{21\cdot5^n\cdot(5^n-3^n)}+\frac{4\cdot3^n}{3\cdot5^n\cdot(5^n-3^n)^2}\,. \end{equation} \end{theorem} } In order to prove Theorem~\ref{ther1} and other main results, we shall first give the following lemma. \begin{lemma}\label{Lemma01} For the Tower of Hanoi graph $H_n$ with $n\geq1$, \begin{equation} \label{sn1sn2a} s_{n,1}(0)=\left(\frac{5}{7}-\frac{5}{7}\left(\frac{1}{15}\right)^n\right)\cdot3^{\frac{1}{4}3^n+\frac{1}{2}n-\frac{1}{4}} \cdot 5^{\frac{1}{4}3^n-\frac{1}{2}n-\frac{1}{4}}\,, \end{equation} \begin{equation} \label{sn1sn2b} s_{n,2}(0)=\left(\frac{2}{7}+\frac{5}{7}\left(\frac{1}{15}\right)^n\right)\cdot3^{\frac{1}{4}3^n+\frac{1}{2}n-\frac{1}{4}} \cdot 5^{\frac{1}{4}3^n-\frac{1}{2}n-\frac{1}{4}}\,, \end{equation} \begin{equation} \label{pn1n2sola} p_{n,1}(0)=\left(\frac{5}{14}\frac{5^n-3^n}{5^n}+\frac{9\cdot5^n+5\cdot3^n}{14\cdot75^n}\right)\cdot3^{\frac{1}{4}3^n-\frac{1}{2}n-\frac{1}{4}}\cdot5^{\frac{1}{4}3^n+\frac{1}{2}n-\frac{1}{4}}\,, \end{equation} \begin{equation} \label{pn1n2solb} p_{n,2}(0)=\left(\frac{1}{7}\frac{5^n-3^n}{5^n}-\frac{9\cdot5^n+5\cdot3^n}{14\cdot75^n}\right)\cdot3^{\frac{1}{4}3^n-\frac{1}{2}n-\frac{1}{4}}\cdot5^{\frac{1}{4}3^n+\frac{1}{2}n-\frac{1}{4}}\,, \end{equation} \begin{equation} \label{pn02sola} p_{n,0}(2) =\frac{1}{14}\left(1-\frac{1}{15^n}\right)\cdot3^{\frac{1}{4}3^n+\frac{1}{2}n-\frac{1}{4}}\cdot5^{\frac{1}{4}3^n-\frac{1}{2}n+\frac{3}{4}}\,, \end{equation} \begin{equation} \label{pn02solb} p_{n,1}(2)=\frac{5}{14}\left(1-\frac{8\cdot3^n}{5\cdot5^n}-\frac{12}{5\cdot15^n}+\frac{3}{25^n}\right)\cdot3^{\frac{1}{4}3^n-\frac{1}{2}n-\frac{1}{4}}\cdot5^{\frac{1}{4}3^n+\frac{1}{2}n-\frac{1}{4}}\,, \end{equation} \begin{equation} \label{pn02solc} p_{n,2}(2)=\frac{12}{7}\left(1-\frac{2\cdot3^n}{5^n}+\frac{6}{15^n}-\frac{5}{25^n}\right)\cdot3^{\frac{1}{4}3^n-\frac{1}{2}n-\frac{1}{4}}\cdot5^{\frac{1}{4}3^n+\frac{1}{2}n-\frac{1}{4}}\,, \end{equation} \begin{equation} \label{ln02sola} l_{n,0}(0) = \frac{5}{14}\left(\frac{5^n-3^n}{5^n}+\frac{9}{5\cdot15^n}+\frac{1}{25^n}\right)\cdot3^{\frac{1}{4}3^n-\frac{1}{2}n-\frac{1}{4}} \cdot5^{\frac{1}{4}3^n+\frac{1}{2}n-\frac{1}{4}}\,, \end{equation} \begin{small} \begin{equation} \label{ln02solb} l_{n,1}(0)=\frac{15}{28}\left(1-\frac{12\cdot3^n}{5\cdot5^n}+\frac{7\cdot9^n}{5\cdot25^n}+\frac{9}{5\cdot15^n}-\frac{16}{5\cdot25^n}\right) 3^{\frac{1}{4}3^n-\frac{3}{2}n-\frac{1}{4}} \cdot5^{\frac{1}{4}3^n+\frac{3}{2}n-\frac{1}{4}}\,, \end{equation} \end{small} \begin{footnotesize} \begin{equation} \label{ln02solc} l_{n,2}(0)=\frac{3}{14}\left(1-\frac{8\cdot3^n}{3\cdot5^n}+\frac{5\cdot9^n}{3\cdot25^n}-\frac{9}{2\cdot15^n}+\frac{5}{25^n}+\frac{25\cdot3^n}{6\cdot125^n}\right)3^{\frac{1}{4}3^n-\frac{3}{2}n-\frac{1}{4}} \cdot5^{\frac{1}{4}3^n+\frac{3}{2}n-\frac{1}{4}}. \end{equation} \end{footnotesize} \end{lemma} \begin{proof} Based on Figs.~\ref{fn},~\ref{pn},~\ref{ln}, and~\ref{lnplus}, we can establish the following recursive relations \begin{equation} \label{sni0a} s_{n+1,i}(0) = 3s_{n,i}(0)s_n^2+2p_{n,i}(0)s_n^2+4s_{n,i}(0)s_np_n \,, \end{equation} \begin{small} \begin{equation} \label{sni0b} p_{n+1,i}(0)=s_{n,i}(0)s_n^2+p_{n,i}(0)s_n^2+6s_{n,i}(0)s_np_n+4p_{n,i}(0)s_np_n+3s_{n,i}(0)p_n^2+s_{n,i}(0)p_nl_n\,, \end{equation} \end{small} \begin{align} \label{sni0c} p_{n+1,i}(2)&= s_{n,i}(0)s_n^2+2p_{n,i}(0)s_n^2+3p_{n,i}(2)s_n^2+l_{n,i}(0)s_n^2+ \nonumber \\ &\quad 2s_{n,i}(0)s_np_n+2p_{n,i}(0)s_np_n+4p_{n,i}(2)s_np_n+s_{n,i}(0)p_n^2 \,, \end{align} \begin{align} \label{sni0d} l_{n+1,i}(0)&= s_{n,i}(0)s_n^2+2p_{n,i}(0)s_n^2+2p_{n,i}(2)s_n^2+l_{n,i}(0)s_n^2+ \nonumber\\ &\quad 8s_{n,i}(0)s_np_n+12p_{n,i}(0)s_np_n+12p_{n,i}(2)s_np_n+\nonumber\\ &\quad 4l_{n,i}(0)s_np_n+12s_{n,i}(0)p_n^2+8p_{n,i}(0)p_n^2+6p_{n,i}(2)p_n^2+\nonumber\\ &\quad 2s_{n,i}(0)s_nl_n+2p_{n,i}(0)s_nl_n+2p_{n,i}(2)s_nl_n+4s_{n,i}(0)p_nl_n\,. \end{align} Using the initial conditions $s_{1,1}(0)=2$, $s_{1,2}(0)=1$, $p_{1,1}(0)=1$, $p_{1,2}(0)=0$, $p_{1,0}(2)=1$, $p_{1,1}(2)=p_{1,2}(2)=0$, $l_{1,0}(0)=1$, and $l_{1,1}(0)=l_{1,2}(0)=0$, the above recursive relations are solved to obtain Lemma~\ref{Lemma01}. \end{proof} From Eqs.~(\ref{so:sna}-\ref{so:snc}) and Eqs.~(\ref{sn1sn2a}-\ref{ln02solc}), we can prove Theorem~\ref{ther1}. \subsection{Determination of $S_{n,i}(\bm{\alpha})$ with $\bm{\alpha}$ being connecting vertices} We proceed to calculate $S_{n,i}(\bm{\alpha})$ with $i=1,2,3$, where $\bm{\alpha}$ are the six connecting vertices, the length of whose labels is two. By definition, the six connecting vertices are 01, 10, 02, 20, 12, 21. We obtain that $S_{n,i}(01)=S_{n,i}(02)=S_{n,i}(10)=S_{n,i}(12)=S_{n,i}(20)=S_{n,i}(21)$. Since connecting vertices only exist in $H_n$ for $n\geq 2$, we only need to determine $S_{n+1,1}(01)$ for $n\geq 1$. Thus, { \begin{theorem} For the Tower of Hanoi graph $H_n$ and $n\geq1$, \begin{equation} \label{Sn1101a} S_{n+1,1}(01) = \frac{1}{14}5^{1-2n}\cdot(15^n-1) \,, \end{equation} \begin{equation} \label{Sn1101b} S_{n+1,2}(01)=\frac{1}{42}\left(30+6\cdot5^{1-2n}-3^{2+n}\cdot5^{-n}-23\cdot5^{-n}\right) \,, \end{equation} \begin{equation} \label{Sn1101c} S_{n+1,3}(01)=\frac{1}{42}\left(12-3\cdot5^{1-2n}-2\cdot3^{1+n}\cdot5^{-n}+23\cdot5^{-n}\right), \end{equation} \begin{equation} \label{pn120a} P_{n+1,1}(01)= \frac{3\cdot5^{1-2 n} \left(5^n-3^n\right) \left(15^n-1\right)}{14\left(5^{n+1}-3^{n+1}\right)}\,, \end{equation} \begin{equation} \label{pn120b} P_{n+1,2}(01)=\frac{7\left(\frac{9}{5}\right)^n+5\cdot3^{1-n}-2\cdot3^n-19\cdot5^{-n}-3\cdot5^{n+1}}{7\cdot3^{n+1}-7\cdot5^{n+1}}\,, \end{equation} \begin{small} \begin{equation} \label{pn120c} P_{n+1,3}(01)=\frac{49\cdot3^{1-n}-28\cdot3^{n+1}+3^n 5^{3-2 n}-56\cdot5^{1-n}+42\cdot5^n+2\cdot 5^{2-n}9^n}{14 \left(5^{n+1}-3^{n+1}\right)}, \end{equation} \end{small} \begin{equation} \label{hn120a} P_{n+1,1}(02) = \frac{3\cdot5^{1-2 n} \left(3\cdot5^n-3^n\right) \left(15^n-1\right)}{14\left(5^{n+1}-3^{n+1}\right)} \,, \end{equation} \begin{footnotesize} \begin{equation} \label{hn120b} P_{n+1,2}(02)=\frac{19\cdot3^{1-n}+19\cdot3^{n+1}+2\cdot3^{n+1} 5^{1-2 n}-113\cdot5^{-n}-2\cdot5^{n+2}-5^{-n}9^{n+1}}{14 \left(3^{n+1}-5^{n+1}\right)}\,, \end{equation} \begin{equation} \label{hn120c} P_{n+1,3}(02)=\frac{75^{-n} \left(106\cdot3^n 5^{n+1}-125\cdot9^n-453\cdot25^n-2\cdot5^{n+2} 27^n+184\cdot225^n-86\cdot375^n\right)}{14 \left(3^{n+1}-5^{n+1}\right)}, \end{equation} \end{footnotesize} \begin{equation} \label{h4n420a} P_{n+1,1}(20) = \frac{25^{-n} \left(5\cdot3^n+21\cdot5^n+7\cdot3^n 5^{2 n+1}-5^{n+1} 9^n\right)}{14\left(5^{n+1}-3^{n+1}\right)}\,, \end{equation} \begin{footnotesize} \begin{equation} \label{h4n420b} P_{n+1,2}(20)=\frac{55\cdot3^{-n}-19\cdot3^{n+1}+3^n 5^{1-2 n}-11\cdot5^{1-n}+2\cdot5^{n+2}+5^{-n}9^{n+1}}{14 \left(5^{n+1}-3^{n+1}\right)}\,, \end{equation} \begin{equation} \label{h4n420c} P_{n+1,3}(20)=\frac{75^{-n} \left(95\cdot9^n-38\cdot15^n-77\cdot25^n-14\cdot3^{n+1} 125^n+38\cdot135^n+52\cdot225^n\right)}{14 \left(3^{n+1}-5^{n+1}\right)}, \end{equation} \end{footnotesize} \begin{footnotesize} \begin{equation} \label{h46u420a} L_{n+1,1}(01) = \frac{25^{-n} \left(37\cdot3^n 5^{3 n+1}-25\cdot9^n+38\cdot15^n+39\cdot25^n-2\cdot3^{2 n+1}25^{n+1}+5^{n+2} 27^n\right)}{14 \left(3^{n+1}-5^{n+1}\right)^2}\,, \end{equation} \begin{align} \label{h46u420b} L_{n+1,2}(01)&=\frac{75^{-n} \left(-3^{4n+3} 5^n+27\cdot5^{3 n+1}-29\cdot3^{2 n+1} 5^{3 n+1}+2\cdot3^n 5^{4n+3}\right)}{14\left(3^{n+1}-5^{n+1}\right)^2}\nonumber\\ &\quad +75^{-n}\frac{20\cdot27^n+8\cdot25^n 27^{n+1}-13\cdot45^n-188\cdot75^n}{14\left(3^{n+1}-5^{n+1}\right)^2}\,, \end{align} \begin{align} \label{h46u420c} L_{n+1,3}(01)&=\frac{75^{-n} \left(-319\cdot3^{n+1} 25^n+62\cdot3^{3 n+1} 25^n+65\cdot27^n\right)}{14\left(3^{n+1}-5^{n+1}\right)^2}\nonumber\\ &\quad +75^{-n}\frac{199\cdot45^n+789\cdot125^n+26\cdot405^n-562\cdot1125^n+254\cdot1875^n}{14\left(3^{n+1}-5^{n+1}\right)^2}. \end{align} \end{footnotesize} \end{theorem} } \begin{proof} Based on Fig.~\ref{fn}, we have the recursion relations for the connecting vertex 01: \begin{equation} \label{length1a} s_{n+1,1}(01) = s_{n,1}(1)s_n^2+p_{n,0}(2)s_n^2 \,, \end{equation} \begin{equation} \label{length1b} s_{n+1,2}(01)=s_{n,2}(1)s_n^2+2s_{n,1}(1)s_n^2+4s_{n,1}(1)s_np_n+p_{n,1}(1)s_n^2+p_{n,1}(2)s_n^2 \,, \end{equation} \begin{equation} \label{length1c} s_{n+1,3}(01)=2s_{n,2}(1)s_n^2+4s_{n,2}(1)s_np_n+p_{n,2}(1)s_n^2+p_{n,2}(2)s_n^2\,. \end{equation} Since the quantities on the right-hand side of Eqs.~(\ref{length1a}-\ref{length1c}) have been explicitly determined, according to the relation $S_{n+1,i}(01)=s_{n+1,i}(01)/s_{n+1}$, we obtain Eqs.~(\ref{Sn1101a}-\ref{Sn1101c}). Analogously, we find $P_{n+1,i}(\bm{\alpha})$ and $L_{n+1,i}(\bm{\alpha})$, when $\bm{\alpha}$ are connecting vertices. It is obvious that $P_{n,0}(\bm{\alpha})=L_{n,0}(\bm{\alpha})=0$. Note that $l_{n,i}(01)=l_{n,i}(02)=l_{n,i}(10)=l_{n,i}(12)=l_{n,i}(20)=l_{n,i}(21)$, $p_{n,i}(01)=p_{n,i}(10)$, $p_{n,i}(02)=p_{n,i}(12)$, $p_{n,i}(20)=p_{n,i}(21)$. Using Figs.~\ref{pn},~\ref{ln}, and~\ref{lnplus}, we can establish the recursive relations \begin{equation} \label{length2a} p_{n+1,1}(01) = s_{n,1}(1)s_np_n+p_{n,0}(2)s_np_n \,, \end{equation} \begin{align} \label{length2b} p_{n+1,2}(01)&= s_{n,2}(1)s_np_n+s_{n,1}(1)s_n^2+5s_{n,1}(1)s_np_n+s_{n,1}(1)s_nl_n+ \nonumber\\ &\quad 3s_{n,1}p_n^2+p_{n,1}(1)s_n^2+3p_{n,1}(1)s_np_n+p_{n,1}(2)s_np_n \,, \end{align} \begin{align} \label{length2c} p_{n+1,3}(01)&= s_{n,2}(1)s_n^2+5s_{n,2}(1)s_np_n+s_{n,2}(1)s_nl_n+3s_{n,2}(1)p_n^2 \nonumber \\ &\quad p_{n,2}(1)s_n^2+3p_{n,2}(1)s_np_n+p_{n,2}(2)s_np_n\,, \end{align} \begin{equation} \label{length3a} p_{n+1,1}(02) = s_{n,1}(1)s_n^2+3s_{n,1}(1)s_np_n+p_{n,0}(2)s_n^2+3p_{n,0}(2)s_np_n \,, \end{equation} \begin{align} \label{length3b} p_{n+1,2}(02)&= s_{n,2}(1)s_n^2+3s_{n,2}(1)s_np_n+3s_{n,1}(1)s_np_n+s_{n,1}(1)s_nl_n+ \nonumber\\ &\quad 3s_{n,1}(1)p_n^2+p_{n,1}(2)s_n^2+3p_{n,1}(2)s_np_n+p_{n,1}(1)s_np_n \,, \end{align} \begin{align} \label{length3c} p_{n+1,3}(02)&= 3s_{n,2}(1)s_np_n+s_{n,2}(1)s_nl_n+3s_{n,2}(1)p_n^2+p_{n,2}(2)s_n^2+\nonumber\\ &\quad 3p_{n,2}(2)s_np_n+p_{n,2}(1)s_np_n \,, \end{align} \begin{equation} \label{length4a} p_{n+1,1}(20) = s_{n,1}(1)s_n^2+s_{n,1}(1)s_np_n+2p_{n,1}(1)s_n^2+p_{n,0}(2)s_n^2+p_{n,0}(2)s_np_n \,, \end{equation} \begin{align} \label{length4b} p_{n+1,2}(20)&= s_{n,2}(1)s_n^2+s_{n,2}(1)s_np_n+2p_{n,2}(1)s_n^2+s_{n,1}(1)s_np_n+\nonumber\\ &\quad s_{n,1}(1)p_n^2+2p_{n,1}(1)s_n^2+5p_{n,1}(1)s_np_n+p_{n,1}(2)s_n^2+\nonumber\\ &\quad p_{n,1}(2)s_np_n+l_{n,1}(1)s_n^2 \,, \end{align} \begin{align} \label{length4c} p_{n+1,3}(20)&= s_{n,2}(1)s_np_n+s_{n,2}(1)p_n^2+2p_{n,2}(1)s_n^2+5p_{n,2}(1)s_np_n+\nonumber\\ &\quad p_{n,2}(2)s_n^2+p_{n,2}(2)s_np_n+l_{n,2}(1)s_n^2 \,, \end{align} \begin{align} \label{length5a} l_{n+1,1}(01) &= s_{n,1}(1)s_n^2+6s_{n,1}(1)s_np_n+s_{n,1}(1)s_nl_n+4s_{n,1}(1)p_n^2+\nonumber\\ &\quad 2p_{n,1}(1)s_n^2+8p_{n,1}s_np_n+p_{n,0}(2)s_n^2+6p_{n,0}(2)s_np_n+\nonumber\\ &\quad p_{n,0}(2)s_nl_n+4p_{n,0}(2)p_n^2 \,, \end{align} \begin{align} \label{length5b} l_{n+1,2}(01)&= s_{n,2}(1)s_n^2+6s_{n,2}(1)s_np_n+s_{n,2}(1)s_nl_n+4s_{n,2}(1)p_n^2+\nonumber\\ &\quad 2p_{n,2}(1)s_n^2+8p_{n,2}(1)s_np_n+2s_{n,1}(1)s_np_n+s_{n,1}(1)s_nl_n+\nonumber\\ &\quad 8s_{n,1}(1)p_n^2+4s_{n,1}(1)p_nl_n+p_{n,1}(1)s_n^2+10p_{n,1}(1)s_np_n+\nonumber\\ &\quad 3p_{n,1}(1)s_nl_n+10p_{n,1}(1)p_n^2+p_{n,1}(2)s_n^2+6p_{n,1(2)}s_np_n+\nonumber\\ &\quad p_{n,1}(2)s_nl_n+4p_{n,1}(2)p_n^2+l_{n,1}(1)s_n^2+4l_{n,1}(1)s_np_n \,, \end{align} \begin{align} \label{length5c} l_{n+1,3}(01)&= 2s_{n,2}(1)s_np_n+s_{n,2}(1)s_nl_n+8s_{n,2}(1)p_n^2+4s_{n,2}(1)p_nl_n+\nonumber\\ &\quad p_{n,2}(1)s_n^2+10p_{n,2}(1)s_np_n+3p_{n,2}(1)s_nl_n+10p_{n,2}(1)p_n^2+\nonumber\\ &\quad p_{n,2}(2)s_n^2+6p_{n,2}(2)s_np_n+p_{n,2}(2)s_nl_n+4p_{n,2}(2)p_n^2+\nonumber\\ &\quad l_{n,2}(1)s_n^2+4l_{n,2}(1)s_np_n\,. \end{align} From Theorem~\ref{th:solve} and Lemma~\ref{Lemma01}, we obtain the exact expressions for $p_{n+1,i}(01)$, $p_{n+1,i}(02)$, $p_{n+1,i}(20)$, $l_{n+1,i}(01)$, and thus for $P_{n+1,i}(01)$, $P_{n+1,i}(02)$, $P_{n+1,i}(20)$, $L_{n+1,i}(01)$. \end{proof} \subsection{Determination of $S_{n,i}(\bm{\alpha})$ for an arbitrary vertex $\bm{\alpha}$} { We finally calculate $S_{n,i}(\bm{\alpha})$ for an arbitrary vertex $\bm{\alpha}$. Note that a vertex $\bm{\alpha}$ in $H_n$ has a label $\gamma_1\gamma_2\cdots\gamma_p$ with length $p$, where $1\leq p \leq n$ and $\gamma_z \in \{0,1,2\}$ for $1\leq z \leq p$. In the preceding subsections we have determined the degree distribution among all spanning trees for the three outmost vertices corresponding to the case $p=1$ and the six connecting vertices associated with the case $p=2$. Next, we will show that for any vertex $\gamma_1\gamma_2\cdots\gamma_p\gamma_{p+1}$ in $H_{n+1}$ with label length $p+1$, $S_{n+1,i}(\gamma_1\gamma_2\cdots\gamma_p\gamma_{p+1})$ is obtained from some related quantities for the vertex $\gamma_1\gamma_3\cdots\gamma_p\gamma_{p+1}$ in $H_{n}$ with label length $p$.} { Let $\gamma$ be a sequence of $\{0,1,2\}$, and let $\|\gamma\|$ be the length of $\gamma$ satisfying $0\leq \|\gamma\|\leq n-1$. Then, all vertices in $H_n$ have the label form $0 \gamma$, $1\gamma$, or $2\gamma$, while all vertices in $H_{n+1}$ have the label form $0k\gamma$, $1k\gamma$, or $2k\gamma$ with $k \in \{0,1,2\}$, corresponding to vertices in $H_{n}^1$, $H_{n}^2$, and $H_{n}^3$ that form $H_{n+1}$. Below we are only concerned with $S_{n+1,i}(0k\gamma)$, since $S_{n+1,i}(1k\gamma)$ and $S_{n+1,i}(2k\gamma)$ can be easily obtained from $S_{n+1,i}(0k\gamma)$ by symmetry.} For an arbitrary vertex $\bm{\alpha}$ in $H_n$, we define the following row vector, which contains all quantities we are interested in: \begin{align} \label{Matrix0a} \bm{M}_{n,i}(\bm{\alpha}) = \left[\begin{matrix} S_{n,i}(\bm{\alpha}) & P_{n,i}(\bm{\alpha}) & T_{n,i}(\bm{\alpha}) & R_{n,i}(\bm{\alpha}) & L_{n,i}(\bm{\alpha})\end{matrix}\right],\nonumber \end{align} where $n\geq1$. Then, our task is reduced to evaluating $\bm{M}_{n+1,i}(0k\gamma)$. Before giving our main result for this subsection, we introduce some matrices. Let $\bm{E}_0$ be the $5 \times 5$ identity matrix, and let $\bm{E}_1$ ($\bm{E}_2$) be an elementary matrix obtained by interchanging the third (second) column and the fourth column of $\bm{E}_0$. In other words, \begin{align} \bm{E}_0=\left[\begin{matrix}1&0&0&0&0\\0&1&0&0&0\\0&0&1&0&0\\0&0&0&1&0\\0&0&0&0&1\end{matrix}\right],\quad \bm{E}_1=\left[\begin{matrix}1&0&0&0&0\\0&1&0&0&0\\0&0&0&1&0\\0&0&1&0&0\\0&0&0&0&1\end{matrix}\right],\quad \bm{E}_2=\left[\begin{matrix}1&0&0&0&0\\0&0&0&1&0\\0&0&1&0&0\\0&1&0&0&0\\0&0&0&0&1\end{matrix}\right]. \nonumber \end{align} Moreover, for any non-negative integer $n$, the matrix $\bm{C}_n$ is defined as \begin{equation} \label{CN} \begin{split} \bm{C}_n=\hspace{13.3cm} \\ \left[\begin{matrix} \frac{2\cdot 5^n+ 3^{n}}{3\cdot5^n} & \frac{3\cdot25^n-9^n}{5^n (5^{n+1}-3^{n+1})} & \frac{3\cdot25^n-9^n}{5^n (5^{n+1}-3^{n+1})} & \frac{(5^n+3^n)^2}{2\cdot5^n (5^{n+1}-3^{n+1})} & \frac{6\cdot25^n-2\cdot9^n}{(5^{n+1}-3^{n+1})^2}\\ \frac{5^n-3^n}{6\cdot5^n} & \frac{9^n-4\cdot15^n+3\cdot25^n}{2\cdot5^n (5^{n+1}-3^{n+1})} & \frac{(5^n-3^n)^2}{2\cdot5^n (5^{n+1}-3^{n+1})} & \frac{25^n-9^n}{2\cdot5^n (5^{n+1}-3^{n+1})} & \frac{7\cdot 125^n+45^n+27^n-3^{n+2}\cdot25^n}{2\cdot5^n (5^{n+1}-3^{n+1})^2}\\ \frac{5^n-3^n}{6\cdot5^n} & \frac{(5^n-3^n)^2}{2\cdot5^n (5^{n+1}-3^{n+1})} & \frac{9^n-4\cdot15^n+3\cdot25^n}{2\cdot5^n (5^{n+1}-3^{n+1})} & \frac{25^n-9^n}{2\cdot5^n (5^{n+1}-3^{n+1})} & \frac{7\cdot125^n+45^n+27^n-3^{n+2}\cdot25^n}{2\cdot5^n (5^{n+1}-3^{n+1})^2}\\ 0 & 0 & 0 & \frac{2\cdot25^n-9^n-15^n}{5^n (5^{n+1}-3^{n+1})} & \frac{2\cdot(5^n-3^n) (3\cdot25^n-9^n)}{5^n (5^{n+1}-3^{n+1})^2}\\ 0 & 0 & 0 & \frac{3\cdot(5^n-3^n)^2}{2\cdot5^n (5^{n+1}-3^{n+1})} & \frac{3\cdot(2\cdot5^n-3^n) (5^n-3^n)^2}{5^n (5^{n+1}-3^{n+1})^2} \end{matrix}\right]. \nonumber \end{split} \end{equation} Then, by alternatively computing $\bm{M}_{n+1,i}(00\gamma)$, $\bm{M}_{n+1,i}(01\gamma)$ and $\bm{M}_{n+1,i}(02\gamma)$, we obtain $\bm{M}_{n+1,i}(0k\gamma)$, as the following lemma states. \begin{lemma}\label{Theo3} For the Tower of Hanoi graph $H_n$ and $n > 2$, \begin{equation}\label{Matrix0b} \bm{M}_{n+1,i}(0k\gamma)=\bm{M}_{n,i}(0\gamma)\bm{E}_k \bm{C}_n \end{equation} holds for all $i=1,2,3$ and $k=0,1,2$. \end{lemma} \begin{proof} We first prove the case $k=0$. For this case, based on Figs.~\ref{fn},~\ref{pn},~\ref{ln}, and~\ref{lnplus}, we can establish the following relations: \begin{align} \label{vectora} s_{n+1,i}(00\gamma) = 3s_{n,i}(0\gamma)s_n^2+p_{n,i}(0\gamma)s_n^2+t_{n,i}(0\gamma)s_n^2+ 4s_{n,i}(0\gamma)s_np_n \,, \end{align} \begin{align p_{n+1,i}(00\gamma)&= s_{n,i}(0\gamma)s_n^2+p_{n,i}(0\gamma)s_n^2+6s_{n,i}(0\gamma)s_np_n +3p_{n,i}(0\gamma)s_np_n+ \nonumber \\ &\quad t_{n,i}(0\gamma)s_np_n+3s_{n,i}(0\gamma)p_n^2+ s_{n,i}(0\gamma)s_nl_n \,,\nonumber \end{align} \begin{align} t_{n+1,i}(00\gamma)&= s_{n,i}(0\gamma)s_n^2+t_{n,i}(0\gamma)s_n^2+6s_{n,i}(0\gamma)s_np_n+p_{n,i}(0\gamma)s_np_n+\nonumber \\ &\quad 3t_{n,i}(0\gamma)s_np_n+3s_{n,i}(0\gamma)p_n^2+s_{n,i}(0\gamma)s_nl_n \,,\nonumber \end{align} \begin{align} r_{n+1,i}(00\gamma)&= s_{n,i}(0\gamma)s_n^2+p_{n,i}(0\gamma)s_n^2+3r_{n,i}(0\gamma)s_n^2+t_{n,i}(0\gamma)s_n^2+\nonumber \\ &\quad l_{n,i}(0\gamma)s_n^2+2s_{n,i}(0\gamma)s_np_n+p_{n,i}(0\gamma)s_np_n+\nonumber \\ &\quad 4r_{n,i}(0\gamma)s_np_n+t_{n,i}(0\gamma)s_np_n+ s_{n,i}(0\gamma)p_n^2 \,,\nonumber \end{align} \begin{align} l_{n+1,i}(00\gamma)&= s_{n,i}(0\gamma)s_n^2+p_{n,i}(0\gamma)s_n^2+2r_{n,i}(0\gamma)s_n^2+t_{n,i}(0\gamma)s_n^2+\nonumber \\ &\quad l_{n,i}(0\gamma)s_n^2+8s_{n,i}(0\gamma)s_np_n+6p_{n,i}(0\gamma)s_np_n+12r_{n,i}(0\gamma)s_np_n+ \nonumber \\ &\quad 6t_{n,i}(0\gamma)s_np_n+4l_{n,i}(0\gamma)s_np_n+12s_{n,i}(0\gamma)p_n^2+4p_{n,i}(0\gamma)p_n^2+\nonumber \\ &\quad 6r_{n,i}(0\gamma)p_n^2+4t_{n,i}(0\gamma)p_n^2+2s_{n,i}(0\gamma)s_nl_n+p_{n,i}(0\gamma)s_nl_n+\nonumber \\ &\quad 2r_{n,i}(0\gamma)s_nl_n+p_{n,i}(0\gamma)s_nl_n+4p_{n,i}(0\gamma)p_nl_n.\nonumber \end{align} By definition of $S_{n,i}(\bm{\alpha})$, $P_{n,i}(\bm{\alpha})$, $T_{n,i}(\bm{\alpha})$, $R_{n,i}(\bm{\alpha})$, and $L_{n,i}(\bm{\alpha})$, we have \begin{align S_{n+1,i}(00\gamma) &= \frac{2\cdot 5^n+ 3^{n}}{3\cdot5^n} S_{n,i}(0\gamma)+\frac{5^n-3^n}{6\cdot5^n}P_{n,i}(0\gamma)+ \frac{5^n-3^n}{6\cdot5^n}T_{n,i}(0\gamma)\,,\nonumber \end{align} \begin{align} P_{n+1,i}(00\gamma)&= \frac{3\cdot25^n-9^n}{5^n (5^{n+1}-3^{n+1})}S_{n,i}(0\gamma)+ \frac{9^n-4\cdot15^n+3\cdot25^n}{2\cdot5^n (5^{n+1}-3^{n+1})}P_{n,i}(0\gamma)+\nonumber \\ &\quad \frac{(5^n-3^n)^2}{2\cdot5^n (5^{n+1}-3^{n+1})}T_{n,i}(0\gamma)\,,\nonumber \end{align} \begin{align} T_{n+1,i}(00\gamma)&= \frac{3\cdot25^n-9^n}{5^n (5^{n+1}-3^{n+1})}S_{n,i}(0\gamma)+ \frac{(5^n-3^n)^2}{2\cdot5^n (5^{n+1}-3^{n+1})}P_{n,i}(0\gamma)+\nonumber \\ &\quad \frac{9^n-4\cdot15^n+3\cdot25^n}{2\cdot5^n (5^{n+1}-3^{n+1})}T_{n,i}(0\gamma)\,,\nonumber \end{align} \begin{align} R_{n+1,i}(00\gamma)&= \frac{(5^n-3^n)^2}{2\cdot5^n (5^{n+1}-3^{n+1})}S_{n,i}(0\gamma)+ \frac{25^n-9^n}{2\cdot5^n (5^{n+1}-3^{n+1})}P_{n,i}(0\gamma)+\nonumber \\ &\quad \frac{25^n-9^n}{2\cdot5^n (5^{n+1}-3^{n+1})}T_{n,i}(0\gamma)+ \frac{2\cdot25^n-9^n-15^n}{5^n (5^{n+1}-3^{n+1})}R_{n,i}(0\gamma)+\nonumber \\ &\quad \frac{3\cdot(5^n-3^n)^2}{2\cdot5^n (5^{n+1}-3^{n+1})}L_{n,i}(0\gamma)\,,\nonumber \end{align} \begin{align} L_{n+1,i}(00\gamma)&= \frac{6\cdot25^n-2\cdot9^n}{(5^{n+1}-3^{n+1})^2}S_{n,i}(0\gamma)+\nonumber \\ &\quad \frac{7\cdot125^n+45^n+27^n-3^{n+2}\cdot25^n}{2\cdot5^n (5^{n+1}-3^{n+1})^2}P_{n,i}(0\gamma)+\nonumber \\ &\quad \frac{7\cdot125^n+45^n+27^n-3^{n+2}\cdot25^n}{2\cdot5^n (5^{n+1}-3^{n+1})^2}T_{n,i}(0\gamma)+\nonumber \\ &\quad \frac{2\cdot(5^n-3^n)\cdot(3\cdot25^n-9^n)}{5^n (5^{n+1}-3^{n+1})^2}R_{n,i}(0\gamma)+\nonumber \\ &\quad \frac{3\cdot(2\cdot5^n-3^n) (5^n-3^n)^2}{5^n (5^{n+1}-3^{n+1})^2}L_{n,i}(0\gamma),\nonumber \end{align} which can be rewritten in matrix form as \begin{equation} \label{SPLM} \bm{M}_{n+1,i}(00\gamma)=\bm{M}_{n,i}(0\gamma) \bm{C}_n=\bm{M}_{n,i}(0\gamma)\bm{E}_0 \bm{C}_n\,. \end{equation} In this way, we have completed the proof of the case $k=0$. For the other two cases $k=1$ and $k=2$, the proof is completely analogous to the case $k=0$, we omit the details here. \end{proof} The first column of the matrix in Eq.~(\ref{Matrix0b}) gives $S_{n+1,i}(0k\gamma)$ for any vertex $0k\gamma$, which is recursive expressed in terms of the related quantities for vertex $0\gamma$. Let $\bm{e}_1$ denote the vector $(1,0,0,0,0)^{\top}$, from Lemma~\ref{Theo3}, we have the following result. \begin{theorem}\label{Theo4} For the Tower of Hanoi graph $H_n$ and $n > 2$, \begin{equation}\label{Matrixa} \left[\begin{matrix}S_{n+1,i}(00\gamma)\\S_{n+1,i}(01\gamma)\\S_{n+1,i}(02\gamma)\end{matrix}\right]= \left[\begin{matrix}\bm{M}_{n,i}(0\gamma)\bm{E}_0\bm{C}_n\\\bm{M}_{n,i}(0\gamma)\bm{E}_1\bm{C}_n\\\bm{M}_{n,i}(0\gamma)\bm{E}_2\bm{C}_n\end{matrix}\right]\times \bm{e}_1 \end{equation} holds for all $i=1,2,3$. \end{theorem} By symmetry, we can obtain the recursive relations for $S_{n+1,i}(1k\gamma)$ and $S_{n+1,i}(2k\gamma)$. Since for arbitrary $n$ and $\|\gamma\|=0$ and 1, the terms on the right-hand side of Eq.~(\ref{Matrixa}) have been previously determined, we can repeatedly apply Theorem~\ref{Theo4} to obtain $S_{n,i}(\bm{\alpha})$ for any vertex $\bm{\alpha}$ in $H_n$. \section{Conclusion} In this paper we have found the number of spanning trees of the Hanoi graph by using a direct combinatorial method, based on its self-similar structure, which allows us to obtain an analytical exact expression for any number of discs. The knowledge of exact number of spanning trees for the Hanoi graph shows that their spanning tree entropy is lower than those in other graphs with the same average degree. Our method could be used to further study in this graph, and other self-similar graphs, their spanning forests, connected spanning subgraphs, vertex or edges coverings. We have used it to provide a recursive solution for the degree probability distribution for any vertex on all spanning tree configurations of the Hanoi graph. \section*{Acknowledgments} The authors are grateful to an anonymous reviewer for its valuable comments and suggestions, which have contributed significantly to the readability of this paper. This work was supported by the National Natural Science Foundation of China under grant No. 11275049. F.C. was supported by the Ministerio de Economia y Competitividad (MINECO), Spain, and the European Regional Development Fund under project MTM2011-28800-C02-01. \footnotesize	{ "redpajama_set_name": "RedPajamaArXiv" }	9,944
Q: How to make screenreader read the aria-label of a button while clicking I'm working on improving the accessibility of an HTML page. I have a "refresh" button. Is it possible that every time I click the button, the screenreader will read out "refreshing". This is my HTML code: <button id="refresh_btn" title="refresh the content" aria-label="refresh" class="btn btn-default btn-xs"><i class="fa fa-refresh"></i></button> A: You have to investigate the aria-live attribute: <div aria-live="polite" id="ele"></div> Each time you press the button you can populate the above tag with the text you want using javascript: <div aria-live="polite" id="ele">Loading</div>	{ "redpajama_set_name": "RedPajamaStackExchange" }	6,562
Readers love the Ren Faire Romances by A.J. MARCUS The Falconer's Lure "It was a wonderful story and I cannot wait to read the rest of the series. A. J. has a wonderful gift of telling a story and I was proud to have a chance to read this book." —MM Good Book Reviews "There's something magical about Ren faires, and AJ Marcus manages to capture it in this book" —Shameless Book Club "I am a big fan of AJ Marcus, and I love this series." —The Novel Approach The Satyr's Song "...a good, strong story with good-natured characters and an optimistic message. Recommended." —Top 2 Bottom Reviews "If you adore reading beautiful love stories and crave a little extra, this is the book for you. A fantastic read and one I will be returning to again and again." —Gay List Book Reviews The Jouster's Lance "This was a fun read..." —Literary Nymphs Reviews By A.J. MARCUS Animal Magnetism (Dreamspinner Anthology) Embracing Change Soul Survivors Throwaway Card REN FAIRE ROMANCES The Archer's Arrow The Falconer's Lure The Jouster's Lance The Satyr's Song Published by DREAMSPINNER PRESS http://www.dreamspinnerpress.com Published by DREAMSPINNER PRESS 5032 Capital Circle SW, Suite 2, PMB# 279, Tallahassee, FL 32305-7886 USA http://www.dreamspinnerpress.com/ This is a work of fiction. Names, characters, places, and incidents either are the product of author imagination or are used fictitiously, and any resemblance to actual persons, living or dead, business establishments, events, or locales is entirely coincidental. Throwaway Card © 2015 A.J. Marcus. Cover Art © 2015 Paul Richmond. http://www.paulrichmondstudio.com Cover content is for illustrative purposes only and any person depicted on the cover is a model. All rights reserved. This book is licensed to the original purchaser only. Duplication or distribution via any means is illegal and a violation of international copyright law, subject to criminal prosecution and upon conviction, fines, and/or imprisonment. Any eBook format cannot be legally loaned or given to others. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without the written permission of the Publisher, except where permitted by law. To request permission and all other inquiries, contact Dreamspinner Press, 5032 Capital Circle SW, Suite 2, PMB# 279, Tallahassee, FL 32305-7886, USA, or http://www.dreamspinnerpress.com/. ISBN: 978-1-63476-126-0 Digital ISBN: 978-1-63476-127-7 Library of Congress Control Number: 2015902238 First Edition June 2015 Printed in the United States of America This paper meets the requirements of ANSI/NISO Z39.48-1992 (Permanence of Paper). This book is dedicated to S.J. Tucker, the wonderful gypsy fairy bard whose music touches so many people. You inspire so much magic in our world. Keep up your awesomeness and thanks for "River's Wild Child," which sparked the idea that matured into Throwaway Card. You are the greatest. # 1 "WELL, LAFOUX, are you going to bid or fold?" Shank asked. Sweat dripped down Hugh Lafoux's hard-set face. He glanced at the other men around the poker table. The early summer heat had them all sweating, even in the cooling evening air that wafted slowly through the calico curtains, moved about by a gentle breeze off the river and slowly turning ceiling fans powered by the huge boiler that moved the boat's massive paddle wheel. His opponents ranged from the soft banker out of Saint Louis, to a cowboy who wandered into the game at the last minute, to Al Shank, the swarthy owner of the riverboat Bayou Belle, who organized the game. Of all the men, Shank was the only one Hugh knew well enough to dislike. Hugh looked at his cards, not a winning hand, not by a long shot. He glanced at the pile of coins on the table. A decent pot, but not the biggest of the evening. If he was going to get enough money to move on west, he needed more. He stacked his cards and laid them on the green felt in front of him. "Fold." Shank smiled as he reached for the pot. "I knew you were just bluffing. You keep claiming you're a big-time gambler, but your face is an open book, at least to me." "You're just having a lucky streak tonight, Shank." Hugh tried not to frown and show his irritation with the riverboat owner. He glanced at his pocket watch. Not yet nine o'clock. The player calliope in the corner cut off and the petite evening singer, Susie Sweet Tones, took the stage in a swirl of bright-colored skirts, a low-cut bodice, and curly brown hair. As Shank began shuffling the cards, she broke into a sultry song that drew the attention of almost every man in the bar. "She's worth every penny I pay her." Shank chuckled as he passed the cards to the cowboy to cut. "She'll make sure every man on this boat is ready for my top-deck ladies by the time she's done with them." The cowboy smiled. "She does have a sweet voice. Nicer than some of them singers in the saloons out west. If you ask me, most of them women were just dropped off some wagon train when their menfolk couldn't handle their screeching any longer." Hugh nodded slowly as the first card came his way. "I heard some of the little songbirds in Atlanta before she burned. Now there were some fine voices." He waited patiently for all five to be dealt before he picked up his cards. The singer didn't distract him like she appeared to do to the cowboy. He knew her, and they were friends, nothing more. Neither of them had anything the other was interested in. "She says she used to play the bigger houses in Atlanta." Shank shrugged as he finished dealing. "I've got no way to check. Since the war there's not much left, but her voice is fine enough and she's honest." His gaze landed on Hugh. "Honesty is hard to come by in these parts nowadays, what with all them damned carpetbaggers coming down to help us rebuild and taking a good portion of what they want for themselves." Then he laughed while he studied his cards. "But we all know that. So, gentlemen, I think I'll open the bid with a dollar." A silver coin hit the table's green felt with a soft thud. Everyone anted up, cards were discarded, and new cards were studied. Although he didn't need to, Hugh sighed as he stacked his cards in his hands, set them on the table, and tapped them. Shank slid two silver dollars into the pile of coins in the center of the table. "We're up to two dollars, gentlemen." Hugh studied his cards again. He had a full boat with queens high. It would be hard to beat. He tapped the cards and looked uncertainly at the other players. Shank smiled. The banker studied his cards, stacked them in his hand, then spread them out again as if uncertain what he had there. Leaning back in his chair, the cowboy sighed and put his cards down on the table, a contented look on his rugged features as he slid two silver dollars across the green felt. Hugh slid five coins into the pot. "Raise to three dollars." "Must have a good hand there, Lafoux." Shank grinned harder. "I'll see your three dollars and raise to five dollars." The cowboy nodded and slid two more coins into the growing pile, as did Hugh. "I don't know." The banker shook his head before he added his coins to the pile. Making a show of glancing at his cards, Shank nodded. "I think I'll take one more card. Anyone else?" "Nope." The cowboy didn't even pick up his cards. "I'm fine here." With a heavy sigh, Hugh picked up his cards and glanced nervously at the cowboy. It's possible to beat a full boat, but he's being too forward about it. He's bluffing. Hugh shook his head. "I'm good." He stacked the cards again and set them on the table in front of him. "Three." The banker slid three cards to the discard pile with a shaking hand. Shank slid the requested cards to the nervous man, then looked at his own with a blank expression. The banker frowned at his cards, pulled out a silk handkerchief from his pocket, and wiped his sweating brow. I bet he's just a bank teller, Hugh thought to himself. He's too nervous to be in charge of a bank. I bet he'd wet himself if he ever got held up. Just the type to hand over everything without even trying to put up a fight. I bet he's from back east and trying to hide his accent. He's probably terrified just being west of New York. "So let's raise the bid to ten dollars." Shank moved his coins over. The cowboy looked at his cards, then at the pile of coins. "I'll see that." He didn't have many coins left after he slid his out onto the table. Hugh felt comfortable with his winnings so far and added to the pot with a slow nod. The large pot would add nicely to the money he was gathering to head west in hopes of starting a new life. "I fold." The banker tossed his hand onto the discard pile. "I think I need a drink." "Don't take too long if you want in on the next hand." Shank glanced at his cards, then at the pot. "Looks to me like you both have good hands." The cowboy leaned forward, and a bit of hay floated off his black hat. "I might, and I might not. Why, are you thinking about making this interesting?" Shank's gaze rested on Hugh. Hugh shrugged. "What's on your mind, Shank?" He'd sat across the table from Shank too many times to trust him. "It's been a lively game. Our friend from the range here is looking a bit low in funds. It might be time to open up the bidding a bit." Shank's flabby face remained unreadable, but Hugh knew the kind of bargains the riverboat owner made to people when they were short of funds. Many of his employees had run out of money in a poker game and found themselves working it off for years on end. "If it means I can walk out with this here pot, you've got my attention." The cowboy smiled. The two missing teeth in the front and the yellow tobacco stains ruined his rugged handsomeness. "What have you got beyond your dwindling stack of coins, cowboy?" Shank looked him over. The move reminded Hugh of the way plantation owners used to look at slaves during an auction. It felt worse than how lonely, desperate men fresh off the trail looked at whores. The cowboy frowned. "I ain't putting up my horse. He's been with me too long. Now my saddle's worth a good twenty-five dollars. My rifle's worth thirty. It's got one of them newfangled mini spyglass scopes on it. I can hit a rabbit at half a mile with it, thanks to some adjustments that a tinkerer back in Saint Louis did to it. He added a removable chamber that can hold a lot of bullets. Best gun I ever fired. Even with all the bullets, it's lightweight." "We can start with the rifle." Shank slid twenty coins into the pot. "Bid's at twenty." "But the rifle's worth thirty." The cowboy looked at his cards. "Fine. Twenty." Hugh wondered what he'd do with another rifle. He tried to avoid gunfighting if he could. "I'll see the twenty." Hugh thought about raising but decided to wait until the cowboy was out of the game. He didn't want to take advantage of his obvious desperation, at least at the poker table; then, remembering the missing and yellow teeth, Hugh mentally shook his head. No, I wouldn't even take advantage of him that way. Shank called the next round. The cowboy turned over two pair, aces and kings with a queen trailing. Hugh breathed a little easier as he turned over his full boat, queens high. "Nice hand." Shank chuckled as he turned over his own full boat, jacks high with two fives. "Well played, Lafoux... well played. I guess you get a new rifle with a fancy scope on it." The banker came back over, clutching a glass of whiskey, as Hugh raked the pot over to his side of the table. I won that one fair and square. Unfortunately the cowboy is about empty and the banker doesn't have much in him, even if he does have some cash. I'll need to take this next hand as high as I can. It's liable to be the last hand. I'm not about to play Shank just the two of us. A QUARTER hour later, as Susie finished up her set, Hugh smiled at Shank, the cowboy, and the banker. "Well, gentlemen, it's been a good game." He raked the coins into his hands. At least the previous hands were honest enough that they don't realize how much I took them for in the last hand. "It's always good to have you stop by at the Bayou Belle, Lafoux." Shank chuckled, but there was something under it that sent chills through Hugh. "It's just nicer when you leave with your pockets lighter, not heavier with ill-gotten gain." Shit! Hugh forced himself to remain calm as he put his winnings into his pocket. "Just a lucky night, I guess." He knows I switched cards that last hand. I don't know how, but Al knows. I need to get out of here. I hope we're close to the dock. Not in the mood to swim for shore tonight. "We'll need to go up to my room to get my rifle," the cowboy said. Hugh glanced at Shank. If he didn't go with the cowboy, it would look suspicious. He could bow out of taking the rifle once they got away from Al and his men in the bar. If he was lucky, he'd make it to shore before too many of Shank's men were on his tail. "Okay, let's go. I've got a room waiting for me near the river, so I need to get going as soon as we dock." That was a safe story; there were plenty of rooms along the river in Memphis, but his was closer to the center of town. He waved at Susie as she made her way to the bar. If he didn't, Shank might realize he was going to try to run. Susie waved back but stopped to talk to the bartender. A short, skinny Negro rushed into the room, nearly knocking the cowboy down as he made for Shank. He said something Hugh couldn't hear above a strange chugging out on the water. "What!" Shank roared. "I can't believe that." "Which floor you on?" Hugh asked as he and the cowboy walked out of the bar and into the mezzanine in the middle of the boat. The lights of Memphis were still a short distance away. Too far for his liking. Back in the bar, it sounded like Shank was getting madder. "Second deck, over the engine room," the cowboy replied and started toward the stairs going down. That would be bad. In the distance, a church bell tolled ten. "Hey, tell you what, I really don't want your rifle." "You won it fair and square." The cowboy shook his head emphatically. "My momma, rest her soul, always told me not to gamble. I just can't help myself." "Pardner, you keep your rifle with its fancy new scope. I really need to be going. I'll lose my room if I'm not there by ten fifteen." Without waiting for a reply, Hugh turned toward where the gangplank would be shortly to jump off the boat, if necessary. Two men stepped out of the shadows as he neared the wooden path to freedom. "Now, Lafoux." Shank's voice came from behind him. "You're not going to run off before you collect all your winnings, are you? I'm sure our friend here wants to make sure you have everything you won fair and square." "We've already worked out something, Al. You don't need to worry yourself about anything. My pardner here and I are perfectly happy with our agreement." Shank put his flabby arm over the cowboy's shoulder. "Surely you haven't been on the range so long you're willing to take this no-account instead of any of my lovely ladies. Or did he even bother telling you all the conditions of him not wanting your gun?" The cowboy stepped away from Hugh with a harsh frown. "What are you talking about?" "Never mind." Shank shook his head. "Just leave him to me. We'll see him off the boat. Keep your rifle and don't worry about anything the rest of the night." He turned the cowboy toward the stairs. The sweat running down Hugh's back had nothing to do with the steamy night air that had lost most of the pleasantness he'd first felt when he walked outside. "Now, Shank. Can we talk about this? What split would you like?" If Shank had caught him cheating, he might as well not deny it. He didn't mind cheating, but out-and-out lying was something he didn't like to do, even to a snake like Shank. Shank waited until the cowboy had disappeared down the stairs. "Split?" He spun toward Hugh faster than expected. His fist connected with Hugh's jaw. Hugh rocked backward and hit his head against the heavy wooden beam on the corner of the wall. His head pounded and he saw stars. He struggled to stand, grasping the corner he'd hit so hard. "Come on Al, let's talk about this." He reached into his pocket and pulled out a handful of coins with a shaking hand. He carefully left the majority of his winnings hidden, hoping to get away with something for his evening. "Here, take it. It's not worth my life." From the rumors he'd heard recently about Shank, his might not be the first life to feed the gators in the Belle's wake. Shank laughed. "The money's not worth your life. You're right. But I think it's time I made an example of you." As the coins fell to the deck with an almost musical clang, Shank stepped away from Hugh. "Lafoux, too many people think they can come onto one of my boats and cheat me. Sometimes it's just me and sometimes it's the house. I need to show people I'm not going to put up with cheaters anymore." He gestured to his heavies. The first one struck Hugh with a blow to the gut that doubled him over. "I'll spread the word that your disappearance is tied to your cheating tonight. I'm sure no one will really miss you." Thrusting his hand into his pocket, Hugh grasped the handle of his derringer pistol. He straightened and didn't bother pulling the gun from his pocket; he just pulled the trigger. The thug on his right stumbled away as the bullet grazed his leg. "Shit! He shot me!" The other heavy yanked Hugh's arm painfully out of his pocket. The little gun fell back into the pile of coins still in his pants. A few more coins clinked to the deck. "No more of that." He punched Hugh in the face. Hugh stumbled backward, hoping someone heard the shot and might come to his rescue, but it was Shank's boat. A wall stopped his retreat, and the thug he'd shot hobbled over to him. The next blow, which struck him in the groin, was harder than any he'd suffered before, outside of the cannonball that had taken his leg. Hugh stopped trying to stand. He fell to the deck and hoped the beating would stop. A ringing started in his head as one of the heavies kicked him hard, leaving the iron taste of blood in his mouth. He curled himself into a fetal position, trying to protect his head, but they just kicked him in the back. Finally, in the distance, Shank called them off. "Boys, I think anyone watching has the point. Now get rid of him. It's time to throw this card away like the joker he is." Rough hands lifted Hugh from the deck. His legs slowly unfolded, almost on their own. His black leather boots dragged on the wooden deck as they half carried him, half pulled him toward the rear of the boat and the giant paddle wheel that churned there. "Lafoux, you weren't even the best cardplayer I ever had on my boat." Shank stepped in front of the men carrying Hugh. "I'm sure somewhere, someone might miss you, but I doubt they'll shed many tears for you." He stepped away from Hugh, and the thugs lifted him over the rail. The air cooled for a moment as Hugh fell from the ship toward the murky depths of the Mississippi River. The wheel hit his back hard before the water engulfed him. The paddle wheel spun and tossed up water around him, but he somehow missed the turning death Shank had planned for him. He came up in the shower of water dripping from the wheel, gulped air twice, then a current pulled him down. # 2 THE WARM arms of the night river enveloped Cotton Freeman as he pushed the raft he'd spent lots of time modifying down the Mississippi, keeping close to shore where the gators would be prowling. The raft moved easily in the water. The metal augmentations he'd given it—a wide, shallow keel, a special smooth prow with metal rungs made especially for tying ropes—made it much safer for his occupation, gator hunting. It was nearly impossible for a struggling alligator to upset the raft, like had happened to him before he'd modified things. He was a little closer to Memphis than he liked, but he'd heard rumors of a white gator south of the docks there. He could get a really good price for a white gator skin. The nearly full moon sitting high in the cloudless sky cast enough light that it was almost daylight bright on the river. It made the hunting easier but also left Cotton feeling exposed. He preferred lower light when he hunted. There was less chance of being spotted and questioned when it was darker. Lately it always seems there's someone out there wanting to know what everyone else is up to. It makes earning an honest living hard. Holding his pole tight in his big brown hands, Cotton pushed off a cypress root, keeping his keen gaze on the water and where the slight waves met the muddy shore. That was the best place to look for gators, but he made sure to look amidst the tree roots too; smaller ones often rested there to avoid the larger beasts that lived in the river. Cotton poled on toward the docks. The thick nasty smell of the tanneries and stockyards filled his nose, pushing out the more comforting odors of the humid forest along the river's edge. Ahead of him, something large moved in the water. He stopped poling and let his raft glide along as he scanned the water. Nothing resurfaced. Listening as hard as he could, Cotton tried to block out the sounds of the people on the docks. But even then he couldn't spot what had made the noise. Must've been a gar. He moved his pole and pushed his way under the first dock. Maybe I'll have better luck to the north. "Cotton Freeman, is that you, boy?" a voice called down to him. Coming up on the north side of the dock, Cotton looked up. A friendly dark face peered down at him. "Timmy Birmingham? What are you doing down here on the docks tonight?" Cotton stuck his pole in the mud to keep the raft from drifting as he stopped to talk. "Lordy, Cotton, it is you," Timmy replied. "I thought that was your shiny hair I saw. I suppose I should be asking you what you're doing out here, but I bet you're a-hunting gators." "Keep your voice down," Cotton hissed. "You know we ain't supposed to be huntin' gators around the docks. The sheriff thinks it scares off the good folk." Timmy chuckled. "Like we care what the good upstanding folk of Memphis want. Most of 'em still mad we be walkin' round without our collars on no more." Timmy rubbed his neck. "They still be like, 'boy, go do this' and 'boy, go do that.'" That prevailing attitude of people was one of the reasons Cotton liked to keep to himself in his cabin south of town and just above the flood plain. It was a wild area near the swamp, and there weren't many folks who liked to venture out there without good reason. For Cotton, the lack of people was good, because there weren't many blacks who were as friendly to him as Timmy. He was too white. And all the whites just saw another colored, even if his skin was closer to theirs than most of the former slaves he knew. Cotton shook his head. "So you didn't say why you're up there on the pier." "I'm a-waitin' for the man coming down from Saint Louis tonight." Timmy puffed out his narrow chest a bit. "He's a-testin' a new boat. It's a boiler boat. Runs on steam, but it ain't like nothing seen on the river before. He regulates the speed through some kinda jet thing that moves it through the water. Claims it's faster than a paddleboat, so he racing the Bayou Belle. If he makes it, he wants my help making more of them." "Your help?" Cotton stared at his friend. "Yeah. He says I got a sharp mind and strong arms. He might even take me on as an apprentice and maybe eventually a partner if his boat takes off. We figures now that the war's over, folks is going to be looking fer faster ways to get around. He's also got some ideas for a horseless carriage but figures a faster boat will take off quicker, particularly with folks wanting to get out West now. 'Specially with all dem folk dredging out new rivers and such." Cotton nodded. "I ken see where that might be good. If you decide you need some gator hide for these new faster boats, you know where to find me." Timmy smiled at him. "You still out there in the swamp south o' town?" "A little east of the swamp, but yeah. I ain't too hard to find if you look in the right area." Loud talking alerted Cotton to more men coming toward them. "Looks like you're about to have some company. I better get going." In the distance, the church bell chimed nine. "Good luck, Cotton. If you decide you want to come out of the swamp, check with me. If this boat takes off, we'll need a few more strong hands, and they don't get much stronger than yours." Cotton waved as he poled away toward the next dock, hoping to disappear into the shadows again. "I'll keep that in mind." SOMEWHERE AHEAD something large slid into the water. Cotton froze and listened. There was the sound of water being displaced by something swimming. With years of practice, he homed in on the light movements. His new spear lay at his feet. Without diverting his attention, he picked it up as he laid his pole down. The eight foot metal and wood weapon was heavier than his pole but rested easily in his hand. When the sound of the gator moved closer, he took a slow centering breath before launching the spear at his target. It hit with a satisfying thunk. Water splashed up as the gator lurched out of the water. Cotton thrust his maneuvering pole through a hole in the raft and into the shallow, muddy river bottom before he leapt off the raft into the water. He grabbed the spear and swam toward the shore. His feet found the mud, and he yanked the spear toward him. The huge gator came up out of the water, lunging at Cotton. It couldn't get very far, as the spear held it back. It took all Cotton's strength to wrestle the beast free of the water and onto shore. Once there, it struggled to get back into the safety of the river. The spear had hit it near the joint of its front leg and body. Good, the skin will still be good. I hate it when I put a hole in the middle of the skin. Cotton pulled out his knife and, grabbing the gator's mouth to hold it closed, stabbed it through the eye, granting the creature a quick death. He dove back in the water to retrieve his raft. Chugging loudly, something shot down the river, heading toward Memphis, and its wake sloshed large waves over him. His raft rolled toward him, knocked free of his simple mooring. He ducked under the water as the raft passed over him, heading toward shore. Damn it! Was that the new boat Timmy was talking about? Cotton resurfaced and grabbed for his raft. If it was, I don't like it. It's too fast. Life on the river is supposed to be slow and laid-back. With his strong grip, he got his raft under control, and by that time the water was shallow enough he could walk it up to the shore. The gator had stopped twitching. Cotton pushed the button on the spear that caused the special spikes on it to retract so he could easily pull it free. When he'd made the weapon, he figured it would make hunting easier, and he'd been right. It didn't take Cotton long to gut the gator and load it onto his raft. Leaving the guts on the shore helped reduce the chance of attracting unwanted scavengers to the raft, but he could always use another hide. If this big boy is an indication of what I can find north, I might come back here more often. He poled his way south. The ones south are getting smaller and harder to find. I can also keep my eyes out for that white one on the way up there. He set himself a good rhythm when the church bell sounded ten. The sound of a paddleboat to the north made him look over his shoulder. The Bayou Belle was drawing close, but it was far enough away he could easily avoid it by poling slightly closer to shore. Lights from the boat made him uncomfortable as it passed. It don't seem right to light things up like that. God made the night for a reason, and we shouldn't be trying to undo it. A shot rang out as the boat cleared him. Cotton stared up at the boat. He couldn't see anyone nearby, but the shot had been close. The familiar sounds of someone getting hit carried across the water, even over the sounds of the paddle wheel. Cotton shuddered, remembering the many times as a child he'd felt hard fists pounding into him. He'd been thankful that by the time the war was over, he'd grown big enough most people didn't want to mess with him. It ain't right to hit another human like that. "Good riddance, Lafoux!" a gruff voice shouted from the boat. Something heavy hit the water. For several seconds the sound of the riverboat filled the night. Then someone gasped for breath. Like he did when hunting the gator, Cotton focused on the sound. No one deserves the river's embrace. He jammed his pole down into the mud before he dove off the raft, trying to follow the gasp. The moonlight didn't reveal anything on the surface. Other scavengers, obviously recognizing the sound, rushed from where they lay hidden on the shore into the water. Cotton dove down into the murk. Human life is precious. If I don't get him, the gators will. Reaching out with each stroke and straining his eyes in the darkness, Cotton searched for the person thrown from the boat. Something glistened ahead of him. He swam toward it as his lungs began to burn for air. He brushed something with his fingers. It felt like wet cloth. Taking a handful, Cotton pulled toward the surface. The resistance was the right weight for a man. Breaking into the air, Cotton took a deep breath and filled his burning lungs. Then he hauled the person above the water. A deep inhalation of breath rewarded his effort. But the form still felt limp. Cotton turned his focus to dragging them both to shore before the gators got them. It would be easier for him to drag the man out of the water on shore than trying to get him onto the raft. For a moment, he wished that he'd finished his tinkering on a bottle of air that could help a man get through the water faster. A loud groan and hiss greeted him as he got to shore. His spear lay on his raft, now out of his reach. "Back!" Cotton shouted at the top of his lungs. Two smaller gators glared at him from the bank. He splashed water at them, wishing he had his weapon, pole, or even a rock. Luckily, they were small enough they backed away from him. Cotton sighed as he dragged the man clear of the water, out of the range the gators would normally pursue. Pausing, Cotton looked at his refugee of the river. He was a tall, well-built man in nice clothes. Red swollen lumps misshaped his face, and his right leg hung at an odd angle. I wonder if he was even worth saving. Cotton shook his head as heavy, ragged breath came from the bloated lips. Cotton ran into the water and hurried toward the raft. I guess I'm lucky that there aren't a lot of huge gators out tonight. Sounds like I got the biggest one already. I've got to get the raft back. It took him a couple of minutes. As he climbed aboard his simple transport, a scaly hide brushed his foot. Cotton jerked his lower body free of the water and scrambled to his feet. Thankfully the adjustments he'd made to the raft's basic design, like the low metal keel down the middle, helped keep it right-side up. If he was lucky, he'd manage to save the gator he'd killed and the night wouldn't be a total loss. Poling toward the shore, Cotton shouted several more times as the smaller gators moved back toward the man lying there. The man was smaller than a lot of the gators Cotton killed, so getting him onto the raft wasn't overly difficult; then they were heading down the river. Cotton moved farther into the river current than he normally did as they reached the docks at Memphis. He wanted to stay as far away from the Bayou Belle as he could. At his feet the man shivered and coughed. "Don't worry none," Cotton said, hoping his voice wouldn't carry across the water. "I've got ya. You gonna be okay now. I'll get you home and see about patching you up. Don't you worry none, Lafoux." His name sounds like he's from N'awlins. I bet he's just had a run of bad luck. Cotton pushed questions out of his mind as he poled his raft toward the shore again, happy to leave the lights and reek of Memphis behind him. # 3 COTTON LOOKED at the man, Lafoux, on his bed. Once he'd gotten the man home, stripped, and dried off, he'd wondered why anyone would've beaten such a man. The damaged right leg was also a mystery. This is a fine piece o' work. Other than being metal, it looks just like a regular leg. I wonder if them bolts holding it on hurt where the skin is growing on them. Is it a war injury? With a name like Lafoux, he probably fought for the rebs. He'd managed to stop the bleeding around Lafoux's face, but there was some swelling on the man's broad, powerful back that didn't look good, and a fevered sweat soaked him. This is more than I can deal with. If I don't get some medicine for him, he'll be dead by the end of tomorrow. Fix him, then I'll try and fix his leg. It looks really complex. Not like some of the pegs I've seen others in town with. "Lafoux, you stay in my bed." Cotton walked toward the door, grabbing the lantern on the way. "I'll be back as soon as I can. I hope Miss Cassandra can help you." He paused for a moment and debated taking his raft back up to the docks in Memphis but decided to take the trails instead. Miss Cassandra lived far enough from the docks it wouldn't help much to travel by the river. For once, thankful for the moonlight that was bright enough he didn't need the lantern on paths he knew, Cotton took off at a run. Around him the night forest was alive with sound. Owls hooted to each other, a fox barked in the distance, and he was close enough to still hear the frogs and gators calling in the swamp. The route he ran was little more than a game trail at first. Eventually it merged with a more-traveled path he knew led to other folks who lived away from the hustle and bustle of Memphis, but he turned toward the city. When the moon dropped below tree level, he stopped, lit the lantern, and resumed running. He made a turn off the harder path onto a softer trail that led to Miss Cassandra's. The trees opened up, revealing open fields and a huge house. If the place had ever had a name like so many of the large houses of the South, he'd never known it. After the war, the master had never returned and the freed slaves had taken it over. Miss Cassandra now controlled it, and everyone who lived there answered to the old woman who generously helped out anyone in need. "Hey!" Cotton stopped a good distance from the house. "I need to speak to Miss Cassandra!" He waited. Late at night it wasn't a good idea to go running into a house without announcing yourself. Cotton didn't want to be shot and killed, leaving Lafoux to die in his cabin. A light came onto the sweeping veranda that encircled the house. "Who calls on Miss Cassandra this late at night?" a gruff male voice shouted back. "It's Cotton Freeman. I live down near the swamp." "Cotton Freeman. The mulatto who hunts gator?" "That's me. I've got a sick man who needs help." Cotton took a cautious step toward the veranda. A large black man stood on the porch holding the lantern. He had a shotgun held casually over his shoulder. "Is this something that ken wait till morning? Miss Cassandra has already turned in for the night." Cotton shook his head. "He was beaten by someone on a riverboat and tossed in the river. I fished him out and dried him off, but he's still feverish. I don't know if he'll still be alive come morning." The man shook his head. "Them riverboat men think thems above God's law. Come on in. I'll send someone to fetch Miss Cassandra." He motioned Cotton toward the front door. "Ben, who you bringing into the house at this hour?" a woman asked right before the gaslight in the foyer brightened. "Cotton Freeman." Ben set the rifle by the door. "He's got a sick man he fished outta the river and needs Miss Cassandra right quick." The woman, nearly as dark as Ben, nodded. "I'll fetch her. She ain't been abed long. She'll want ta help." "Thank you, Helen." Ben smiled at her. "We'll wait here." He cast a dark glance at Cotton, the first aggressive move the man had made. "Won't we, Cotton?" "Sure will." Cotton nodded. Helen hurried up the stairs without another word. He'd never been inside Miss Cassandra's house. From the little he could see from the gaslight, the old woman managed to keep the glory of the place. The rug he stood on was soft and intricate, the wallpaper was fancy, and the gaslight itself had an elegant fluted glass chimney. Here and there were a few spots where the wallpaper was torn and curling, possibly a scar from the war if there had been any fighting in the house proper. He'd heard of people leaving some of the scars to remind them of what had happened and those who had been lost, both slave and freeman alike. Soft steps on the stairs pulled Cotton's attention away from the minor tear in the wallpaper near the gaslight. Helen came down with Miss Cassandra in tow. Miss Cassandra was dressed in a riding skirt and had a large black bag in hand. Her steel gray hair, pulled back in a tight bun, was tied off with a gingham bandanna. "I fell asleep waitin' for ya to git here, Cotton Freeman," Miss Cassandra said, her soft voice strong. "But don't ya fret none. I knew you was a-comin', not when exactly." Cotton nodded respectfully to the old woman. "Thank you for comin', Miss Cassandra. How'd ya know I'd be here tonight? I didn't know until a little while ago." She gestured him toward the door. "Ben, bring my horse please, and one for yourself. We've got a bit of a ride tonight. Cotton, did you ride? I didn't hear a horse come up." He shook his head. "No, Miss Cassandra, I ran here. I'd feel better running back, if you don't mind none." "Not at all." She stopped on the veranda. The moon had finished its path across the sky and the stars were all that provided light beyond the lanterns. "So tell me about this man ya fished outta the river. Anythin' special about him?" Her question took Cotton back a moment. He scratched his head. "He got a metal leg. I reckon it's a war injury." She shook her head. "No, I think there may be something special 'bout him, else why would the spirits send you to him like this? Let me think about it. It'll come to me. Maybe when I see him." Helen touched Miss Cassandra's arm. "Ma'am, is there anything else you think you'll need tonight?" Miss Cassandra shook her head again. "No, Helen, I should be fine. You git yerself onto bed now. Ben and I will be out for a while. Don't you worry none. We'll be home before sunrise. It'll be just fine." Ben returned with the horses as Miss Cassandra patted Helen's arm and walked down the wide stone steps onto the lush green grass. "Cotton, why don't you lead us back to your cabin? I think I know where it is, but you know the way better than I." She swung onto her horse without waiting for Ben or Cotton to offer her a hand up. Sitting there, sidesaddle, she was the dark vision of a proper southern lady. Cotton nodded. "Yes ma'am, Miss Cassandra, right this way." He took off running again, his callused bare feet moving easily over the uneven ground. HIS CABIN was just like he'd left it as Cotton jogged up. Behind him, the two horses kept up the steady beat they had all the way from Miss Cassandra's house. Not waiting for the other two, Cotton hurried through the door and hung his lantern on the hook near the bed. Lafoux's skin was still dripping with sweat, dark damp stains spread out over the thin blanket he lay on. "Step aside, boy. Let me take a look at him." Miss Cassandra pushed on Cotton's shoulder to get closer to the bed. "Lordy." She sighed. "They beat him good." She looked back at Ben. "Grab a bucket and go fetch me some water, Ben. I ken see where Cotton got most of the river off him, but I need to cool him off some." Setting her bag down, she stared at Cotton. "Cotton, step back and give me room to work here. You was right to come git me. He's in bad shape. Good Lord willin' he'll make it through the day." When Ben returned with the bucket of water, she motioned to both of the men. "Let me get a look at his back. See what damage there is there. I bet they kept beating him even when he was down. That riverboat man didn't want him to git back up." Cotton and Ben rolled Lafoux on his side as gently as possible. Miss Cassandra moved the lantern closer and touched each of the bruises that discolored the pale skin. Shaking her head, she straightened, gestured for them to lay him back down, and put the lantern back on its hook. "He didn't moan or cry out when I touched them, so hopefully he ain't beat up on the inside none, but it'll be a miracle." "So what we need to do?" Cotton asked. "I don't like his fever, but being beaten and tossed in the river will do that." She opened her bag and pulled out a small linen package. "Do you know how to make tea, Cotton?" He nodded and accepted the small bag. "Yes ma'am, Miss Cassandra." "Start by putting some on for him while I check his head. There's so much swelling, I might not be able to tell much." Cotton hurried out the front door to his fire pit and stirred up the coals to get it going again. After putting a couple of new logs on the fire, he got a pot of water and put it on to boil under the coils he used to help pressurize things he worked on. As he'd done more than once, he wished the fire could be inside, but the cabin was too small and cramped. With the heat and humidity, it would get too hot inside if the fire was there. When he walked back into the cabin, the sharp smell of alcohol hit him. Miss Cassandra wrung out a rag in the water bucket while Ben held a large bottle of something. "I cleaned the wounds on his face the best I could." Miss Cassandra shook her head. "You did a fair job of it before. I can't tell if we're lucky there weren't any leeches in the river or not. If the swelling don't go down in a couple of days, we might need to leech him." She tapped Lafoux's metal leg. "I'd like to meet the person who made this. It's a real work of art. Ain't never seen anything so complete and lifelike. It weighs the same as his other leg. They even put in lines like hair. It musta been very expensive. Shame it's at an odd angle here. If that were a real knee joint, I might be able to put it back straight." Cotton nodded. "Iffen he wakes up, maybe he can tell you. I was gonna look at the leg tomorrow in the light. See iffen I can fix it." "Good luck. I know a lot of boys on crutches who'd like to have one." She sighed and started putting her things back in her bag. "Now, give him a cup o' that tea every few hours, along with lots of water. Keep him cool. I'm hoping the tea will help the fever break. Cotton, I can't promise he'll make it. He was beat really bad. Even if he does, he might not be right in the head. I'll stop by tomorrow afternoon and see how he's doing. It we're lucky, he'll be awake by then. The longer it takes him to wake up, the less chance there will be that he does." "I understand." Cotton opened the door so Miss Cassandra and Ben could walk out. "Thank you for coming. I don't know who he is, but I couldn't let the river have him. It jest didn't seem right. Nobody deserves to die in the river." Miss Cassandra stopped next to her horse. "The river don't give up those it tries to claim easily. I want you to remember that, Cotton. He's been touched by the river now. He'll be a different man than he was before." "I didn't know him before, so how'll I be able to tell?" She swung up on her horse. "You might not, but he will." Cotton stood there and waited as they rode off in the direction they'd come from. In the distance, a gator roared, reminding him of the one he still needed to finish cleaning and skin. Other than trying to get the tea into Lafoux, there wasn't much more he needed to do before going to bed. He retrieved the lantern, sparing a moment to look at Lafoux lying in the pool of his own sweat. He's a handsome man. Nice body, even with the metal leg. I bet he's got a good story to go along with it, maybe as good as the one about why those riverboat men tossed him into the river tonight. I hope he makes it. # 4 SOMEWHERE IN the darkness, something moved. Hugh couldn't make it out. Other than the heat and the oppressive moisture, Hugh couldn't make anything out. His head hurt. His back hurt. His ribs hurt. The only thing that didn't hurt was his fake leg, which surprised him; he often had phantom pains from it. He struggled to sit up. Something cooler than his surroundings slid down his face as a wave of nausea swept over him from the pain that wracked him. He dropped back to the rough pillow under his head, and more pain shot through his back. A moan escaped him, forcing its way out of swollen lips, and the darkness took him again. THE BRIGHT light streaming through the windows of what had once been a greenhouse blinded Hugh. The smell of ammonia and opium flowed around him. How did I get back here? He remembered the place. Glancing down, he saw his metal leg wasn't there; neither was his flesh and bone leg from before. This can't be right. "Can someone tell me what I'm doing here?" "Ah, Lieutenant Lafoux, you're finally awake." A buxom nurse rushed over to his side. "We were beginning to think you weren't going to wake up." Hugh blinked, recognizing the nurse from the field hospital that had been set up in the plantation house west of Chattanooga during the war. "This can't be right." "Now, Lieutenant, I know it looks bad, but don't worry. We've got an artificer who's working on getting you a new leg. He said it will be an exact duplicate of the one you still have." She blushed. "Well, it won't have hair or skin, but it will be just the same." "No!" Hugh shook his head. The room swam. "That's not what I mean! How did I get here? I'm not supposed to be here! I've already been here." "Now, Lieutenant, you need to calm down." She pressed a ceramic cup to his lips. "Here, drink this. It'll make you feel better." The tea was bitter as she poured it down his throat. He coughed as the familiar taste of opium flowed across his tongue. Then the drugs in the tea took effect and oblivion claimed him. THE BARN door opened. Hugh remembered walking through the door many times in his youth. The smells of hay, grain, and livestock were good memories. There was just the barest hint of light glowing from the hayloft. Heart pounding, Hugh hurried to the ladder and squirrel-quick scampered up it. Jonathan, the boy next door, lay sprawled on the hay, waiting wistfully. His young body stirred more memories and reactions. Hugh stopped and stared. "This can't be. Jonathan, you're dead." The emotional wound he'd thought closed years earlier bled again as Jonathan sat up and looked at him. It was a look that tore at his heart. "What are you talking about, Hugh? I'm not dead, at least not as long as your daddy don't find us up here." Jonathan laughed. The light, cheerful sound was just as Hugh remembered it. Shaking his head, Hugh stepped back toward the ladder. "No, Jonathan, you're dead. I saw you die. A Yankee cavalryman rode you down. I couldn't get there in time." Hot tears rolled down Hugh's face, and he turned away from Jonathan. "This isn't real. Did I die in the river and I'm in purgatory, or worse, hell? The preacher always said if I didn't change my ways I'd go to hell." Jonathan touched Hugh's shoulder. "Why are you talking like that? You don't care what ol' Father Steadman says. You never have. I been waiting for you up here. Now come on, we ain't got a lotta time before folks will come looking for us." Jonathan pulled at Hugh's shirt. As he'd never done in life, Hugh pushed Jonathan away. "No! This ain't right. Jonathan, you're dead. You died on the battlefield, in my arms. You can't be here. We can't be here!" Hugh started to step back on the ladder, but he lost his balance when his metal leg disappeared, and he dropped down into the hole in the hayloft floor. He didn't even scream as he fell. The falling seemed to take forever until the darkness claimed him again. HUGH FELT the cool damp on his forehead again. He lay there afraid to move lest the pain return. "Hey, you awake?" a strong voice asked. Hugh tried to look toward the voice, but his head throbbed when he tried to move it. The lantern hung behind the speaker shadowed what little he could see. The light glowed through pale, nearly white hair. For a second Hugh tried to answer, but his throat was very dry and his lips felt too large for his face. "Just a second," said the voice. "I'll go get you sump'in ta drink." When he stood, the speaker blocked out the light for a moment. Then he was gone. Somewhere nearby a door opened, closed, then seconds later opened again. The man stood by the side of the bed. "I reckon it's a good time fer some more o' Miss Cassandra's tea." Strong hands gently lifted Hugh's head off the pillow. Fighting back the pain from his head, back, and chest, Hugh forced himself to swallow. The bitter brew slid down his throat. It did little to help his parched state. He tried to push the other man away when he had enough of the tea, but he couldn't lift his arms. He was too weak. Coughing, he tried to turn his head as the cup left his lips. "Guess that's all you can get in ya right now. Well, it's more than ya got before." "Am I in hell?" Hugh forced the words out. The man laughed. It was a light, cheerful sound. "Golly, I hope not. I pulled you outta the river and brought you here. Miss Cassandra said if you woke up, there was a good chance you'd live." The voice lacked any sophistication. It reminded Hugh of some of the slaves from his father's plantation. But it was too young to belong to an old man, and the last he checked, Negroes didn't have yellow hair. "Who...?" He tried to get out more but didn't have the strength. "Cotton Freeman, Mr. Lafoux." Before he could ask how the stranger knew his name, his vision blurred and he went back to sleep. # 5 COTTON ROLLED up the tanned gator hide and carried it into the small shed where he stored things he didn't want to get wet in the rain but didn't have room for in the house. It also served as his main workshop. Most of his tools and metal parts were in there. "Almost got enough to take into the mercantile," he said to himself. "I reckon iffen it gets lonely enough out here, you talk to yourself, don't ya?" Timmy appeared in the shed's doorway. Taking a deep breath, Cotton willed his heart to slow down from the fright of the unexpected voice. "Timmy, whatcha doing out this way?" "Coming to spread tales of the river." Timmy smiled and leaned against the doorframe. "Seems Big Al from the Bayou Belle been tossing folks overboard again. This time was some gambler they say was cheating Big Al. I think he was just mad losing the race to that new boat o' ours." Cotton glanced nervously at his cabin. He hoped Lafoux stayed unconscious and didn't draw Timmy's attention. He didn't want anyone beyond Miss Cassandra and her people to know he was here. The swamp folk south of Memphis were a gossipy group, always coming to their own conclusions about what their neighbors were doing. "I ain't heard nothin' 'bout nobody being tossed into the river lately." Timmy cocked an eyebrow. "Really? You do stay in the swamp more than you used to. It's all over the docks right now. Seems he's been tossing people out right and left, but he's trying to keep it quiet, until last night. At this point I think most of us Negroes would rather pole up to Saint Louis than ride his boat of death. He's mad about the South losing the war and determined to bring back the way things was. Stay away from the Bayou Belle." Timmy paused and sighed. "But that weren't the reason I come out here today. Since the new boat beat the Bayou Belle into the docks last night, we're going to swing into production, and I thought I'd see if ya might be interested in helpin' out. Would get you outta the cabin here. It's a mite safer than gator huntin' too. The boats won't try an' eat you. Ya never know, you might like workin' on bigger things than spears an' rafts." "No, thanks." Cotton shook his head. "I like it out here. Fewer people to be botherin' me." He ran a hand through his pale hair. "Fewer people a-lookin' at me too. Not everyone is okay talking with me like you are. Plus, I don't wanna do bigger things." Timmy waved his concern away. "Folks'll get over it. This is a new country now the war's over and all us slaves is freed. Eventually even the people like Big Al Shank will be acceptin' of everyone and everything. You mark my words. The days of black folk, white folk, yellow folk, and mixed folk being treated all different-like are about over. I heard something the other day about a mix couple gettin' hitched. That ain't common but it do happen. Who knows, one day we might even have ourselves a colored president of these here United States." Walking past Timmy and out into the bright afternoon sun, Cotton shook his head again. "I doubt I'll ever see anything like that. I can't see as why any colored man would want to get messed up with all those fools in politics." Timmy laughed. "I'll 'member that when I become mayor of Memphis, or maybe even governor of Tennessee." "I'm sure if you became governor, then some fool like Big Al Shank would have you killed. We'd find you a-hanging from a magnolia tree on the main road outta town two days after you won. There'd be a sign warnin' the rest of us not to get uppity." "So whatta ya say? At least think about it." Timmy squared his shoulders and stood as straight as he could. "I think things is a-changing. Now would be the time to make your move outta the swamp." A deep sigh escaped Cotton. "I still don't think so, but I'll ponder it a while." "Right." Timmy grinned. "Just don't lose no fingers to no gators, okay? You'll need all of them to help us build boats and git rich. Now the war's over, there's money to be made, and it don't involve carpetbaggers." "Thanks for thinking of me." Cotton walked over to his tanning board and started rolling up the next skin dry enough to put away. "Hey, we might be different shades, but we come from the same place, Cotton Freeman. I ain't like some'a them other Negroes who don' like you none just cause who your momma slept with." Cotton stopped rolling the skin and looked at Timmy. "My momma didn't sleep with the master's boy—he raped her. You 'member that. She didn't choose to make me this way." It had been a long time since the old anger about his birth had boiled out of him. When he'd been younger, it had been a constant battle with the other children around the plantation, many of whom were just as mulatto as he was; they were just darker-skinned and didn't have his very telling pale hair. "Hey, Cotton, ya don't need to get mad at me." Timmy backed up two steps in the face of his anger. "I'm sorry for my wordin'. Your momma was a decent woman. She'll always have a good spot in my memories. I know she's a-looking down on us right now and smiling at us being free men and all." Cotton took a deep breath. "I'm sorry, Timmy. That's still a sore spot." He looked at the ground and shook his head. "I shouldn't take it out on you. You've always been a good friend." "Damn right." Timmy looked into Cotton's eyes and smiled. "And don't you forget that. Why do you think I walked all the way out here to offer you a job? But don't you mind none, I've got a couple other folks to talk to too. Just wanted to talk to you first." He glanced up at the sky. "Guess I'd better head back to Memphis." "So where ya setting up shop?" Cotton hoped a bit more interest in Timmy's venture would help put things to rights again. "In that old blacksmith shop out on the east end of Main Street." Timmy beamed a bit talking about the shop. "You know the one—it burned during the war, and then the ol' smith, McIntire, passed on a couple a years ago and all his sons had died in the war. My partner was a friend of one of his boys, so after talking to the widow McIntire, deals was struck and we get to use the shop and set up business there." Timmy nodded thoughtfully. "It gives us the room we need to make most of the newer-fangled parts we're experimentin' with." "Then I'll come looking for ya there first, should I change my mind." Cotton finished rolling the gator hide, then turned back toward the shed. "You do that." Timmy grinned. "I can see you're busy with the skins. But don't you forget, you decide to leave the swamp and there's a place for you in the city. I'll make sure of that." "Thanks." Cotton stopped just outside the shed door. "It's nice you thought of me. I do appreciate it." "You're welcome." Timmy strolled for the footpath that led to the larger trail. "Be safe out here, Cotton." "I will." Cotton put the skin next to the others and thought about what Timmy had said. He'd always heard rumors that some of the riverboat men weren't the nicest folks around, and there were still a lot of folk who didn't like the outcome of the war. Even some colored folk would rather the South had won. They had been comfortable in the lives they'd led. Some of them had kind masters. The fear of the unknown kept many where they had been all their lives. They'd been told they were stupid so long that they believed it. Since being freed, some folk were having problems adjusting to their new lives. Not to mention, there were a lot of whites sore about the changes and determined to take it out on everyone. Cotton paused and looked out over the magnolia and cypress trees that marked the edge of the swamp, so close to his cabin. Most of the Carsons hadn't been too bad, but there were the ones who enjoyed their whiskey. Those had been the bad ones. According to his mother, it had been one of the Carson cousins, with his platinum blond hair, who caught her between the house and the slave quarters one night when he'd been drinking and raped her. At least she said he'd been drinking the first time it had happened. He shuddered a moment. He didn't like thinking about his mother and how her life had played out, so he went back to work on his skins. HOOFBEATS, SOFT on the path, drew Cotton's attention as he knelt by the cook fire stirring a pot of gator gumbo. His dinner had just reached the point the fresh savory aroma of the herbs was drifting up and making his mouth water. He looked up as Miss Cassandra and Ben rode into the small glade where his cabin sat. "Miss Cassandra." Cotton stood and smiled at her. "I wasn't sure when you'd get back out here. Would you like some dinner? I can always throw a bit more on if I need to." She reined her horse in and shook her head as she slid down to the ground. "Thank you, Cotton, but no. I'm sure by the time we get back to the house, Helen'll have our dinner ready, and I wouldn't want to put a strain on your supplies. How's our patient? Has he woke up yet?" Cotton moved his pot away from the flames. "For a little while, never very long at a time, though. He keeps dropping back to sleep right after I get that tea o' yours inta him." She graced him with a tight smile. "That's a good sign. He needs to sleep off what happened to him. Has his fever broken?" He walked ahead of her toward the cabin door. "Yeah. At least I think it has. When I checked on him a while ago, he wasn't as hot as before. Not sweating as much neither." "Even better." She walked into the cabin and gestured for Cotton to leave the door open. "It'll give me some more light to see him by." Cotton glanced at Ben, who only nodded. Miss Cassandra walked over to the bedside and looked down at Lafoux. She touched his brow and smiled, then held her hand to his chest. "Ben, hand me my 'scope please." Ben dug into the black bag Miss Cassandra had carried the night before and handed her a strange device that had a metal cup on one end with what reminded Cotton of ice tongs on the other end, all connected by small tubes. She put the tong end into her ears and held the cup end in the brown hair that covered Lafoux's chest. Closing her eyes, she looked like she was listening to something. She moved the cup around, then pursed her lips. "Sounds like there might still be a little bit of the river inside him. If we're lucky, it won't cause him too much trouble. But his heart sounds strong. That's important." She handed the device back to Ben. "It's still too early to tell if he's going to survive. The fact he's been awake gives us some hope. I'd water that gumbo down a bit if I was you before you give him any. We have no way to know if he can handle the spices. But if you ken get him to eat something, it'll improve his chances. Keep giving him the tea. It'll help him rest." Cotton stood there and just nodded. "Should I try to wash him? The sweat done set up a stink. I'm afraid a wolf or coyote might think there's someone dead in here." "Sure. It can't hurt. Just be careful not to let him take a chill. After that fever, if he takes a chill it'll be all over." "I'll make sure to dry him off right properly." "Good. I'll check back on him in a couple of days. Iffen things get worse, don't hesitate to come git me." She walked toward the outside. "Have you been able to find out anything else about him? Was there anything in his clothes?" Glancing at the untouched pile of garments near the foot of the bed, Cotton shook his head. "No. But Timmy Birmingham stopped by earlier. He said rumor on the docks was Big Al Shank tossed some cheating gambler off the Bayou Belle last night. It might be him." Miss Cassandra huffed. "If he was cheating Al Shank, then good for him. I keep warning all the Negroes around Memphis to keep well away from that boat. Too many of our people either end up disappearing after taking a ride on that boat, or he puts them to work, claiming they owes him money for some made-up expense. He always treats them worse than when they was slaves." She shook her head. "Maybe that's why the river gave this one back. She don't approve of Al Shank any more than the rest of us do." Miss Cassandra stopped and stared into the fire for a moment. Silence filled the glade until she shook her head. "I know there's something about this man. I just can't figure it out. It'll come to me." She walked over to the horses. "Come on, Ben. Let's get back to the house." She mounted her steed without help from either man. "Thank you for stopping by, Miss Cassandra, ma'am." Cotton smiled at her. "I sure do appreciate it." "There's something happening here, Cotton." She looked down at him from her horse. "I think it'll be good in the long run. The winds warned me you were coming last night. The river gave you this man. There must be a reason for it, and it's a good reason. I'll keep my eye on it, 'cause I don't like unknowns around my house. Take care of him and yourself." "I will, Miss Cassandra." Cotton touched her hand for a second. He didn't know why he touched her hand. He'd never done that before. Her skin was soft and dry, like any other old woman's. She patted his hand. "Good." Turning her horse, she gestured for Ben to follow her, rode down the path, and quickly disappeared in the thick trees. # 6 THE LIGHT coming in from the open door was painfully bright to Hugh when he opened his eyes. He closed them quickly, then slowly opened them again, letting himself adjust to the brightness. There was enough light for him to finally see a little more of his surroundings. The cabin was small, from what he could tell, but it was tidy. It looked more to be for sleeping than anything else. He couldn't even see a cookstove or a table. From the distance came the sound of someone chopping wood. As he lay there, he realized it was the first time his bed was dry since he'd awakened after his beating. His skin didn't feel clammy either. Shifting slightly, he found the pain that had seared his back was lessened. It still hurt, but he could almost see himself fighting through the pain enough to sit up. He tried to raise his head, but it throbbed heavily, so he laid it back on the pillow. Where am I? Who saved me? I remember someone with pale hair and strong hands. An urgency in his bladder made him struggle to sit upright. The effort left him sweating and his head pounding. The sandy floor was gritty under his bare foot. He tried to stand, but his senses swam and he sat back heavily, fighting to remain sitting. When his head stopped reeling, he looked toward the door. The sound of an ax striking wood had stopped. "Hey!" Hugh shouted as loudly as his parched throat and dry lips would let him. It wasn't much, and he hoped whoever was chopping wood could hear him. Footsteps outside the door rewarded his efforts. A tall, broad-shouldered man with honey-colored skin and pale blond hair stood there. Sweat dripped down the contours of his muscular chest. "Lordy, you're trying to get up." The man rushed to the bed. "I need to pee and didn't see a chamber pot." Hugh forced the words out. The man shook his head. "Ain't got no chamber pot, Mr. Lafoux. I can help you to the privy, though." A second of modesty swept over Hugh. "Are there others around?" "Nah, just us. Ain't nobody going to see you out here." The man walked to the bedside. "Ya wanna try leanin' on me, or should I just carry ya? I ain't tried to fix ya metal leg yet. It ain't in no condition to support ya." "Let's try leaning, if you can help me stand." Hugh reached for the man's thick, cord-like arm. The effort of standing, even with help, left Hugh faint. He forced himself to lean on the strong man who was slightly taller than he. Each step was a major ordeal as his muscles complained about time unused and his head wavered from step to step. The urgency in him grew too, now he was upright. Luckily it wasn't far from the cabin to the outhouse. Unfortunately the small wooden building wasn't designed for two, and the big man had to lean in to help Hugh get seated over the hole. The odd angle of his prosthetic made it even more awkward. The metal limb banged into the wall and sent shivers through his right side. "Do you want the door closed?" asked the man as Hugh's body began releasing. "It doesn't matter," Hugh said. "I guess you've been wiping me down." The man nodded. "Yeah." Hugh felt better as his bladder emptied. "So who are you?" "Cotton Freeman." A crooked smile crossed the handsome face. "I told you two days ago, but Miss Cassandra says the fever would do things to your head. Make ya different." "Cotton." Hugh sighed. "I seem to recall something about a Cotton something recently, but it seems so far away." It felt good to sit there on the cool, smooth wood, even with the odors of the privy wafting up around him. "Well, Cotton, I'm Hugh. You must've figured out the Lafoux part." Cotton nodded. "I heard someone shout it when they threw you off the riverboat." "So you managed to fish me out of the river?" Hugh scratched at several days' worth of beard on his chin. "I guess I owe you for pulling me out and saving my life." "Not really." Cotton shook his head. "I heard them men beating on you, then throw you overboard. It ain't right for folks to be beating on one another." He frowned. "I've been on the receiving end too many times. I had to do what I could. We're just lucky the river decided to give you to me. Otherwise you'd be feeding the gators and gars." Hugh reached for the doorframe to pull himself up after he finished. "There is that." His head swam, and he grabbed for Cotton's strong arm again. "I'd offer to get out of your hair, but I don't think I'm going to be up for going anywhere for a few days at least." Cotton caught him and helped him stay standing. "No fuss. It's just one of you, so you won't bother me too awful much. Besides, it's nice to have someone besides the gators and crows to talk to." Cotton wrapped a supportive arm around Hugh's waist, and together they moved slowly back to the cabin. "You mentioned Miss Cassandra. Who's that?" "She lives up in the big house. She helps folks out with healing and the like." He paused for a moment. "Some folks say there's a mite more than a little bit of voodoo in her, but we don't bring that up none in polite company." Hugh nodded. He knew more than a few of the former slaves were very superstitious, even among their own. "So she came to try and heal me?" They reached the cabin, and Cotton angled through so they could both clear the door. "She didn't try, she did. Well, maybe it was more her tea than her. She'll be back by in a few days to see how you're doing." They reached the bed, and Cotton lowered Hugh down gently. The walk from the outhouse had drained Hugh of the little strength he had. As Cotton helped him stretch out again, he grabbed Cotton's strong hand. "Thank you, Cotton. I'd be dead without you." Cotton squeezed his hand back and smiled at him. "Don't you worry none about that. The river ain't a good way fer nobody to die. Maybe one day you'll have the chance to pull someone from her too. Then we'll be balanced." Hugh smiled back and nodded weakly. "Balance is a good thing." He sighed and watched Cotton turn and walk out the door. The light and shadows played nicely off Cotton's defined, muscular back. I've never even looked twice at a colored man. This one shapes up nicely. Since the war, everything is changing. I know my whole world has, more than just losing my leg and family. If I can find true interest in a black man, anything is possible. # 7 COTTON STROLLED into the cabin carrying his ball-peen hammer, a thin steel pry bar, and a heavy pair of pliers. "Hugh, are you up for me taking a whack at fixin' your leg?" He bounced the hammer in his hands to hide his nerves. He hadn't done much more than help Hugh from the bed to the privy since he woke up. Hugh stared at him in the cabin's low light. "Do you think you could? It would be nice to get around a little easier. With this thing bent like it is, it's almost worse than not having it." "I reckon it is." After setting the tools on the bed next to Hugh, Cotton turned on the oil lamp. "If it weren't cloudy out, I'd say let's git ya outside, but it won't help today." "What do you need me to do?" Hugh pushed the thin blanket off, revealing his bent right leg. The intricacies of it still baffled Cotton. It was complex and familiar. The maker who'd shaped it had done a wonderful job making it look like a real leg, with just a bit of metal bone about twice the size of a silver dollar where the kneecap should've been. The brass of the leg sparkled in the lamplight, showing the delicate grooves that looked like the hair on Hugh's real leg. The metal kneecap was bent on the inside of the leg, pushing against the lower part of the articulation. "I think this is part of the reason it's hanging wrong." Cotton pointed to the bend. "Let's start there." He picked up the pry bar and hammer. The leg moved easy enough for him to get the pry bar under the cap. He strained his muscles trying to return the damage to a shape that looked like the undamaged side of the kneecap. Pausing, he glanced at Hugh. "What's wrong?" Hugh arched his eyebrows. Cotton swallowed as fear for Hugh rushed through him, followed by a bit of fear for himself. He'd seen what happened when a colored man inadvertently hurt a white man. The colored man always paid the price, if he was at fault or not. But he really didn't want to cause Hugh any pain; he'd feel terrible if he did. "I don't want to hurt you." A sad chuckle rolled out of Hugh. "I haven't had any pain in that leg since I woke up in the hospital after losing it. Unless you count the phantom pains, which I don't. So bang away." "If you're sure." Cotton pushed harder on the pry bar. The kneecap shook and popped off. "Lawdy." Cotton jumped back from Hugh and scrambled to find the piece of metal where it rolled under the bed. He found it and brought it back out. "Maybe this will be easier to fix now. But I didn't mean to break it." A warm smile lit up Hugh's healing face. "It's okay. From the looks of it, there are a few springs holding it on. If you've got some the right size, it should be an easy fix." He reached down and moved the lower part of the leg and was able to get it almost back to a proper position. "I think I've got some more springs. If I don't, I can take them off of my spear and then git more when I goes into town." Cotton hurried from the cabin to check his shed for what he needed. He muttered to himself about breaking Hugh's fancy leg as he went. But at least he don't seem mad at me. I wouldn't want ta make him mad. White men ain't friendly when they gets mad at colored folk. Finding what he needed, Cotton dashed back to Hugh. "I gots the springs." "Good." Hugh was still smiling at him. "Let's get this back together and see if it works." Cotton spent a few minutes with his hammer, returning the kneecap to its proper shape. He made sure Hugh approved. When he went to put it on, the small rings on the kneecap for the springs didn't line up with the ones on the lower part of the leg. "I think it's bent, just a bit." Cotton frowned as he studied the slight angle the leg still had. "I wonder if we work together iffen we can bend it back enough to make it work." He glanced at where the bolts in the top of the brass held the leg to Hugh's thigh. Along the edge of the leg, and the base of the bolts, it looked like his skin had grown over the metal. "It might be easier if we could take it off, but I don't wanna mess with them bolts." Hugh shook his head emphatically. "I don't either. Let's just try this. I'll hold the top. You try and move the bottom." "Iffen you're sure." Cotton took a firm hold of the middle part of the lower articulation. "I'm sure." Hugh gripped his metal thigh. "I just wish I had more leverage or stability." Cotton's muscles strained as he put ever-increasing pressure on the leg, trying to slowly bend it back into shape. It moved. Ever so slowly, the metal yielded to their efforts. "Try that." Hugh put a warm hand on Cotton's shoulder to stop his effort. The touch sent urgent tingles through Cotton. Picking up the mended kneecap, Cotton hooked the springs on, first to the upper leg, then the lower. It all lined up, not perfectly, but good enough. "Looks good." Hugh swung the leg off of the bed, and it hung correctly next to his regular leg. "Let's try it out. Can you support me?" Cotton held out his arms to Hugh like he'd been doing to help him to the outhouse. "Come on." Hugh eased up. His smiled broadened. "I'm up." "Yeah, ya are." Cotton didn't take his hands from Hugh. He didn't want him to fall over. "Now let's take a step or two." Hugh shifted his weight. The movement was slightly different from the way a man with two good legs would move, but he lifted the metal leg off the ground and it swung forward a few inches. Then he moved his good leg up next to it. Cotton backed up, trying to give him room to move while maintaining a hold on him. They took a few more steps before they reached the door. Hugh's face was pale with effort. "It's working. That's good. I think I need to lie back down." He huffed and rolled his eyes with a pained look. "I'm not used to standing again. I promised myself when I got out of the hospital that I wasn't going to get in this shape ever again." "Then let's get you back in bed." Cotton helped him turn around and head back to the bed. Their minor triumph bolstered his day. The fact that Hugh hadn't gotten mad when he'd broke things worse gave him even more hope. Maybe Hugh is different from the other whites in the South. COTTON HUMMED softly to himself as he skinned the alligator he'd killed the previous night. He'd been busy enough with taking care of Hugh he hadn't maintained his normal production of skins, but he had enough food and there weren't any supplies he needed presently, so it didn't really matter. There was also something about taking care of Hugh that made him happy. When he realized he was humming, he stopped. I don't normally hum while I work. It reminds me too much of the singing in the fields. But I feel happy. Is it wrong to hum when I'm happy? It's not as lonely with Hugh here. I never thought I'd like taking care of another person, but it makes me feel needed, and that's nice. Focusing on nailing the damp skin to a piece of board, Cotton pushed thoughts of Hugh out of his head for a little while. "Anything I can do to help?" Hugh startled Cotton. He wasn't used to having people around as he worked. He turned and stared at Hugh leaning against the cabin's doorframe. He'd put on his pants, covering up his metal leg and other things, but was still bare chested. Copper-colored toes were visible below the cuff of the black pants. The bruises and cuts from Big Al's attack were fading slowly, leaving behind a lean, shapely form that had known work, but not the hard labor Cotton had endured. Cotton leaned the board up against the shed wall next to the other skins that dried in the sunlight and wind. "I don't think. Not much ta do right now. I ken get the gator meat cut up so it ken dry." When an almost lost look crossed Hugh's handsome but still slightly swollen face, Cotton realized he needed something to do. "How 'bout getting the vegetables ready fer tonight? Cooking fer two is taking a little more time then I'm used ta." "I can do that." Hugh walked gingerly from the cabin to the wooden table near the cooking fire. He looked almost relieved after he lowered himself down onto the bench there. He sighed heavily. "This leg's a little harder to drag around when I'm not feeling good. It almost reminds me of learning to walk with it." "Ya must do pretty good at it." Cotton smiled at him. "Ya haven't asked me to get ya a walking stick." Hugh shook his head. "I haven't used a cane since I got used to the leg. The artificer who made it did an excellent job. But then, the amount of money my father paid him for it, he had to." Hugh tapped his leg; even through the fabric covering it, there was just a hollow metallic sound. "Compared to some of the others I've seen, it's a work of beauty. All in all, it works just like a regular leg. I just have to be careful how I set it down sometimes." Cotton put some okra, squash, and carrots on the table for Hugh. "So how did you get it anyways? Iffen I ain't being too forward asking." "No." Hugh picked up the small knife lying on the table before reaching for a piece of okra. "I don't mind saying. Cotton, you've done so much for me, you could ask me just about anything." For a second, Cotton's heart skipped a beat. Since Hugh was well enough to clean himself, Cotton had missed the feel of the lean muscles under his hand. He figured asking to be able to touch Hugh more would be too much. It was obvious Hugh was from a Southern family with money, and money meant slaves before the war. Miss Cassandra did say the river might've changed him. Maybe he'd be open. Hugh continued to cut the okra. "There's an old saying, you can't win a race with a cannonball. I can tell you from personal experience, it's true. It was the battle of Fort Jackson. I was part of the battalion under Brigadier General Johnson K. Duncan. Them Union ships came up the river at us. I remember the cannons going off. We didn't really stand a chance. We did our best, but in the end it took standing up to Duncan and forcing him to end the futility of it all. A lot of good men died there. The first day or so was all I really remember. Filled with smoke and constant cannon fire. Many of my troop were killed. That first day, I was running back and forth, helping the wounded while trying to keep up my end of the firing. We were all exhausted, and the Union just wouldn't let up. So many friends died in each other's arms. Then everything changed in my life. I was holding on by a thread after the cannonball hit me. I was in and out of it for the last several days of the battle. After everything got quiet, the next thing I knew I was waking up in a plantation house converted to a field hospital clean across the states, near Chattanooga. My father was already there and had made arrangements for my new leg. He'd had me moved before they even knew if I was going to live. Compared to a lot of the ones I've seen, it's a really nice one. Better than a single piece. Unless you happen to bump up against it, or see me without my pants, you'd never know it's not real." Cotton nodded. "But don't it get cold during the winters?" "I guess a little." Hugh shrugged. "The bigger problem, and I was going to ask you about getting some oil, is rust. I've got to wipe it down once a week or so and add a bit of oil to the knee and ankle joints." For a second Cotton thought about it, trying to remember if he still had some, but then realized he'd used the last of his supply in cleaning his gator spear the night before and shook his head. "I ain't got no oil right now. If I did have, I would've used some when we did yer repairs, but I bet my friend Timmy has some. He's working with a guy in Memphis making this new kinda boat that's faster than paddleboats." "I bet he's the man who was racing the Bayou Belle that night." Hugh finished with the okra and started on the carrots. Cotton nodded. "That's him. I could run into town tomorrow and talk to him. Any sorta oil you prefer?" Hugh added carrot tops to the pile of okra ends. "Not really. Any kind of machine oil will be fine. I just don't want to stiffen up and have trouble walking." The sound of hooves coming down the path alerted them to visitors; they turned together to watch two people ride toward them. "It's okay." Cotton took a couple of steps from the table. "It's Miss Cassandra. She said she'd stop by to check on ya some more." The older woman swung down from her horse and walked toward them. "Well, well, y'all look a sight better than ya did the last time I saw ya, Mr. Lafoux." Setting his knife down among the half-finished vegetables, Hugh smiled at her. He started to rise, but a pained look crossed his face and he sank back to the bench. "Miss Cassandra. Cotton says I have you to thank for my health." She stopped a few feet from Hugh and looked him over. "I think Cotton is more to thank than I. He's the one pulled you from the river, then come and fetched me. It's good to see you up and around." Hugh gestured for her to join him at the table. "It takes a lot to put me down for the count. A cannonball couldn't do it, and neither can Al Shank. But I'll be forever in your debt." He looked up and smiled at Cotton. "And Cotton's." Miss Cassandra settled herself on the bench opposite Hugh. Ben stood protectively at her shoulder. "Be careful with your words, Mr. Lafoux. I might just have to take you up on them." "Please call me Hugh. Mr. Lafoux sounds too formal for our surroundings. Anything I can do for you or yours, just let me know." A grim look crossed Miss Cassandra's face. "It seems between you and that newfangled boat, Big Al Shank has crossed the line of decency several times the past week." Hugh straightened on the bench. "What do you mean?" "First, two Negroes have disappeared from his boat between Memphis and Saint Louis. Now it might've been someone other than Big Al, but Ben talked with a couple of the men working in the kitchen, and they said there was some kinda scuffle. The two who went missing were complaining about being forced to ride up on the upper deck during the rain, and Big Al thought they was being uppity." Hugh nodded. He knew Shank well enough to know he, like a lot of other Southerners who thought themselves above others, didn't like it when folks acted in ways he thought inappropriate. "Then last night, soon after the Bayou Belle left Memphis, the old blacksmith shop burned again." Cotton stared at Miss Cassandra. "Is Timmy Birmingham okay?" She nodded. "A few minor burns from where he tried to save some of their work, but he and everyone else got out." Again Hugh nodded. "I can see Al burning down someone he felt was competition. He wasn't real happy about something right after the poker game, and I bet that new boat design giving him a six-hour head start and then beating him into port was it. Come to think of that, it might've had something to do with his violent attack on me. It doesn't excuse it, but it probably added fuel to the fire." Miss Cassandra sighed. "We can't have him hurting people just because he gets mad. Unfortunately the sheriff ain't likely to do anything to him, not on our word, at least." "Do you need me to go talk to the sheriff?" Hugh sounded uncertain, and Cotton wondered why. "I doubt that would do much good either." Miss Cassandra picked up an uncut carrot and seemed to study it for a moment. "But we need a way to stop Big Al from terrorizing people along the river. There's only so much colored folk can do to white folk without incurring the wrath of the other white folk. But white folk can do whatever they like to each other without starting another war." Hugh frowned at her. "Are you suggesting I go kill Shank for you? I'd still get thrown in jail." He shook his head. "Yes, I owe you for saving my life, and I owe Al back for throwing me in the river, but I don't want to go to jail." Miss Cassandra pointed the carrot at him. "Now, Hugh Lafoux, I ain't askin' ya ta go ta jail fer us. I wouldn't ask jail of anyone. Besides, last I checked, killing was a hanging offense. The river gave you to Cotton for a reason, and I don't think I'd be right sending you to dangle on a rope. Odds are I'd rightly upset the river to no end." She waggled the carrot at him. "No, we need to come up with a way of making it look like an accident. Even with an accident, we can spread the word along the river it happened 'cause he weren't treatin' people right. That'll make others think twice before they go abusing folk." "An accident." Hugh sighed. "Miss Cassandra, I'm a gambler with a metal leg. There's only so much I can do in such a situation. I don't know if I could cause an accident that would kill Al Shank." "I wouldn't be asking ya to do it by yourself." A light smile graced Miss Cassandra's lined face and seemed to wash years away from her. "I bet Shamus Culpepper would be willing to help, probably Timmy Birmingham, Cotton, and a few others." Cotton raised an eyebrow. "Shamus Culpepper?" "The artificer Timmy is working with." Miss Cassandra laid the carrot back on the table. "Think about it. It's gonna be another couple of weeks afore you're back to normal, Hugh. I reckon we should all be thankful there weren't more extensive damage. But I'll be interested to find out why the river gave you to Cotton." She stood, looked back at Ben, and nodded toward the horses. "Now why don't we get back to the house? Ya think on things for a while, Hugh. Cotton knows where to find me. From the looks of you, I won't be needing to come back out here and check on you none." She and Ben quickly mounted, turned their horses, and trotted off up the trail away from the house. Cotton glanced at the half-prepped meal and then at Hugh. "Hugh, I'm gonna run into town and check on Timmy. He's a good friend. Can ya handle finishing dinner on yer own? The gator meat done cut up, and all ya gotta do is put it in that pot with the vegetables and water. Light the fire and let it simmer till it smells good." Hugh nodded. "I can handle that. You go on and check on Timmy. I'll have it ready when you get back." Cotton smiled at him. It had been a long time since he'd had someone fix dinner for him. "Thanks." Cotton took off running down the trail. # 8 THE SMELL of smoke and ash still lingered around the charred bones of the blacksmith's shop. A small group of people stood around talking softly. It didn't take Cotton long to spot Timmy talking to a scrawny man with red hair. He walked up and stood patiently waiting for his friend to notice him. "Hey, Cotton." Timmy waved at him and excused himself from the conversation. His right hand was bandaged, but otherwise he looked fine. "What brings you to town?" "Miss Cassandra told me about the fire a little while ago. I wanted to come and make sure y'all were fine." Cotton tried not to stare too hard at the remains of the blacksmith shop. The entire roof had collapsed in and burned. The anvil, the fire pit, and the chimney were all the structural parts that remained. "Can you believe it? We was just 'bout ta finish our second boat too." Timmy shook his head. "Most of us don' think it were an accident neither. Everything was cool to the touch when we went to the saloon down the street last night fer dinner. We hadn't been down there more'n 'bout fifteen minutes before the fire bells started ringing and someone ran in screaming the place was afire." "Who ya think might've done it?" Cotton wanted to hear if Timmy's opinion matched Miss Cassandra's. Timmy glanced around and dropped his voice. "Big Al Shank. He might not've done it hisself, but I bet ya my freedom he were behind it. Everyone knows he was mad about Shamus beating him in the race, even with a head start. If we ken be making faster boats, then the paddle wheels will be done for. Simple rule of commerce, he who can git the stuff there faster will make more money. Riverboat men like Al don't wanna change none. They want things just like they is." "Did anyone see anything?" "No." Timmy shook his head. "Not that anyone would say anything for an Irishman and a Negro when an upstanding member of Memphis society is claiming innocence. We don't stand a chance against Big Al." Cotton nodded. He hadn't realized Shamus Culpepper was an Irishman. The last name didn't sound Irish, but if he was the red-haired man, he looked Irish. "So what can you do?" "Shamus's talking about rebuilding, but he's not sure he's got the money to build it back the way it was. It might be a lot smaller." Timmy sighed. "For a while we might just be a blacksmith shop and have to wait to try and build the boat again until we've got more money raised. By then, someone else might have constructed a better one." "That could happen." A wave of sadness passed through Cotton for his friend. It was hard for a Negro to get a break like Timmy had, and all too often the break disappeared as quickly as it had come, leaving the man with nothing. And unlike Cotton, Timmy had a wife to think about. "Hey, iffen I can do anything to help out, let me know. I ain't got much, but I'll do what I can." Timmy smiled at him. "I'll keep that in mind. I might be fairly busy as we try and rebuild, and me with a bad hand and all. I could come asking for a bit o' gator from time ta time. I know Rubi would appreciate the extra meat." "Sure, I can run some into town tomorrow afternoon, if you like." Cotton liked the idea of being useful to his friend. "That would be nice. I'll let Rubi know, so she ken expect ya." Someone shouted for Timmy. "I need to be goin'." "Sure." Cotton turned from his friend, then turned back. "Hey, any chance you might still have a bit o' machine oil around that didn't burn up?" Timmy scratched his head. "I don' think so." He turned toward the Irishman. "Shamus, that cabinet with the machine oil in it burnt up too, didn't it?" Shamus frowned and nodded. "With everything else." He looked at Cotton. "If ye're a needing some machine oil, the mercantile often has some. With everyone trying their hand at tinkering nowadays, ye'll find it more often than ye used to." "Thanks." Cotton waved to Timmy and hurried down the street toward Olsen's Mercantile. Olsen's Mercantile was the largest store in Memphis. They knew Cotton. He sold his alligator skins there, and they gave him a fair price, not like a bunch of folks who would ship them to the factories in the East to be made into shoes, belts, and more. It wasn't the first time he'd gotten tinkering supplies there. "Hey, Cotton," said Sherman Olsen, oldest son of the first Olsen to run the mercantile. Olsen's was one of the few businesses to survive the war. Since they'd been working class for generations and hadn't been real fond of slavery, they'd never had problems with the freedmen and women they now dealt with directly as opposed to as agents for the plantation owners. "Hello, Sherman." "Have you heard about the fire last night?" Sherman leaned across the counter toward Cotton. "Yeah." Cotton walked over so they wouldn't be easily overheard. "I just talked with Timmy Birmingham down there. He's hoping they can rebuild." "I done told Shamus Culpepper if he needs anything on credit with me, he can have it. We need more men like him and Timmy in this town. Showing folks what a colored man and an Irishman can do working together. It's a good thing." "I agree." Cotton straightened up a bit and raised his voice to normal levels. "I need a bit of machine oil." Sherman scratched his thick brown beard. "Yeah, how much do you need?" He walked out from behind the counter. "Are you still hunting gators?" "Yeah. I made me a new spear that's got some moving parts to it. It works really nicely. I used up my can on it." He still didn't want folks knowing Hugh was out at his cabin. The world thought Hugh was dead. It might be better to keep that illusion going. "So you shouldn't need too much." Sherman led him over to an aisle with a lot of springs, gears, and other things tinkerers might need. Every time I come in, there is more and more stuff here. There really must be a lot of folks experimenting with things. Sherman picked up a strange shaped metal can with a long pointed spout running off the top. "When you need more, come back in. Bring the can in, and I can just refill it and save you a little money. I'm trying this refill thing instead of just selling larger cans. A lot of the tinkerers around seem to like it. Saves folks shelf space that the bigger ones take up. There's more on your account than this, so I'll just subtract it off for you." Cotton took the can. "Thanks." "So, Cotton," Sherman dropped his voice again. "You be careful while you're out there hunting gators. Stay out of the way of the riverboats. Them men who run 'em are getting more and more ruthless." "Okay." Cotton nodded. "I'll remember." He turned to go. "Oh. When can I expect more skins? Some of these artificers like your leather for some of their contraptions. I can pay you more than what I have been." "If ya don' mind a partial order, I ken bring you some tomorrow. I promised Timmy Birmingham I'd bring Rubi some gator meat in. I could drop 'em by at the same time." A wide, bright grin split Sherman's beard. "That would be good. Right now I think I could sell everything you could bring me." "I reckon I needs to spend more time in the swamp, then." Cotton grinned back. "Don't kill yourself, but anything extra would be appreciated." Cotton turned and strolled out the door. THE OILCAN caused an odd, uncomfortable bulge in Cotton's pocket, and he wished he had brought his pack with him. He wanted to stroll down to the docks and see if he could pick up any information or gossip before he headed back to his cabin and Hugh. There were a couple of barges pulled up to the docks and workers, mostly colored with a few whites in the mix, moved up and down the docks unloading the cargo. Cotton slowed and tried to look like he'd just come down to see the river and gawk at the things like the trackless steam locomotive with wide metal wheels. Men from a barge were loading boxes into the boxcar behind it. "This is safer," one worker mumbled to another. "Shore is," another replied. "You won't catch me taking no ride on a paddle wheel. Them captains is more ruthless then ours be. I'll stay floating up and down on the barges. Don't need no faster no how." One of the others laughed. "You're just trying to stay away from your wife in N'awlins anyhow." "Don't forget his one in Saint Louis," added another. "I ain't got no wife in Saint Louis!" the second one objected without breaking the line as he dropped the bag of grain he carried onto the wagon waiting for it. It was a new kind of metal wagon with only two horses instead of six. It was supposed to be lighter for the horses to move. His coworkers all laughed. "Next thing you'll be telling us," the first one said, "is that you don't visit them hoes from the Bayou Belle. We all know you stop in there any time you get the opportunity. The rest of us know them hoes has been worked over so badly by Big Al they ain't worth half the price he charges for 'em." Cotton walked on but stopped to stare at the trackless locomotive. It had to be the biggest conveyance he'd ever seen. Its smokestack was taller than any of the buildings in town, including the three-story inn. The body of the thing was longer than the barge it was unloading. The engine house made up a good quarter of its length with a wood stack filling a section right behind the engine. Two men worked on getting wood into the boiler and steam poured out of the smokestack in a steady white plume. The rest of the thing was a long cargo bed that was rapidly being filled up with the efforts of the men unloading the barge. "Boy." A man leaned out of the engine and gestured at Cotton. "If you're looking for work, we could use a hand. Not as many folk around the docks today as usual." Cotton shook his head. "Thank you, but no. I've got to get back to the house. Got what I needed from town." He patted his pocket and the oilcan pressed into his leg. "But if I need work, I'll keep an eye out for you." The man nodded. "Good." Having seen everything he figured he was going to, Cotton turned himself back toward the swamp. He was right. There were a lot fewer people around the docks today than there normally were. I wonder if it has to do with the Bayou Belle being in dock yesterday. Big Al's getting a bad name, and folks are staying away when he's around. Miss Cassandra might be right—it might be time to do something. It ain't right for folks to feel this uncomfortable. It's a big river. Folks might start to move up or down it. The houses fell away as the forest crept in and the trail thinned. Cotton jogged out of town slower than he'd run into it to check on Timmy. Regardless, he relaxed as his feet carried him away from Memphis and the comforting feel of the swamp closed in around him. # 9 HUGH TOOK a deep breath, inhaling the savory aroma of the gumbo he'd cooked for several hours. He'd never been a good cook, never really had much of a chance to practice over a campfire like Cotton's except when he was riding between towns. At home there had always been slaves, and in the army there had normally been the mess tent. But when there hadn't been an inn or saloon to stop in, he'd had to make do with his own culinary efforts. The sound of Cotton's return was softer and slower than his exit had been. It was almost like he wanted to approach his cabin unheard. Hugh turned and looked at the trail. Cotton's blue shirt hung open with sweat dripping from it. His almost white hair was plastered to his head. The sight touched Hugh's heart. In the short time he'd been awake and around Cotton, he'd never seen the man so tired. "You look exhausted." Cotton nodded and pulled a small can of oil from his pants pocket. "I am. Running to and from Memphis can wear on a fella. But I 'membered your oil. All Timmy's had burned up, but they had some at the mercantile. I used a bit of my credit with 'em to get it. Boy, that gumbo sho does smell good." Hugh's fingers brushed Cotton's as he took the oil. "Thanks. I'll pay you back. For the oil, the nursing, and everything you've done for me." "Don't worry about it." Cotton shook his head. "You cooked dinner. I ain't had nobody cook me dinner in a long time." "Well, I think it's ready." Hugh set the oil down on the weathered table before handing Cotton one of the dented, military-surplus metal bowls they'd been eating from. "I should warn you, I'm not the best cook in the world, but gumbo's easy as long as you don't overseason it." Cotton laughed wearily. "It smells good, and I didn't have to cook it. Right now I don't care." He put the bowl down. "Let me run get some water first." Hugh shook his head. "No, let me get it. You just ran all the way to Memphis and back. Get some food and sit down." For a moment Cotton stared at Hugh. "Hugh, it ain't right for a white man to be serving a colored man. I can get it." "No." Hugh put a hand on Cotton's shoulder. A strange feeling passed through him. For a moment he wanted to do more than just touch Cotton's shoulder. "There isn't anyone out here who will see anything we do." He snatched Cotton's wooden cup before Cotton could touch it, carried it over to the water pail, and dunked it down to fill it. Careful not slosh the full cup, he walked slowly back to the table and set it down in front of Cotton. How long before everyone realizes that folks are equal and it doesn't really matter who serves who? The Negroes haven't been freed that long. It will take time. Hugh paused and smiled at Cotton. It wasn't that long ago that I never would've thought about serving a black man. But this is Cotton. He's done so much for me. I don't really care who sees it. Cotton stood there, stone still with his mouth slightly open. "Thank you. But you don't need ta be serving me. It ain't your place." Grinning harder, Hugh handed the bowl back to him. "Get some food, or do you want me to serve you that too?" With a slow shake of his head, Cotton took the bowl and went to the pot of gumbo bubbling over the fire. Once Cotton had his, Hugh got some for himself, then seated himself on the other side of the table. "Cotton, a couple of weeks ago, hell, a week ago, I would've agreed with you and let you serve me. But, you're a good man, a free man, and you don't have to serve me just because I'm white and you're not, at least not completely. You've done so much for me—let me do a few things for you. It doesn't look like you've got anyone around here to do things for you." With his spoon halfway to his mouth, Cotton paused. "No. I ain't." He finished moving the gumbo-laden spoon into his wide lips and chewed slowly. "Most folks don't like me much. I'm too white for the colored folk and all white folk see is another colored man, even if I do have this pale hair." "But Miss Cassandra and your friend Timmy?" "Miss Cassandra helps any and all. She don' care none 'bout what we are, as long as we're good people and willing to pass her help along to others. Timmy... well, Timmy and me go a ways back. Our mamas was house slaves at the same plantation, so we grew up together. We've always been friends. Timmy also hopes that one day whites and coloreds can live together peacefully, without all the hate and fightin'." He took another bite of the stew. "This is pretty good." Hugh smiled. "I'm glad you like it. I can do a little bit around a campfire." He liked the fact Cotton was opening up to him. "So there haven't been any women who caught your eye? You're a big, strong guy, handsome even." For a second Hugh paused. He'd never called a colored man handsome before. "I bet the girls all loved you." "No." Cotton frowned. "I think I looked a little too much like my father. He'd been the master's cousin... before he was killed in the war. Or at least that's what my mama always told me. The whole family had the same light blond hair, so it was hard to say who my daddy really was. But all the girls... they always laughed when they thought I couldn't hear them. Not that I really ever thought about them." A hope rose in Hugh at Cotton's tale. He really didn't think about them? Might he be interested in men instead? "Why didn't you think about them?" Cotton shrugged as he set his spoon down and took a long drink of his water. "Don't rightly know. It might've had something to do with the other boys at the plantation. Other than Timmy, they was always beating us, me and Timmy, telling us we didn't have no right to be looking at the girls. They wanted them all to themselves." Hugh chewed his mouthful of gumbo slowly before saying anything else. "So Timmy never found a girl neither?" "Nah, Timmy married Rubi a few years ago. She's a nice gal. She was a house slave at the next plantation over. She'd always been kinda sweet on Timmy and when we all got freed, the first thing he did was ask her to marry him. Miss Cassandra performed the ceremony since we couldn't get no white preacher to do it, what with them being colored an' all. Rubi thought I should get hitched to one of the other house girls, but I felt uncomfortable around her and decided to come down here to the swamp and hunt gators." For a moment he stared off into the forest. "I like the peace and quiet around here. It suits me. I can't see me gittin' hitched and havin' no kids. Out here, they'd all git eaten by the gators iffen they weren't careful." "I don't think most women would appreciate that." Hugh chuckled slightly. "But don't you get lonely out here?" "Not really." Cotton swallowed his food, then brought the bowl to his lips and drank down the broth. "So, you asking about me. What about you, Hugh Lafoux? You got a wife and kids waiting for you somewhere?" It was Hugh's turn to shake his head. "Nope, not me. The war came up before my mother could manage to marry me off to any of the belles that were always flitting around the house. After the war, I managed to stay on the move. Since my family lost everything, I haven't found anything worth settling down for. I just don't have it in me to try and rebuild things from the ashes that the war left behind. I want to head west. There's new land and new opportunity out there. So far I haven't found anyone I really clicked with. Most women are just too soft and fragile. At least in my opinion." Hugh stopped eating and watched Cotton's face to see if the man caught the real meaning of what he'd said. For a moment it looked like Cotton was trying to think about it. Then he stood and walked back to the stew pot for a second bowl. "Yeah, a lot of women do look more fragile than men." A strange look crossed his face. "But a lot of the men are too rough. They don't know how to be gentle." What's he mean by that? Hugh finished off his bowl of gumbo. Part of him wanted to probe more, and the rest of him, a larger part, wanted to leave it alone, at least for a while. He sat there and studied Cotton as the last rays of the evening sun disappeared into the swamp. The firelight cast strange colors against Cotton's dark honey skin, and his pale hair, slowly drying from his early exertion, caught the light in an almost angelic glow around him. When he turned, the firelight danced through the sparse hair on Cotton's chest. Hugh wanted to feel that hair, find out if it was soft or coarse. "Don't you want any more gumbo?" Cotton asked. "It's pretty good, lessen ya don't like yer own cooking." Hugh shook his head. "I'm full. Still getting my strength back. I don't think I can eat too much." Cotton nodded. "I got sick right after I built the cabin. I was bad for a while, could barely eat. Miss Cassandra says iffen you don't feel like ya ken eat something, then don't force it. You'll eat more as time goes by." "Sounds like what my mother used to say." He stretched and, unbidden, a wave of tiredness washed over him. "So I'm thinking I might go lie down. Lately I haven't been up as much as I have today." Cotton set his bowl down after he drained the broth again. "Okay. If you want to." Hugh paused before he rose. "Cotton, I haven't asked before. Where are you sleeping? I presume the bed is yours, and I haven't seen another one." "There ain't no other one." Cotton shook his head. "I been sleeping out here near the fire. It keeps the night prowlers at bay." "Cotton, the bed's big enough. Why not sleep in there with me?" Pausing, Hugh thought about the possibilities of Cotton sleeping in the bed with him. Hope stirred inside him. "I wouldn't want to crowd ya none." Cotton picked up his bowl and Hugh's before Hugh could object. A chuckle escaped Hugh. "Cotton, it's your bed, not mine. You're a freeman, who deserves all the rights of any other man. I don't know if Lincoln said every man deserves to have a bed, but I'm sure if he didn't say that, it's something he would have if he'd thought about it. I don't want you to have to sleep out by the fire. When I go to bed tonight, will you come sleep in your bed with me?" Cotton juggled the eating utensils from hand to hand. "You're not completely healed yet. Don' ya think ya'd sleep better without me sweating all over ya?" Something tells me you sweating all over me might be really nice. "Tell you what, let's try it tonight. If it's too uncomfortable, then I can sleep on the cabin floor or out by the fire." "No." Cotton shook his head emphatically. "Hugh, it really wouldn't be right with you being a white man and all to sleep on the ground whist I be sleeping all comfortable in my bed." "I won this argument last time before dinner." Hugh laughed. "I bet I could win it again. Tell you what, if I can't get a proper amount of sleep with you in the bed, I'll tell you. Tomorrow night we can make other arrangements if it don't work tonight." Cotton scratched his smooth chin and carried the bowls and spoons over near the water bucket. "If ya insist. We'll try it. Iffen anyone asks, we'll tell them you insisted. That way it don't look like I'm getting uppity. Folks around here don't like uppity colored folk." Hugh smiled and nodded. "I take it you're not going to let me help you clean the bowls?" "No." Cotton shook his head again. "It's bad enough you cooked dinner and got my water. I ken clean our bowls." # 10 COTTON STOOD out by the fire, hoping Hugh would be asleep by the time he decided to go into the cabin and lie on the bed. Staring at the glowing coals, Cotton sighed. I don't know iffen he'd welcome my advance or not. I'm colored. An' it ain't natural for a man to want to touch another man. Master Carson always flew into a rage when he'd catch folk doing it. I never understood. From the forest, an owl screeched, sounding more like a horse than a bird. In the distance another answered it. Cotton glanced at the cabin door, where the lantern light still shone brightly. The coals were low enough they wouldn't be a problem but would still provide a basis for the next day's fire. With a heavy swallow, Cotton walked toward his door. Hugh sat naked on the side of the bed with the oilcan in one hand and an old rag in the other. The oil made the copper-colored leg glisten in the lantern light. He looked up and smiled at Cotton. "Sorry, this is taking a bit longer than I figured it would. There was a bit of rust starting in the knee joint that took me a while to get out. Never had that happen before, but then I haven't gone for a dip in Big Muddy since this happened either." Trying to ignore Hugh's fit form, Cotton walked to the foot of the narrow bed. "Don't worry. It took the fire a while to burn down." He didn't bother saying he'd hoped Hugh would already be asleep. "I can stop now and finish up in the morning," Hugh offered. "Either way, it won't take long." Cotton sat down on the foot of the bed. It was easier to look at Hugh's broad back than it was his chest and groin. "Go ahead and finish. I don't mind. Just want you to be able to get around okay." "Thanks." Hugh bent to finish the task of applying the oil. "Since I've had this leg, I haven't gone this long without oiling it. It gets to be a habit after a while." "Is it a lot of work?" Cotton stretched out on the bed and watched the play of Hugh's muscles as he worked the rag across his leg. "What's it feel like?" Hugh straightened for a moment, looked over his shoulder, and smiled at Cotton. "If I had a nickel for every time a guy asked me about what the leg feels like.... It was strange at first. I had to relearn how to walk, but now, most of the time, I don't even have a limp. If I bring it down too hard, it's jarring and hurts where it attaches to my leg bones. But I've had it long enough I don't really feel anything." He turned back to his work. "Every so often I do feel my toes move, which is weird. But I've talked to other men who've lost limbs—a lot of folks did in the war—and they call it phantom pains, or movements. Sort of like remembering what it was like when you still had your limb. It's part of life for me now." Cotton shook his head as it settled on his threadbare pillow. "Sounds spooky to me. I'm not sure I'd be able to git used ta having a metal leg." "Like I said before, I got lucky and got a nice one." Hugh worked the rag in between two of the moving parts of the knee. "There were more than a few guys out there who ended up with just a single piece of metal," Hugh continued, "or worse, just a piece of wood. It all depended on what they could afford." For several minutes, Hugh grew silent and the only sound in the cabin was the rag moving across the smooth metal that gleamed copper in the lantern light. Then Hugh sighed. "I often wonder if my father thinks he threw away the last of his money on my leg. For the last couple of years of the war, there weren't any crops on the plantation for him to rebuild his fortune with. I can't say as I ended up as the kind of son he wanted. After my brother was killed in the war, he wanted me to take over the family plantation down near New Orleans, but I didn't want it. Even if there had been anything left of it, or if most of our sl... workers stayed on as sharecroppers, I'd had enough of commitment and responsibility. Most of it was burned. I can't remember who taught me to play cards, but I'm good at that. I hopped on the first paddle wheeler heading north and haven't set foot in Louisiana since." There was a lot of heavy loneliness in Hugh's words. They pulled at Cotton, and sitting back up, he reached a tentative hand out to him. Hugh's shoulder was cool to his touch. "I understand. That's part of why I live out here. To get away from things and people." Maybe we're more alike than we realize. So we're different colors—inside we're alike. Hugh didn't jerk away from Cotton's touch. It felt good to Cotton to touch him again, even if it hadn't been that long. "I guess that's the biggest part of both our lives, getting away from people. You came out here on the edge of the swamp, and I ride the boats up and down the river, never staying in one saloon too long." Hugh laid his rag across his leg and turned gently under Cotton's hand. "It does get lonely after a while." Cotton nodded. "Yeah. It does." His heart raced as his gaze fixed on Hugh's brown eyes. Then he turned away. It ain't right to look inta his eyes like that. After a second, when the only sound was the owls screeching in the distance, Hugh took Cotton's hand. "You've got strong, gentle hands." He kissed Cotton's fingers. Part of Cotton wanted to jerk back. He'd never had anyone kiss his fingers before, but the movement was easy and sent pleasant tingles across his skin. Times is a-changing, but is this too much to ask for? Will he just leave me like my daddy did Momma? Hugh stopped and looked into Cotton's eyes again. "Is this all right?" The question caught Cotton off guard. He blinked. "What?" What is he asking me? White men don't ask. They take. Momma always told me that the masters take what they want. Iffen we want it or not. Do I want it from Hugh? Without turning loose of Cotton's hand, Hugh pulled back slightly. "I normally ask my partners if it's okay to proceed before I go too far." He chuckled softly. It was a very pleasant sound. "It's too easy to get into a situation, then have someone decide they don't really want to do what we're doing. I bet you're not used to being asked, particularly from a white man." Cotton shook his head, even more confused than he had been. Heat flowed up his arm from where Hugh continued to hold his hand. "Iffen you're askin' what I think you're askin', I've never been asked before. The bigger boys always just took what they wanted from me, until I got big enough to stop them. I ain't never been with a white man before." An expression that might have been revulsion crossed Hugh's face. Cotton wondered if his admission had changed Hugh's mind until he spoke again "I'm sorry about that. You're a good man, Cotton. You don't deserve to have anything happen to you that you don't want. I presumed, when you put your hand on my shoulder, you might be interested in being with me tonight." He squeezed Cotton's hand. Squeezing back, Cotton nodded ever so slightly. "Hugh, I won't lie to you. I liked taking care of ya. I wanted to touch ya. I've been a-wanting to touch ya all day. I think you're one of the best-looking men I've ever seen. There's something about ya that pulls me to ya. Maybe that's why the river put me in your current that night." His heart pounded. "I don't rightly know all the answers to your question since I don't know exactly what you're asking, but I want to touch ya. I want to find out what this feeling inside me is." Hugh grinned and kissed Cotton's fingers again. Another wave of tingles washed up Cotton's arm and his heart pounded harder. "Then please, touch me. I want to touch you too. We can take things slowly if you want. Right now I don't have anything waiting for me out in the world beyond this cabin." With his free hand, Hugh touched Cotton's chest and ran his fingers across it. Where Hugh's touch passed, a line of fire scorched its way across Cotton. He mirrored Hugh's actions, and the brown hair on Hugh's chest tickled his fingers. His breath caught when Hugh touched his nipple. He shivered slightly when Hugh rubbed it gently. "Let me kiss you," Hugh whispered. Without stopping to think about it, Cotton leaned closer. Hugh's lips were soft against him, and there was the faint taste of gumbo. Hugh touched the back of Cotton's head as their kiss lingered. When they finally separated, Cotton caught his breath and stared at Hugh. "That was really nice." Hugh ran his fingers down Cotton's jaw. Swallowing hard, Cotton nodded into Hugh's hand. "Yes. Yes, it was." He ran his hands across Hugh's chest, letting his fingers dance across Hugh's nipples. Under his hand, Hugh's heart pounded with a strong, steady beat. Somehow, even though his own heart raced, it surprised Cotton that Hugh's should be doing the same thing. He thought his was just because he'd never been a willing participant before. Before he could really think about it, Hugh's mouth was on his again, and he surrendered to their joint need to not be alone. Hugh pushed Cotton back on the bed and began kissing down his neck and across his chest. New, stronger sensations passed through Cotton when Hugh's mouth closed on his nipples. Energy shot through him so intense he arched his back and hugged Hugh's head to his chest. Chuckling, Hugh pulled away for a second. "I think you like that." As his breath came in ragged gasp, Cotton nodded. "Yes." "Then you're in for a big surprise in a couple of minutes." Without further elaboration, Hugh lowered his head back to Cotton's chest. After working his way across to the other nipple and eliciting more sounds of pleasure from Cotton, he kissed and licked his way down Cotton's stomach. All the while, his hands untied the cord that held Cotton's pants up. It was all Cotton could do to not jump when Hugh slipped a hand in his pants and touched his cock. He'd never been touched like that before. Even when the other boys at the plantation had been abusing him, they'd never touched his cock. They'd only made rude comments about the curly blond hair at its base and how much smaller than theirs his was. Hugh pushed Cotton's pants down and squeezed his cock. "Not bad. I wasn't sure what to expect. Seems you got a little from both sides." He smiled at Cotton. Cotton stared down at his dick in Hugh's grasp. It was so hard it hurt, but it seemed to fit in Hugh's hand perfectly. "What cha mean?" Before he answered, Hugh bent over it and took it in his mouth. Cotton leaned back as waves of pleasure shot through him. Is it right to feel this good? Will he let me do this to him? Will it feel this nice to him? He moaned as his breath quickened. Then Hugh pulled off him with a quick lick around his cockhead. "You're long and thick. Overall, a very nice dick you have here." Cotton didn't know how to reply before Hugh's warm mouth engulfed him again. He gasped. Hugh grabbed hold of Cotton's sac and pulled. Cotton's back stiffened, and he reached for Hugh's head. For a moment, as his heart raced harder than ever before, he thought he might be about to die. He couldn't breathe and his balls tingled. Then the waves of pleasure peaked. His dick surged in Hugh's mouth, and he collapsed on the bed. Hugh gagged slightly, then lifted up from Cotton's cock, pausing to lick the head of it again. He grinned at Cotton. "Wow! That was some load. I take it it's been a while since you came." Trying to catch his breath, Cotton just nodded. "Yes. I didn't know that's what it felt like." For a second, Hugh stared at him. "What do you mean... wait, are you saying you've never even masturbated before? You've never had anyone pleasure you like that?" "No. Never. The preacher at the Carson Plantation always said it was evil to touch ourselves, and nobody ever cared enough to make me feel like that." He combed a hand through Hugh's hair as his heart slowly returned to normal. "I thought I was dying, but it felt so good." Again Hugh chuckled. "It does feel good. You also taste very good." Cotton cocked an eyebrow as an idea hit him. "So how do you taste?" "If you want a taste, you're welcome to it. I'll understand if you don't want to. But I've been told I have a very tasty cock." Hugh straightened up with his legs on either side of Cotton. The metal leg was cool and slick from oil against Cotton's skin. Glancing down Hugh's body, his cock stood out from a nest of brown hair. It was narrower than the cocks Cotton had encountered on the slave boys and shorter too. When he'd seen it before, while taking care of Hugh, it had always been soft and small. It had grown some, but not as much as he expected. He wrapped his fingers around it. It disappeared in his hand, but he squeezed slightly and Hugh rewarded him with a soft moan. It was warm and hard in his grasp. "How do I do it?" Cotton all but whispered. He never thought about putting a man's dick in his mouth, let alone a white one. "Gently," Hugh replied. "If you want to lie there, I can move it up to you. I can lie down and you can do it like I did. There are a few other ways we could do it." Cotton ran his free hand up Hugh's flat stomach and across his hard chest while he started stroking Hugh's cock. "Why not like you just did mine? It might be easier on ya." A warm smile graced Hugh's lips. "Okay." He eased himself down on the bed next to Cotton, pausing to kiss him. The kiss tasted more salty and musky than before. Is that because of my cock in his mouth? Cotton wondered as Hugh rolled them over so Cotton lay on top. Lying on Hugh's chest, Cotton tried to remember everything Hugh had done to him that felt good. He licked and sucked at Hugh's large nipples. The hair on Hugh's chest felt odd but pleasing against his lips. He remembered to lick the head of Hugh's cock before he took it in his mouth. It tasted similar to Hugh's last kiss. But it was muskier. Cotton sighed as he lowered his mouth down until his lips touched the hair at the base. A low moan escaped Hugh, and his strong hands closed around Cotton's shoulders. "That feels really good." Knowing he made Hugh feel good inspired Cotton to grab Hugh's balls and pull slightly. Hugh moaned louder as Cotton slid up and down on his cock, flicking his tongue around it as he did. He had to work Hugh's cock longer than Hugh had to work his, but finally Hugh's breath deepened and quickened. Hugh thrust up, burying his cock in Cotton's mouth, then a thick salty fluid flowed from it. Reflexively, Cotton swallowed as he slowed his efforts. Hugh shuddered and gently lifted Cotton's head off his cock. "I get really sensitive after I cum." He pulled Cotton up so they could lie side by side on the bed and kissed him again. "You did that really well. What did you think? How did I taste?" Cotton let out a long happy breath, feeling more contented than he had in a very long time. "Like nothing I've ever tasted before, but I liked it." Hugh kissed him again, spreading the warm contented feeling through him. "Good. I liked it too." He ran his hand through Cotton's short curly hair. "Let's settle right here and get some sleep. I hope I don't keep you up all night." "With what?" Cotton stared at Hugh for a moment. "Your snoring's not that bad." Caressing Cotton's chest, Hugh wandered his hand down to Cotton's half-hard cock again. "No, but after a little while, I might want more of this." "Oh," Cotton replied. "I bet we can work something out with that." He hugged Hugh before kissing him again. It felt like he'd found something he'd been missing his whole life. He really liked the feeling of Hugh there in his arms. In the distance the owls continued their calling, and a gator roared. For a moment Cotton felt like answering that roar with one louder and more demanding, but that would mean shifting from the comfortable position he was in with Hugh, so he lay there and continued to run his hands across Hugh's body, enjoying each touch and tingle. # 11 HUGH STROLLED along the road leading to Memphis. The day was hot and muggy. Beside him, Cotton had on a knapsack with alligator hides tied to it and a large parcel of gator meat inside for Timmy's family. Hugh had offered to help with the load, but Cotton had refused. "It's been a long time since I felt this good." Hugh rubbed his hands through the beard that darkened his face. "Do you still think the beard is enough to change my look? I'd hate to be recognized and have it get back to Al that I'm still alive." Cotton nodded as they reached a more heavily traveled section of the road. "That, with the haircut I give ya, ain't no one gonna recognize you. But iffen you like, we can pick you up a hat at the mercantile. Every time I wear a hat, everyone says they don't recognize me. I don't know if that's true or if they're just fooling with me." Thinking about it, Hugh had to nod too. "Yeah, I can see that. I think a cowboy hat would definitely change my look. And don't worry about buying it for me. I got the money that was still in my pockets when Al threw me into the river. It ain't a ton, but it can get me some new duds." After a second he added, "That's not a bad idea. If I look like a cowboy, I know nobody will recognize me. Around here everyone just overlooks cowboys." The day felt like a whole new chapter in his life; why not adopt a new look? He'd been a Southern dandy most of his life, when he wasn't a soldier. "Iffen you had darker skin, we might be able to pass you off as a freed slave," Cotton added. "But even with your tan, you're too light. Folks wouldn't even take you for a Mexican, not that they're really welcome in these parts right now. You scream white man." Hugh chuckled. "Last night you had me screaming." He winked at Cotton. Cotton flushed. It turned his honey-dark skin a deep burgundy. He looked down at the road and kept walking. "Hey, don't be ashamed of it." Hugh ran his fingers briefly along Cotton's cord-like arm. "What other folks don't know can't hurt us. Besides, it's natural to want to enjoy ourselves." And they had, several times over the course of the night. It had been a while since Hugh had so much sex in a short period of time. Once he'd gotten Cotton to relax, he felt like he'd unleashed a wildcat. "We should make sure we keep it at the cabin." Cotton looked around, but they hadn't seen another soul since they'd been on the road. "Folks can be cruel. I don't want to cause ya to get hurt again." Then he flashed Hugh a slight smile. "I just got done patching ya up." Hugh smiled back. "And you did a great job of it too. So will you wait around for me if I go see a friend of mine? I'm not sure I can find my way back to the cabin without you." Cotton nodded. "Sure. It'll give me a chance to talk with Timmy and Rubi for a while." "Good. Let's stop by the mercantile first, then see what information we can dig up." Hugh knew what Miss Cassandra had told them about Al Shank was probably true, but he wanted to check some of his sources and find out. Hopefully the Bayou Belle would be docked at the river. TUGGING THE black cowboy hat into a comfortable position on his head, Hugh sauntered up the gangplank to the Belle like he owned the ship. Two of Shank's men stood at the end of the plank and studied him as he walked toward them. "Hey, fellas, I hear there's a nice bar on this here boat." He did his best to lose his more sophisticated Southern drawl and sound like most of the cowboys he'd met in recent years. The bigger of the two men shifted like his leg was sore. Hugh thought about the derringer in his pocket. Nice to know Shank's man still bore scars from their encounter too. "Yeah, there's a bar. Are you planning on going upriver with us tonight? You'll need to check in with the captain and get a ticket." Hugh shook his head. The hat was a little bigger than he was used to and moved oddly, but it didn't fall off, so he didn't touch it. "Nah. I just wanna see what yer bar's like. Been hearin' the riverboats have better whisky than most of the saloons around here. Thought I'd stop in fer a couple o' drinks and see fer myself." "We cast off at five," the other man said. "Make sure you're off by then, or we'll be charging you extra for traveling without a ticket." Hugh touched the brim of his hat as he nodded. "You've got my word. I'll be off by then. The wife'll have my hide if she catches me here after she's got dinner on the table. You know how it is." The bigger man gestured toward where Hugh knew the bar was. "Go on. Git your drinks, then get back on dry land." "Thanks." Hugh strolled onto the deck and to the bar. A grateful sigh escaped him as he walked inside. On a stool, next to the piano, sat Susie Sweet Tones, belting out a sultry ballad of the glory of the South, just like Shank liked to hear. A quick glance around the bar showed Hugh the riverboat owner wasn't there. He eased up to the bar and ordered a shot of whiskey and a glass of beer. Like he knew it would be, the whiskey was more water than alcohol, and the beer was only slightly better. He knocked back the shot at the bar, then carried the beer to a table near Susie, put his boots on the table, and listened to her sing. The depth of Susie's talent never ceased to amaze Hugh. He'd known the singer for years. She could've had a career in a major opera house on the East Coast but said she preferred the laid-back life traveling on the river. She'd worked several other boats before she got a job with Shank. With her alabaster skin, sparkling blue eyes, long curly brown hair, and perfect teeth, she helped keep his customers in a good mood with her ready smile and incredible vocal talents. He paid her well, even if she didn't help service customers the way the girls on the third floor did. As he finished his beer, she completed her set, walked over, and turned on the auto-player calliope. With a puff of pent-up steam, the thing started cranking out music in sharp metallic tones and the occasional delicate flutelike whistle as she headed for the door. Hugh stood and headed toward her. He dropped his voice and his fake accent. "Susie, you got a minute?" She whirled on him. "I'm sorry, I don't do private performances." Before she could move away, he stepped closer and touched her arm. "Sue, it's Hugh." He moved the cowboy hat back so she could look into his eyes. "Hugh?" Her soft blue eyes grew wide. "My God. Hugh." She threw her arms around his neck and hugged him. "I heard you were dead." Her voice was louder than he liked. He looked around, but no one appeared to be paying them any attention. "And I'd like to keep that rumor alive for a while. Can we go take a walk, off the boat for a few minutes?" She nodded. "Sure." She hooked her arm in his and headed out of the bar. At the gangplank, the two big men stepped in front of them. The one with the limp looked down. "Susie, do you know this man?" She laughed. "Of course! This is my cousin Harry." She patted Hugh's arm. "I bet you thought he was just some cowboy come to sample the whiskey. Harry, did you lie to these poor boys about why you were here? You really are the joker, aren't you?" Hugh shrugged. "You know me, cuz. Always trying to get one by on folks." "We're going to go take a little walk during the break." Susie slipped between them onto the gangplank, pulling Hugh along. "I'll be back in a few minutes. If Mr. Shank gets to looking for me, tell him where I went." Without waiting for a reply, she continued down the gangplank and onto the dock. Hugh waited until they were well out of earshot of the Belle before he said anything. "Thanks for the cover there." "No problem. What are friends for anyway?" She giggled slightly. "Besides, I like giving those two lunkheads a hard time." "So what do you know about what's happening on the Bayou Belle?" Hugh asked as they headed up one of the streets going away from the docks. "Like what? Shank keeps me fairly busy lately. I've heard a few ruckuses, like the night you disappeared, but I always seem to get there too late." "I've heard rumors he's treating the coloreds on board badly and know from experience he's dumping folks in the river. Apparently more than a few folks have gone missing of late." She nodded with a heavy sigh. "Yeah, I think you're right. There always seems to be new staff in the kitchen and even with some of the third-floor girls. It got worse after you disappeared. He wasn't happy losing that race with the newfangled boat." "Speaking of the boat, do you know if the Belle was docked the night the blacksmith shop burned down?" "That was a couple nights ago?" she asked thoughtfully. He nodded before she continued. "We were just leaving dock when the fire bells started ringing. Shank has started liking to travel the river at night. Says he knows where all the snags and sandbars are and the passengers like the cooler air for a majority of their trip. So I didn't think anything of it." Hugh frowned. "So he could've hired someone to burn the place down for him." She nodded. "I suppose." She stopped in the road, let go of his arm, turned and stared at him. "Hugh Lafoux, this almost sounds like you're thinking about doing something to Shank. Like you're giving up your gambling ways and becoming a lawman." A deep laugh escaped Hugh. "A lawman." The laughter felt good. "Sue, you know me better than that. Some friends of mine, one of whom saved my life and nursed me back to health after he pulled my battered body out of the river, asked me to look into stuff. They've had friends and family affected." For a second it felt odd calling Cotton and Miss Cassandra "friends." He'd never called colored folk friends before. But after his night with Cotton, he might want to call Cotton more than a friend. Grabbing his arm again, she resumed walking, leaving him half a step behind. "So you're coming around, Hugh. I like that. It shows you've actually got a bit more backbone than I would've expected." It was his turn to stop. "Wait a minute. What are you talking about? I've got backbone." She chuckled, then pulled him forward. "Yeah, right. Hugh, ever since I've known you, the main focus has been helping yourself, normally to the biggest poker game you could find, or the biggest cock. You're the embodiment of a Southern gambler. Now you sound like you've gotten a cause." "Maybe I just want a bit of revenge on Al Shank for tossing me in the river after his thugs beat me." "Nope." She shook her head. "This is more than that. You started out asking questions that had nothing to do with revenge on Shank. I know you don't like him. Revenge makes sense, but this is more. And since when do you have friends in Memphis who would be affected by Shank tossing a few colored folk into the river?" She paused. "Not that I approve of that kind of behavior." He patted her arm. "I know you don't. That's why I came to you. I know this gig on the Belle is just a job for you. You've got the talent. You can find a new job without any problem." "Yeah." A thoughtful line creased her forehead. "Wait a minute. Your new friends are colored folk, aren't they?" Hugh swallowed. "Yeah. But Sue, they helped me out big time. I would've died without them." "Good for you, Hugh." She smiled at him. "It's about time you started growing up and seeing the world more than you have in the past. There may be hope for you yet." He walked at her side, dumbfounded for a minute. "Wait, you don't care?" "Hugh, I've known you for how many years, since we met at my sister's cotillion back in New Orleans. We might not see each other as often as I'd like, but I know you well enough that as long as you're happy, I don't care." "Thanks." The church bell rang four, and they headed back toward the docks. "So Sue, can you just keep your eyes opened? Don't do anything to make Shank suspicious you're watching him. I don't know what we're going to be doing yet. It might turn into nothing. I'll check in with you once a week or so. Whenever you're docked, keep an eye out for me. Hopefully I can get past Limpy and Growly without too much trouble and see you." She nodded. "Of course. You be careful too. There's going to be some people who aren't going to like the idea of a white man helping colored folk. There could be trouble before you even move against Shank." "Yeah, luckily I'm staying out near the swamp right now. Folks will have to really look to find me, except when I come into town. But thanks for caring." She stopped just shy of the dock. "Of course I care." She patted his beard-covered check before kissing it. "And keep the beard. It looks good on you." She smiled, then in a swirl of multicolored skirts sashayed up the gangplank and disappeared. Hugh stood there at the edge of the docks for a moment and looked at the spot where Susie disappeared. If I were into women, she'd have been the one for me. A shotgun blast rang out in the distance. Hugh hurried toward the sound. For a moment he was terrified something might've happened to Cotton. # 12 SHOUTING IN the street below Timmy and Rubi's rooms drew Cotton's attention. It had been a great day, waking up with Hugh's arms around him, then a leisurely walk to town and a pleasant visit with Timmy and Rubi. She'd been happy to get the salted meat, and he'd immediately promised to bring her more as he got it. Then he and Timmy had sat around discussing Timmy and Shamus's plans to rebuild the blacksmith shop that was visible outside the nearby window. "Maybe we don't want you here!" a man shouted from the street. Cotton heard Shamus's voice but couldn't make out his response. Timmy looked nervous. "Rubi, stay away from the windows." She clutched his arm. "Timmy, don't go. Let Shamus deal with it." "No." Timmy shook his head. "He's my partner, and I'm going down there to stand at his side." "Irish, you and your Negro should just count yourselves lucky you made it out alive!" another voice shouted. "Go back to Ireland and leave the jobs to the Americans. We need them more than we need you." Cotton stood and followed Timmy. "I'll go with you. Maybe if there's more of us, they'll leave." Timmy shrugged. "You never know. We had some people harassing us before the fire, but it got worse yesterday. It's almost like Big Al's paying them ta make sure we leave." He hurried down the stairs to the alley that ran alongside the building. The church tower tolled four. In the street a dozen men had Shamus backed up to the burned front of the blacksmith shop. Shamus looked small and afraid. Cotton knew fear was what they wanted. Fear would only serve to drive them to greater harassment. Cotton squared his shoulders and followed Timmy. "Be careful," he whispered. "Go home, Irish. We don't want your kind here!" a man shouted. "Why don't you go home?" Timmy shouted as they drew even with the men. "We're here rightfully. We're freemen trying to run an honest business." "Yeah, all you colored folks is always going on about being free nowadays, ain't ya?" A big, swarthy man stepped to the front of the group. Cotton recognized his voice as the first shouter. "Well, I've always been a freeman, and I don't like you coming in here and forcing us to pay you for the work you've always done happily for room and board. It ain't right." "Maybe you should take your complaints about that to Washington," Timmy replied, stepping in front of Shamus. "They're in charge of things like that again. You don't like it, start there making changes." The swarthy man stood his ground. "We can't change anything there, but we can make sure you two don' git this here shop up and going again. We don't need your strange little boats coming outta Memphis. Go somewhere else. Maybe they'll like your freeman speech up in Chicago or someplace." A shotgun blast echoed down the road. Sherman Olsen stood in the street before the mercantile loading another round. "You men break this up!" he shouted. "We're a peaceful town here in Memphis. If you want to act like lawless hoodlums, then take yourselves west. Shamus and Timmy are good members of this city. Now break it up and leave them alone!" "Go back to your shop, Sherman!" one of the men in the back shouted. "We don't want no trouble with you." "Then stop harassing my friends!" He fired another blast in the air. Sherman's wife came out of the shop carrying something that looked like a cross between a rifle and a small cannon. It had a wooden stock with a huge gleaming barrel and a heavy scope on the top. "Is this what you wanted?" He turned and took it from her, handing her the shotgun. "That's it." Snapping it down, then up, he leveled the big contraption at the group of men. Tripod legs folded out from it as if to give it balance. "Now then. I suggest you disperse so I don't have to use this. It might not hit all of you, but I assure you, it will make an impact on those it does hit and it will hit more than one of you." The grim set of his face made Cotton shiver. He'd never seen the shopkeeper so angry. Several of the gathered men raised their hands in surrender and ran down the street. The swarthy man and three others looked from Sherman to Shamus and Timmy and back again. Seconds ticked by. The swarthy man snarled at Shamus and Timmy, "Fine. But this ain't done. You'd best leave town while you can. Mark my words, you'll live to regret it if you don't." He gestured to the men behind him and they walked off the street, disappearing into a nearby alley. For several minutes nobody moved. Sherman Olsen lowered the massive weapon and headed back toward his shop. "Sherman, thanks for the help!" Timmy called. "No problem." Sherman set down the contraption and waved. "I didn't see that lily-livered sheriff of ours or any of his deputies coming to help, so I figured I should lend a hand in keeping the peace." With the gun comfortably balanced against one of the roof support poles, Sherman started toward them. "I just wish this wasn't happening. We need inventive minds like yours, Shamus. I hope you don't leave 'cause of all this. I want to do what I can to help you guys rebuild." Shamus nodded, obviously still shaken from the encounter. "I know. There's jest so much a man can take afore he breaks." Timmy stood next to Shamus. "I'm here with you, Shamus. We ain't gonna let the town bullies railroad us outta here. We got the river here, and it's the perfect place to work. That an' we got friends like Sherman and Cotton here too." Cotton nodded. "That's right." He looked down the main street and spotted Hugh in his new cowboy hat hurrying toward them. His heart leapt at the sight. He'd never been so pleased to see another person before. It was a good feeling. "What's going on?" Hugh asked, slightly short of breath. "Jest some ruffians trying to push people around," Shamus said. "Nothing ta worry yerself about." Hugh nodded and looked at Cotton. "You okay?" "Yeah. It didn't come to blows. It might've if Mr. Sherman hadn't showed up with his shotgun." Just having Hugh there helped Cotton relax. Hugh glanced back, and his gaze passed over the large weapon on the boardwalk in front of the mercantile. "That's some shotgun." Sherman chuckled. "I call it a peacemaker. It'll either make peace or pieces. So far I've been lucky and haven't had to fire it at people. It's got a real kick to it, so the longer I can go without firing it, the better." "Custom job?" Hugh asked. "Yeah. Luckily I do a bit of inventing myself." Sherman looked proud as they all walked back toward the mercantile. "Even the rounds are homemade. I'd been meaning to get together with you, Shamus, to see about making a few more of these girls. I can think of some folks who might like to keep them on hand, just in case problems like this come up. They work a lot like a shotgun, but with a much larger spray area and a whole lot more force. It's a good name too. I hope nobody comes along and steals it from me." When they reached the boardwalk, Sherman picked up the peacemaker and hefted it to Hugh, who took it and nearly dropped it. "Wow, that thing weighs a bit more than I was expecting. If it's got a kick to it, I can see why you don't want to fire it on a regular basis, even with the pop-out tripod." He lifted the massive stock to his shoulder, and his head all but disappeared behind the side of the barrel. "Good idea, putting the mirrors in the scope like that. With the size of the barrel, it would be hard to aim." The roughness of it told Hugh it was completely homemade. It didn't have the smooth, polished lines of something that had been mass-produced like many of the guns Hugh had handled during the war. But it had a more advanced experimental feel, like Sherman was trying to employ both new cartridge technology with old tried and true shapes and forms in the barrel. Sherman chuckled. "Don't really need precision aiming with this beast. If you're in the general direction, you're going to hit something." Hugh lowered the thing and offered it to Shamus. "What do you think? Is this something you and Timmy could make?" Shamus took the gun with raised eyebrows. "We might be able ta, once the shop is rebuilt. Who ere ye anyway?" "Oh, I'm a friend of Cotton's." Hugh tipped his hat. "You can call me Harry." Cotton fought back the surprise on his face. Although he knew Hugh wanted Big Al to think he was still dead, he didn't understand why he was giving Shamus a fake name. Shamus seemed to relax. "A friend of Cotton's. Timmy's never mentioned ye, but then I jest met Cotton the other day." Sherman came to their rescue. "He was in the shop a while ago with Cotton." Several townsfolk emerged from nearby buildings and headed their way. Hugh glanced at Cotton, then nodded toward the south. Cotton nodded in agreement. He wanted to get back to the peace of the forest as soon as they could. "Timmy, I think I'm going to head home. Iffen ya need anything, ya know where to find me." "I guess I'll see ya in a few days when you got more meat for us." Timmy grinned at him. "Thanks for bringing that by. Rubi really appreciates it." "Just happy to help." Hugh was already heading across the street without saying good-byes to anyone. Cotton hurried after him just as a group of curious bystanders reached Timmy, Shamus, and Sherman. The questions started before he was out of earshot. He was happy to stroll at Hugh's side as they started down the road that would eventually lead to them the trail back to his cabin. The stress of the incident dropped away from him the farther they got from Memphis. "So why did you tell Shamus your name was Harry?" Cotton asked after they passed the last house close to the city proper. "Sue made it up for me earlier and I thought, just to stay safe, in case someone was listening nearby. Hugh isn't a real common name, but Harry is a bit more so. At least for a while, we'll use it, even with your friends. I just want us all to be as safe as we can while we get a plan worked out and give Shank what he deserves." "So ya found out some of the things ya were hoping to?" Cotton wanted to ask who Sue was, but figured if she was important, Hugh would let him know. Hugh nodded. "Yeah. Things are as bad as Miss Cassandra made them sound. Now we gotta figure out what we're going to do. If you like, we should go see her tomorrow and get started on this." "We could stop by on our way back to the cabin," Cotton offered. "She's not far off the path." "No." Hugh yawned. "It's been an exciting and busy day. Busiest I've had since my last encounter with Shank, and we both know how that one ended. I think I'd like to get back to the cabin, relax, and get my thoughts in order before we see her." "We ken do that." A comfortable silence fell over them as they walked along the path and the trees slowly worked their way closer and closer. As they closed in, Cotton felt even more relaxed, and Hugh being there with him just made everything better. # 13 HUGH SNUGGLED tight against the warmth of Cotton at his back. Even as the morning light came through the cracks in the cabin wall, he didn't want to get up. He wanted to stay in bed with Cotton. It had been a long time since he'd actually slept with anyone. Most of his dalliances were over quickly and his man of the night disappeared before the moon rose very high. Two nights of sex with Cotton had proved invigorating, and he was willing to claim his rapid improvement was due in part to the contented feelings that bloomed around him when he was in Cotton's company. He glanced at the muscular arm draped over his side. It was several shades darker than his skin, but it didn't matter. Cotton was waking up feelings in him he never thought he'd have for another human being. Each day he wanted to have Cotton around more and more. He'd never felt so right with anyone. They were from such different worlds but fit together so perfectly. Cotton stirred slightly. He ran his hand across Hugh's chest, leaving pleasant tingles in its wake. Hugh hugged Cotton's hand to him, pulling them tightly together. Trying not to break their embrace, Hugh rolled over so he could kiss Cotton's soft lips. The kisses still sent shivers through him. "You're already awake." Cotton grinned at him. "I was afraid to move. Afraid I'd wake you." "No." Hugh hugged him again and planted another warm kiss on his lips. "I was just lying here, enjoying the feel of you next to me." Cotton combed a gentle hand through Hugh's bed-tangled hair. "It is nice having ya right here. What cha wanna do today?" "I thought we were going to try to see Miss Cassandra and figure out what we're doing about Big Al." Hugh traced his fingers down Cotton's side. Cotton squirmed slightly when he reached a sensitive spot. "Yeah. We need to do that," Cotton agreed. "But it does feel nice just laying here with you." Hugh let out a happy, contented sigh after Cotton kissed him again. IT WASN'T the largest plantation house Hugh had ever seen. It was closer in size to some of the homes in the garden district of New Orleans than one of the large country homes, but the house Cotton led Hugh to was obviously the central house for a good-sized estate, at least before the war. The sprawling veranda was in good repair, much better than most of the larger places after the Yankees finished their march through the area. The grounds around the house were also well kept, a vision of Southern splendor. For a moment Hugh wished his family's holdings had looked as good after the Union boys had finished with them. The large colored man, who'd been with Miss Cassandra when she'd come out to Cotton's cabin a few days before, stood on the porch, a shotgun resting in the crook of his massive arms. "Cotton, Mr. Lafoux." He nodded at them as they walked up the wide white steps. "Ben." Cotton stopped at the edge of the porch. "We've come to talk with Miss Cassandra about Big Al." Ben nodded. "She said to expect you sometime today." He turned and walked to the door, opened it for them, and shouted. "Helen!" He didn't enter the house but gestured for them to walk in as a woman in blue gingham appeared. "Oh, Cotton Freeman and friend." She smiled at them. "Miss Cassandra said y'all'd be coming today. She's in the back parlor. It's cooler back there. If you'd come with me?" For a moment Hugh wanted to ask Cotton how Miss Cassandra knew they'd be coming when they hadn't told anyone and just made up their minds the previous evening, but he'd heard rumors all his life that some of the colored women knew things others found unsettling. Somehow, as he thought about it while following Helen through the house, it didn't surprise him any that the local curing woman might show some of those mysterious gifts. Overall, the house was in pristine shape. Here and there were little things like torn wallpaper that showed signs of wear and possibly of the war that had ravaged the area only a couple of years before. Helen paused at a pair of double doors and brushed her hands down the front of her dress before opening them. Hugh had seen slaves do similar things before entering rooms where the plantation owners and family might be, but everyone in this house was free, and the gesture seemed strange. Maybe it's just her habit. "Miss Cassandra," Helen said as she opened the doors. "Cotton Freeman and friend are here as ya said they'd be." "Thank you, Helen. Please let Ben know I'd appreciate his input on this situation. I'm sure the house will be safe enough while he's away from his post." Miss Cassandra sat in an old wooden rocking chair and looked out over the lush green lawn that sloped off toward a creek behind the house. Without a word, Helen turned and retreated, leaving the doors open to the hall. "Miss Cassandra." Cotton walked toward her. "Thank you for seeing us today." She shook her head. "No, Cotton, thank you and Hugh for coming so quickly. I presume Hugh has come to a decision about helping us with the problem of Al Shank." A narrow bench sat near the window, and they walked over to it and settled before Hugh said anything. "Yes. I did some checking yesterday, and it appears there's a good chance Shank had a hand in the burning of the blacksmith shop, and some of the disappearances aboard the Bayou Belle extend to the third-floor girls. But only the colored ones." Miss Cassandra pursed her lips. "That's worse than I heard, but I'm not surprised. It seems our women have always been easier to lose track of than our men, and that hasn't changed." Hugh nodded. "But we need to figure out what we're going to do. I've got a friend on the Bayou Belle who's going to keep an eye on things and let me know if there's anything going on or if there are weaknesses we can exploit." Ben came into the room. "Weaknesses are going to be needed. The more we can find, the better. But we have to do something that's going to tell the other riverboat men we ain't gonna put up with actions like Big Al's. Just 'cause we have a different skin color don't mean we be any different. That's what Lincoln said when he freed all us. It just looks like we gonna have to fight to get them rights." Hugh studied Ben. "Ben, you look like hired muscle, but you sound like a politician." "I'm sure there's more than a few white men out there would say I's a bit uppity, and I don't care." Squaring his shoulders, Ben looked even larger. "Miss Cassandra has shown us we're just as good as any white man. We can read, write, and think just as well as anyone else given half a chance. The problem is so many people don't want to give us the chance. If they wants to put us back in chains, they'll find a fair number of us are willing to fight back. People like Big Al need to be shown we ain't just throwaways anymore. Our lives mean something." Miss Cassandra held up her wrinkled hand for silence. "Very good, Ben. You have no idea how it warms my heart that I've managed to stir such passion in you and the others who stayed here with me. But now we need to plan." She rose from her chair. Hugh quickly rose to offer her a hand, but Cotton beat him to it. She smiled at them both as she tucked her arm into Cotton's. "Come this way. I believe we might want to make a few notes as we plan this out. Hugh, I think your hand may be clearer than some of the rest of us. Ben's is good, but when he gets excited, it's hard to make out." She led them to a small study with a grand rolltop desk. The desk was already open with a sheaf of paper lying there as if it were waiting for them. Next to the paper was an inkwell with a strange tube that looked like a pen lying next to it. Hugh sat at the desk; the wooden chair was so used, the seat was worn smooth, but the casters didn't squeak. Miss Cassandra and Cotton settled on the settee near the desk with Ben taking up an almost guard-like position behind them. "Now, Hugh, you said you have a contact on the Bayou Belle?" Miss Cassandra began. Hugh nodded. "Yes, ma'am." "That'll be useful. We'll have to see what information she can get for us." Before he picked up the strange pen, he stared at her. He hadn't said anything that hinted his contact was a woman. "But we'll need more than just that. When you say you're thinking of making this a message to the other riverboat men that they can't continue to abuse the colored folk, something tells me you're thinking of destroying the Bayou Belle." "That is true." Her voice grew soft, barely above a whisper. "The more extreme the destruction, the better people will take notice and remember. Big Al Shank will be judged harshly for what he's done, but we need to warn people not to follow in his footsteps." Hugh jotted down on the paper Destroy the Bayou Belle. "So how do you propose we destroy the Bayou Belle, particularly without hurting innocent people? There's a lot of people on and off that boat who don't know about Al's abuse of the coloreds. Some of them probably don't care." "That I'll leave in your hands. You're correct, we need to do what we can to limit the number killed, while making sure Big Al Shank goes down with his ship." She stopped for a moment and frowned. "That might be harder than it sounds, but I'm sure your gambler's nature can help find a way to make that happen. You're a very resourceful man, Hugh Lafoux." "Is there any way to discredit him before we sink him?" Cotton asked. "Maybe if people thought he was evil, they'd stop dealing with him. Other riverboat owners might take notice and make sure they don't do the same thing Big Al does." Hugh shook his head. "Discrediting Al will take longer. I'm not sure we want to take the time. Also the longer we take, the more likely it will be he'll realize I'm not dead. I wouldn't put it past him to come after me when that happens." Miss Cassandra patted Cotton's arm. "I must be spreading my political leanings out to the swamp too if you're thinking that way. But I agree with Hugh. We don't really have time to discredit Big Al. The longer this takes, the more lives will be lost. I want to see his blood disperse down the river, not have the river run red with the blood of our people. I hate the idea that some innocents may be lost." There was a sudden dark edge to her voice that somehow made it feel very personal. "But if the war has taught us anything, it's that not all the innocents can be saved. Sometimes examples must be made. I wish there was an easier way, but if he just disappears, it won't help protect more of us from others of his ilk. The Lord above may judge me by our actions, but I feel it is worth it, if we are to shape a better future." Who has she lost to Al? Hugh added quickly to his list on the paper. # 14 COTTON FOLLOWED Timmy down to the docks. Memphis was sleepy and mostly empty while in the distance the church bell rang nine. "It's a good thing I do most of my hunting by moonlight," Cotton whispered. "Yeah, you're having an easier time of it than I am," Timmy agreed. "Most honest folk is asleep. I used to think I was honest folk." "You are." Cotton paused when Timmy stopped ahead of him. He listened and couldn't hear anything. "What's wrong?" Timmy shook his head. "I thought I heard something. I guess I was wrong." He motioned for Cotton to follow him. They slipped down to the river's edge, below the dock. The shadows were deeper there. It didn't take them long to near the Bayou Belle. Timmy reached in his knapsack and pulled out a pair of strange goggles. He slipped them over his head and connected them to a small gaslight he held in his hand. Then he tossed a delicate bottle smaller than his fist at the riverboat. It hit the side of the hull, just above the waterline, with a soft shatter. After a couple of minutes, Timmy lit the light and moved his head like he was scanning the boat for something. "Anything?" Cotton asked. He wasn't sure how the whole thing worked, although Timmy and Shamus had said something about a gas in the vial that would flow into the weak spots of the boat's hull, and Timmy would be able to see them through the goggles. Timmy nodded. "Yeah. I'm amazed this boat manages to float up and down the river. Sinking her ain't gonna be no problem." He turned off the gaslight. After he had his gadgets packed away, he motioned for Cotton to follow him along the riverbank to a narrow ladder that led up to the northern dock. "The catch is going to be doing it in a spectacular way. I don't know what Miss Cassandra has planned, but after the blacksmith shop burned, Shamus and I have very limited resources." Cotton shrugged. The sound of footfalls on one of the docks caught his attention and he grabbed Timmy's arm, pulled him deeper into the shadows, and held a finger to his lips. Timmy nodded and they held still. For a second, Cotton reflected on how different it felt to touch Timmy than touching Hugh. Timmy didn't elicit the same waves of anticipation and pleasure Hugh did. "I told you I heard something," said a rough voice. "I'd swear it was a couple of colored folk talking." "There's no one out here," replied a smoother voice. "I guess you were hearing things. Let's get back and keep our watch on the gangplank. Shank won't like it if he comes out and we're not standing there making sure folks don't get past us without good reason." "Yeah. I must've been hearing the ghost of that guy we beat up last night on the way here. You know, beating up that gambler a while back was nice, but he shot me in the leg. These niggers are a lot easier to put down. More fun too." Cotton's breath caught as his blood chilled. These are the men who hurt Hugh. There are two of us, but Timmy's not much of a fighter. If I had my spear, it would help. The men walked away. Cotton waited until their footsteps faded in the distance before he gestured for Timmy to continue down the bank toward the ladder. Even though the men had moved away, Cotton still moved as silently as possible and kept his ears open for the slightest noise. Years of hunting gators in the swamp had attuned him to the least little sound. But he was surprised by Timmy's shout as they climbed the ladder. Right after his shout, Timmy's legs above Cotton disappeared as someone yanked him the rest of the way up to the dock. "Let go of me!" Timmy shouted. Cotton scrambled onto the dock, squaring his wide shoulders and trying to look as imposing and scary as he could. "Put him down!" Several deep laughs answered him. Five large white men stepped out of the shadows next to the two who held Timmy. Cotton knew the odds were against them. If I dive in the river, they won't be able to get me. But I don't want to leave Timmy behind. He's my best friend. "Will you look what we caught?" One of the men holding Timmy glared at Cotton. "It's the scrawny little nigger from the blacksmith shop and his half-blood friend, out for a walk under the docks at night. Boys, we might want to check and make sure they haven't sabotaged the docks. Can't think of any other reason a couple of niggers would be out after dark but to cause trouble. Maybe we need to show 'em what we do to troublemakers." "I said let him go!" Cotton charged the smaller of the two men holding Timmy. He caught the man around the waist and took him to the ground. "Get off me, nigger!" the man yelled and beat at Cotton. But Cotton was bigger than he was and easily kept him on the ground. He brought his knee up hard in the man's groin. The man yelped and folded up on himself. Cotton smashed his fist down on the side of the man's head for good measure. Someone shoved him to the side before he could get to his feet. He fell, and the hard boards of the dock scraped against his back. He crab-walked backward, trying to get enough distance from his attackers to regain his feet. "You're a feisty little nigger. It's amazing how fast you lot forgot your place in things around here," the gruff voice was saying. The sound of a fist hitting flesh rang out, followed by Timmy's cry of pain. Cotton surged to his feet, but someone grabbed his shoulders and shoved him roughly backward. He hit against a firm, fleshy obstacle. He shoved an elbow into the man's ribs and was rewarded with a satisfying huff of released air. Shoving forcefully to the side, he managed to throw the man off the dock and into the shallow river below. Before he had time to do anything else, two more had hold of him. He struggled but they were both as big as he was and nearly as strong. Without proper leverage he couldn't break free. A thick, heavy fist pounded into his stomach. Pain spread through him as more blows followed. He remembered how the bullies of his childhood loved it when he cried out in pain, so Cotton refused to utter a sound as the white men beat him. Nearby, the sounds of Timmy's sobs tore at him, but he couldn't defend himself, let alone his friend. "Hey, why ain't Zeb come back up the ladder yet?" The rough-voiced man asked. "Harley, stop beating on that nigger and go see if Zeb needs help." The roar of a bull gator came from below the dock. A man screamed. Water churned. The white men stopped their assault and stood still as their friend died. Through his throbbing, pain-filled head, Cotton recognized the sound of more gators showing up to join the first one in the bloody feast. Soon their grunts and roars filled the night. "You killed Zeb!" Rough Voice yelled at Cotton. "It's still a crime for colored folk to kill white men! We all saw you do it. Boys, get a rope. These niggers ain't going see sunrise." Cotton struggled against his captors, but they lifted him off the ground, and he couldn't get a blow worth anything in on them. "You can't—" One of them punched him in the throat, cutting off his words as he gasped for breath. "Yes, I think we can." The one who punched him laughed. "It's been a couple years since we had a good ol' fashion lynching. The last time I saw one, it was a Yankee who'd just raped a proper Southern lady. He twitched real nicely as he dangled from the magnolia tree." "Clem, go get a couple of ropes!" Rough Voice ordered. "Meet up north o' town. You know that clearing with the big tree? Yeah, that same one the Yank danced from. It's still strong enough for these two." The man Cotton had laid out struggled to his feet and hurried off, moving in obvious pain. I can't believe this is happening. Despair washed over Cotton as they carried him and Timmy away from the docks. Timmy wasn't moving or moaning anymore. There's nobody who'll save us. It'll just be my word against theirs as to what happened to Zeb. Hugh's at Miss Cassandra's. He won't know what's happening until it's too late. At the thought of Hugh, his despair grew. I'll never be able to find out if what I'm feeling for Hugh is love or not, or find out if he loves me too. This isn't fair. "Hey, this one's heavy. We need a breather." His captors set Cotton down. His legs didn't want to hold him up at first. He took a couple of deep breaths and willed himself to stand. "We can't take too long," Rough Voice admonished. "If the sheriff catches us, these two might have to stand trial or something. If we can hang 'em before he finds out, we can get away with it and they'll be dead. Two less uppity niggers we'll have to deal with in Memphis." Cotton's ribs hurt from the beating, but he pushed the pain back. I have to get free. The river wouldn't have given Hugh to me just to have me die now. Bracing his feet, he yanked his arms away from the men holding him. The men staggered forward. Cotton swung as hard as he could at the one on the right. His fist hurt from the impact with the man's jaw, but the man's head jerked back and he fell to the dirt. Cotton tried to shout for help, but his abused throat refused to make much more than a whisper. He turned toward the other man, but before he could swing, someone tackled him from behind. His legs fell out from under him, and he crashed to the ground. Dirt filled his mouth right before someone hit him hard in the side of the head and everything went black. "CAN'T YOU stand 'em up any better than that?" Rough Voice's words and harsh hands on his shoulders brought Cotton awake. His hands were loosely bound at his back, but there was already a noose around his neck, and it felt like they were trying to stand him on a tree stump or log. "Why are you worried about that? All we have to do is let 'em go and the rope will finish them off." It sounded like one of the men who'd dragged Cotton from the docks, but his head was pounding so hard, he couldn't be sure. "Shut up!" Rough Voice shouted. "Is that horses?" They all got quiet. "Shit! I think you're right. We need to get out of here," said a man off to the left. "Don't worry how they're standing," Deep Voice replied. "Just knock the logs out from their feet and disappear. I wanted to watch 'em dance but don't want to have to explain what's happening. Big Al won't like us having to explain ourselves to nobody." Cotton shifted his hands as the grip holding him on the log let go and the wood rolled away. The rope jerked tight around his neck. His breath caught, but his neck didn't snap. Frantically gasping for breath as the men ran off into the forest, he wiggled his hands and wrenched them free. He reached above his head and got hold of the rope. Pulling as hard as he could, he managed to relieve some of the pressure on his neck. Weak from the beating, Cotton couldn't pull himself up high enough to slip free from the noose. As he hung there, clinging to the rope with all his might, he tried to think of some way out of the fix. Beside him, Timmy's jerking slowed. Tears flowed down Cotton's checks. I'm sorry I couldn't save you, Timmy. There were just too many of them. If I can't find it in me to climb the rope, I may end up hangin' here with you. The sharp report of a gun being fired shook the forest. Cotton braced himself for the bullet. He'd failed Timmy and was more than willing to follow his friend into the afterlife. # 15 "I WISH I could've gone with them." Hugh paced Miss Cassandra's parlor. It had been a couple of hours since Cotton had left to meet Timmy so they could use some contraption Shamus invented that would show them flaws in metal and wood. He'd hated staying behind, but Miss Cassandra had been very insistent. She felt it was too dangerous for Hugh to spend much time down around the docks. Even with his new cowboy hat and beard, she couldn't shake the feeling Big Al Shank might somehow recognize him. The bloodred sunset blazed on the western horizon. The sight gave Hugh shivers. Miss Cassandra, who appeared to be sleeping in one of the many wooden rocking chairs around the house's ground floor, suddenly sat up, her eyes unfocused. "Good Lawd! We've got to get to Memphis." "Miss Cassandra, did you see something?" Helen hurried to her side. "We must hurry." The old woman took a couple of unstable steps toward the door. "Helen, go tell Ben to saddle the horses." A strange feeling of dread settled over Hugh. He didn't know where he was going or he would've run for the stable and helped saddle the horses. Miss Cassandra grabbed his arm. "Hugh, lend me a hand. It's been a long day, and I think it's going to be a longer night." "Do you know what happened?" She shook her head. "I never know exactly what or when things are gonna happen, just they gonna happen. I got no control over the visions that take me. All I know is, if we don't hurry, Timmy and Cotton are going to swing from the ends of ropes tonight. There is a tree, north of town, near the river, where they hung a Yankee soldier. We have to get there." Hugh swallowed hard and resisted the urge to pick the old woman up and carry her out to the horses. I can't lose Cotton. We haven't known each other that long, but I don't want to go on without him. He's like no man I've ever known. By the time they reached the veranda, Ben was there with three saddled horses. Hugh didn't wait for Miss Cassandra to mount; he picked her up as if she weighed no more than a pillow from her parlor and placed her on the saddle of the horse she'd ridden to Cotton's cabin, days before. Then he vaulted into the saddle of a larger horse. He wanted to kick the horse into a hard gallop, but didn't exactly know where he was going, so he let Miss Cassandra set the pace. AS THEY reached the first houses of Memphis and the church bell tolled ten, something in the slow, deep tones made Hugh shiver even in the still-warm summer night. "Ben." Miss Cassandra broke the silence they'd been riding through. "Go find the sheriff. Get him out to the tree. Hugh and I will ride on." "Hugh, you might want this." Ben tossed his rifle to Hugh and followed it with a small leather pouch of bullets. "I'm trusting you to guard her, with your life if needed." "Go on, Ben. My life isn't at stake tonight." She turned her horse toward the docks. Hugh raised the rifle in salute to Ben and spurred his horse after hers. Around them the town of Memphis slept, as most towns did once the sun went down. In the brightness from a gaslight, Hugh caught Miss Cassandra shaking her head as she rode. "What's wrong?" A heavy sigh escaped her. "I feel the river has tasted more blood this night. I don't believe we are too late, but we must hurry." She spurred her horse to a faster gait. Breaking into a gallop in the dark, even on the well-traveled main streets of Memphis, worried Hugh. He'd hate to have the horse stumble and fall, delaying his reaching Cotton in time. His heart raced as a sweat of fear coated his back and hands. The path grew rougher as they sped out of Memphis. When the trail narrowed again, Miss Cassandra slowed their gallop to a trot. Over the pounding of hooves, Hugh thought he heard voices. The moon shone brightly in the clearing they entered. A large magnolia tree dominated the far side of the clearing. From a branch on the left side of the tree, two figures hung. One was still and limp. The other had its hands above the noose and appeared to be trying to pull free of the rope. The moonlight sparkled off light hair. Hugh pulled the horse to a rougher stop than he would normally do. He brought Ben's rifle to his shoulder and targeted the rope just below the branch where the man struggled. He fired. As his heart pounded, he fired a second time. When the second bullet cut the rope, the man fell to the ground. The other rope took two shots as well. By then, Miss Cassandra was across the clearing and dismounting. Hugh kicked his horse hard to clear the distance quickly. He threw himself off the horse and stumbled as his metal leg sank into the soft ground. Miss Cassandra knelt at the side of the man who'd been struggling. "He's alive." "Cotton." Hugh dropped beside him. "Cotton, talk to me." He caressed Cotton's cheek, and laid Cotton's head in his lap; then Cotton's eyes opened slowly. "Hugh." His voice was a harsh whisper. "You found me." A grim smile spread across Hugh's face. "Of course I found you. You found me, now I found you. I'll take care of you this time." Beside them, Miss Cassandra released a heavy sigh. Hugh turned toward where she knelt at Timmy's side. For a moment, the old woman seemed to fold in on herself. "We were too late for Timmy." Hugh swallowed. Glancing down, he watched as silent tears flowed from Cotton. At least we saved Cotton. I don't have to lose him. The sound of more horses running toward them brought his attention to the clearing's south side. Hugh reached for the rifle, secure that its enhanced chamber still had enough bullets for a few more shots, before he recognized the large man on the leading horse as Ben. Two other men followed him. "What's going on here?" the man who dismounted next to Ben demanded. Miss Cassandra appeared to have recovered. She stood, straightened, and stomped toward the sheriff. "What has happened here, Sheriff Buchannan, is two men were hanged tonight. Luckily we arrived in time to save one of them. These were good, upstanding men of this community. Unfortunately we don't know who did this." "Miss Cassandra." There was an element of surprise in the sheriff's tone, although Hugh figured Ben would've told him she was involved. "How did you know this was happening?" "How did I know your wife was having a child and would've died if I hadn't gotten to your house in time? The spirit moved me. Unfortunately, it didn't move me in time to save both these fine men. We need to take Timmy Birmingham to the undertaker. I'll see to his arrangements once I've made sure Cotton Freeman is going to be all right. Once he can speak again, I suppose he might be able to give you some information on the men who assaulted them tonight." "He can't speak?" For a second, Hugh thought there was a bit of hope in the sheriff's voice, replacing the surprise from earlier. Miss Cassandra put her hands on her hips. "Of course he can't speak at the moment. Not five minutes ago he was dangling from this rope." She picked up the hangman's noose she'd pulled off Cotton as Hugh had been riding across the clearing. She thrust the rope at the sheriff. "If the knot had been tied correctly, the odds are Cotton would be dead now. Thankfully the men who tried this ain't the smartest folk Memphis has to offer." The sheriff looked at the rope. "Yeah, not enough loops in this to be effective. But it would've been a painfully slow death if you folks hadn't come by when you did." Over by Timmy, the other man shone a bull's-eye lantern on the still form. "Sheriff, they worked this one over pretty good. He might've been dead before they hung him." "We'll look him over better at the undertaker's. Maybe Charlie will have some ideas on that. Go fetch a wagon and we'll take him back to town." The sheriff waved the man off. "Tonight, sir? Wouldn't it be easier if we wait and do that tomorrow?" A heavy sigh escaped the sheriff. "Are you going to stand watch over the body and make sure none of the local wildlife carry it off? Go get a wagon. If you want, go ahead and wake up Charlie, and he can come get it. He'll need to get it settled in his place anyway." The man nodded. "Yes, sir." He mounted his horse and hurried out of the clearing. During the exchange, Hugh stayed quiet and kept a hand on Cotton's shoulder. He wanted to pick him up and carry him away before things got any worse. The sheriff turned from Timmy and finally saw Hugh. "And who are you?" "Sheriff Buchannan." Miss Cassandra stepped between them. "This is Harry Goodman. He's a good friend of Cotton's. He was with me this evening when the urge to come here hit." Frowning, the sheriff looked Hugh over in the moonlight. "So I suppose you weren't involved in tonight's incident, Mr. Goodman?" Hugh nodded. He gently helped Cotton to sit. "That's right, sheriff. Cotton had some things he wanted to bring to Timmy's family tonight, but needed to get some things to Miss Cassandra as well. I offered to take the gator meat to her while he came into town." Turning his gaze from Hugh to Cotton, the sheriff rubbed his chin. "That's who you are. Cotton Freeman, the gator hunter who lives in that little cabin near the swamp. Any chance you know the men who did this to you?" Cotton coughed, then gagged slightly before raising his hands in a sign of confusion. Shaking his head, Sheriff Buchannan looked at Miss Cassandra. "Cassandra, like most of the community, I respect you. Do me a favor. Keep an eye on Cotton until he's well enough to talk to me. It doesn't look like his throat is so damaged he'll never speak again." He paused and turned back to Cotton. "Boy, I don't suppose you can read and write?" Frowning, Cotton shook his head. "That would've made things at least a little easier." The sheriff looked at Ben. "Any chance you can stay here with me and help me with Birmingham's body? I'm sure Miss Cassandra will want to make sure one of your people is here so everything's done on the up-and-up." "I can stay," Ben replied. He fixed his eyes on Hugh. "Make sure you continue to guard her." "We'll be going back to the house, Ben." Miss Cassandra patted his arm. "I'll be fine. Once you've seen to getting Timmy settled, please go and give the bad news to Rubi. Tell her I'll be by tomorrow to see that he's laid to rest properly." A long breath escaped her. "I know the white preacher won't want to do it for him." "I'll do that." Ben looked at Cotton. "Do you think you can ride my horse?" Cotton shook his head again. Hugh tried to remember if Cotton had mentioned ever being on a horse before. "I can carry him in front of me. We'll have to go slow." "I'm not up for another gallop through town, Mr. Goodman," Miss Cassandra said as she walked over to her horse. "Ben, if you'd be a dear and help me up, we'll get started back to the house. Sheriff, if you need Cotton before he makes it into your office, he'll be staying at my place until he's well." Hugh helped Cotton stand. Then, like Cotton had done for him just days before, he helped Cotton walk to the horse. He mounted first; then Ben helped Cotton up in front of him. A wave of relief spread through Hugh as he wrapped his arms around Cotton to take the reins. He's alive. Hurt, but alive. We're heading back to Miss Cassandra's, and we'll get him well again. # 16 COTTON CUDDLED closer to the warmth at his back. He didn't need to roll over to know Hugh was in bed with him. The bed itself was odd to him. It didn't have the threadbare blanket and too-flat pillows. The sheets were thick and the pillows fluffy. A light breeze came from the slow-moving fan above the bed. He blinked a couple of times before he realized he must be in Miss Cassandra's house. At least here we're safe. Folks won't worry that Hugh's white. And they already know that we're more than just friends. Before the war, I coulda been hung for being with a white man, unless it was my master. He didn't move his head much, but it still throbbed, and his throat was still painfully sore. A heavy, pulsating ache came from his battered hands. I just hope those men feel as bad as I do this morning. With a groan and a movement of sheets, Hugh rolled over, his arm wrapped around Cotton. For a second a sharp pain raced through Cotton's chest at the contact. It was all he could do to not cry out, but he didn't want to wake Hugh. Having never had another person share his bed, he found Hugh's presence there more comforting than he would've expected a few days earlier. The main door to the room slowly opened. Cotton turned his head toward the sound, and it pounded more. Helen walked slowly to the bed. "Miss Cassandra was wondering if you'd woken up yet," she whispered. "I'll inform her you have but Mr. Lafoux hasn't. I'll check back shortly. She wants to visit with ya once you're awake." Cotton started to tell her he could come and leave Hugh asleep, but his dry throat tightened and hurt so much he couldn't get the words out. Without saying anything else, Helen turned and left the room as quietly as she'd entered. There was no reaction on her face. Cotton knew attitudes were changing. But it made him feel good to be reminded of it. Sighing in frustration, Cotton eased deeper into Hugh's embrace. Hugh feels so good, and he came to rescue me. I heard 'em say something about Miss Cassandra had a feeling I needed help. A darkness flowed over Cotton. But they were too late to save Timmy. I don't know what we're going to be able to do for Rubi. I need to go see her. It was Big Al's men who killed Timmy. She needs to know that. The sheriff needs to know that. He remembered crying himself to sleep in Hugh's strong arms. Cotton was a little surprised the tears hadn't returned when he woke. Hugh shifted slightly and tightened his arm around Cotton. Cotton flinched. "Not so tight," he managed in a hoarse whisper. Kissing the back of Cotton's neck, Hugh answered, "Sorry about that." The kiss sent shivers of pleasure through Cotton. It felt good every time Hugh kissed him. "So how are you feeling?" Hugh sat up on an elbow and looked at Cotton. Cotton shrugged, trying to ignore the discomfort the movement caused. "Hurt," he managed to get out. After a careful kiss on Cotton's cheek, Hugh straightened. "Why don't I go get you some water? Wetting your whistle might make it easier to talk." "'Kay." Cotton settled back on the pillow. Hugh swung out of bed. He still had his pants on but had put his shirt across the chair near the bed. Cotton watched as Hugh pulled on his clothes. There was a slight disappointment at the disappearance of Hugh's muscular physique under the fabric. Then Hugh smiled at him. The smile warmed Cotton in a way he never thought a smile could. "I'll be right back." As the door closed behind Hugh, Cotton stared up at the fan turning slowly above him. For a few minutes, he lost himself in its movement. His gaze tracked the leaflike blades as they spun around. There was also a thick cloth band that ran from the gleaming central motor of the fan over to a coppery steam pipe near the wall. The fan, cloth, and pipe all looked fairly new, like they'd been added since the war, part of the many enhancements that were sweeping the country. "Here you go." Hugh hurried back into the room with a carafe of water and two glasses. "Miss Cassandra is right behind me. She wants to talk to you." "And Helen will be in shortly with some breakfast." Miss Cassandra appeared in the doorway. "I didn't figure you were up for anything heavy. I know I wasn't after our long night." The water was cool and refreshing going down Cotton's abused throat. After the first swallow, he shifted to sit up, and Hugh helped him get the pillows behind his back. Miss Cassandra waved her hand at him. "There's no need to sit up. Just be comfortable. Can you talk?" "I can try," Cotton managed to get out. The water had helped his dry throat, but it was still sore from the beating and hanging. "Don't press it too much." Hugh settled on the bed next to him. "Definitely, don't press it." Miss Cassandra frowned. "We don't need everything today. Although the sooner we know what happened, the better. Do you know who attacked you and poor Timmy?" Cotton shook his head. "They mentioned Big Al, but I didn't recognize'em." Miss Cassandra nodded thoughtfully. "I'm not surprised they mentioned Big Al. This started at the docks, I presume?" "Yeah." Cotton nodded. "Grabbed Timmy on the ladder." Helen walked through the door with a small plate of cut fruit. "Here ya go, Cotton. This should be easy on yer throat, lessen you'd prefer some broth or somethin'." He shook his head. "This's fine." "I'll be back with some tea shortly and some biscuits for Mr. Lafoux." She turned and left the room. Silence descended for several minutes while Cotton ate some melon and peach slices. At first the food hurt going down, but he managed to get enough to help him feel stronger by the time he was done. "You know Sheriff Buchannan is wanting to talk to you," Miss Cassandra continued when Cotton finished. "If you're not up to it today, we can probably delay him until tomorrow. Since Timmy was colored, he's not overly worried about finding the folks who did this. If you'd both been white, he'd most likely already have them behind bars and be talking to the judge. Even with the information that they mentioned Big Al, he's not going to move quickly. If anything, he'll move a little slower. But he shouldn't be a problem with our plans either." Cotton frowned. "We have to stop Big Al and his men." Miss Cassandra nodded. "I agree. And I think we've got more allies in this than we probably realize. Unfortunately your injuries might slow us down a bit." "No." Cotton shook his head. It pounded hard for a minute, and he had to wait to continue. "I'll be fine in a couple of days." He touched Hugh's hand. "I'll have Hugh with me. That'll help." "Okay." She didn't look happy. If anything, her wrinkled face looked tired. "We still have to get through today. Timmy's funeral is this afternoon. Do you think you can make it?" "Yes." Cotton looked at Hugh. "Especially if Hugh can help me." "I'll be there." Hugh patted his hand. "I'll get Ben to get the buggy ready." Miss Cassandra rose. "I don't think you should try and sit a horse or walk right now. For the moment you rest, and we'll talk more later." Hugh started to rise, but she waved him down. He smiled as he settled back at Cotton's side. "If you need me to do anything, let me know." Miss Cassandra shook her head. "Right now I think we've got everything under control. The Bayou Belle left the docks last night heading toward Saint Louis. I'd like you to try and speak to your contact there when she returns." "Of course." Hugh nodded. Running a hand down the front of her dress to settle it, Miss Cassandra turned and walked out of the room. "Do you need anything right now?" Hugh asked, smiling at Cotton. "No, just want to lay here a little while longer." Cotton made to remove one of the pillows from behind him so he could stretch out on the bed. Hugh leaned forward and snagged it for him. They were close enough for Hugh's musky scent to fill Cotton. Hugh gently kissed him. It was a short kiss, but it helped relax Cotton. "I'm glad I didn't lose you last night," Hugh murmured. "Me too." Cotton smiled. It was the first motion he'd made that hadn't hurt. "Just found ya." "Yeah. I want to keep you around." Hugh eased a finger across Cotton's brow. "I'd hate to lose you." Cotton didn't know what to say. He squeezed Hugh's leg. "The river likes me. I'll be hard to get rid of." Hugh nodded, then kissed him again. "Last night, on the way home, Miss Cassandra called you the river's wild child. I think she may be right." "I like the sound of that." Cotton relaxed even further. The bed's soft embrace, and knowing Hugh would be there watching over him, made it easy for him to drop back into a deep sleep. # 17 HUGH STOOD quietly at Cotton's side while Miss Cassandra performed the last of Timmy's funeral. He felt awkward; there were only two other white men there. The rest of the fifty people were all colored. Being in the minority was a new situation for him. Instead of focusing on being uncomfortable, he paid attention to Cotton. Timmy's death was hitting Cotton hard. Through most of the service, Cotton had cried softly, not that his abused throat would allow much more. Cotton's big shoulders drooped, and Hugh wanted to put an arm around him to show some support and comfort, but this wasn't the time or place. Even with him sharing their grief for the loss of a member of their community, it would be difficult for Cotton and him to show any sign of affection, even though Cotton appeared closer to white than colored and Hugh was as pale-skinned as they came. Several times during the service, Cotton had grabbed his hand for a minute or so, and Hugh couldn't bring himself to do anything more than squeeze Cotton back, hoping the gesture was enough to express his support and caring. Timmy's wife stood at the edge of the grave as several men lowered the coffin into the ground. Her sobs were just short of screams as the simple wooden box disappeared into the silent earth. Cotton started toward her, but Shamus Culpepper beat him there. The artificer put an arm around her shoulder in a more familiar way than Hugh would've expected the wife and a business partner should have. Rubi's so upset, I doubt anyone is really noticing. She doesn't need any kind of scandal to add stress to the day. Cotton, two steps ahead of Hugh, put a hand on Rubi's arm. "Rubi, if I can do anything, please let me know." She looked up, her tear-streaked face showing more pain than a human face should. "Find those monsters." She grabbed hold of Cotton's hand like a woman clinging to a tree limb before the river washed her away. "You were always the stronger one, Cotton. Honor my Timmy's memory and make 'em pay for what they did to him. He was your friend as well as my husband." Cotton swallowed and nodded. If he said anything to her, it was too soft for Hugh to hear. She stepped out of Shamus's arm and hugged Cotton tightly. For a moment they were able to publicly share their grief in a way Cotton and Hugh were denied. Hugh forced back the jealousy that swelled up in him. Then Miss Cassandra joined them. She made her final condolences before sweeping Hugh and Cotton off to her open-air buggy where Ben stood waiting for them. Already there were people on the short walk back to Memphis. It was a stark reminder to Hugh how much further the colored folk had to go before they'd be equal. Miss Cassandra was the only one with either horses or a buggy at the service. Ben carefully kept their speed slow enough for folks to get out of the way before they passed. Most people waved to Miss Cassandra. Some called out words of encouragement and thanks. Once they were free of the stream of mourners, Ben flicked the reins and the horses bounded forward. "That's one of the things I dislike having to do for the community." Miss Cassandra folded a white lace handkerchief in her lap. It was a sharp contrast to the black dress she wore. "Unfortunately, until we can convince the white preachers to accept our folk into their congregations or we can get some of our folk trained in the way so we blend in better, it'll continue to be my duty." Her tired gaze fell on Cotton. "You do me a favor, Cotton—stay alive. I don't want to have to do this for you anytime soon." Cotton nodded. "I'll try." His voice was weaker than it had been. Since they were away from the crowds in the swiftly moving buggy, Hugh took Cotton's hand in his. "And I'll do what I can to keep him alive. You have my word." "Good. Now, Cotton, are you up for talking with the sheriff? We can go by his office if you are." Cotton sighed. "Maybe. My throat still hurts." "I'll try and make sure it stays a short visit." Miss Cassandra turned and tapped Ben on the shoulder. "Stop by the sheriff's office, please." He nodded. "Yes, ma'am." SHERIFF BUCHANNAN didn't look overly happy to see the three of them walk into his office. He didn't even bother getting out of his chair or taking his boots off his desk. "So, Cotton Freeman, feel like telling me what happened last night?" Cotton sat down in one of the chairs on the opposite side of the desk. Miss Cassandra settled in the other one while Hugh stood between the two of them. Standing over them made him feel like he was protecting them, especially amongst the variety of weapons the sheriff had on display. The wall behind him was covered in firearms of all sorts; simple, nearly rusty flintlocks and black-powder rifles hung amidst shiny pistols and what could've been an early prototype of Sherman Olsen's peacemaker. There were no prisoner cells evident, but there was a huge door that looked more like a piece of clockwork art than a jail door. Hugh didn't doubt it could easily prevent anyone getting past, from either side. "I suppose." Cotton's voice was soft. With a bang, the sheriff's boots hit the floor and he leaned across the desk. "Boy, you're going to need to speak up more if you expect me to be able to hear you." "Sheriff." Miss Cassandra put a hand on the desk and stared at the sheriff. "Cotton is still recovering from his assault. His voice is weak. Not to mention we buried Timmy Birmingham a few minutes ago." Glaring, the sheriff settled back in his chair. "Yeah, according to Charlie Goldthwaite, Timmy was most likely dead before they tried to hang him." Cotton nodded. "They beat him really bad." "Do you know who beat you?" asked the sheriff. "No." Cotton shook his head. "It was dark." "Then why are you here, boy?" Miss Cassandra glared back to him. "To give you what information we have." "But if he didn't know who they were, what good is it?" "Maybe you can put it together with some of the other information you might or might not have." The steely look the old woman focused on him wasn't one Hugh wanted to ever turn his way. It gave him shivers. "If you don't want the little information he has, then maybe we should just leave." Sheriff Buchannan sighed. "No, if he ain't got much, this won't take long. Come on, Cotton, boy, what do you have?" "Big Al Shank's men. They mentioned Big Al." Cotton's tone shifted from tired to angry. "Not enough. A lot of people around here talk about Shank. They always have. It ain't nothing new." "They said he wouldn't want questions coming up," Cotton added. "Everyone knows Shank don't like people poking their noses in his business." The sheriff straightened in his chair. "Is that what you two colored boys were doing? Sticking your noses in Shank's stuff, and he sicced these boys on ya?" Cotton shook his head. The sad look made Hugh want to reach out and put a supportive hand on his shoulder, but he couldn't. They'd already decided it wasn't a good idea to let the sheriff know they were investigating the Bayou Belle for flaws. "I was showing Timmy how to hunt gators. There's been a few around the docks lately." He paused. "Like someone's feedin''em." The sheriff huffed. "Like who would feed the gators near the docks? That would take a whole lot o' stupid." "No one ever said any of the people around the docks are the smartest bunch in Memphis. But it might explain some of the missing people of late." Miss Cassandra rose from her chair. "That's the information we've got for you. I doubt you're going to do anything with it. We all know Timmy was just another colored man who managed to git hisself hung. Ain't that what yer thinking?" Sheriff Buchannan cocked an eyebrow as if trying to figure out if he'd heard her right but didn't reply. He did have the decency to look a bit nervous. Hugh knew it wasn't her normal diction, but hadn't expected Miss Cassandra to use such a simple thing to try and make the sheriff uneasy. Miss Cassandra gestured to Cotton and Hugh to follow her out of the office. No one said a word until they were back in the buggy and Ben had it turned around, heading back toward the house. "Wow," Hugh muttered. "I never realized how hard it is for...." He scrambled for words. "Colored folk? Ex-slaves? Our people?" Miss Cassandra finished for him. "Don't be shy around us, Hugh. You're part of us now, and don't think the sheriff won't paint you with the same tarred brush he used for us. He'd be happy if we'd just go away. In his mind Timmy doesn't matter. One less colored man, particularly one who was brave enough to be a business partner to an Irishman, is a good thing. Timmy's one less potential problem he has to deal with, or in the case of Buchannan, one he'll have to look the other way with while others deal with him. Even after my help birthing his last child, he still holds tightly to the old ways that permeate this part of the country." Hugh nodded. He'd been part of the problem not long ago. "But why don't you move to the North?" "This is our home. Even if we spent years in chains and working the fields for others, this is our home. We ain't leaving it." There was a fierce determination in Miss Cassandra's words. "Would you leave what you've known all yer life just to make life a little easier for yerself?" Swallowing, Hugh nodded again. "When I lost my leg, I left and never looked back." The fact that there wasn't anything to go back to made it easier. She huffed. "Then it's a good thing you emerged from the river different than when you went in. We don't need no stuffed-shirt fool right now. We need the man you're becoming. I'm not sure I would've liked you before the river had her way with ya." Her words stung Hugh. He shifted in his seat next to Cotton. Did the river really change me? Or was it Cotton? The Mississippi River is just a body of water flowing north to south, cutting its way between the east and the west. It didn't do anything to me. It was all Cotton. If some white man had pulled me out, I'd be the same man I was when I went in. Wouldn't I? The silence that settled over them lasted until they pulled up to Miss Cassandra's house and they all got out of the buggy. # 18 COTTON STOOD and stretched. After three days, his body still hurt, but it wasn't as bad as it had been, and he was growing tired of spending most of his time either sitting or lying. At least we finally left Miss Cassandra's last night. He looked around his small rustic cabin. It might not be as fancy as the plantation house, but it's mine. I built it with my own two hands. I don't need much more. Hugh walked in and smiled. Sweat gleamed on his broad chest. "I figured I'd let you sleep again. How are you feeling this morning?" At the sight of Hugh, Cotton's heart pounded and an unbidden smile spread across his face. Maybe I have found something I need more than this little cabin. "Better. Still hurting a bit." "Well, don't push it. Miss Cassandra wants us to lie low for a few days while Shamus works up a couple of things he thinks might help us." Hugh shook his head. "I hate waiting." Cotton walked out to the table, pausing to kiss Hugh on his way past. "I do too. But at least it looks like things are quiet right now. I think tonight I'll head out and do a bit o' gator huntin'." Hugh frowned at him. "Are you up for that?" "Don't really have much of a choice." Cotton seated himself on the bench nearest the fire. "We gonna need some more food soon, especially with what I give away recently. Iffen I don't go hunting, I'll have to use some of my credit at Olsen's Mercantile, and I'd rather hold on to that for things we... I can't get on my own." He was getting used to having Hugh around; it wasn't the first time he'd caught himself using we when talking about things in their lives. "Do you have to go as far as the river?" Hugh sat on the bench at the table next to Cotton. "I could've sworn I heard gators closer than that." Cotton nodded. "There are, sometimes. But to get the larger ones, I need to be out in the river. The ones closer in are fairly small. I don't get as much for their hides." Hugh touched Cotton's arm. "Can I go with you, at least? That way if you get too tired, I can pole the raft home." The concern in Hugh's voice touched Cotton more deeply than his hand on his arm. I've never had anyone care if I could get home or not. Dear River, thank you for this gift you have given me. "Yes, you can go with me. Just try and stay on the raft. I don't want to be pulling you out of the river again. She might decide to keep you the next time." THE MOON was nearing dark, and the inverted crescent hovered just above the tree line on the west bank of the Mississippi River as Cotton poled his raft from the swamp into the river proper. In the distance, a coyote howled. To the north, a gator roared, and another answered. Not wanting to end up near the Memphis docks, he turned the raft toward the south. "Is the hunting better this way?" Hugh asked. He sat in the center of the raft, holding Cotton's mechanical spear and an older one that didn't have the fancy springs in it. Two lanterns also sat next to him. Cotton shrugged. "Lately there're too many hunters. The gators are getting harder to catch. That's why I hunt at night. It's a little riskier, but there's more critters out. I'm glad we came out tonight. With the dark moon coming on, it'll be harder to find things. If we're lucky, we'll catch a couple and have enough meat for a few days." "That would be good. Do you ever get tired of eating gator?" "Sometimes, but then I'll go catch a rabbit or possum. Brought down a big buck last year. That was some good eatin'." The sound of something swimming near them silenced Cotton. He listened hard, but the sound vanished as quickly as it had come. "Sometimes I think I should get me a rifle. That might make it easier for things like deer." "You brought down a deer with a spear?" Amazement clouded Hugh's voice. Smiling, Cotton nodded. "It's what I had. You ambush them right, it's not as hard as it sounds. I just had to make sure the blow was true to the heart so it didn't suffer. I don't like critters to suffer. It spoils the taste of the meat." He hoped Hugh wouldn't think him stupid for such a comment. Many people didn't care if their meal suffered, but he always thought he could tell if something died clean or not, just by the taste of the meat. "One of my old nannies used to say things like that," Hugh replied with a thoughtful tone in his voice. "I can't say as I've ever noticed a difference one way or the other." Nearby, something splashed from the shore into the river. The loudness was right for a large gator. Cotton listened for the sound of the critter swimming along. There it was, the faint swish of the tail through the water. For a moment everything in and on the river seemed to fall silent as Cotton focused on the movements. A slight ripple moved in the faded moonlight. Since they were going south, the current carried them along without too much help from the pole, but Cotton pushed off the bottom hard to gain a bit of speed, then laid the pole on the raft and reached for his spear. Hugh handed him the spear and picked up one of the lanterns. "Tell me when," he whispered. Cotton pushed everything out of his mind except the gator swimming in front of the raft. Experience told him where it was as the tip of its tail came into view. He took a slow, centering breath and flung the spear. A good solid thunk rewarded him. Water splashed and the gator roared in pain. "Now." Hugh lit the lantern and turned in the direction Cotton had thrown the spear. The gator spun in the water, trying to dislodge the weapon. The blow hadn't been clean. Snatching his other weapon from Hugh, Cotton threw it, trying to finish what the first had started. The second spear struck the alligator in the stomach. Even though his body was already complaining about his exertions, Cotton leapt into the water. In seconds he had his hands on the first spear. The spikes were extended, and he couldn't pull it out. He grabbed the second spear and ripped it free of the gator's belly. The gator's tail caught him in the legs. The blow knocked him under water. Cotton couldn't catch a good breath before going under and came up sputtering. His head pounded. "Cotton!" Hugh shouted from the raft. With the older spear in hand, Cotton thrust it hard at the gator's head. The thing's thrashing yanked the spear away from him. More blood filled the river. With a tremendous roar, the gator lunged at Cotton. Then something hit it and it dropped below the water's surface. Splashing through the water, Hugh caught Cotton in his arms. "Are you okay?" Cotton nodded. "I think so." He realized that Hugh had hit the gator and stopped it from injuring him. He'd never had anyone try and save him before. His heart swelled. Hugh kissed him. "I thought that thing was going to take you down before you had it under control." "It was a bit harder than normal." Cotton pushed away from Hugh. "That shoulda done it in. Help me git it on the raft before more show up. There's always more gators waiting to eat the wounded and dead." The warm water closed over Cotton's head as he dove down into the murky depths. Thankful they were still in the shallows and not in the central channel, he found the new spear first, then the lifeless body of the gator. Cotton grabbed the spear and used it to pull the gator back to the surface. Hugh was there, holding onto the raft while treading water. Cotton felt weak as it took both of them to haul the gator onto the raft. When he managed to climb back on and take a good look at the critter, his breath caught. It was the biggest gator he'd ever caught, easily ten feet long. The tip of its tail hung over the raft's edge. He scrambled to catch the lanterns as they rolled toward the water due to the gator's rough landing. Once both he and Hugh were back onboard, Hugh caught Cotton up in a big hug. "I almost lost you again." Hugh kissed him with so much vigor Cotton's breath caught. "Cotton, I don't want to lose you. I just found you." Hugh swallowed. "I love you." Cotton caressed Hugh's wet body. The words he'd been trying to find ever since that night he'd fought to stay alive in the noose came to him. "I love you too." He kissed Hugh back. "Thanks for saving me." Nearby, another gator roared. "I think we need to get moving." Cotton reluctantly stepped out of Hugh's embrace. "Iffen we don't, we might end up fighting off a few of these big boys who want this guy fer their own." After another quick kiss, Hugh nodded. "Yeah. Makes sense. There's a lot of meat on this big fella." Cotton started to pole them back up the river when his arm spasmed and he nearly dropped the pole. He paused and rubbed his sore bicep. "Here." Hugh lifted the pole out of his hands. "This is one of the reasons you let me come along. That big bruiser was more than you planned on bringing in tonight. I can get us back to the cabin." "Thanks." Cotton smiled at Hugh, then sank down to sit in front of him, beside the gator. It felt good having confessed to Hugh the feelings that were building up in him, even if it did feel strange to have someone else poling the raft home with a huge gator on it. # 19 HUGH WATCHED as Cotton finished cutting the gator meat into chunks and putting them into salt barrels to dry for a few days; then they would take some to Miss Cassandra and Rubi. Blood coated both of them. The process of skinning and butchering the gator had left them both smelly and covered in slime. But it didn't matter. They'd admitted their feelings for each other. I never thought I'd tell a colored man I loved him. But I do. When I thought that alligator was going to kill him, I almost died. It was almost as terrifying as seeing Cotton swinging from that tree. I don't want to be without him. Cotton closed the door to the drying shed. "Come on." "Where?" Hugh stared for a moment. Covered in blood and gore, Cotton looked like something out of a preacher's tale of hell. "There's a spring nearby. The water's clean enough there so we can get this blood off us." He grabbed Hugh's hand. For a moment a wave of revulsion washed over him; then he remembered his own hands were in a similar shape. The path to the spring was narrow, but Cotton must've known it well. He led Hugh easily and neither of them stumbled in the darkness. The spring produced enough water that a creek flowed away from it. The water was warm and inviting. There was a pool near the source. Cotton stopped just downstream of the pool and dropped his pants. "Get clean here—that way we don't have to wait for the dirty water to move downstream before being able to relax in the spring." He sat down in the waist-deep water and spent several minutes rubbing himself. It took Hugh a minute longer to follow Cotton; he had to pull off his boots. Hugh wasn't used to warm water anywhere except in a house where the servants brought the heated water, or occasionally in better saloons and inns. As the blood came off, he began to feel cleaner than he had in some time. By the time he was content he had most of the grime off, he looked up to find Cotton grinning at him. For a second Hugh stared at Cotton. "What?" Cotton's grin faded. "I just like watchin' ya. If it makes ya nervous, I'll stop." Hugh shook his head. "No, don't stop. I just didn't know what was making you grin. Most of the guys who've grinned at me like that were drunk. I like watching you too." "Come on." Cotton grabbed Hugh's hand as he rose. The moon had long since set, but the stars were bright enough it was easy enough to see all the details of Cotton's incredible physique. Even though they had been sleeping together for over a week, he still wasn't used to the sight, and seeing it wet with clean water stirred Hugh. The water in the pool was nearly neck deep and slightly warmer than the water just outside it had been. Cotton turned and hugged Hugh tight. Hugh returned the embrace, enjoying the sensations of Cotton pressed up against him. Their kiss lingered. Cotton combed his hand through Hugh's damp hair. "Did you mean it?" For a second confusion ran through Hugh's mind before he realized what Cotton was asking. He nodded. "Yes, I love you. You've done more for me than anybody ever has. You're not like anyone I've ever met. You're so real and honest. That's hard to find. The idea of losing you scares me to death. I've almost lost you twice now. I want to just take you away somewhere and protect you, keep you safe from all the hateful people out there and the gators too." A deep, pleasant laugh escaped Cotton. "You can't protect me from everything, ya know. But it's nice ya want to. I still can't believe the river gave you to me. Sometimes I wake up in the morning and just look at you and wonder why a white man would care about me. But my heart, my heart tells me it's true." He kissed Hugh again. "I think I realized it when I thought I was going to die. I wasn't sure of the right words, if two men could even use the words and have them mean anything. I love you, Hugh. I never want to be without you ever again. My life out here, it might be away from people, and I like that, but it do get lonely sometimes." Hugh nodded and hugged Cotton tighter. Between them, their cocks hardened and the touch of Cotton's dick quickened his pulse. "Gambling can be lonely in a more superficial sorta way. I don't know what I want to do, but when this is over, I'd like to take you away somewhere." "As long as we're together, that's what I want." Cotton ran a strong hand down Hugh's back. "Take me with you and always love me. That'll make me happy." "That'll make me happy too." They stood there in the warm water, wrapped in each other's arms for several minutes. Hugh reveled in the warm, moist feeling of Cotton's lips on his, but the excitement of killing the alligator and their statements of love stirred the need for more in him. He was hot from more than just the water, and he could tell Cotton was too. "Cotton, I want you inside me," he whispered with his lips less than an inch from Cotton's ear. Confusion reigned on Cotton's face. "What do you mean?" Hugh reached between them and squeezed Cotton's cock. "I want you to bury this inside my ass." "But won't that hurt you?" The confused look deepened. "I know when the boys on the plantation would do it to me, it hurt bad." "No." Hugh shook his head. "If you don't want it, it can hurt. But I want this. It's been a while since I wanted a man the way I do you. I know you'll be gentle." Cotton nodded, but his face didn't relax much. "If it's what you want." For a second his lower lip quivered and his chin wrinkled. "Oh yes, it's what I want." Hugh kissed Cotton to still his fears. "Right here in the water." Hugh wrapped his legs around Cotton's narrow waist, lifting himself up slightly on Cotton's broad shoulders. "You'll need to guide it in." "How do I do that?" Cotton's voice quavered. "They always took me from behind." "See, this is going to be different. This isn't from behind." Hugh kissed Cotton. "Find my hole with your finger, then guide your cock up there. When I feel you entering me, I'll lower myself down farther." Clumsily, Cotton found Hugh's hole. Hugh was already so relaxed, the finger barely registered. Then Cotton's cockhead found him. Knowing Cotton would react badly if he showed any signs of pain, Hugh kept his face neutral as fire seared him. Using his hands on Cotton's shoulders for leverage, he lowered himself down on Cotton's dick until it was all the way in. Hugh let out a soft moan and willed his body to relax further. "Let's let it set there for a minute." He kissed Cotton. Cotton ran his hands up Hugh's back. "Are you sure I'm not hurting you? It feels really good to me." His voice was more relaxed than it had been seconds earlier. A wide grin spread across Hugh's face. "It feels good to me too. You've really never been on the giving end of this, have you? And never out of love." "No." Cotton shook his head. "But if you like this, I want to do it more." "Oh yes, we'll definitely be doing this some more." Hugh locked his lips on Cotton's and rose up to the point where Cotton's cock almost popped out of his ass; then he lowered down on it again. A heady moan escaped Cotton. "I don't know how long I can do this until I cum." Hugh pulled up again. "I'm with you. You feel amazing." For a moment he wished they weren't standing there in the pool of water and were in the bed where Cotton could use a little more force on him. After several more movements, Cotton straightened in Hugh's embrace. "Oh man!" In the tight passage of Hugh's ass, Cotton's cock thickened and pulsed. Hugh slammed his ass down as hard as he could. "Cotton, grab my cock, yank on it, make me cum." He leaned back slightly with his legs still wrapped around Cotton's waist and his hands on Cotton's shoulders, trying to give Cotton access to his cock, which was screaming for attention. Cotton's hand closed around him. There was something about having the warm water surrounding them that made the touch that much more energizing. It didn't take long, with Cotton's still-hard cock in his ass, for his balls to tingle. His ass tightened like a vise around Cotton's dick as his balls emptied their load into the warm pool. "Holy shit!" Hugh leaned his head back and shouted as his body shook long and hard. When it was over, he laid his forehead against Cotton's. Sweat ran between them as he kissed Cotton. "That was incredible." "Yeah." Cotton nodded. "When you were coming, I thought your hole was going to cut off my dick. Does it always get tight like that?" Hugh chuckled. "When there's a cock like yours in it, it does." He lifted himself up so Cotton's cock popped out; then he unwrapped his legs and stood against Cotton. "That was the best fuck I've ever had. I love you, Cotton." Cotton kissed him hard and passionately. "I love you too, Hugh. I'm so happy I pulled you out of the river and Big Al didn't kill you." "I am too." Hugh gave a long contented sigh. "I am too." He kissed Cotton again, then laid his head on Cotton's broad shoulder. "If life could stay like this, everything would be fine." "Yes, it would." Cotton ran his hands through Hugh's hair. "I wish things didn't ever have to change from this." But they will. They always change. We still have to deal with Big Al Shank. I wish I could just take Cotton and disappear, but that wouldn't be fair to the people who are counting on us. Hugh kissed Cotton again. He really has changed me, or maybe it was the river. But other people are now more important than my own needs and wants. # 20 COTTON HANDED Shamus the tool he'd asked for and carefully avoided the puddle of sludge that now stained Miss Cassandra's barn floor. They'd been working for two days on improvements to Shamus's boiler boat. If their plan went badly, Shamus was supposed to get in and help rescue people. The new gaslights were installed, and Shamus was working on some adjustments to the motor. With Timmy gone, it fell to Cotton and Ben to help out while Hugh met with his contact on the Bayou Belle in hopes of gaining new information. "We're going ta need ta get her inta some water soon, so I can test the adjustments." Shamus wiped a skinny hand across his sweaty forehead. "We won't know it's ready until then." "So if you aren't racing the Belle, how can we tell if it's actually fast enough?" Cotton asked. Shamus leaned against the narrow bow. "We ken time it. I've got a pocket watch." He chuckled. "I'd have beat Shank by several hours as opposed ta just a few minutes on the last run if he hadn't left Saint Louis half a day before he was supposed ta. I was giving him a two-hour head start, but he left before sunrise. I didn't notice him gone until I'd gotten up for breakfast. I still waited until the time I had scheduled to leave." A frown darkened his brow. "I guess I was trying to play fair. Shank isn't. That's part of the problem, isn't it?" Cotton nodded as he wiped his greasy hands on a red handkerchief he pulled from his pocket. "Folks like Shank don't like to play fair. A lot of'em don't even think rules apply to them. That's why we're taking him down, to show the others even if the authorities won't do anything, the people will." "Yeah." Shamus nodded weakly. "I jest hope we all get out of this with our skins intact. It's not gonna be easy, even with the gizmos I've rigged up into the boat. There's a lot of variables we can't take inta consideration." For a second he stared at Cotton, then at Ben. "That's the point where Timmy would normally explain ta me how everything would work out just fine." He swallowed. "I miss him." "I miss him too." Cotton touched Shamus's shoulder. "He was my best friend." "Mine too. He gave me the encouragement ta git out there and make this boat happen. Did ya know we'd gotten three orders for boats since we won the race?" He paused, and a frown creased his freckled brow. "At least before the shop burned down. Timmy was sure we'd get things rebuilt and then git caught up on the boats. Now I don't know if I'll be able to get them out at all." "I'm sure something or someone will come along and help you find a way. Timmy really wanted this to be big for the two of you. I've never seen him so excited, not even when Rubi married him." "I'd begun to think the boats and business meant more to him than I did." Rubi stood in the doorway to the barn. After Timmy's funeral, Miss Cassandra had offered to take her in for a while to give her time to figure out what she wanted to do. Shamus shook his head and walked toward her. "Rubi, ye know Timmy loved ye. Yeah, he got obsessed with the boats, but ye were his true love. I've ne'er seen a man so in love as he was with ye." "Yes, I know." Her voice cracked. "I was happy about how excited the boats made him. You gave him as much hope as being freed at the end of the war had. If nothing else, he died while he was happy. There ain't a lot of folks that can say that." "Exactly." Shamus wrapped his arms around her and gave her a big hug. Cotton turned away from them. They'd been hugging a lot over the past few days. He didn't know what, if anything, it meant, but he wasn't sure it was the right way to honor Timmy's memory. "So are you all done for a little while?" Rubi sounded closer to Cotton than she had been. "I think so." Cotton turned back to them. She was only a few feet from him. Her delicate face looked conflicted about something. "Then could I steal you away for a little while, Cotton? There's something I need to talk to you about." Shamus nodded when Cotton glanced at him. "I guess so." Rubi hooked her arm in his and steered him toward the barn door. "I'll try not to take too long." A nervous feeling ran through Cotton as they walked outside the barn door and Rubi headed them across the lush lawn. He'd not been alone with a young woman before. Having no idea what Rubi wanted, he felt uncomfortable even though he knew no one from outside Miss Cassandra's trusted few would see them. "How you holding up, Rubi?" Cotton started, hoping if he could get her talking, they could get their discussion wrapped up quicker. She shrugged. "Not sure how I'm supposed to be holding up. I miss Timmy something awful. He was always so good to me." She sniffled. "I loved him. He was my life." "He loved you too." Cotton patted her hand on his arm. "I know." She sighed. "Having Shamus around is helping. I think he cared more for Timmy than he realized. I hope we're not starting too much gossip, being around each other so much, but right now I need someone. Almost everyone I knew growing up, except Timmy and you, died in the war. And now Timmy." She pulled a small piece of cloth from the front pocket of her blue dress and dabbed her eyes. After a short pause, she blew her nose. "So Cotton, I think it's nice that you and Hugh are getting along. I always knew you were a little different from normal folks." Her words puzzled Cotton. "Different?" "Not that there's a real problem with it. I mean, the good book talks about Sodom and Gomorrah and the sins committed there, but since you're not exactly white and not colored neither, I don't know if the good book applies to you. Especially since slavery, which the book says is acceptable, is now illegal here in the South, I wonder what that means to any of us right now. I looks about an' see everything turning upside down. But it feels good. Don't you think? Did Timmy tell you he saw two mens holding hands a couple of weeks ago? They'd gotten off that new steam-powered stage that runs from Nashville to Memphis. That thing make such an awful racket, I jest don' see how folks can ride in it." Cotton stopped and stared at her for a moment. "Rubi, what are you going on about? Are folks talking about me and Hugh?" She shook her head. "No—well, not amongst the colored folk. I don't talk with no white folk but Shamus, so I don't know if they be talking about ya or not. I reckon it ain't nobody's business but y'all's." Patting her hand, he angled her toward one of the benches that signified the boundary between the yard and what had once been the ladies' garden, now mostly overgrown as the forest began reclaiming the land. "Rubi, you're babbling more than just a little bit. Is there something on your mind?" As she sat on the wooden bench, she sighed. "A couple things. If you and Hugh are happy with each other, I wanted to let you know I'm happy for you. I know Timmy would've been too. He was always worried you might be lonely out there in your cabin all by yourself." Cotton smiled at her. "Yes, Hugh and I are happy with each other. I didn't realize I was lonely out there in the cabin until he came along." She returned his smile. "I'm glad. Cotton, you're a good man and you deserve to be happy, like Timmy and I were." Then her face fell. "Cotton, this is harder, much harder than I thought it would be. It's probably why I'm babbling more then I usually do." She shook her head. "So out with it." Cotton squeezed her hand. "You haven't babbled like this since the funeral." Rubi swallowed hard. "I know. I'm sorry for the babbling. I wanted you to know before I told Shamus. I'm hoping the two of you can help me figure out what I should be doing about this." "About what?" At his question, a silence fell over them. In the distance a hawk screamed. "Cotton, I was a married woman, so you can't judge me none." She swallowed again. "I'm pregnant." At her words, his eyes grew wide. "It's Timmy's." She glared up into his eyes. "Of course it's Timmy's. I ain't no whore!" He patted her hand again. "I ain't saying you a whore, Rubi. You're Timmy's love. I knew it was his baby. What do you want to do?" "What do you mean?" "I've heard talk about things women ken do to lose babies." She stood and jerked her hand out of his. "Cotton Freeman! How dare you think I might want to get rid of this baby? It's Timmy's. It's the last part of him I'll ever have, and I'm keeping it." He reached out for her, then drew her back down next to him when she accepted his hands. "I wasn't sure. Life ain't easy for a woman with no man around, or is that what you wanted to talk to me about?" Nodding, she dabbed at her eyes again. "Yes. I want our baby to have a family. It's a hard world for a baby that ain't got both a mam and a father. You should know something about that, with your daddy unknown'n' all. Yeah, all the house slaves doted on you something fierce, but that ain't the same as having a daddy, particularly when the boys started picking on you for being half-blood." "But this baby ain't half-blood. You and Timmy are both full colored and that's what this baby will be." "Yeah, but I want to make sure you'll help look out for us. Timmy ain't here no more, and we're going to need someone. I don't know if Shamus will help out or not. He's talking about heading up to Chicago or maybe Ohio when we're all done here. I don't know if we'll be welcome along or not. It ain't all that strange nowadays to see whites and blacks together. It's one of them thangs that changed with the war. So many changes." Cotton put his arm across his shoulder. "Rubi, if you don' go with Shamus, you can go with Hugh and me, or maybe stay here with Miss Cassandra." Rubi shook her head. "Now don' go getting me all wrong here. Miss Cassandra is good to all us colored folk around Memphis parts, but I'd rather not have my baby brought up around some of the strange mumbo jumbo stuff she do. It's spooky. The way she knows stuff. How did she know you two was being hanged?" "I don't know. Some folks say the river itself speaks to her." "Exactly. Ain't nothing for a baby to be brought up around. I'd rather be out in the swamp with you." "But I think you'd rather be a going with Shamus. He's your first choice?" "Lord's own truth, Cotton, you're my first choice, but if Shamus would take me in and make me happy, that would be better fer me, even if he is white. Folks is more accepting, now that we free. From what I hear, they even more accepting up North. You'd only be a friend. That's all you could ever be, particularly with Hugh around." The meaning of her words struck him. Then he thought back to before she'd married Timmy and how she'd acted interested in him, but he hadn't been interested back. I never made a choice to be with Hugh. It's just right. Like breathing. I don't know if I could be with Rubi or not, but Hugh makes me happy. I ain't never looked at a woman the way I do Hugh, and that's the truth. Cotton patted her hand again. "Rubi, the important things right now is for you to be happy and yer and Timmy's child to be safe and loved. I couldn't make you completely happy, but I do know I could love Timmy's child liken it was my own. I can't speak for Hugh, but as far as I'm concerned, if you want to go with us when this is over, you're welcome to." She threw her arms around him as a fresh round of tears flowed out. "Thank you, Cotton. You're the best friend anyone could ask for." She sobbed into his shoulder. He held her there on the bench while she cried. It wasn't hard to tell her tears were for Timmy more than anything else. Cotton had never thought of himself as a strong person, but he knew he would have to be strong for Rubi and maybe for her baby. Luckily he had Hugh who could be strong for him. Together, they could all survive the coming fight with Big Al and make the river safe for everyone. # 21 HUGH KEPT his head down as he walked up the gangplank. It was his third visit, so Shank's guards were getting used to his cowboy cousin disguise, but he was still nervous when he went past the men. He had no idea what might clue them off to his true identity. But they didn't do more than give him a cursory look as he strolled past them. He was running late, so by the time he reached the bar, the steam calliope was already playing and Susie was leaning against the bar chatting with the bartender. Hugh walked up alongside her. "Hey, cuz. Sorry I'm running late. Just got into town." She flashed him a bright smile. "No problem. You can walk me down to the mercantile. I need a couple things from there and also wanted to stop in at that new dress shop that just opened up. Going with you will be faster than going with one of the girls." "Sounds like a couple hours out of here." He offered her his arm. With a parting smile at the bartender, she accepted his arm. "If you've got time for dinner tonight, I've got the night off." Hugh cocked an eyebrow as they walked through the door and out onto the main deck. "Really?" Susie nodded. "Yup." She slowed as they approached the top of the gangplank and Al's men. "Boys, don't worry if I'm not back before dark. Since we're docked all night, Harry's going to take me for some different grub." The one that had been limping straightened slightly. "Sure thing, Susie. If Al gets to looking for you, I'll let him know you're with your cousin again." She smiled at them but didn't bother with a reply as she resumed her walk down the gangplank. "Beautiful weather we're having right now. I hear they're having one of those big storms come through New Orleans. It's downright frightful, if my sources are correct." "I thought the river was running a bit high for late summer." Hugh kept his surprise to himself. She didn't usually bother with things like the weather. For a moment he wondered if it was a cover for the men on the gangplank. Then Al Shank stepped out of a carriage at the end of the dock. It took all Hugh's confidence in his changed appearance to keep walking toward the man who'd ordered his death. Al had never seen him as anything other than a Southern gentleman, cleanly shaven with a bare head, or on rare occasions in a top hat. His scruffy appearance should be enough to hide him. "Ah, Susie, off to enjoy your evening?" Shank strolled toward them, looking larger than the gator Hugh and Cotton had hauled out of the river several nights earlier. He leaned heavily on his cane, and sweat dripped down his jowls. "Yes, Al." Susie smiled at him. "My cousin Harry is taking me into Memphis. I wanted to stop in at that new dress shop and figured we could get something to eat while we were in town." He grinned at her like a man watching his prize mare walk past. "If you need more money than you have, don't worry about telling the dress shop to send me the bill. We'll work it out." The look he gave her made Hugh want to punch the smugness off his flabby face. Susie's smile never faltered. "Thanks for the offer, but I think I have enough for what I'm looking for. I'll be back later." Shank nodded. "All right. Have a good evening. I think we all need a rest. Come to think of it, I might even come into town tonight for dinner. It's been a while since I ate anywhere but on the Belle." "We'll keep an eye out for you." She patted Hugh's arm. "Come along, Harry. Let's get on to the dress shop." Although they hadn't been introduced, Hugh touched the brim of his cowboy hat and inclined his head. "Pleasure to meet ya, Mr. Shank, sir." Shank nodded slightly and resumed his walk up the gangplank without the slightest hint of recognition. Two blocks away from the docks, Hugh finally let out a pent-up sigh of relief. "I could've done without running into Shank on the dock." "I guess we're just lucky you haven't run into him the last two times you've stopped by." Susie steered him along the main street. "I think the storm surge is supposed to hit tonight. That's why he wants to stay docked, or at least close to Memphis. That way, just in case something happens, he can get to safety." Hugh nodded. "Sounds like Shank. It still amazes me how they can figure out when the storms are going to strike." "I had someone try and explain it all to me a while back. It was after one of my sets and I don't know if he was overly drunk, or if it was just beyond me. Stuff about air pressure and winds." Susie shook her head. "I don't get it." "But with everything changing so much, I'm sure we'll all understand more and more over time. So anything else interesting going on?" "If you ask me, there's less colored folks riding the Belle the last few trips back and forth. You wouldn't know anything about that, would you?" Hugh shrugged. "Not directly. Although I have heard there are rumors going around that colored folks aren't safe on the Belle and if they can take another boat to Saint Louis, then they should. There might even be folks on the north end spreading the same tale. There are enough boats making the run right now, it isn't too inconvenient." Susie chuckled. "Yeah, sounds about right. Al's a little put out right now 'cause since the rumors about you have circulated, instead of driving off the cheats, it's driving off all the gamblers. He hasn't had a good game in nearly a month." "Has it been that long?" Hugh held the door to the dress shop open for her. It didn't feel like a month, but then he'd been down for over a week, or so Cotton said. They'd had just over a week before Cotton was attacked and Timmy was killed, and that was just shy of a week ago. Three weeks is nearly a month. Susie nodded as the heavily perfumed air of the shop wafted out around them. "Yes, it has." "Oh my dear!" An elderly shopkeeper in a bright blue satin dress hurried toward them. "You're that singer from the riverboat. Come in, come in." The shopkeeper's attention ended their conversation until Susie had picked out a couple of dresses and petticoats. She promised to wear the dresses in Saint Louis and make sure others knew where she'd gotten them. The ordeal left Hugh standing around, occasionally offering his opinion on a dress's color or style. But it did give him time to think about Cotton. Every day seemed to bring them closer together. He'd never spent time thinking about another man the way he did Cotton. Ever since the war, his thoughts had mostly revolved around spotting a handsome man and contemplating how to get him into bed for a few hours, or barring that, at least bent over a hay bale in a deserted barn. Cotton was different. He could really find himself settling down somewhere with Cotton, or at the very least traveling with him. He could teach Cotton to play poker, and the two could work some good scams on folks. Even as he thought about Cotton helping in some of his card shark schemes, the idea felt wrong. Cotton was too innocent and honest to be part of something like that. Cotton would do almost anything he asked of him. He knew that from the talks they had as they were falling asleep each night wrapped in each other's arms. But he didn't want to betray that trust by asking. The plot to destroy Al Shank was pushing things where Cotton's honesty was concerned, but Timmy's death had given Cotton a greater need to free the river from Shank and men like him. "Come on, Harry." Susie patted his arm. "You look like you were daydreaming." He shook his head, slightly startled from her approach. "Sorry. Yes. A bit. What, no packages?" She giggled. "You really don't have a clue how women work, do you? Mrs. Bolívar will have her seamstress deliver my purchases to the Belle shortly. They'll be waiting for me in my cabin when I return." Her brown curls bounced as she shook her head. "Men. Now, come along. We need to stop in at the mercantile for a few more things, and then you'll have to take me to that quaint restaurant that opened up a few months ago. I was just informed they have the most divine Cajun cuisine. Most of the recipes come straight from their family who live in the French Quarter. You know how much I miss the garden district." He held the door for her as they sauntered from the perfumed closeness of the small shop out into the humid openness of Memphis, with its aroma of fresh horse manure and dumped chamber pots. "I didn't realize you missed the garden district that much." The door closed. "I really don't, but I do miss the food. Mrs. Bolívar has a cousin there, and we were chatting about it. It makes her happy to think other people miss it as much as she does." She sighed. "Honestly, for a gambler, you really don't understand working people, do you?" "I've never really had the urge to work women like that. What did she give you, a better discount?" A wide grin graced Susie's face. "But of course. Now then, how are your plans to sink Al coming along? I take it you want to do more than just ruin his business." Hugh nodded. "We do. Particularly after some of his guys killed Timmy and almost killed Cotton. We don't have a firm schedule yet. When we do, I'll try and let you know so you can be off the Belle when she goes down." Susie frowned as Hugh opened the door to Olsen's Mercantile for her. "You realize if I'm not there one night, particularly a night when she's sailing, that might upset Al and blow your plans." Before Hugh could reply, Sherman Olsen walked up to them. "Harry, Miss Susie, what a pleasant surprise. I didn't know the two of you knew each other." Susie's frown deepened for a second. "We're old friends. Sherman, there's a few things I need to pick up." She pulled a small piece of paper from her beaded handbag and passed it to him. He glanced over the list. "Yes, I think I have everything. Give me a couple of minutes, and I'll gather them up for you. Please look around while I take care of this." He turned and hurried off with the paper. "You didn't warn me that Sherman knows you." Susie dropped her voice and hissed at him. Hugh shrugged. "Cotton sells skins here. I've come in with him a few times." He touched the cowboy hat. "This is where I got the hat." She shook her head with an exasperated look. "You've got to be careful. Sherman is one of the people who ships a lot of things with Al. I don't know if he'd warn Al about your plans, if he knows of them, but he might." For a moment Hugh watched Sherman moving about gathering the things on Susie's list. "He helped fend off some guys who were threatening Timmy and Shamus a week or so ago. He doesn't seem to trust Shank any more than the rest of us do." "Just because he doesn't trust Shank doesn't mean he won't rat you out if he thinks there's money in it for him." She gave him a completely exasperated look. "You need to be careful who you trust in this. There's a lot of things that could go wrong. Loose lips can sink ships, or in your case, not sink ships." Hugh grinned at her. "You know, you should put that in one of your songs some time. Maybe if you write a ballad of our adventure." She glared at him. Sherman waved at them from the counter. The storekeeper's easy demeanor made it hard for Hugh to think of him as the type of man who could cause problems for their endeavor. He honestly seemed to deplore the plight of the colored folks in Memphis and appeared to want Shamus to rebuild the blacksmith shop for more than greed. The couple of times he'd been with Cotton, he'd even seemed pleasant when a lot of the folks around town, white and colored, were less than tolerant of him. As Sherman went over the list with Susie, his wife appeared from the back of the shop. She hurried over to Hugh, grabbed his arm, and pulled him back among the shelves, out of easy earshot of the counter. "Harry, you do know who she works for, don't you?" Hugh nodded. "Yes. Susie and I are old friends. I know she works on the Belle, singing." "Just be careful. She might spill the beans if you tell her too much. Word from the docks is she's Big Al's girl all the way." "I don't think so. I trust her. She's giving me information on Al and what he's been up to." As he spoke he realized Susie hadn't given him a whole lot of information, but he doubted she was holding out on him. She was just a singer on the boat. There was a limited amount of stuff she'd be able to get out of Al, unless she was sleeping with him. Hugh shivered. He hoped Susie wasn't desperate enough to sleep with Al. Mrs. Sherman patted Hugh's arm. "Okay. Just be careful who you trust. We all want this to work with as few problems as possible." She turned and hurried back behind the burlap curtain. Hugh strolled back toward the counter, where Susie stood with a medium-sized bag clutched in her hand. She smiled at Hugh. "So what was that all about?" He opened the door and gestured for her to walk out onto the boardwalk. As he took her arm, he chuckled. "She wanted to warn me you work for Shank and I shouldn't trust you." Susie stopped with a loud clack of boot heels. "I oughta go back in there and give her a piece of my mind." With another chuckle, Hugh patted her hand. "She's just trying to look out for me and for the plan. I appreciate it. Just like I appreciate you doing the same thing by warning me about Sherman doing business with Shank. I know you wouldn't betray me to Shank. I trust you and I trust the Olsens. They want what's best for the folk of Memphis. They'll keep quiet, and this whole thing is going to go off just the way we want it to. Now we just need to work out a plan to get you off the Bayou Belle on the night we want to blow her up. It would be nice to be able to get everyone off, but that would tip Shank off something was about to happen." Hugh sighed as they stepped off the boardwalk and headed down a less-traveled street toward the restaurant where Susie wanted to eat. "That's the biggest problem I'm having with the plan—getting everyone but Al and his men to safety when this goes down." "Like I said before, you're changing, Hugh. There was a time, not long ago, the only person you really cared about was yourself. Now you're worried about other people, some of whom you don't even know. What's happening to you?" As he opened the door to the Cajun restaurant, Hugh shook his head. "I don't know. Miss Cassandra keeps saying sometimes the river changes people. I don't know if it was the river, Cotton pulling me out of it after I almost died, or something about Cotton. But I know I'm changing. I hope it's a good thing." "I hope it doesn't get you killed for good this time," she finished in a whisper as a maître d' appeared. Hugh didn't bother adding he hoped it wouldn't get him killed either. He'd finally found a life he was more than a little bit interested in exploring, one that felt more real to him than anything, even the war. He wasn't ready to die for real. # 22 WARM RIVER water splashed up around Cotton as he stood in the sharply angled metal bow of Shamus's speeding boat. He'd never been in anything that moved as fast as the boiler boat did. Steam belched in the stern where Shamus stood, steering with the huge wooden wheel that looked out of place amidst the metal that made up most of the rest of the boat. The boat was easily three, maybe four, times the size of his raft "Cotton, we need more wood in the boiler!" Shamus shouted. Cotton dashed back to it and threw in several rounds of heavy maple. The fire blazed even brighter and the heat made him take a couple of steps back before he slammed the boiler door closed. After a minute the cloud of steam thickened and the boat moved even faster. "That's it!" Shamus cheered. "I knew those adjustments we made would work. She's even faster than she was before. The tweaks in the turbine are really helping move the water through her, as opposed to just her through the water." "How can you tell?" Cotton looked around, trying to see indications of their movements. The trees forming the shoreline were almost a blur. "See the hills?" Shamus pointed to two hills disappearing to the north. "Yeah." Cotton nodded but didn't understand. "I timed us. When ye put the wood in, we were approaching the north hill. It's one of the landmarks Timmy and I used previously to figure out our speed. After ye put the wood in and we took off, we passed the south hill a good ten seconds faster than our best attempts before. With that calculation, I've no doubt I could make the run from Memphis to Saint Louis in eight, maybe nine hours. Almost over twice as fast as the Bayou Belle." He grinned like a fool. "Coming back would be even faster. There won't be any problem in us following the Belle from Memphis. Then after she starts to go down, we ken get in quickly an' help rescue folks." "That's good." Cotton looked out over the river as they continued to race past the shoreline. He shook his head. The speed made him a little bit dizzy. "So we can head back now?" Shamus spun the wheel, and the boat turned almost instantly north. "Sure. This was a good shakedown outing fer her. I may make a few more adjustments before our big night." He smacked his forehead. "We're forgetting ta test the cannon. I can't believe we're forgetting ta test the cannon." Cotton walked back to the bow, where they'd mounted the heavy iron cannon Miss Cassandra claimed had been left on the plantation during the war. Shamus had added a sighting scope along with a smokeless firing mechanism. Both Hugh and Cotton were suspicious of where it had really come from, but the armament was welcome, so it was quickly added to the boat. "Hold her steady, Shamus. I'll fire it." He simply aimed it ahead of them, knowing there wasn't anything other than gators and gars they couldn't see at a distance by starlight. He packed in the gunpowder packet the way Shamus showed him, then rolled in the ball. The fuse slid into place easily; then he used the new flint-and-steel rotary lighter Shamus had given him. It took him three tries since the wind of their passage kept blowing the sparks away from the fuse. Then one caught. Sparks flared out from the fuse. Cotton turned his back and covered his ears until a deafening boom erupted from the iron barrel, causing the boat to shake. He looked up as the cannonball disappeared into the darkness ahead of them. Then a loud splash rolled down the river. Grinning like a fool, he turned to Shamus. "Well, it works." His words echoed in his head since his ears were still ringing from the blast. Looking shaken, Shamus had his hands firmly wrapped around the big wooden wheel. "That thing really bucked the boat more'n I expected. If we're lucky, we won't have to use it." Shamus's voice sounded far and away, but Cotton still made out most of it. "With luck." It didn't take long before they were back at the inlet that led into the swamp and back toward the cabin. Cotton opened the boiler door and pulled several levers to cut the steam and slow the boat. He let out a heavy, relaxed sigh as the boat returned to speeds he was comfortable with. COTTON SHIFTED uncomfortably in the saddle as he and Shamus rode their borrowed horses back toward Miss Cassandra's. It was only the third time in his life that he'd ridden a horse, and he wasn't sure he liked it at all. But it was faster than his own two feet. As they reached the point in the path where a trail turned toward the plantation house, another horse cantered toward them. Even in the dark, Cotton recognized Hugh's cowboy hat, and a wide grin spread across his face. "Hugh!" he shouted and waved. "Cotton, Shamus." Hugh's horse picked up the pace as they stopped to wait for him. "So how did the changes to the boat go?" "Well," Shamus replied. "She's faster than ever. The cannon even works. Although hopefully we won't have to use it." "I've never moved so fast in my life." Cotton wished they weren't on horseback and he could give Hugh a hug. "If it helps us make sure few innocents are lost, that's the important thing. Even with Miss Cassandra and Ben working to get folks to the shore, it might be hard to get everyone out of the water." Hugh's horse pranced slightly as it came alongside the other two. They all headed toward the plantation house. "So why are you just coming in so late?" Cotton asked. "Susie had the evening off, and I took her to a new restaurant she wanted to try. Seems the Bayou Belle is staying at dock tonight due to a storm that hit New Orleans. She'll be here until the storm surge passes." Cotton rubbed his chin. "Is that why the river was so quiet tonight? I thought the new boat had scared everything away, but if there's a storm surge coming, then the gators'll be headin' to higher ground." "Could be." "Now that you mention it, things were really quiet out there," Shamus agreed. "I never really pay close attention. Most of it just becomes background noise to me." "Listen to the river," Cotton said. "She'll tell you what's a-going on." He wondered if the incoming storm was going to be a good thing for them or a bad thing. Storms always brought change, not all of it positive. MISS CASSANDRA smiled at them after they all made their reports to her. "I think we can use the storm to our advantage. We can get everything set while everyone's trying to stay in and dry. Then when Big Al sets off, all we have to do is sink the Bayou Belle. Do you think everything's ready, Shamus?" The Irishman nodded. "Yeah, pretty much. I got the explosives from Olsen this morning. We both had a bit of a chuckle that they'd come down from Saint Louis on the Belle. If we ken get alongside her in a storm, I'd like to do it before or after the swell hits. Trying to get everything in place on her hull during a storm swell is going to be asking fer trouble." "When we get done here, head back to the cabin with Hugh and Cotton. Get ready and move when the time is right." She walked over to her desk, pulled out a red-flannel-wrapped package, and carried it over to the table where they all sat. "I think it's time to see what lies ahead for us." She set the package on the table. After resuming her seat, she unwrapped the package with careful reverence. It was a deck of cards. Miss Cassandra picked up the cards and began to carefully shuffle them. "Sometimes, when it's something really important, I consult the cards as to what lies ahead." Cotton's breath caught. He never expected to see Miss Cassandra actually do anything magical in his presence. If he hadn't known her so well, he would've gotten up and left the room. His mother had always told him to be wary of magic and those who practiced it. It wasn't a good or safe thing. He nearly jumped when she set the cards down next to him. "What?" "Cut the cards." She smiled at him. "You're very involved in what's going on. I need your energy in this throw. Then pass them to Hugh, and Hugh can pass them to Shamus. When Shamus's done, he can hand them back to me." Staring at the cards, Cotton had to force himself to touch them. They didn't feel like anything other than regular cards, although there appeared to be more of them than the ones Hugh had played with one night after buying them at the mercantile. He cut the stack into two piles, then put the bottom pile on the top pile and pushed them over to Hugh. Hugh appeared more relaxed as he cut the cards into four piles and, faster than Cotton could follow, had them back into a single stack before handing them over to Shamus. "Been a while since I've seen a deck of those. I used to know some women who read cards back in New Orleans." Shamus looked almost as nervous as Cotton. When he handed the cards back to Miss Cassandra, he crossed himself. "Don't do nothing to anger the fae." With a soft chuckle, Miss Cassandra shuffled the cards again, but just once, before she set the deck on the table in front of her. She picked up a card and looked at it. An unreadable expression covered her wrinkled face. The flickering glow from the gaslights didn't help. The card she placed in the center of the table had a picture of a young man with a walking stick and a dog at his heels. "The fool," she said softly, then glanced at Hugh. "There's a journey afoot. Or perhaps a life change. We're all on journeys of some sort, particularly those who've been touched by the river." Pulling another card, she smiled. A large golden cup occupied the card she laid across the fool. "Ace of cups. New emotional beginnings. A journey delayed by the heart, or maybe started by the heart. The cups also sing of the river. Like calls to like." The next card had a man holding a stick while other sticks were thrusting at him. "Conflict." She nodded and placed the card below the fool. Two dogs barking at a smiling moon were on the card she placed above the fool. "Cycles. Everything is meant to come and go in our lives. It makes the journey interesting." Her voice sounded more trancelike with each card she turned over. The card she placed to the right of the fool had a man with his arms full of swords while two more lay behind him. "Things forgotten or left behind." She shook her head. A naked man and woman reached for each other as an angel looked down on them. She placed the card to the left of the fool. "The lovers. Two unlike forces coming together." A soft smile graced her face as she looked from Cotton to Hugh. "Joining to make the journey easier." She paused and studied the cards. "The fool has a journey of the heart to make. It won't be easy. There will be things to leave behind as he battles the conflicts of the past, but he won't make the journey on his own." She picked up another card and laid it to the right of others. A bright bolt of lightning struck a black tower, and people fell from either side. A soft chuckle escaped her. "At least the world will see the disaster we're going to rain down on Big Al." Without further comment she laid another card above it. She nodded at the wheel with its various creatures around it. "We won't know what's happening until it happens and the wheel of fortune finishes turning. There are many times when the fates do not want us to see what lies in store." The next card depicted a rainbow covered in cups with joyous people below it. "We are hoping for prosperity and happiness from our endeavor." She shook her head again. "Of course we are. That's what everyone wants from their endeavors." Resting her hand on the cards, she sighed. "There is a lot o' things we're hoping for from this. Let us hope the fates are kind to us." She turned over the last card and laid it at the top of the row. A woman stood holding a rod in each hand. She was encircled by a green wreath, and animals rested on clouds in the corners of the card. "There will be a large number of opportunities open to us. This is good. If we all died in the end, there wouldn't be any opportunities for us." Miss Cassandra sat back in her chair, set her elbows on its padded arms, and her hard gaze never left the table. She nodded several times and mumbled to herself. Cotton's heart pounded and he wanted to question her, but he couldn't bring himself to. Hugh cleared his throat. "Well, from what I know of all this, it looks fairly good." "And what do you know of this, Hugh?" Miss Cassandra looked up from the cards spread before them. "Like I said, I've known a few card readers in the past." He gestured to the cards, one by one and gave a quick overview of how he saw things, wrapping up with, "The good number of major cards in the throw are also important—they tell of fate, something we're all destined to do and cannot escape." Miss Cassandra smiled, then tapped the crawdad Cotton hadn't noticed on the card with the moon on it. "And what happens if the lobster should bite one of the dogs while its focus is on the moon? The law of cycles says every time something rises, something else must fall. That's why the dogs are two different colors." Cotton swallowed. As she spoke, a vision of death filled his mind. "But we already lost Timmy. Maybe he's the one that has to fall in all this." "Maybe." Miss Cassandra's gaze turned toward Cotton, and he shivered at the cold distance of it. "But maybe not. It's also possible the lobster won't bite anyone and he's just there to bask in the glory of the moonlight." She looked away and shook her head. "There are too many unknowns. There's a chance everything is going to go smoothly and we'll sink the Bayou Belle and get Big Al out of the way, and there's also the chance something will go wrong and we'll lose one of our own. I don't like the wheel of fortune where it is." She sighed, scooped up the cards, returned them to the deck, and carefully wrapped the red flannel around them again. Hugh shook his head. "The wheel of fortune has always been kind to me. I'm good with it crowning the venture." Miss Cassandra didn't look up as she continued to put away her cards. "I think it would be best if we all get as much sleep as we can. When the storm breaks over us tomorrow, you need to be ready to move. I'll make sure none of the colored folk in Memphis are on the Belle when she leaves dock tomorrow night. I think the storm swell will hit us after midnight, and the storm will still be raging at dawn. Luckily it won't be as bad here as it will be on the coast. But it should be enough to cover your actions, if by nothing else than making noise and keeping everyone from wanting to be outside until it clears." Once the cards were carefully wrapped, she placed them in front of her and put her hands on them. "Since we know there will be whites on the Belle, that means the potential for injuries, and it can't be helped. Hugh, do your best to help out, and I'll have people ready north o' town to do what we can after the explosion. If we're very lucky, the river will be with us on this and we can get those who need saving to shore." Hugh nodded. "I hope so. We don't need the blood of the innocent on our hands." A dark and scary look crossed Miss Cassandra's face. "Hugh, it's been a very long time since there have been truly innocent people in this world, and those few I've encountered would never set foot on a boat like the Bayou Belle." Cotton shivered from the look. He wanted to grab Hugh's hand and pull him out of the room, but Hugh only smiled. "So, Miss Cassandra, I've been meaning to ask you for a while, and I figure now's a good time to do it, before we all carry out this dangerous plan. What is your real beef with Al Shank? Your hatred of him goes beyond that of a healer of those he's injured. This feels personal." "If you feel the need to ask me the question, then I suppose I should answer it." Her voice softened. "We all have debts Big Al Shank owes us. He nearly killed you. His men killed Timmy and tried to kill Cotton. The Belle has left a bloody streak down the Mississippi for too long. The debt he owes me is my husband and son. During the war, Al Shank came to be the owner of the Belle after a duel in the streets of Memphis. The Yankees had just come through. They'd killed the sheriff at the time and left a state of lawlessness. My husband and son were trying to help others. Al was having an argument with Porridge McBride, the previous owner of the Belle. Their conflict carried out into the street. My men tried to break it up. My boy was the first to die from Al's gun that day. My husband and Porridge died moments later. Al declared himself owner of the Belle and continued his reign of bullying. So for me, sending Big Al to the gates of whatever hell will have him is personal." Cotton touched Miss Cassandra's hand. "I'm sorry. I'd never heard what happened. There was so much death at that time." She patted his hand. "Cotton, there was nothing you could've done then. You were hiding out in the swamp, hoping the war would just pass you by. At least you came out of it alive. There were times that was all any of us wanted. Just like now. We can count our success by how many of us gather at this table when it's all said and done." # 23 HUGH HUGGED Cotton as tight as he could. It was nice Cotton didn't flinch at his strength and could return it as well. Outside the cabin the wind began to howl. Shamus snored softly from the floor. Cotton hugged Hugh nice and tight and softly kissed him. Both movements sent shivers of pleasure through him. "I don't want to let you go," Cotton whispered. "I'm afraid one of us won't come back." "I understand." Hugh kept his voice low as he kissed Cotton. He hoped they would all get enough sleep to get them through the coming day. "At least the cards looked positive." Cotton shook his head. "I don' trust the cards none. My mama always told me to never trust no magic. It's too easy for the magic to lead us astray. We're good people, Hugh." With another kiss, Hugh silenced him. "We're going to be okay. We just have to believe that. Otherwise I won't be able to let you go and everything'll fall apart." THEY LAY there in each other's arms as the wind outside the cabin blew harder until a fine mist of rain was forced through the cracks. Neither of them dropped off to sleep as the storm raged, fanning the flames of their fears. Cotton finally gave Hugh a parting kiss and got out of bed. Hugh caught his arm. "Where are you going?" Cotton smiled down at him. "To check and see if the storm surge has passed already. It's easy to tell here near the swamp." He squeezed Hugh's hand, then hurried out the door. Shamus sat up suddenly. "What's happening?" "It's okay, Shamus." Hugh swung his legs out of the bed. He still had his pants on; neither of them had felt comfortable getting completely naked with Shamus asleep on the floor just a few feet from them. "Cotton just went out to check if the storm surge has passed. The wind's getting worse out there." "If it's passed, we need to get moving. How long until daybreak?" Hugh reached for the lantern and lit it. "You've got the watch. Mine never came up from the river bottom." Shamus pulled out his pocket watch, opened it, and tilted it so the light from the lantern hit the face. He frowned. "Nine in the morning. Why's it so dark out there?" "The storm must be heavier than we anticipated." Cotton hurried back in. "The storm surge is past. There's lots of fresh grasses and branches along the bases of the trees closer to the swamp. The storm's really going out there. We should git going." With a heavy, almost weary groan, Shamus stood and dusted himself off. "I got to thinking about it while I was drifting off to sleep—another plus to going during the storm is, the heavy rain will help hide some of the steam. Not all of it, but some, just in case anyone is looking our direction at the wrong time. Hopefully the rain on their tin roof will cover some of our noise too." Hugh pulled on a shirt, then stopped himself. This will be drenched in seconds, from the sound of the rain. Better to go without. I can warm up at Miss Cassandra's after this is over. He took the shirt off and left it lying on the rumpled bed. A nervous grin crossed Cotton's face. "Well, let's go. The sooner we're done with this part, the better." They hurried outside. The wind-driven rain lashed at Hugh. The coldness of it took his breath away. He followed Cotton and Shamus to where the newly improved boat was moored. The surge had washed a large amount of debris up around the boat. Cotton was already pulling at the branches and working to get it so they could move the boat into deeper water. Hugh splashed into the water and joined him. "Everything looks fine up here!" Shamus shouted from the boat as Hugh helped Cotton wrestle a large tree trunk away from the hull. Shamus's lantern splashed light around. "We've almost got it free!" Cotton yelled back. "Fire up the boiler." Another couple of limbs and the bow of the boat was free to enter the swamp. Cotton motioned for Hugh to climb aboard. The rail was a little higher above the waterline than most of the riverboats Hugh had been on. He grabbed the metal rail and pulled himself up. "Hugh, a hand here!" Shamus's shout barely carried over the sound of the rain hitting the deck. Hugh rushed over as Cotton climbed aboard. Shamus held a large tarp up and was trying to get wood out while not letting the rain in. "What can I do?" Hugh asked. "Hold the tarp while Cotton and I get the wood," Shamus replied. "It won't do to get the wood wet." Taking the edge of the tarp, Hugh turned his back to the wind so the cold rain wasn't slapping him in the face. It didn't take long for Cotton and Shamus to get enough wood in the boiler. The big metal box quickly put out enough heat to help counter some of the chill of the storm. "Hang on—this may be a bit rougher than normal." Shamus pulled a lever and grabbed the big wheel. The boat lurched violently, then settled into a nice smooth motion as it plowed through the swamp. "Cotton, light the lanterns in the bow. They might not do much, but any help they can give will help." Cotton hurried forward, and moments later twin beams of light illuminated the dark waters. "It could be worse." Cotton said, returning to the where Shamus steered the boat. "How so?" Hugh asked. "It could be at night in the rain," Cotton smiled. "It's not dark enough to be night anymore." "It's after nine in the morning, probably close ta ten now," Shamus snapped. His grip on the wheel was so tight his knuckles were white. "But it's still dark out here." "Big storms'll do that." Cotton stood next to Hugh near the boiler. "There's only been a few this dark, but it looks like night will never end, then the rain will stop and the sun comes out." "We'd better hope that doesn't happen until after we leave the Belle," Hugh said. He put a wet arm across Cotton's damp shoulders. The contact helped his efforts to remain calm. Inside he wanted to panic, but he knew that wouldn't help the situation. It's just like a poker game. Keep bluffing for as long as possible. People can smell fear. Cotton leaned against his side. "We're doing this. It's going to work." Hugh nodded. "Yes, we are." "Cotton, we're inta the river, I think," Shamus announced. "I can't see well enough to be sure, but the going just got smoother." After a quick kiss on Hugh's neck, Cotton hurried to the bow and peered into the water. "Looks like it. Head north." Shamus spun the wheel and the boat turned. "We ken add more wood now. The faster we go, the sooner we get there and then can get back." THE SHADOW of the Bayou Belle rose up out of the rain in front of them. Shamus cut speed when they heard the church bells chiming ten. They'd gone a lot faster than Hugh realized. The constant downpour and dark skies made it impossible to judge time or distance. Shamus pushed the lever he'd pulled earlier, and the boat's speed dropped even more as it slid along the port side of the riverboat. As they passed beside the big, still paddles, Hugh remembered his previous up-close sight of them when Shank's men had dropped him overboard in hopes he'd die either in the paddles themselves or in the river. He fought back a shiver of dread. Then Cotton tied them off to the water's-edge railing of the Belle. Through the wind-lashed rain, it was hard to see anything on the riverboat that wasn't directly in front of them. Hugh grabbed a box of explosives and the hand drills. He handed a tool to Shamus and one to Cotton. The two set about boring holes just above the water line in the boat's thick wood. As they finished each hole, Hugh carefully filled it with the explosive that Shamus had explained, but, in the excitement, he couldn't remember. A small waterproof fuse ran from hole to hole, and Hugh capped them off with a strange clay mixture Shamus said he'd come up with. It would help keep the explosives dry and direct the blasts into the ship proper, causing more damage. They were almost halfway through when the sound of footsteps caught Hugh's attention. He paused, his heart hammering. The footsteps grew closer. He took the explosives with him as he slipped onto the lower deck of the riverboat. With a quick gesture, he warned Cotton to be still. The man Hugh had shot in the leg came around the corner. He had on a thick oilskin coat and a wide-brimmed hat, but Hugh recognized his shape and slight limp. Carefully, Hugh set the explosives down. As Hugh straightened, the man looked at him. "Hey, what are you doing out on deck in this storm? You should be in your cabin." Hugh rushed forward. The man backpedaled but slipped on the wet deck. He crashed hard. Hugh landed on his chest and hit him in the jaw. His knuckles hurt, but he hit the thug again. Memories of the beating he'd received at the man's hands flashed through his mind. He wanted to keep up the beating but didn't have time. Hugh aimed a brutal blow to the man's temple and his head rocked sideways as he fell unconscious. Before he stood, Hugh listened for sounds of anyone else coming his way. The deck was silent. For a moment he looked at the man he knelt on. If I leave him here, he might recover and tell Shank there was something suspicious going on. I've got to dump him in the water. Cotton eased up next to Hugh. "That sounded like the guy who tried to hang me," he whispered. "Was he?" Hugh's doubts about what to do with him vanished. Standing on the slick deck, with the wind hitting him hard, wasn't easy, and it took Cotton's help to get the man over the edge of the riverboat. They gently lowered him into the water. His head bumped off Shamus's boat, and he floated away on the rain-dark waves. Hugh nodded in satisfaction, knowing at least one of Shank's heavies was out of the way and heading for the gators. "Let's get this finished," he whispered as Cotton and Shamus went back to work drilling holes. Hugh finished packing in the explosives and curled the fuse in a tight knot at the last hole so he could reach it later and ignite it. The rain was beginning to let up as they made it back to Shamus's boat and cast off. They floated on the angry river until they were well clear of the docks before throwing more wood in the boiler and heading back to the cabin. By the time they reached the swamp, the sun was peeking out from behind the clouds and the cold rain of the morning was fading to a distant memory. # 24 COTTON TRIED not to shiver as Hugh rubbed the only towel over him. It felt so good to get dry. The cold, pounding rain had chilled him to the bone, but he didn't want Hugh or Shamus to know how cold he really was. "I would suggest we get your fire going outside, but we need to get to Miss Cassandra's and let her know we have everything in place," Hugh said as he pulled the towel away to run it through his own hair for a moment. "Grab dry pants and a shirt. That will help you warm up a bit." Cotton stared at him for a second. "How did you know I was cold?" "Goose bumps. You're covered in them, and I know how cold I am." Running his hand over his arms, Cotton frowned. "Yeah, I guess you're right." He went to the wooden chest at the foot of the bed and pulled out his only other pair of pants. "It's a good thing I've got two pairs of pants. Otherwise I'd either have to go naked until the other pair was dry or wear them wet. It wouldn't be the first time I ran around in wet pants." Hugh smiled at him. "And you look good in wet pants, but I'd hate for you to catch your death of cold just as we deal with Shank." He hugged Cotton, and the warmth of their skin touching spread a pleasant, comforting feeling through him. "We could just crawl back into bed." Cotton chuckled softly. "Maybe Miss Cassandra and Ben can finish the job with Shamus's help. That way I'd know you're safe and sound." "No." Hugh shook his head. "I think we're committed now. If we don't go blow up the Bayou Belle, the explosives might accidentally go off as they age, and innocent lives might be lost if it happened when the boat was full and in the center of the river. I don't want to think I caused that many deaths. Killing one of Shank's men or soldiers during a war is one thing. Accidently killing a boatload of people because we weren't men enough to finish something we started isn't something I could live with." Cotton ran his hand along Hugh's chest. "I understand. But that doesn't keep me from wanting to make sure we're both safe." Hugh nodded. "I agree." He grabbed his shirt off the bed and pulled it on before Cotton could find another reason to delay them. Since Shamus didn't have any dry clothes at the cabin, he was already en route to Miss Cassandra's house. The horses moved nervously in the makeshift corral Shamus and Cotton had rigged up using a bit of rope and some tree branches. Cotton looked at them with a little trepidation. He'd ridden more in the past week than he had his whole life. He was used to running places. The horses were faster, but he didn't think they were as reliable as his own feet. Hugh untied one of the ropes and stepped into the corral with both bridles in his hand. "I'm kinda glad we left the saddles at the barn. There's no way we could've kept them dry in that storm, and saddle leather doesn't do well when it gets too wet." He walked up to one of the horses and slipped the bridle on before he handed the reins to Cotton. Cotton led the horse out of the corral before mounting. Seconds later Hugh rode alongside him and they headed for Miss Cassandra's. "Hugh, there's something I wanted to talk to you about," Cotton said as they rode side by side through the forest. "What's on your mind?" "I talked to Rubi the other day. I would've mentioned it sooner, but we've either been busy or had people with us the whole time. Rubi's pregnant. It's Timmy's and she wants to keep it." Hugh looked confused. "And what does this have to do with us?" "Maybe nothing. It depends on how her talk with Shamus goes. It sounds like Shamus might be more than a little interested in taking care of Rubi now that Timmy's gone. But if he's not, she wants me... us to." "What?" "Don't worry about us. I done told her she and I couldn't be no more than friends." He reached over and took Hugh's hand. "I'm with you, Hugh. I love you. I ain't interested in women. You know that." Hugh nodded but confusion still etched his handsome face. "But she wants to make sure her little one has a home and someone to call daddy. Timmy was like family to me." A hard lump rose from Cotton's chest and tried to wedge itself into his throat. He swallowed hard. "I'd do almost anything to help Rubi, but I told her you'd have to be okay with it too." Hugh squeezed Cotton's hand; then the horses sidestepped, ripping them out of each other's grasp. "I think I understand. But we don't know what's going to happen after we're done here." He paused and pushed his horse closer to Cotton's, close enough their legs brushed against each other. "I mean, we're going to be together. That much I know. But we don't know where. We really haven't even discussed the 'where' part. I don't know if I want to stay in Memphis or even in Tennessee. It's still changing due to the aftermath of the war. But there's a lot of land opening up out west. You're not worried about being out somewhere alone?" Cotton shook his head and patted Hugh's leg. "As long as you're there with me, I can be anywhere." A bright smile graced Hugh's face. "That's how I feel too. But I also know that in a lot of areas, our kind—men who prefer other men—aren't really welcome to be out in the open. It might be easier to be on the frontier, out by ourselves." "I hadn't thought about that, but it sounds like a good idea." Cotton was new to the idea of love, let alone the concept that folks wouldn't approve. But he did know, thanks to his parentage, what the disapproval of others could mean for a life and how hard it could make things. He didn't want things with Hugh to be hard. He wanted them to be easy and happy. "Right before my run-in with Shank, I heard about something that at the time didn't sound interesting, but now, with you, it does." "What?" "The government is opening up the Oklahoma Territory for settlers. Or there's Kansas, or Colorado Territory. We could homestead in any of those. I think it might be easier to get away from folks in Jefferson. The mountains there could hide us. I've even heard rumors of gold up in some of the mountains. Maybe we could become gold miners." It was something Cotton had never considered. "Maybe. Trapping up there wouldn't be that much different from hunting gators down on the river, and I'm good at that." Hugh patted his leg and squeezed his hand. "Exactly. We could make a good life out on the frontier. I suppose if Rubi wants to go with us, she would be welcome. I just wouldn't want her to get lonely." Cotton nodded. "Yeah, lonely wouldn't be good for any of us. I'll talk to her about it. See if she's talked to Shamus." They turned off toward Miss Cassandra's. Ahead of them the parting clouds revealed a huge rainbow that stretched across the expanse of the lawn. Cotton stopped his horse and stared. He'd never seen such a bright, perfect rainbow before. "Wow," Hugh muttered. "That's gorgeous." For a moment all the concerns about sinking the Bayou Belle and what would come after flashed away. Cotton turned and grinned at Hugh. "At least I got to see it with you. I hope it's the first of many wonders I can see at your side." Hugh nodded in agreement. "Yeah, sharing things like this with someone is what being in love is all about. There's so much more we can do and see. We just have to get through the night." Inwardly Cotton cursed the horse. He wanted to lean over and kiss Hugh, but being bareback, he didn't trust his balance. "I love you, Hugh." "I love you too." # 25 HUGH WALKED up the gangplank of the Bayou Belle. The air was even more humid than normal. It gave the evening a very oppressive atmosphere. He pushed back the nervous feeling that crept up from the pit of his stomach. The feeling had grown ever since he left Cotton at Miss Cassandra's house. Cotton and Shamus headed back to the boat at the cabin, while Miss Cassandra rallied her people to ride north of Memphis and wait for the boat to explode. Hugh's part was the hardest—set off the explosives, make sure Shank went down with his ship, and get off the Belle and to the boat with Cotton and Shamus. "Coming up awful late tonight, Harry," said the one guard he recognized at the top of the gangplank. The man standing on the other side must've been a replacement for Limpy, who was by now alligator meat. "Susie arranged for me to ride to Saint Louis this trip," Hugh replied. It was all he could do to force a smile at the men. "She said there might even be a poker game, if I got lucky. It's been a while since I played much. It might be a nice way to spend the evening." The new guard smiled. "We'll let Mr. Shank know you're looking for a game. If there are others riding tonight, you might get your wish." Hugh touched the brim of his cowboy hat. "Much obliged." He walked on into the bar, where the soulful sounds of Susie's voice rolled out the open door. Instead of heading to the bar first, Hugh made for an empty table. If Shank acted according to his nature, he'd come looking for a poker game fairly quickly. Plus he'd warned Susie if he came in and sat down at a table, it was a warning sign she needed to get off the boat before it left dock. When Susie's gaze passed over him, she frowned but didn't interrupt her song. She rolled from the tune into one that glorified the Confederacy. While she sang on, Hugh grew more nervous. A slight shudder ran through the riverboat. It had cast off from the dock. A heavy hand landed on Hugh's shoulder as he got out of his chair to head over to Susie. "I hear you're looking for a poker game tonight, cowboy." Glaring up into Shank's heavy jowls, Hugh swallowed a protest and deepened his voice in hopes that it wouldn't give him away. "Shore thang. My cousin Susie said you have some o' the best games on the river." He laid on a thick accent. Shank smiled at him. "That we do, that we do. I've even been able to find a couple other people who want to play along with us. Four players is always so much more interesting than two." Hugh glanced at Susie. She looked nervous. "Yes sirree." Two other men appeared in Shank's wake. They weren't anyone Hugh had seen before. There was something odd about one of them. He looked rougher than the men Shank normally played with, almost like one of his hired hands. The other man dressed like a Southern gentleman, but he looked uncomfortable and just a tad young. "Then why don't we move this over to my private table," Shank suggested with a gesture toward the green-felt-top table in a corner away from the bar. "We can be more relaxed over there." For a moment as they walked over to the other table, Hugh wondered who was walking into whose trap. He knew how easy it was to lose a lot of money to Shank, but as long as he could keep Shank at the table, the better the chances of making sure he was in the middle of things when the explosion happened. Susie sang a ballad about the battle of Sabine Pass. Shank looked at her, smiled, and pulled out his cards. "Okay, boys, game's five-card draw. Standard rules. No wild cards." HUGH FROWNED at his cards. Never in his life had he deliberately played so badly. But he'd left his card rig in the cabin. He wore short sleeves that wouldn't have covered the slick device for hiding cards. But his goal wasn't to win at the card game; his goal was to beat Shank at the game of life. "I fold." He laid the cards face down on the green felt. The young man next to him raised a bushy blond eyebrow. "I'll call and raise." He tossed three silver dollars onto the pile of coins. "Too rich for me," the ruffian replied. Shank grinned. "Looks like this might be your night, Mr. Mulgrew." Shank tossed the required coins into the pot, then flipped over his cards. "Two pair, tens high." His joy radiated from Mulgrew's face. "Four jacks." He reached for the pot, the third one he'd won so far. In the distance a steam whistle blew three short blasts. Hugh's heart raced. That was the signal from Shamus that he and Cotton were in position. An odd look crossed Shank's face. "So we're not the only boat on the river tonight? I guess others couldn't wait until dawn to get on the way. Storms always mess things up for shipping." It was his turn to deal, so he began shuffling. Noticing Susie had gone quiet, but the calliope hadn't come on, Hugh glanced over his shoulder. She stood at the bar, talking with the bartender. She looked more nervous than before. "Harry, are you playing or not?" Shank asked, drawing his attention back to the table. Hugh's cards lay on the table in front of him. The others already had theirs in hand. He snatched up his cards and looked at them. The ace, king, queen, jack, and ten of clubs sat there in his hand. His eyes grew wide. It was one of the best hands he'd ever been dealt. When it came around to his turn to bid, he upped to five dollars. The ruffian immediately folded and then sulked in his chair. Shank looked dubious. "I'll see your five and raise you three." Mulgrew frowned and folded. Shank grinned. "How many cards would you like?" "None." Hugh shook his head. I might as well win one hand before we blow this boat. For a moment Shank contemplated him. He rubbed his jowls. "None? I'll take two." He tossed two cards to the side and pulled two from the deck. The gleam that sparked in his eyes told Hugh he'd gotten good cards, but it would be impossible to beat a royal flush. "I'll raise five." Shank tossed more coins into the pile. Hugh did the same. Tapping his cards, Shank stared at Hugh. "So, Harry, what do you say we make this interesting?" Hugh shook his head. He didn't have time for interesting. "I'd like to keep it simple. The evening's young yet. I think most of us still have a lot to lose. I'll call." It wasn't a huge pot, but it would offset what Hugh had lost so far. Shank frowned at him. "As long as you keep playing. I don't like it when someone wins a hand, then walks away from the table. It makes me feel like I've been had. Or that you aren't serious about winning." "I'll keep playing." Hugh picked up his cards and fanned them out before he plopped them down on the green felt. "Nice hand." Shank glared as he revealed a full house, two aces and three nines. He gathered up the cards while Hugh raked the coins over. It was Mulgrew's deal. The young man handled the cards with a fair amount of skill and dealt quickly. Hugh got another good hand. I can't play this one out. It's getting time to blow the boat, or we'll be too far upstream for Miss Cassandra's folks to help save people. He discarded his two best cards and asked for three. The new three were even better. The pot rose. Finally, on the second round of bidding, Hugh laid his cards on the table. "I fold." He pushed his chair back. Shank looked alarmed. "Where are you going?" "The beers are starting to hit." Hugh patted his stomach for effect. "While you all play out this hand, I'll go to the facilities. I'll be right back." "We won't hold the next hand too long for you," Shank snapped. Hugh knew how much Shank hated having a game held up, even for something like bodily functions. Nodding, Hugh hurried from the room. Susie followed him out the door. "Hugh, you can't mean to do this tonight." He pulled her into the shadows near the rail. "I can and I do. Everything's in place, except you're still on the boat. You need to get off now." She shook her head. "I can't. Al will kill me if I'm not here." He didn't bother trying to keep the exasperation out of his voice. "And if you are here, there's a chance you'll die. We put enough explosives on this boat to blow her sky-high. You need to get off here. Head to the east shore. Some of Miss Cassandra's people are waiting there to help with rescue efforts." "You don't understand." Hugh let out a heavy sigh. "Then you better explain it to me, and quickly. If I'm not back at the table in a few minutes, Shank's going to look at the cards I discarded and realize I'm up to something. That was a really good hand I threw away." "I'm pregnant." A slow tear ran down her check. "And why didn't you tell me this yesterday?" "I just realized that I missed my second period during the storm. I must be pregnant." Frustration rose up in Hugh. "And why does that stop me from blowing up the boat?" "It's Al's baby." The tears were causing her makeup to run. Rubbing the bridge of his nose, Hugh tried to figure out what to say. "Why are all the women in this mess turning up pregnant? So help me, if Cassandra announces the impending arrival of a baby, I think I'll scream. Look, you know and I know Shank will just dump you, baby and all, over the side of the boat and let you fend for your own with the alligators. Get off the boat and get to shore. I'll find you after the explosion, and we'll figure out what we're going to do." "Hey, did you see that cowboy cousin of Susie's?" Shank's voice carried around the corner. Hugh dropped his voice, "Go tell Shank you haven't seen me. Then get off the boat." He gently shoved Susie toward Shank and dashed down the deck toward the spot where he'd set the fuse. He had to lie on his belly and hang over the side to reach the fuse. It was awkward, but Hugh managed. A hard slap of storm-tossed waves splashed up near the fuse so he had to hold it up the best he could to keep it out of the water so he could get it lit. The lighter Shamus had given him was more awkward to use at the odd angle, and it took several tries to get a spark to reach the fuse. Shamus had assured him that once lit, the water-resistant fuse would burn even if it got wet. He hoped the artificer was correct. The fuse sparked. "Hey! What are you doing there?" a gruff voice shouted at Hugh. Hugh scrambled to his feet and took off running for the back of the boat. He had a better chance of getting free if he were toward the rear, where the explosions would happen later than the ones in the bow. "Let me go!" Susie's voice shrilled as Hugh ran past the mezzanine that led to the gangplank. He skidded to a stop. Shank struggled with Susie, one of his beefy hands around her neck as he forced her against the wall. "Tell me where that cousin of yours got off to, or I swear I'll snap your beautiful neck and throw you to the gators myself. I can replace you as easily as I found you." "Let her go, Shank." Hugh didn't bother adding the accent or the deeper voice he'd been using. Shank's face paled in recognition. "You. You're dead. My men threw you in the river after they beat you to near death." Hugh rushed him, slamming a hard fist into Shank's soft face. "Yeah, about that." Staggering, Shank somehow managed to keep hold of Susie. She slammed the heel of her boot into his foot. He yelped in pain, and Hugh hit him again. "Fine, have the bitch!" Shank shoved Susie at Hugh. With some quick footwork, Hugh managed to keep on his feet as Susie's small frame slammed into him. He spun. "Get in the river, now!" He pushed her toward the rail. The boat shook as the first explosive went off. Shank's fist connected with Hugh's jaw in the next second; then the boat lurched forward. Stars filled Hugh's vision and he fell to the deck. # 26 COTTON WILLED the boiler boat to go faster. Twilight was long on the river, but it created shadows that weren't normally there. "We've got to be careful," Shamus said. "The storm surge may've moved some o' the sandbars and such around. It won't do to run aground on anything." The boat lurched and stopped. "Damn!" Shamus pushed the lever to cut power. "See, I was worried something like this might happen." Cotton ran to the bow of the boat and looked into the water. Several large tree limbs stuck out and appeared to have caught the boat in their grasp. "Get me the hatchet! I'll get us free!" Cotton dove overboard. The river water was colder than he remembered. He pulled at several of the branches that broke easily, but there were several he couldn't get to move. "Come on, we have to get moving again. Hugh needs us." The hatchet handle appeared just above his head. "Here. Do ye need any help?" "I don't think so." Cotton grabbed the hatchet. He managed to make quick work of the first limb, but the second was farther down. He took a deep breath and dove into the murky water. It was harder to swing the hatchet underwater—the water itself seemed to be softening the blows. He quickly figured out that shorter swings were more effective. He had to resurface and dive four times before the branch fell away, drifting down the angry river. Luckily, the third big limb cut through easily. Cotton braced his feet the best he could on the tree trucks, still underwater, but deep enough to not impede the passage of their shallow-bottomed boat. He pulled on the hull, and it slid easily forward. "Ye got it!" Shamus shouted. Cotton nodded as he grabbed the edge of the boat and pulled himself up on deck. "Now, let's get going again. Hugh needs us in place before he blows those explosives." To the north, the church bell rang. Cotton was too nervous to count the chimes. It didn't really matter. Hugh wouldn't do anything until they gave him the signal they were in place, but they couldn't wait too long. If they were too far north, Miss Cassandra and her crew wouldn't be able to help get people out of the river. Shamus pulled the lever and the boat shot forward. "Gimme more wood." Without responding, Cotton pulled up the tarp and started adding wood to the boiler. The boat gained speed and was soon zooming past the Memphis docks. There was no sign of the Bayou Belle. "We've got to hurry," Cotton said. "Those trees slowed us down." His heart pounded harder than he'd ever felt it before. We have to get there in time. If Hugh is to survive the river again, I've got to be there. She might not let him up for anyone else. "I think she's going as fast as she can," Shamus replied. "We'll get there." The bottom of the boat grated on something, but it didn't slow down. "Cotton, get the lanterns out front lit. We're going to need some light if we're going to avoid snags and stuff." Shamus held steady to the wheel. Cotton rushed forward and got the lights lit. As the second one came on, it illuminated a huge tree right in front of them. "Left!" he shouted. "There's a tree." The boat jerked hard enough that Cotton was forced to scramble to stay on his feet. Water splashed over the bow, but they avoided the tree. "Stay up there and keep watch!" Shamus yelled. "Remember, it's port and starboard, not right and left." "No," Cotton muttered to himself as the water splashed around them. "I can't remember that. You handle right and left!" Then lights appeared north of them. "We've got lights! It might be the Belle!" Cotton peered as hard as he could. He wished the boiler and motor didn't make so much noise; he strained to hear the distinctive sound of the paddle wheel. There hadn't been any other paddle wheelers at the docks during the storm. The only paddle wheel boat heading north would be the Bayou Belle. When he finally heard the distinctive whoosh of the big wheel bringing water up and dropping it, Cotton breathed a little bit easier. But they were rapidly approaching the spot where Miss Cassandra was going to meet them. "That's the Belle!" he yelled back to Shamus. "Slow down and pace her." The slowing process was nearly instantaneous as Shamus hit the levers to cut the steam power and the current of the river helped drop their speed. Cotton ran back to the boiler and pulled the chain attached to the whistle near the top of the stacks. He gave three quick pulls, their signal they were in place and Hugh could blow the boat at any time. COTTON PACED the deck. As the minutes ticked by, he paced faster and faster. Why hasn't Hugh set off the explosion? Has something happened to him? He stalked over to Shamus. "Do you think you could drop me off on the deck so I can go make sure Hugh is all right?" "I don't know if I ken match their speed just right. It'd be really tricky. We should wait a few more minutes." "What about if you pulled alongside them and I jumped off? The lower deck is close enough to the water I could catch the railing and pull myself up." "And what happens if the explosions start right then? Ye'll be in the same shape as Hugh." Across the water, a commotion started. "Hey! What are you doing there?" a gruff voice shouted. Cotton's heart leapt. "That's one of the guys who killed Timmy and tried to hang me!" "Let me go!" a woman shouted. "Shamus, we need to catch up to the Belle!" Cotton ran toward the bow of the boat. "Cotton, we have ta wait. If we get caught up in the explosions, it could take out the boiler, and then we'd be in trouble too." Stopping, Cotton turned and glared at Shamus, but he knew the Irishman was right. His shoulders slumped. The next shout sounded like Hugh, but he couldn't make out the words. Then the first explosion lit up the left side of the Belle. The loud splash of someone hitting the water rolled across the river before the second explosion sounded. Cotton wanted to dive in and find out who was in the river, but he waited with clenched fists as each explosion sounded in what felt like faster and faster succession. Pieces of wood and metal flew out toward the western shore of the river, and the riverboat began to list that same direction. Mighty Mississippi, spirit of the great river, please be kind to Hugh. I love him, and I don't want to lose him. By the time Shamus finally put their boat in motion, Cotton was at his wit's end with worry for Hugh. Ahead of them people were yelling and screaming from the water, and Cotton couldn't detect the one voice he wanted to hear the most. # 27 HUGH CRAWLED on his hands and knees toward the railing and the river beyond. Ahead of him Susie jumped into the cold, angry water. He could only hope she could swim until she was safe or Cotton and Shamus arrived with rescue. "What did you do to my boat?" Shank shouted behind him as a second blast rocked the vessel. A heavy hand caught Hugh's ankle and jerked him back. With his metal leg, he kicked out as hard as he could. A cry of pain from Shank rewarded his effort. Hugh lunged forward, still on his hands and knees. If I can get to the railing and over it, I can swim for it and make sure Sue makes it out too. Cotton's out there somewhere on the river, waiting for us. A foot smashed into the small of his back. Pain shot through him but was short-lived as the third blast, closer than the previous two, ripped through the boat. Wood shot up around them, knocking his assailant backward. Hugh could see water from where he lay. He knew the next blast would happen almost right under him. Shoving himself off the deck as hard as he could, Hugh dove for the river. Pieces of the Belle scattered around him. He plunged deep into the water, hoping it would protect him from the next blast. The pressure in his ears changed, and for a moment he thought they might have burst. He headed for the surface, trying to direct his path toward the front of the Belle, where the explosives had already detonated. By the time he surfaced, his lungs were burning for air. Fire blazed on the listing riverboat. It cast an eerie orange glow across the river. Hugh gulped for air and treaded water. Above him, from the third and fourth floors, people were screaming. He stared at them. "Jump! Get off the boat!" He couldn't believe they weren't thinking about their own lives. A heavy chest splashed down near him. Hugh looked up. One of the working girls was trying to get another chest over the railing to follow the first one. "Don't worry about stuff, just get off the boat." Another explosive detonated. The girl lost her hold on the chest, and as the Belle listed toward Hugh, the chest came at him. He frantically swam out of the way. We hadn't thought about which way the damned boat would roll as it sank. Hugh swam to the west, away from the eastern shore where Miss Cassandra and her people waited. I've got to get out of the way before it rolls over on top of me. Several people hit the water near him. One looked like the girl who'd been pushing the chest. "Mister, I can't swim!" She batted at the water in an attempt to keep her head up. Wrapping an arm under her arms to keep her afloat, Hugh said, "We've got to get out of the way of the boat. It's coming this way." "Oh Lawdy!" She clung to him like a lover, her legs entwined with his. "Let go!" He fought to keep them both above the water. "Let me hold you. You latch on to me like that and we're both going under." "Lawdy, mister, don' let me drown! Don' let me drown!" It became like a mantra to her. Hugh ignored her words and swam on to the west. I hope Susie got clear okay. Another blast sent more debris flying. There was an awful moaning from the boat. It sounded like a giant wounded animal in a great deal of pain. The boat toppled on its port side. Waves splashed over Hugh. The girl in his arm screamed. Something heavy rushed past his leg, and then he made the surface again. A bright light from downriver passed over him. His heart jumped. Shamus and Cotton are coming! The wreckage of the boat lurched as another explosion shook it. Waves washed over them again. Kicking to stay afloat, Hugh lifted his arms out of the water. "Over here! Cotton! Shamus! Over here!" The lights turned toward him. His heart slowed its frantic beating, and for a moment he just focused on staying afloat with the girl in his arm as the sound of Shamus's boiler grew louder. The fire from the Belle made Cotton's hair look almost red when he leaned over the bow of the boat. "Hugh!" The relief in his voice brought a smile to Hugh. "Cotton! Thank God. Here, help me get her out of the water." He grabbed hold of the edge of the boat with his free hand and lifted the girl up toward Cotton with his other arm. Cotton hoisted the girl out of the water and onto the boat. She clung to him like she'd tried to do to Hugh. "Oh, thank Gawd, thank Gawd. You're my angel." Hugh started out of the water, but a hand grabbed his belt and pulled him back in. "No, you don't!" # 28 COTTON TRIED to untangle himself from the girl's arms, but she held tight. "Ma'am, please let go. I need to help Hugh." Something had yanked Hugh out of sight. Cotton's heart raced. He thrust the girl away from him so hard, she nearly fell back in the river. She caught herself on the cannon. Cotton stared over the edge of the bow and saw the hulking form of Big Al Shank trying to push Hugh down in the water. "No! Hugh!" Cotton turned and grabbed his gator-hunting spear from where it lay near the cannon. Big Al bent over slightly, and Cotton hoped Hugh had managed to get in a good blow. He pulled back his arm and threw the spear at Big Al's meaty back. Big Al jerked upright as the spear went in; then he fell forward into the water. Cotton dropped into the water. "Hugh!" He dove down. The lights from the boat and the fire from the Belle made it easier to see than it had been the first time he'd pulled Hugh from the river. Hugh's form floated just a couple of feet below where Al slowly sank. Cotton grabbed his arm and pulled him to the surface. As their heads broke the water, Hugh coughed. Cotton hugged him. "Hugh, you're all right." Hugh nodded. "Now that you've saved me again." Cotton swam the short distance to the boat. "The river gave you back to me. I was afraid she wouldn't give you back a second time." "We're going to be fine." Hugh's hand held on to the boat next to Cotton's. "Let's get out of this water and find the other survivors. I lost track of Susie. She was still on the Belle when the explosions started." Easily pulling himself out of the water, Cotton knelt on the deck and helped Hugh out. He hugged Hugh again. "You're safe." "Okay, we got more people to get out!" Shamus shouted. "Hugh, tell me where to start." "Susie!" Hugh shouted at the top of his voice. "Susie, where are you?" From the west came a small female voice. "Over here, Hugh!" Cotton turned one of the lanterns toward the voice. A woman waved at them. "I'll get you." Hugh laid a hand on Cotton's shoulder. "I can get her." With a small shake of his head, Cotton dove back into the river. When he surfaced, he glanced back at Hugh. "You look for others. I can do the swimming, since you did the fighting." Then he swam as hard as he could toward the woman. She smiled at him as he drew near. "I can swim to the boat, if you like." "Let me help you. Hugh's worried about you." "You must be Cotton." Confused by her statement, he nodded as he treaded water. "Hi, Cotton, I'm Sue. Let's get to the boat. Do you want me to hang on to your neck?" Cotton nodded. "Sure. Just don't choke me. It ain't no fun getting choked when you're trying to save nobody." She wrapped her arms around his neck, but most of the pressure was on his chest. "How's that?" "Good. Now hold on. We need to get out o' here before the gators show up." He started swimming as fast as he could. Her weight, light as it was, slowed him down a bit, and he was out of breath by the time he reached the boat and Hugh lifted her free. As Cotton climbed out of the river, Hugh let Susie out of the embrace he folded her into. Cotton realized she had lost part of her clothes. "Miss Susie, what happened? You're just in your underclothes." She ran a hand through her wet brown hair. "I took them off after Hugh pushed me in the water. It's easier to swim without them. But even then, I was in the river a bit longer than I like." Hugh turned her toward the boiler. "Go stand over there—it's a lot warmer. We've got more people to get out of the water." They turned the lights back toward the rolled bulk of the Bayou Belle. Chunks of wood floated all over the river. Some of them had people clinging to them and some didn't. Then more lights appeared from the bow of the Belle. Small boats and rafts floated toward them, each with at least two people, all searching for survivors. "Slow and easy, Shamus!" Hugh called. "A bit to starboard and we'll get the next one." Cotton stood next to Hugh as they drew closer to the wreckage where a woman clung. Together they pulled her out of the cold, dark water. After a grateful hug to both of them, she hurried back by the boiler with Susie and the girl who'd come on with Hugh. It wasn't safe for the boat to go too deep into the wreckage, so Hugh and Cotton took turns diving in and pulling folks out. There were a lot more of them than they had planned on. Every time they went after another one and came back to the boat, Cotton's happiness that Hugh was still with him grew. They worked long into the night collecting people before they declared it done and headed to the eastern shore where Miss Cassandra waited for them. # 29 HUGH DROPPED gratefully onto Cotton's bed. He was bone-tired. He should've rested after the fight he'd had with Shank, but time hadn't allowed for that. They'd had to save as many people as they could. He didn't want the blood of innocents on his hands. The night had been longer and colder than he planned for when they first came up with the scheme. But from what they had been able to tell, they'd gotten all the passengers out alive. They didn't have an exact count of crew, but a lot of them had been there on the shore when they called it done. There were even a couple of Shank's heavies. Miss Cassandra, along with Ben, had taken them aside. Hugh didn't know what had happened to them and didn't want to know. Cotton lay down next to him and immediately engulfed him in another hug. They'd been hugging all night, but it didn't matter. He was so happy to be alive and have Cotton in his arms, he wanted to hug Cotton for all he was worth too. "I love you." Cotton kissed him. It was the first kiss they'd taken time for since Hugh had come out of the river. Cotton's lips were warm and soft against his. "I love you too." Hugh clung to Cotton, and the deep feeling of safety and contentment filled him. "We made it back. I knew we would." Cotton shook his head. "When Big Al pulled you back under the water, I was terrified you were gone and the river wasn't going to give you back this time." Cotton sighed. "I killed Big Al with my gator spear. It wasn't meant for that." Hugh nodded. "I know. But Big Al Shank isn't going to be hurting people anymore on the river. And although the official story is it was all an accident Al caused himself, people are going to know what really happened and that the colored folks around here aren't going to put up with whites thinking it's still before the war. We did a good thing." A big yawn escaped Cotton. "Yes, we did. Now we need to go to sleep. I'm not sure I want to wake up again for three days, maybe a week. All the swimming done tired me out." "I agree." Hugh stroked Cotton's muscular back, enjoying the feeling of the hard smooth ridges under his fingers. We survived. It was close several times, but we survived. AFTER THE first bite of Helen's pancakes, Hugh felt better than he had since he woke up in Cotton's arms. The soft, tasty cakes all but melted in his mouth with just the right amount of butter and syrup. A satisfied moan escaped him. "Helen, these are heavenly!" he shouted toward the kitchen. "Thank you, Mr. Lafoux." She appeared in the doorway. "It's a secret family recipe." Around Miss Cassandra's table the others—Cotton, Miss Cassandra, Shamus, Rubi, Ben, and Susie—ate their breakfast with similar looks of pleasure plastered on their faces. A contented silence filled the room while everyone consumed their food. "What are the officials saying about the accident?" Hugh asked after he'd mopped up the last bit of his syrup and swallowed the final bite of his breakfast. Miss Cassandra looked at him from the head of the table. "Not as much as they could be. Since it happened outside of Memphis, Sheriff Buchannan doesn't have jurisdiction. The sheriff of the next county up doesn't really want to touch it. From what I hear tell, he's found one too many colored folk floating in the river after the Bayou Belle went past for him to really care if she sank in the waters off his county or not. There may be some fallout yet when state officials get wind of it, but unless Big Al had pull with someone who's going to really miss him, I doubt anyone's going to care. The folks who got rescued were just happy we was all out hunting and fishing on the river that night after the big storm. Most of 'em are waitin' fer the next riverboat to come along and take 'em on to Saint Louis." Hugh nodded. "Good. But I think I still want to put some distance between myself and Memphis for a while. A lot of people around here still think I'm dead. I'd like to keep it that way." "I was thinking about that too," Shamus said. "Ever since Timmy died, I've been thinking about going to Chicago. There's a great maker community up there. Lots of new ideas are always coming out of there." He paused and looked at Rubi. "I just don't know if ye want to go with me." Rubi dropped her fork as her face lit up. "You want to take me with you to Chicago?" Shamus nodded. "I want to take care of ye, Rubi. We've grown so close since Timmy died. I know we both miss him, and ye're carrying that little piece of him inside ye. He meant a lot to me, and I'd like to help ye make sure the little one knows how good a man its father was. Maybe it'll show some of his curiosity and ingenuity." She grabbed his hand. "So you really mean it?" "Yes, Rubi, I really mean it. I'd even like to marry you." He looked toward the head of the table. "Miss Cassandra, I'd like you to perform the service if you could." A warm smile spread across Miss Cassandra's face. For a moment it erased the wrinkles on her visage, making her look much younger and very beautiful. "Now that it's legal for anyone who's in love to be married, it would be my honor. We'll need to go to the courthouse to get some papers. When do you want to do it?" Shamus glanced at Rubi. "Tomorrow, if it's not too soon. I'd like the rest of you to be there too. That way you can all share in our happiness." Rubi nodded repeatedly. "Of course. That'll be so great." Miss Cassandra looked at Hugh and Cotton. "And what of the two of you? When are you planning on leaving?" Hugh shrugged. "I don't know. We're thinking of heading west. It would probably be better to get moving fairly soon so we can find a place and make it secure by winter. I hear it can get a mite bit colder out west than it does here along the Mississippi." "I've heard the same thing," Miss Cassandra agreed. She looked at Susie. "And what of you, Sue? Do you know what you're going to do?" Of all of them, Susie looked the most uncomfortable. She shook her head and stared at her half-eaten breakfast. "I don't know." She pushed away from the table and hurried from the room. Hugh squeezed Cotton's hand, then hurried after her. SUSIE SAT on a bench in the yard. Her head was bent and her shoulders shook with her sobs. Hugh sat down next to her and put an arm across her shoulder as she cried. Her tears went on for several minutes before she sniffled and wiped her nose on the dress that looked more like it belonged on Helen than Susie. Its long sleeves were not her style. "Talk to me, Sue," Hugh said softly. "What's going through your head right now?" "Everyone's got this all figured out. But I don't know what I'm going to do. I could be heartless and get Miss Cassandra to give me something to get rid of the baby. Then I could head back East, maybe even get another job on a riverboat." She shook her head. "But I can't do that. It's not who I am inside. All life is precious, even one that came from a foul and corrupt seed like Al." "And you're sure it's his?" Hugh hugged her tight. She nodded softly. "It wasn't like I planned on sleeping with Al, but he kept the other men off me as long as I slept with him whenever he asked. It wasn't so bad, after a while." "So he didn't rape you, then?" When Hugh first heard her say she was pregnant with Al's baby, that was what he had assumed, even if he couldn't imagine Susie staying around Al if that had been the case. "No." She sighed. "Hugh, haven't you ever been lonely enough you'd sleep with just about any guy who made you an offer?" It was his turn to nod. "Yeah, there's been a few questionable times. But, Sue, you could have any man you wanted." "I know, and I did. Until I signed on with the Bayou Belle. It was a good contract. Al was always nice enough to me, but none of the guys would even really look at me. That was okay at first, but you understand people have needs. When I started trying to get those filled, I realized Al had told all the crew to make sure everyone understood I was off-limits. I should've walked then, but I loved the river life. The river sings inside me like nothing else ever has, and riding the Belle was so much fun. After a while I turned to Al. I think he planned it that way. He was never mean or cruel to me. He just wasn't the best lover I've ever had. During the war he got occupied with other concerns. He would actually smuggle troops both directions. He worked for both sides." Hugh sucked in a hard breath. Double agents were the bane of the War Between the States. Due to the nature of the war, it was easy for people to pretend to be one way or the other. "I always figured Al for a staunch Confederate. He was the picture of Southern, not a good picture, but a picture." "He was that. He loved what the South stood for, but he was willing to take money from the North too. I think money was what drove him more than anything. But smuggling troops required a lot of his attention, so he didn't ask as much of me. After the war he wanted more, but he always made sure I had anything I wanted. Like the other day when he said I could charge things to his bill at the dress shop." "I just figured he'd take that out of your pay." She shook her head. "No, it was in trade.... I guess that's a polite way to put it. I've always been good about making sure I never got pregnant. But either I missed a dose of my teas, or this was one of the times it didn't work. But now it's there, I don't want to get rid of it. This baby's not going to be Al's baby. It's going to be mine." She sat a little straighter and squared her shoulders. "I'm glad Al's gone. I really am. I just don't know what I'm going to do." Hugh hugged her again. "Sue, we've known each other for years. I know once you've made up your mind, there's no turning you around. Why don't you come West with us?" "With you and Cotton?" She looked up at him. "But aren't you two...?" "A couple?" He finished for her. "Yes. But I think he'll be good with this if you are. The other day, when he found out Rubi was pregnant, he had a talk with her, and if Shamus hadn't wanted to take her with him, she wanted to come with us. He explained to her it would just be as friends, and she understood and still wanted to come. She said it was because Cotton was such a good friend to Timmy and she knew he'd be good to their child. I agreed with Cotton, although I had a few reservations. I'll need to double-check with him, but I bet he'd still be okay with that kind of arrangement." "I'll need to think about it. Where are you two thinking about going exactly?" He shrugged. "We really hadn't figured it out. There's a lot of homesteading going on west of here—Oklahoma Territory, Colorado Territory, maybe even Texas. I kinda figured we'd head west until something looked good. I hope we don't have to go as far as California." She chuckled, the first happy sound out of her in days. "I hope not. California's a long way away from here." Hugh nodded. If they had to go that far, it would be a long and dangerous journey. He didn't want to put Cotton in any more danger if they could avoid it. # 30 COTTON LOOKED at his good clothes and sighed. "I know I wore these to Timmy's funeral, but I want something nicer for a wedding. Shouldn't a wedding be nicer than a funeral?" Hugh straightened his collar and nodded. "That makes sense, but a lot of this world don't make sense. Unfortunately, we have to go with what we have sometimes. You'll look great." He picked up the white shirt and held it in front of Cotton, then smiled. "Yep, you'll look great. So handsome. Shamus better hope he looks more dapper or everyone will be looking at you." With heat rising in his face, Cotton snatched the shirt away from Hugh and pulled it on over his broad shoulders. The cloth was tight and confining as he buttoned it. "It's just an old shirt," he muttered. "I hope I don't pop a button or nuthin'." "It held up at the funeral." Hugh kissed him and sent butterflies fluttering through him. "It'll be fine. Why are you so nervous about this?" Cotton shook his head. "I don't know. It almost feels like I'm saying good-bye to the last part of Timmy. As soon as they can get packed, Shamus wants to get on the river and head to Chicago. We might never see him, Rubi, or the baby ever again. Not that we've seen the baby yet. They're all we have left of Timmy." He frowned. "I never realized I'd miss him as much as I do." Hugh wrapped his arms around Cotton and held him tight. "It's okay to feel sad. Weddings are a sign of change. Sometimes that change is hard to deal with. I think that's the real reason so many people cry at weddings. They're afraid of the unknown futures. Like anything else in life, it's a gamble." His words brought the barest hint of a smile from Cotton. "And if nothing else, ya know all about gambles, don't ya?" "Yeah." Hugh combed his hands over Cotton's hair. "Some of them turn out better than others. Now, let's get to Memphis. We've got just enough time to get there. We don't want folks holding up things just because we're not there yet." The deep love that filled him whenever Hugh was around flooded out of Cotton, and he hugged Hugh with all his might. "Thank you, Hugh." Chuckling, Hugh hugged him back. "For what?" "For cheating Big Al and making him mad enough to throw you in the river so I could find you and rescue you. And for loving me and bringin' so much happiness into my life. I love you so much." Their kiss lingered. "I love you too, Cotton. Thank you for rescuing me that night and showing me a fool like me isn't really just a throwaway card. We've done good in a short period of time." "You're not a fool, Hugh." Cotton ran his hands down the front of Hugh's soft, light blue shirt. "You're a wonderful man who just needed a bit of a challenge to rise to the occasion." With a huge grin, Hugh took his hand and headed for the door. "See, that's the kind of thing that has really endeared you to me. Thank you so much, Cotton, for just being you." COTTON STOOD in the middle of the main street of Memphis. The lingering mud of the storm mingled with the horse manure and pulled at his new boots, a gift from Hugh. Too many people had showed up for the wedding to have it in the courthouse, so with Shamus, Rubi, and Miss Cassandra standing on the boardwalk, everyone else stood in the street, effectively blocking traffic during the event. Rubi looked perfect in her white wedding dress, the same one she'd worn a couple of years before when she and Timmy had wed. Beside her Shamus looked dapper in his new gray suit, which Cotton was fairly sure he'd seen on a rack at Olsen's Mercantile the last time he'd been in there. Dressed in a simple but elegant green dress, Miss Cassandra stood between them, and when she announced they could kiss, the crowd roared. Theirs was the first mixed-race marriage in Memphis and the crowd, made up of open-minded colored folks and whites, were excited for a new beginning, especially after the sinking of the Bayou Belle and the disappearance of Big Al and most of his men. The attitude of Memphis had shifted slightly. It made Cotton feel good about what they had done, even if they had all had a personal stake of revenge in it. As the folks around them swarmed up on the boardwalk to congratulate the couple, Hugh grabbed Cotton's hand. "Cotton, I've got something to ask you." Cotton stared at Hugh for a moment. "Sure." He took a step away from the crowd. "We can tell 'em congratulations later. The crowd's making me a mite nervous." "Cotton, why don't we get married today too?" It wasn't a question Cotton had ever expected to be asked. He blinked at Hugh and his heart raced. "Can we do that?" He knew it sounded shaky as he said it. It didn't matter; he didn't know any other way to respond. "There's no laws against it." Hugh looked confused by the answer. "A lot of guys do it to make sure property transfers to business partners. I think we're a bit more than business partners." As his head spun with the implications, Cotton nodded. "Yes. It would be great to know we're always going to be there and the law has to acknowledge us." A huge smile dominated Hugh's face. "Good. Let's go get the paperwork filled out. Do you want others with us? We can just do paperwork and not much else, or we could come back out here on the boardwalk and let the whole of Memphis know." "No." Cotton shook his head. "Just us... well... maybe Miss Cassandra, Shamus, Rubi, and Sue. But no more. Let's keep it quiet." "Okay." Hugh gave him a quick kiss. "You go get them, and I'll go have the justice of the peace get the paperwork started." Cotton figured his smile was nearly as broad as Hugh's. "Okay!" With a quick squeeze of Hugh's hand, he pushed his way through the well-wishers gathered around Shamus, Rubi, and Miss Cassandra. He reached Miss Cassandra first. "Miss Cassandra, can ya come inta the judge's office with me? Hugh done asked me to marry him an' I said yes. We want you to be there." Miss Cassandra grinned at him. "Of course, Cotton, let's go." She took his arm. "We want Shamus, Rubi, and Sue with us too." He looked through the throng of people. Shamus and Rubi were still on the boardwalk. Susie stood on the edge of the walk, like she was trying to keep her shoes clear of the mud. Walking slow enough that he didn't hurry Miss Cassandra overly much, Cotton reached her before the others. "Sue, can you come with me to the judge? Hugh asked me to marry him. I said yes. He wants you there. We're doing it right now." Down the block, Hugh walked into the courthouse. Cotton's heart raced so hard, he wasn't sure he'd be able to make it to the judge's office. Susie beamed at him. "Cotton, that's great. I've never seen Hugh as happy as he's been since you've been part of the picture here. Yes, come on." Nearby, Shamus looked up from where Miss Cassandra was talking to him. He grinned at Cotton and whispered something to Rubi, who nodded vigorously. "Folks," Shamus started. For a moment Cotton worried he was about to tell everyone gathered there he and Hugh were also getting married, and his throat tightened. "Rubi and I have something to do real quick. Why don't y'all head over to the saloon, and we'll meet y'all there shortly. Don't eat the wedding cake until we git there." "Don't take too long then, Shamus!" someone in the crowd shouted back. Shamus escorted the two women down toward the judge's office while Cotton, arm in arm with Susie, walked that way too. Shamus held the door open as Miss Cassandra and Rubi entered. Cotton waited for the women to go in first. "This is a great day for all of us." Shamus thumped Cotton on the back. "We all get our happy endings." All Cotton could think to do was nod. "Yeah." His heart throbbed and for a moment he felt faint. Then over the heads of the others, he spotted Hugh standing at the desk, talking with Judge McAllen. At the sight of Hugh, his head spun even more. He put a hand on the door frame to stabilize himself. Is this really going to happen? Are Hugh and I going to be legally bound forever? How did I get so lucky? Hugh looked up and grinned at him. "Cotton, come on over here. The judge wants to ask you a few questions." Their friends opened the way to let him through. It was all he could do to make his feet walk the short distance. A feeling of disconnectedness filled him. The judge looked at him over the top rim of his thick spectacles. "Cotton Freeman, Mr. Lafoux here tells me the two of you wish to be married. Is that how you feel?" Cotton nodded. "Yes, sir, Judge McAllen." "Now, you do realize as two men, this is basically partnership paperwork, so that should you own property, it will pass to each other. This isn't very common in the state of Tennessee, but it has been done. So, to the best of your knowledge, have you ever been married before? There isn't a Mrs. Freeman out there somewhere who will object to this union?" "No, sir." Cotton shook his head. "I think I'd remember being married before." The judge chuckled, as did Shamus. "Judge, I can assure you Cotton Freeman hasn't been married before." Miss Cassandra moved to stand alongside Cotton. Her presence, along with Hugh's, helped stabilize him. "Thank you, Miss Cassandra. Your word is good enough for me." Judge McAllen turned and pulled out a couple of pieces of paper. "What, aren't you going to ask Hugh the same question?" Rubi asked. "I already have." The judge ordered the papers in a neat pile on his desk. "What I haven't asked either one of them is if they want me to officiate the ceremony or Miss Cassandra. Either would be legal." Cotton stared at Hugh, then glanced at Miss Cassandra. "Miss Cassandra, do you mind doing another wedding today? I'd like you to do it, if you have it in you." She hugged him tightly. "Of course I have it in me, dear boy. I'd be honored to perform the wedding." Hugh grinned at her. "Good. So, Judge, let's get the paperwork done. We don't want to keep Shamus and Rubi from their guests at the saloon." Pulling out a long feather quill, the judge chuckled. "Of course not." He dipped the quill in the inkwell on his desk and made several notations on each of the papers, which from what Cotton could tell were all identical. "Now, have the two of you decided on the surname you're going to use?" The judge paused with his quill poised above the paper. "You can choose either of your existing surnames, or pick a new one." Hugh sighed. "We hadn't given it any thought. Freeman doesn't mean much to me. I've always, up until now, been a freeman." He looked at Cotton. "Lafoux feels like a name from a different life for me." His gaze traveled to Miss Cassandra. "Your cards said there would be a disaster or a major change. Getting married is a major change. With a different last name, we'd both be new people." He shrugged. "So, Cotton, who do you want to be?" Cotton grabbed hold of Hugh's hand. "As long as I'm with you, Hugh, I don't rightly care who I am." "If it's okay with you, I'd like to still sound Cajun," Hugh said after a thoughtful pause. "What about Deneaux?" Susie asked. "Do you remember them? We went to school with the kids. The whole family was wiped out in the big storm that hit New Orleans a few years before the war started. They were always a nice family. I liked them. I always wanted to be part of their family." Hugh nodded. "I liked them too. They didn't believe in slaves, and they didn't mind not fitting in with the rest of New Orleans society. They were good people." He held Cotton's hand and stared into his eyes. "What do you say Cotton? Can we be the Deneauxs?" Cotton ran the name over in his head. It sounds nice. Definitely has a Cajun ring to it. But it doesn't sound pompous like some of the plantation families. "I like it." After making some other notes on the papers, the judge passed the first paper, along with the quill, to Hugh. "Mr. Lafoux, if you could sign, please." "Okay." Hugh signed the papers, all in the same spot. When he handed the papers and the quill to Cotton, Cotton stared at them for a moment. He tried to remember the way he'd been told to write his name by his mother. It had been one of the few things she'd shown him in an attempt to make him fit more into the whites' world. With a shaking hand, he scrawled C O T T O N F R E E M A N. After taking four dips in the inkwell, it all ran together a bit, but when he compared it to Hugh's signature, it actually looked clearer. By the third time he signed, he wasn't shaking as much. The judge looked at the signatures as the papers were passed back over the desk to him. He nodded. "Very good. Now, if we can get the signatures of the witnesses. We only need two, but I'll need Miss Cassandra's signature as the one who actually married the two of you." Shamus and Susie stepped up to the desk. Shamus gave Hugh and Cotton a quick nod. "I'll be honored to be a witness to these two fine gentlemen getting married. It's a fine institution, and I think everyone should have the honor of being so blessed." He signed the papers where the judge indicated. "Sure." Susie smiled at Hugh. "Hugh's been my best friend for many years, and Cotton makes him so happy. How can I not witness their wedding?" Her signature was a lot more flowing and pretty than any of the others. The judge looked at Miss Cassandra. "I believe this is your show now, Miss Cassandra." She stepped over in front of the judge's desk and turned to face Cotton and Hugh. "Cotton, Hugh, give me your hands." Cotton pushed back the butterflies that threatened to bend him over in fear as he held out his right hand to her. It made him feel a little better that Hugh's hand shook slightly too. He's as nervous as I am. Miss Cassandra's grasp was wrinkled and warm under his fingers. "It's funny, sometimes, how the river gives us just what we need and takes away that which we don't need. She has blessed the two of you with her grace. There have been several times in the past month when you could've both disappeared into the warm darkness, but you didn't. You stand here strong and proud together. That togetherness is what will see you through the rest of your lives and inspire the future generation." She paused and looked at Cotton, then Hugh. "Is there anything either of you would like to say to the other?" Hugh cleared his throat. "Cotton, we've been told men don't return from the river's grasp as the same men who went in. I can attest to this. I don't know if it was the river or you that transformed me into the man I am now. I know your care and love helped shape me more over this past month than anything has in a very long time. I love you for that, and I'm so thankful you want to spend the rest of your life with me." What do I say? I can't talk as pretty as Hugh or Miss Cassandra. Cotton cleared his throat. "Hugh. I'll always be thankful for the river givin' you ta me. Ya've touched my life and made me see and feel things I never thought I would be able to. I can't make no speech. All I ken say is, I love you, and I always will." He smiled at Hugh. "And that's all you need to say." Miss Cassandra squeezed their hands, then joined them. She held their hands in hers. "We stand here today, near the river that brought them together, and by the light of the Almighty. It is my pleasure to join Hugh and Cotton together, until the last breath has been drawn through their lungs. I now pronounce you married!" Susie and Rubi cheered as Hugh and Cotton kissed. Cotton felt more complete than he ever had before. "I love you, Hugh." "I love you too, Cotton. Now and forever." # 31 THE DRY wind was vastly different from anything Hugh had known in the past. After several weeks on the Arkansas River, heading west in the boat Shamus gave them—a second prototype he and Timmy had been working on and he'd managed to salvage from the ashes of the blacksmith shop—they had the Centennial Divide in their sights. Thanks to the work of the dredgers, there weren't very many shallow spots, and the trip had flowed along smoothly. The river had taken a sharp turn to the north, and was getting harder and harder to navigate even with the steam boiler powering their movements. "So what about here?" Hugh asked, looking up into the sky that blazed a brilliant red and orange after the sun had disappeared beyond the mountains to the west. "Here?" Cotton looked around and smiled. They stood on the banks of the river. A large valley ran between two mountains as far as they could see to the north and the south. They'd passed through a small town on the banks of the river a few hours before they'd given up and come ashore. Tall buffalo grass waved at them in the soft fall breeze. Nearby, trees with bright yellow, orange, and red leaves quaked. "I like it." Sue looked up from the fire. The delicious aromas of dinner wafted around her. "That little town, what was its name, Salida? It seemed nice. A little rough, but it's a frontier town and that's to be expected. It's nicer up here than it was down around Pueblo. That was a little too desolate, even with the river running through it." In the distance an elk bugled. Moments later a wolf howled in the twilight. Cotton nodded. "There's hunting here. That's good. I like staying close to the river. This one's a bit wilder than the Mississippi was, but I could get used to it." Hugh nodded. They echoed his own thoughts about the place. It was different from anything he'd ever known, but then being married to Cotton and having Sue getting ready to have her baby was different too. He wasn't the same man who'd lost his leg in the War. He had rapidly become a new and different man, and it felt good. "I guess tomorrow we can do a bit of exploring, or should we go down into Salida and find the surveyor's office and get a homestead claimed? I haven't seen a fence in a few days." "I hope some cattle rancher hasn't claimed this land," Cotton said. There was a gentle pleading in his voice. "I like it. I think it could be home." Walking up to Cotton, Hugh hugged him. "Anywhere you are is going to be home. Being together is the important part of things." "Together," he glanced at Sue, "as a family." "As a family," Hugh agreed. "I CAN get someone out there to get your land claim on file," the surveyor in Salida said the next day. "We've not had many people claim land out that way yet. The river's too untamed for most folk, and there ain't been gold found between here and Buena Vista. You know winter's coming, and it's going to get cold." The little man talked almost faster than the words could come out of his mouth. Hugh nodded. "Thank you. We really appreciate getting this on file. I think one of the great things about homesteading the territories is how easy it is." The clerk stopped his buzzing about the office and frowned at Hugh. "You do realize you have to make improvements to the property and maintain things for five years or the land reverts to federal hands, don't you?" "Yes." Hugh kept his tone cheerful. "You'll be surprised how quickly we've got things up and working out there. We're in this for the long haul." With a heavy sigh, the clerk went back to getting his paperwork out. "Good. Now you say you're along the river. There is a fairly substantial flood plain there. You'll want to make sure any buildings you put in are well away from that. We have people float down the river every year when the thaw waters reach the house and sweep them past Pueblo." Hugh nodded. "We're from Memphis and New Orleans, so we understand about flood plains and how to keep a house and barn around during a flood. We'll be fine." "Okay. I think I know the area you're talking about." The man made a few notations. "I've got a couple of things to take care of this afternoon, so tomorrow either me or the other surveyor, Fred, will be out your way. You mentioned you have a boat, so we'll look for it. Will it be on the north or south bank?" "South bank." On that section of the river, Hugh had a hard time finding a spot where he could land the boat on the north bank, but the land along the south bank had looked more appealing. Plus from what he could tell, there weren't any streams or rivers that would have to be crossed if they settled on the south bank and wished to reach town. The clerk nodded. "That's some good land over that way. Luckily there haven't been many settlers come through that wanted to fight the river much past town. I doubt it stays that way. And how many adults do you have in your party," the man glanced at Hugh's paperwork, "Mr. Denox?" "It's De-no," Hugh pronounced the name correctly for the man. It still felt a little strange referring to himself by a different name, but it felt good too. It was Cotton's name. Just to confuse people and offer them a little protection, Sue had changed her surname to it as well. They'd figured that would give her child a form of legitimacy and make it easier for anything they all built to be safe. "Sorry, Mr. Deneaux," the clerk replied nervously. "I know it's not something that's seen often, but I'm sure folks around here will get used to it." He smiled at the man. "There are three of us." "Very good. You're each entitled to a full 160 acres of land. That would be 480 acres total. If you decide you want land on both sides of the river, we can work that out when we survey and file your land claim." Hugh nodded, then finished his meeting with the man. As he left the surveyor's office, he caught himself humming. It was a song Cotton spent a lot of time humming. The thought of Cotton broadened his smile as he went about getting the items on the list Cotton and Sue had sent with him. They'd used a lot of their supplies on the trip upriver. Now that they'd found a place they wanted to settle, it was time to replenish some supplies and order a few things delivered to the campsite so they could get started on building their home. EVEN AS a chilly wind blew across him, sweat dripped down Hugh's back. He rolled another log over to the nearly completed wall. Above him Cotton worked with a system of pulleys and chains to get the logs lifted so that a long jointed arm could grip them and hold them in place while a couple of the neighbors from down the river helped knock them into place. Hugh had thanked the men every day that they showed up to help. Without them, there was a bit of doubt that they'd be done with the house before winter set in. As he rolled another log over, Sue rode up in the buggy Cotton had crafted from some of the spare parts they'd found at an abandoned homestead their property encompassed part of. Cotton claimed it was the most complex thing he'd ever built, and if it hadn't been for working with Shamus, on the boats, he never would've been able to make it. It looked a lot like a regular buggy—what it had been built from—but without the horse. He promised, once they got the house finished, he'd see about getting some kind of cover on it, but right then it was open-air, though that at least allowed the smoke from the fire to escape. The miniature boiler that powered it produced a fair amount of smoke and heat as it bounced the buggy across the rough ground. But it made getting to town easier than taking the boat. There just wasn't much dock space there. She held up a couple of envelopes. "We've got mail!" she called as she brought the buggy to a stop, with a huge puff of steam as she turned it off. There was a strained look as she stepped out of it, easing herself down the two rungs beside the wheels. Hugh knew that since she had less than two months before the baby was due, she had growing difficulty getting around, but she refused to let either him or Cotton help much. "What are they?" Hugh asked, wiping the sweat from his brow with his flannel shirt sleeve. "Rubi and Shamus, and one from Miss Cassandra." She paused and straightened her skirt before starting toward him. "Rubi and Shamus?" Cotton grabbed hold of the chain and swung down off the nearly finished wall. He glanced at the neighbors helping them. "You guys take five. I'd like to get this wall finished this afternoon." "If you want to have this house livable by the time the snows really start flying around here, we've got to stay busy," Bill Boni, their closest neighbor, said as he scrambled down to the ground. "That dusting we had this morning ain't nothing like what's going to be here in a few weeks." "Just a short pause," Hugh said. "Like to know how the folks back home are doing." Sue motioned them to the chairs around the fire circle just south of the house. "Rubi's letter was fairly short. She says that they are settling in easily. Shamus set up a shop and has found a couple of folks to work with him. He's already making more of the boiler boats. Sounds like he's in big demand." A happy smile spread across Cotton's sweat-streaked face. "Good. Has she had the baby yet?" Sue nodded. "She did. A boy. They named him Timmy Cotton Hugh Culpepper." "Why did they name him after me?" Cotton glanced between Hugh and Sue. "Mine's not a good name." "Why not?" Hugh asked. "I think it's a good name." "It's a slave name. Little Timmy ain't going to be no slave. He was born a freeman and I hope he always will be." "I'm sure he always will be." Sue pulled out one of the letters and unfolded it. "I think Cotton is a great name. If he knew you, I'm sure he'd feel the same way when he grows up." The look on Cotton's face said he didn't exactly agree. "I hope they make sure he knows his father was a great man too." "They will." Sue looked at the letter in her hands. "The letter from Miss Cassandra is a bit longer. It seems that our actions with the Belle have had the desired effects. Since we left, there haven't been any incidents of local whites hurting any of the colored folk. Ben is now deputy." "That's big," Hugh muttered, not wanting to really interrupt her, but feeling the need to express himself. "It is," Sue continued. "I can't say as I've ever heard of a colored man as deputy anywhere. Ben's a good man and he'll do a good job. Miss Cassandra is hoping it will help make the coloreds and whites get along better." "I'm sure it will." Cotton got a faraway look. "I jest hope someone like Big Al Shank never comes to town and tries to make a point of killin' him." "Even if someone did," Hugh set a reassuring hand on Cotton's broad shoulder. "Even if someone did, he wouldn't get away with it. Not in Memphis. Not after the Belle went down. They would be too worried about reprisals. I wish Miss Cassandra and crew would be able to hold onto things because everyone loves her, but sometimes, a bit of fear makes things easier." "I wish that weren't so too." Cotton sighed. "Hey, so if you two are just going to spend the rest of the afternoon jawing, we can head back to our own places," Bill called out. "We've got some winter preparations to make of our own." Hugh paused. A year earlier and he would've never dreamed of building his own house. He'd wanted to come west, but always figured it would just be a little dugout, unless he managed to end up finding himself someone who already had a house. The work was hard, some of the hardest he'd ever done in his life, but with Cotton at his side, it felt good. They were working toward the rest of their lives that would be spent with Sue and her baby. "We're coming." He glanced at Cotton. "Come on, let's get these walls done so we can get the roof on. I'd rather not still be in the tents when a real snow shows up." Cotton grinned at him. "Me too." It was a look that caused Hugh's heart to beat faster and made him very happy. THE COLD wind howled as Hugh bowed his head against the snow-laden gust. He carried an armload of split wood and followed in Cotton's tracks. Ahead of them smoke billowed out of the stone chimney that marked the central hearth of their cabin. They both stopped and kicked snow off their boots as they stepped under the eaves of the porch before Cotton opened the door. Several lamps lit the cabin's interior. In the hearth, a fire roared. Cotton added the wood he carried to their diminishing supply near the hearth. Sue slumped in the chair near the fire. "Sorry, dinner's going to be late. I think the baby's coming." Hugh dropped his wood on the pile and straightened with a start. "What? You were fine when we went out a couple hours ago." She chuckled weakly. "Really, Hugh, you don't know anything about women, do you?" "Not really." Hugh hurried to her side, but Cotton beat him across the room. "Whatta ya need?" Cotton asked. "I ken get ya some hot towels. My momma was always getting the birthin' woman hot towels. Will that help?" "Maybe." She reached up for Hugh. "Help me get to my bed." Hugh reached into the chair and helped her to her feet. "Will you be warm enough there? Maybe we can move your bed near the fire." They'd decided to build the cabin with separate bedrooms like a Southern-style house as opposed to a rustic cabin, but just used blankets to allow privacy. There weren't fireplaces in the bedrooms. She shook her head. "No, don't worry about that right now. Although if Cotton could move the crib by the fire for a little while to warm it so the little one doesn't have to sleep in cold blankets? That would be nice." She grabbed her swollen stomach and shook. "We're really close." The paleness of her skin worried Hugh. "I can carry you." He made to pick her up. "No." She pushed his arm away. "We don't know if that will hurt the baby. Cotton, get the water going and make sure to boil a knife to cut the cord with." "Yes, Sue." Cotton hurried to do as he'd been told. Hugh pushed the blanket back so Sue could get into her room. Her bed was already changed to the bedding he knew she'd planned to use when the baby came. She'd already lit the lights in there too. "When did you first start having pains?" He helped her lie down. "Right after the two of you headed out to split wood. My water broke about an hour ago." "It looks like you cleaned it up yourself." Hugh hadn't seen any signs of the fluid on any of the floors. "You were busy, so I had to. Don't want the wolves or bears smelling it and trying to get in. We've got enough to deal with right now." Another spasm wracked her body. She clenched her fists and teeth, then let out a long, deep, ragged breath. "It's really close." She raised her legs and pulled her dress up. "See if you can see its head." "Sue, you know I don't know what things down there look like." Hugh walked slowly to the foot of the bed. His heart pounded and a film of sweat started on his face despite the coolness in the room. He looked. A small ball of brown hair looked like it was trying to push its way out of Sue. "Okay, I think that's a head. At least, it doesn't look like anything that should be down there." Cotton appeared in the doorway. He'd taken off the heavy coat he'd been wearing outside. "Water's on to boil. What...?" He paused and stared at her. "Oh Lordy, Sue, I think it's coming." Hugh turned toward Cotton. "You've done this before?" "No." Cotton shook his head. "Like I said earlier, my mamma helped the birthin' woman on the plantation. I seen it a time or two." He started to turn back to the hearth. "Cotton, I've never done or seen anything like this before, not even a dog or a horse. If you can be of more help here, I'll go get the water boiling." For the first time since they'd walked into the house, a wave of relief washed over Hugh. "I think I can help." Cotton moved to the bedside. "Iffen it's okay with Sue." She shuddered again, and the tiny head pushed harder to come out. "It's okay, Cotton. Can you catch the baby?" Her voice took on a shrill tone, almost ending in a scream. He nodded. "Yes. Hugh, go get me a warm towel. They are in the pot on the hearth. Now Sue, if you're ready to push the little one out, I'll catch it." Hugh hurried out of the room and ran for the hearth. He paused for a second and pulled off his coat to drape it over the chair Sue had been sitting in a few minutes before. As he grabbed the hot towel out of the pot, a scream reverberated through the cabin, followed by a loud cry. "Hugh, bring the knife too!" Cotton shouted. He glanced into the pot and spotted the knife there. It was the sharpest knife they had. After the cold outside, the water was almost too hot. Hugh dropped the knife onto the towel and headed back to the bedroom. Cotton held the bloody form of a tiny boy. He gently placed the baby onto Sue's stomach. He smiled at her. "It's a boy." She smiled back at him. "And what am I going to do with three men in this cabin?" Hugh handed Cotton the knife, then started to clean the baby off with the towel. After getting a good breath, the baby cried louder when Cotton cut the umbilical cord. Cotton quickly tied the remainder of the cord into a tight knot. "Hugh, let Sue hold him as soon as she pushes, one more time." "One more time?" Hugh looked at Cotton in confusion. "She's not having twins, is she?" "No," Cotton and Sue said in unison. Sue gripped the blankets and her stomach heaved one last time. A bloody mass came out. Cotton pulled the birthing blanket up around it, then pulled the blanket out from under Sue. He quickly slid another blanket under her. "Hand her the baby and come with me." "Here he is." Hugh handed the little baby, now with a lot less blood and body fluids on it to Sue. "He looks like you." He smiled. "I think that's better than looking like Shank." She stared at the baby for a moment. "I think you're right." Then she pulled her dress down and lowered the baby to her breast. He quieted as he began to suckle. "Hugh, come give me a hand!" Cotton called. "Be right back." Hugh smiled at her. A feeling of warmth and happiness spread through him. He'd been happy a lot since Cotton pulled him out of the river. Somehow the little boy's birth helped that grow into something so much more. He'd never wanted children before, but now that he had the stability Cotton offered and with the happiness their little family filled him with, Hugh was ready to raise the boy as his own and pass on their legacy to him. Cotton had his coat back on and the birthing blanket in his hands. "Come on, Hugh, we need to get rid of this." As he pulled on his coat, Hugh raised an eyebrow. "Why both of us?" "We're giving it to the river. We owe the river a lot, so we're giving her this piece of life, a life that's going to mean a lot ta both of us." "But the spring thaw hasn't hit yet," Hugh objected. "The ice out there is fairly thick." "Yes." Cotton nodded. "That's why we're both going. Plus you need to tell the river thank you for everything she's given you." HUGH WAS half-frozen by the time he and Cotton had chipped a hole in the ice they could get the afterbirth into. He shivered as he dropped the pickaxe onto the ice. "Good." Cotton handed the afterbirth to Hugh. "Now, drop the blood of our son into the river." "Our son?" Hugh stared at Cotton. "Yes, our son. He might not be our blood, but we will raise the little one as if he was. He'll know the love of two fathers. What more could any boy ask? We have the river to thank for this. She gave you to me, and this little boy was conceived while Sue was floating on the river. It all comes back to the river." "And you do realize this is a different river?" Hugh began to unroll the blanket. Cotton nodded. "But the Arkansas runs into the Mississippi. She'll know what we do here tonight and will give her blessings to our son." The bloody pieces rolled out of the blanket and into the hole. They splashed slightly as they hit the water. Hugh knelt at the hole until they were all in there, then he straightened and looked at Cotton. The light of the full moon made the entire area nearly noon-bright as it reflected off the accumulated snow. There was a beautiful light shining in Cotton's eyes Hugh had never seen before. He thought he had learned all about his lover in the months they'd been together, but this new, almost mystical light was different. A slow, heavy sigh came out of Cotton. "It is done. The river is never going to take anything from us. She gave you to me, and now we've given her something back in return." He caught Hugh up in a fierce hug. "I love you so much." "I love you too." Hugh kissed Cotton. The wind around them stilled and a silence filled the night as their kiss lingered. The happiness he'd felt handing the baby to Susie intensified. My life is complete in ways I never realized it could be. I really am more than just a throwaway card. Their lips parted and the cold slammed against Hugh. "Come on. You might keep me warm, but I think we need the fire." Cotton laughed and looped his arm into Hugh's. "You're right. Let's get inside to make sure Sue's all right and figure out what she wants to name the baby." "We are going to make great dads, aren't we?" Hugh fell into step with Cotton. "Yes." Cotton nodded. "As long as we have each other and share our love with Sue and our boy, we're going to make great dads. Together, we can raise this boy up right. All he will ever know is our love." A.J. MARCUS has been writing to pass the time since high school. The stories he wrote helped him deal with life. A few years ago, he started sharing those stories with friends who enjoyed them, and he has started sending his works out into the world to share with other people. He lives in the mountains with his extremely supportive husband. They have a lot of critters, including dogs, cats, birds, horses, and rabbits. When not writing, A.J. spends a lot of time hiking, trail riding or just driving in the mountains. Nature provides a lot of inspiration for his work, and keeps him writing. He is also an avid photographer and falconer; don't get him started talking about his birds because he won't stop for a while. Website: http://www.ajmarcus.com E-mail: andy@ajmarcus.com Twitter: @aj_marcus Facebook: https://www.facebook.com/authorajmarcus Embracing Change By A.J. Marcus Every day Sam Benito watches his marriage fall apart. He and his husband, Charlie, a New York Times bestselling author, fight constantly, catching their teenage son, Iggy, in the middle. If there's any love left, it's hard to find. Charlie, bent on self-destruction, crosses an unspoken line, and Sam realizes it's time to leave as the man he fell in love with is gone forever. After leaving his high-powered corporate job years ago, Sam now works at a small feed store in an effort to keep his family together. It's a job he never thought he would find pleasant, but working with Geary Ellis may have something to do with his job satisfaction. Charlie digs himself deeper, and Sam is helpless to do anything. Torn between his budding love for Geary and his years with Charlie, Sam finds comfort in Geary's arms, but it may not be enough to hold him together as Charlie falls apart. http://www.dreamspinnerpress.com The Archer's Arrow A Ren Faire Romance By A.J. Marcus Former Olympic archer Robin Lockwood quit competing and now runs an archery booth at the Ren Faire. He enjoys his unencumbered life with few attachments but lots of casual friends. Traveling across the country from fair to fair adds spice to his life. John Aquitaine found acting in college and started a comedy show with his good friend, Pete. They are the "Perfect Princes," and it helps John escape real life. The gypsy lifestyle lets him keep people at arm's length until an arrow nearly hits him and he meets the handsome Robin Lockwood. The flame between them sparks quickly, but the relationship is slowed when John's dark past catches up with him. John's Uncle Fred, the source of his horrible memories, appears at one of the Perfect Princes' performances, and it upsets John so much he needs Robin to rescue him. Their love is tested again as Uncle Fred plans to finish what he started when John was a child. http://www.dreamspinnerpress.com The Falconer's Lure A Ren Faire Romance By A.J. Marcus Watching birds of prey soar gives Garret Nicholson a sense of peace. It's exactly what he needs after his recent break-up. His ex never understood Garret's work with the raptors, but the birds have been part of his life for years. Garret spends his time between The Sky's the Limit Raptor Rehab Center and his dad's falconry show at the Hawkwood Fantasy Faire, trying to prove to himself and his father he has what it takes to be a great falconer. Trevor DePalma is in awe, but he isn't sure whether the man or the falcons fascinate him more. Watching the birds perform at the Faire gives Trevor the first taste of joy he's had since his father threw him out two years ago. Bonding with Garret over their mutual love of birds, Trevor eagerly learns all he can, and Garret proves a willing teacher. But as feelings grow, Trevor worries how Garret will react when he learns Trevor is homeless. Life on the street is growing more dangerous for Trevor and his friends. Garret offers him safe space to find his feet. As the world crashes around them, Garret and Trevor will need each other's support in ways they've never imagined. http://www.dreamspinnerpress.com The Jouster's Lance A Ren Faire Romance By A.J. Marcus Dale O'Toole, aka Diederik, the Demon Duke of Denmark, takes his Renaissance festivals seriously. He has been on the jousting circuit for five years and enjoys his gypsy lifestyle, traveling to faires around the country. It's fun and he has good friends. Austin Renfro has worked in a pirate gift shop at the Colorado Renaissance Festival for several years but has a life outside the medieval fantasy world. When Austin spies Dale during the first joust of the season, he knows he must find a way to meet him, even if the jousters and royal cast don't normally associate with the working class. Their first chance meeting causes more than a little embarrassment for both men, but they don't let that stop them. They try to let their budding love find its place while keeping it from becoming common knowledge. But when a particularly conservative knight catches them in flagrante, it's bound to cause problems. After all, jousts are dangerous.... http://www.dreamspinnerpress.com The Satyr's Song A Ren Faire Romance By A.J. Marcus With nothing to lose after getting booted from the Dallas Symphony, concert flutist Adrian Mylonas follows a friend's recommendation to take work as a satyr at Scarborough Renaissance Festival. While playing his pipes, Adrian spots a man unloading elephants. Ed Costa has lived his whole life running elephant rides at various festivals around Texas. He inherited the job from his father, and is teaching the family trade to his five-year-old son Eddy, who is the center of Ed's life. He likes the life he leads, but he begins wondering if he's missing out because he doesn't have someone special to share it with. The songs of the elephants and the colorful life of the faire capture Adrian's imagination, and as he gets to know Ed, the rugged man sets his heart free. He begins to think he could leave his careful and sophisticated life behind for new music, new habits, and new love. http://www.dreamspinnerpress.com http://www.dreamspinnerpress.com http://www.dreamspinnerpress.com http://www.dreamspinnerpress.com http://www.dreamspinnerpress.com http://www.dreamspinnerpress.com	{ "redpajama_set_name": "RedPajamaBook" }	2,168
{"url":"https:\/\/apboardsolutions.com\/ap-inter-2nd-year-physics-important-questions-chapter-7\/","text":"# AP Inter 2nd Year Physics Important Questions Chapter 7 Moving Charges and Magnetism\n\nStudents get through\u00a0AP Inter 2nd Year Physics Important Questions 7th Lesson Moving Charges and Magnetism which are most likely to be asked in the exam.\n\n## AP Inter 2nd Year Physics Important Questions 7th Lesson Moving Charges and Magnetism\n\nQuestion 1.\nWhat is the importance of Oersted\u2019s experiment ? [T.S. Mar. 17]\nImportance of Oersted\u2019s experiment is every current carrying conductor produces a magnetic field around it and which is perpendicular to current carrying conductor.\n\nQuestion 2.\nState Ampere\u2019s law and Biot-Savart\u2019s law.\nAmpere\u2019s law : The line integral of the intensity of magnetic induction around a closed path is equal to g0 times the total current enclosed in it.\n\u2234 $$\\oint \\overrightarrow{\\mathrm{B}} \\cdot \\overrightarrow{\\mathrm{d}} l$$ = \u03bc0 i.\nBiot \u2013 Savart\u2019s laws : Biot \u2013 Savart\u2019s law states that the intensity of magnetic induction (dB) due to a small element is directly proportional to the\ni) current (i)\nii) length of the element (dZ)\niii) sine angle between radius vector (r) and dl and inversely proportional to the square of the point from current element.\n\u2234dB \u221d $$\\frac{\\mathrm{i} \\mathrm{dl} \\sin \\theta}{\\mathrm{r}^2}$$\ndB = $$\\frac{\\mu_0}{4 \\pi} \\cdot \\frac{\\mathrm{i} \\mathrm{d} l \\sin \\theta}{\\mathrm{r}^2}$$\n\nQuestion 3.\nWrite the expression for the magnetic induction at any point on the axis of a circular current-carrying coil. Hence, obtain an expression for the magnetic induction at the centre of the circular coil.\n\n1. Intensity of magnetic induction field on the axis of the circular coil B = $$\\frac{\\mu_0 \\mathrm{ni} \\mathrm{r}^2}{2\\left(\\mathrm{r}^2+\\mathrm{x}^2\\right)^{3 \/ 2}}$$\n2. At the centre of the coil B = $$\\frac{\\mu_0 \\mathrm{ni}}{2 \\mathrm{r}}$$\n\nQuestion 4.\nA circular coil of radius T having N turns carries a current \u201ci\u201d. What is its magnetic moment ?\nMagnetic moment (M) = N i A\nM = N i (\u03c0r2) (\u2235 A = \u03c0r2)\n\u2234 M = \u03c0 N i r2\n\nQuestion 5.\nWhat is the force on a conductor of length L carrying a current \u201ci\u201d placed in a magnetic field of induction B ? When does it become maximum ?\n\n1. Force on a conductor (F) = B i L sin\u03b8\n2. If \u03b8 = 90\u00b0,FMax = BiL\ni.e., the direction of current and magnetic field are perpendicular to,each other, then force is maximum.\n\nQuestion 6.\nWhat is the force on a charged particle of charge \u201cq\u201d moving with a velocity \u201cv\u201d in a uniform magnetic field of induction B ? When does it become maximum ?\n\n1. Force on a charged particle (F) = B q v sin \u03b8.\n2. If \u03b8 = 90\u00b0, FMax = B q v.\n\nQuestion 7.\nDistinguish between ammeter and voltmeter. [A.P. Mar. 17; A.P. Mar. 15]\nAmmeter\n\n1. It is used to measure current.\n2. Resistance of an ideal ammeter is zero.\n3. It is connected in series in the circuits.\n\nVoltmeter\n\n1. It is used to measure RD between two points.\n2. Resistance of ideal voltmeter is infinity.\n3. It is connected in parallel in the circuits.\n\nQuestion 8.\nWhat is the principle of a moving coil galvanometer ?\nMoving coil galvanometer is based on the fact that when a current carrying coil is placed in a uniform magnetic field, it experiences a torque.\n\u2234 current in the coil (i) \u221d deflecting angle (\u03b8).\n\nQuestion 9.\nWhat is the smallest value of current that can be measured with a moving coil galvanometer ?\nMoving coil galvanometer is sensitive galvanometer, it is used to measure very small current upto 10-9 A.\n\nQuestion 10.\nHow do you convert a moving coil galvanometer into an ammeter ?\nA small resistance is connected in parallel to the moving coil galvanometer, then it converts to ammeter.\n\nS = $$\\frac{\\mathrm{G}}{\\frac{\\mathrm{i}}{\\mathrm{i}_{\\mathrm{g}}}-1}$$\n\nQuestion 11.\nHow do you convert a moving coil galvanometer into a voltmeter ? [T.S. Mar. 16, 15, 14; A.P. Mar. 16]\nA high resistance is connected in series to the moving coil galvanometer, then it converts to voltmeter.\n\nR = $$\\frac{\\mathrm{v}}{\\mathrm{i}_g}$$ \u2013 G\n\nQuestion 12.\nWhat is the relation between the permittivity of free space e0, the permeability of free space m0 and the speed of light In vaccum?\nSpeed of light in vaccum (C) = $$\\frac{1}{\\sqrt{\\mu_0 \\varepsilon_0}}$$\nHere \u03bc0 = m0 = permeability in vaccum\n\u03b50 = permittivity in vaccum.\n\nQuestion 13.\nA current carrying circular loop lies on a smooth horizontal plane. Can a uniform magnetic Held be set up in such a manner that the loop turns about the vertical axis ?\nTorque (\u03c4) = $$\\overrightarrow{\\mathrm{M}} \\times \\overrightarrow{\\mathrm{B}}=\\mathrm{i} \\overrightarrow{\\mathrm{A}} \\times \\overrightarrow{\\mathrm{B}}$$ (M = n i A)\nwhere i is current, $$\\overrightarrow{\\mathrm{A}}$$ is area vector, $$\\overrightarrow{\\mathrm{B}}$$ is magnetic field. Area vector $$\\overrightarrow{\\mathrm{A}}$$ acts normal to the loop, so torque $$\\vec{\\tau}$$ cannot act along the vertical axis. The magnetic field is not set up to turn the loop around itself.\n\nQuestion 14.\nA current carrying circular loop is placed in a uniform external magnetic field. If the loop is free to turn, what is its orientation when it achieves stable equilibrium?\nThe plane of the loop is perpendicular to the direction of magnetic field because the torque on the loop in this orientation is zero.\n\nQuestion 15.\nA wire loop of irregular shape carrying current is placed in an external magnetic field. If the wire is flexible, what shape will the loop change to ? Why ?\nFor a given perimeter, a circle has maximum area among all geometrical shapes. So to maximise the magnetic flux through it will assume a circular shape with its plane normal to the field.\n\nQuestion 16.\nConsider a tightly wound 100 turn coil of radius 10 cm, carrying a current of 1 A. What is the magnitude of the magnetic field at the centre of the coil ?\nSolution:\nSince the coil is tightly wound we may take each circular element to have the same radius R = 10 cm = 0.1 m. The number of turns N = 100. The magnitude of the magnetic field is (From Eq.),\nB0 = $$\\frac{\\mu_0 \\mathrm{I}}{2 \\mathrm{R}} \\hat{\\mathrm{i}}$$\nB = $$\\frac{\\mu_0 \\mathrm{NI}}{2 \\mathrm{R}}=\\frac{4 \\pi \\times 10^{-7} \\times 10^2 \\times 1}{2 \\times 10^{-1}}$$ = 2\u03c0 \u00d7 10-4 = 6.28 \u00d7 10-4 T\n\nQuestion 17.\nA solenoid of length 0.5 m has a radius of 1 cm and is made up of 500 turns. It carries a current of 5 A. What is the magnitude of the magnetic field inside the solenoid ?\nSolution:\nThe number of turns per unit length is,\nn = $$\\frac{500}{0.5}$$ = 1000 turns \/ m\nThe length l = 0.5m and radius r = 0.01 m. Thus, l\/a = 50 i.e., l >> a.\nHence, we can use the long solenoid formula, namely, Eq. (B = \u03bc0nI)\nB = \u03bc0 n I\n= 4\u03c0 \u00d7 10-7 \u00d7 103 \u00d7 5 = 6.28 \u00d7 10-3 T\n\nQuestion 18.\nA circular coil of wire consisting of 100 turns, each of radius 8.0 cm carries a current of 0.40 A. What is the magnitude of the magnetic field B at the centre of the coil ?\nSolution:\nHere, n = 100, r = 8cm = 8 \u00d7 10-2 m and I = 0.40 A\nThe magnetic field B at the centre\nB = $$\\frac{\\mu_0}{4 \\pi} \\cdot \\frac{2 \\pi \\mathrm{In}}{\\mathrm{r}}=\\frac{10^{-7} \\times 2 \\times 3.14 \\times 0.4 \\times 100}{8 \\times 10^{-2}}$$ = 3.1 \u00d7 10-4 T\nThe direction of magnetic field depends on the direction of current if the direction of current is anticlockwise. According to Maxwell\u2019s right hand rule, the direction of magnetic field at the centre of coil will be perpendicular outwards to the plane of paper.\n\nQuestion 19.\nWhat is the magnitude of magnetic force per unit length on a wire carrying a current of 8A and making an angle of 30\u00b0 with the direction of a uniform magnetic field of 0.15 T ?\nSolution:\nAccording to the question\nI = 8 A, 6 = 30\u00b0, B = 0,15 T, l = 1 m\n\nThe magnitude of magnetic force\nf = I (l \u00d7 B) = I l B sin \u03b8\n= 8 \u00d7 1 \u00d7 0.15 \u00d7 sin 30\u00b0\n= $$\\frac{8 \\times 0.15}{2}$$ = 4 \u00d7 0.15 = 0.6 N\/m\n\nQuestion 1.\nState and explain Biot-Savart\u2019s law.\nConsider a very small element of length dl of a conductor carrying current (i). Magnetic induction due to small element at a point P distance r from the element.\nMagnetic induction (dB) is directly proportional to i) current (i) ii) Length of the element (di) iii) sine angle between r and dl and inversely proportional to the square of the distance from small element to point P.\n\nQuestion 2.\nState and explain Ampere\u2019s law.\nAmpere\u2019s law : The line integral of the intensity of magnetic induction field around closed path is equal to \u03bc0 times the net current (i) enclosed by the path.\n$$\\oint \\overrightarrow{\\mathrm{B}} \\cdot \\overrightarrow{\\mathrm{d} l}$$ = \u03bc0i\nProof: Consider a long straight conductor carrying current i as shown in figure. Magnetic induction at a distance r from the conductor is given by\n\nB = $$\\frac{\\mu_0 \\mathrm{i}}{2 \\pi \\mathrm{r}}$$ (From Biot-Savart\u2019s law)\nThe value of B is same at all points on the circle.\n$$\\oint \\overrightarrow{\\mathrm{B}} . \\overrightarrow{\\mathrm{d} l}=\\oint \\mathrm{B} \\mathrm{d} l \\cos \\theta$$\n= $$\\mathrm{B} \\oint \\mathrm{d} l$$ = B \u00d7 2\u03c0\n= $$\\frac{\\mu_0 \\mathrm{i}}{2 \\pi \\mathrm{r}}$$ \u00d7 2\u03c0r\n$$\\oint \\overrightarrow{\\mathrm{B}} \\cdot \\overrightarrow{\\mathrm{d} l}$$ = \u03bc0i\nThis proves Ampere\u2019s circuital laws.\n\nQuestion 3.\nFind the magnetic induction due to a long current carrying conductor.\nConsider a long straight conductor carrying a current i. Let P be a point at a distance r from the conductor. Let r be the radius of the circle passing through point p.\n\nMagnetic induction is same at all points on the circle. Consider a small element of length dl.\n$$\\oint \\overrightarrow{\\mathrm{B}} \\cdot \\overrightarrow{\\mathrm{d} l}=\\oint \\mathrm{Bd} l \\cos \\theta$$\nAngle between B and dl is zero i.e. \u03b8 = 0\n= $$\\mathrm{B} \\oint \\mathrm{d} l$$\n$$\\oint \\overrightarrow{\\mathrm{B}} \\cdot \\overrightarrow{\\mathrm{d} l}$$ = B (2\u03c0r) \u2026\u2026\u2026\u2026\u2026\u2026. (1)\nAccording to Ampere\u2019s laws\n$$\\oint \\overrightarrow{\\mathrm{B}} \\cdot \\overrightarrow{\\mathrm{d} l}$$ = \u03bc0i \u2026\u2026\u2026\u2026\u2026. (2)\nFrom equations (1) and (2), B (2\u03c0r) = \u03bc0i\n= $$\\frac{\\mu_0 \\mathrm{i}}{2 \\pi \\mathrm{r}}$$\n\nQuestion 4.\nDerive an expression for the magnetic induction at the centre of a current carrying circular coil using Biot-Savart\u2019s law.\nConsider a circular coil of radius r and carry a current! Consider a small element \u2018dl\u2019. Let O is the centre of the coil. By using Biot \u2013 Savart\u2019s law,\n\ndB = $$\\frac{\\mu_0}{4 \\pi} \\cdot \\frac{\\mathrm{id} l \\sin \\theta}{\\mathrm{r}^2}$$\nHere angle $$\\overrightarrow{\\mathrm{d} l}$$ and $$\\overrightarrow{\\mathrm{r}}$$ is 90\u00b0 (i.e., \u03b8 = 90\u00b0)\ndB = $$\\frac{\\mu_0}{4 \\pi} \\frac{\\mathrm{idl}}{\\mathrm{r}^2}$$ \u2026\u2026\u2026\u2026\u2026 (1)\nAs the field due to all elements of the circular loop have the same direction. The resultant magnetic field can be obtained by integrating equation (1)\n\nQuestion 5.\nDerive an expression for the magnetic induction of a point on the axis of a current carrying circular coil using Biot-Savart\u2019s law.\n\nConsider a circular coil of radius R and carrying a current i. Let P is a point on the axis at a distance x from the centre O. Let r be the distance of small element (dl) from P.\nFrom Biot \u2013 savart\u2019s law\ndB = $$\\frac{\\mu_0}{4 \\pi} \\cdot \\frac{\\mathrm{id} l \\sin \\theta}{\\mathrm{r}^2}=\\frac{\\mu_0}{4 \\pi} \\cdot \\frac{\\mathrm{id} l}{\\mathrm{r}^2}$$ \u2026\u2026\u2026\u2026\u2026\u2026.. (1)\n(\u2235 \u03b8 = 90\u00b0 Angle between $$\\overrightarrow{\\mathrm{d} l}$$ and $$\\overrightarrow{\\mathrm{r}}$$)\ndB can be resolved into two components dB cos\u03b8 and dB sin\u03b8. If we consider another This also resolved into dB cos\u03b8 and dB sin\u03b8.\nThe components along the axis will add up and perpendicular to the axis will cancel.\n\u2234 Resultant magnetic induction at P is\n\nQuestion 6.\nExplain how crossed E and B fields serve as a velocity selector.\nWhen a charged particle q moving with a velocity v in presence of both electric and magnetic fields.\nThe force experienced due to electric field FE = q$$\\overrightarrow{\\mathrm{E}}$$\nThe force experienced due to magnetic field FB = q $$(\\vec{v} \\times \\vec{B})$$\nConsider electric and magnetic fields are perpendicular to each other and also perpendicular to the velocity of the particle.\n\nE = E$$\\hat{\\mathrm{j}}$$,B = B$$\\hat{\\mathrm{k}}$$, v = \u03c5$$\\hat{\\mathrm{i}}$$\nFE = qE$$\\hat{\\mathrm{j}}$$, FB =q(v$$\\hat{\\mathrm{i}}$$ \u00d7 B$$\\hat{\\mathrm{k}}$$) = \u2013 qvB$$\\hat{\\mathrm{j}}$$\n\u2234 F = FE + FB\nF = q (E \u2013 \u03c5B)$$\\hat{\\mathrm{j}}$$\nThus electric and magnetic forces are in opposite directions.\nWe adjust E and B such that, the forces are equal\nFE = FB\nqE = q \u03c5 B\n\u03c5 = $$\\frac{E}{B}$$\nThis condition can be used to selefct charged particles of a particular velocity. The crossed field E and B serve as a velocity selector.\n\nQuestion 7.\nWhat are the basic components of a cyclotron ? Mention its uses ?\nCyclotron is a device used to accelerate positively charged particles like protons, \u03b1 \u2013 particles, deutrons etc.\n\nCyclotron mainly consists of\n\n1. Two hollow D-shaped metallic chambers D1 and D2\n2. High-frequency oscillator\n3. Strong electro magnet\n4. Vaccum chamber.\n\nUses of cyclotron :\n\n1. It is used for producing radioactive material for medical purposes i.e. diagnostics and treatment of chronic diseases. \u201c\n2. It is used to improve the quality of solids by adding ions.\n3. It is used to synthesise fresh substances.\n4. It is used to bombard the atoms with highly accelerated particles to study the nuclear reactions.\n\nQuestion 8.\nDerive an expression for the magnetic dipole moment of a revolving electron. [A.P. Mar. 16]\nSolution:\nConsider an electron revolving in a circular orbit of radius r with speed v and frequency \u03c5. If the electron cross a point P on the circle in every revolution, then distance travelled by electron to complete one revolution = 2\u03c0r.\nNo. of revolutions in one second (\u03c5) = $$\\frac{\\mathrm{v}}{2 \\pi \\mathrm{r}}$$\nThe electric current (i) = $$\\frac{\\text { Charge }}{\\text { Time }}$$ = charge \u00d7 frequency\ni = e \u00d7 $$\\frac{\\mathrm{v}}{2 \\pi \\mathrm{r}}$$\n\u2234 Magentic dipole moment (M) = iA (\u2235 N = 1)\nM = $$\\frac{\\mathrm{ev}}{2 \\pi \\mathrm{r}}$$ \u00d7 \u03c0r2 (\u2235 A = \u03c0r2)\nM = $$\\frac{\\mathrm{evr}}{2}$$\n\nQuestion 1.\nDeduce an expression for the force on a current carrying conductor placed in a magnetic field. Derive an expression for the force per unit length between two parallel current-carrying conductors.\nExpression for the Force acting on a current carrying conductor :\nConsider a straight conductor (wire) of length T, area of cross section \u2019A1, carrying a current T, which is placed in a uniform magnetic field of induction \u2019B\u2019 as shown in fig.\n\nWe know the external magnetic field exerts a force on the conductor.\nThe electrons in effect move with an average velocity called drift velocity \u2018Vd\u2018. The direction of conventional current will be opposite to the direction of drift velocity.\n\nLet us assume that the current flows through the conductor from left \u2018B\u2019 in the plane of the paper makes an angle \u2018\u03b8\u2019 with the direction of current \u2018i\u2019 as shown in fig.\nIf F\u2019 is the force acting on the charge \u2018q\u2019 in B.\n\u2234 F\u2019 = q Vd B sin \u03b8\nIf \u2018n\u2019 represents number of moving electrons per unit volume (\u2235 n = $$\\frac{N}{V}$$)\n\u2234 Current i = nq Vd A\nIf \u2018N\u2019 is the number of electrons in the length \u2018l\u2019\nN = nlA\nTotal force on conductor F = F\u2019.N (\u2235N = nV = n \u00d7 A \u00d7 l)\n= (q Vd B sin \u03b8) (nlA)\n(nqVdA) (lB sin \u03b8)\n\u2234 F = ilB sin \u03b8\nCase (i) : If \u03b8 = 0\u00b0, FMin = 0\nCase (ii) : If \u03b8 = 90\u00b0, FMax = Bil\nExpression for the force between two Parallel conductors carrying conductors :\nConsider two straight parallel conductors AB and \u2018CD\u2019 carrying currents \u2018ix\u2019 and \u2018i2\u2019 and which are separated by a distance \u2018r\u2019 as shown in fig.\n\nIf B1 and B2 are magnetic inductions produced by the current carrying conductors AB and CD. Magnetic induction Bx at a distance \u2018r\u2019 from the conductor \u2018AB\u2019 can be written as B1 = $$\\frac{\\mu_0 \\mathrm{i}_1}{2 \\pi \\mathrm{r}}$$\nIf \u2018F\u2019 is for\u0153 acting on \u2018CD\u2019 clue to magnetic induction \u2018B1\u2018 then\nFCD = i2lB1\nWhere l = length of the conductor\nFCD = i2l $$\\left(\\frac{\\mu_0 i_1}{2 \\pi \\mathrm{r}}\\right)=\\frac{\\mu_0 i_1 i_2 l}{2 \\pi r}$$ \u2026\u2026\u2026\u2026\u2026. (1)\nThe direction of the force can be determined by using Flemings left hand rule.\nSimilarly we can find the force acting on the A conductor AB due to magnetic induction B2.\nFAB = i1lB2\n\u2234 FAB = i1l $$\\left(\\frac{\\mu_0 i_2}{2 \\pi r}\\right)$$ \u2026\u2026\u2026\u2026.. (2) [\u2235B2 = $$\\left(\\frac{\\mu_0 i_2}{2 \\pi r}\\right)$$]\nFrom the equations (1) and (2) FAB = FCD = $$\\frac{\\mu_0 \\mathrm{i}_1 \\mathrm{i}_2 l}{2 \\pi \\mathrm{r}}$$\n\u2234 Force between two parallel, straight conductors carrying currents,\nF = $$\\frac{\\mu_0 \\mathrm{i}_1 \\mathrm{i}_2 l}{2 \\pi \\mathrm{r}}$$\nForce per unit length $$\\frac{\\mathrm{F}}{l}=\\frac{\\mu_0 \\mathrm{i}_1 \\mathrm{i}_2}{2 \\pi \\mathrm{r}}$$\n\nQuestion 2.\nObtain an expression for the torque on a current carrying loop placed in a uniform \u2018 magnetic field. Describe the construction and working of a moving coil galvanometer.\nTorque acting on a coil carrying a current kept in a uniform magnetic field : Let a rectangular current loop ABCD of length l = AB = CD and width b = AD \u2013 BC carrying a current \u201ci\u201d be suspended in a magnetic field of flux density B.\nThe normal ON drawn to the plane of the coil makes an angle \u2018\u03b8\u2019 with the magnetic field B.\n\nForce on arm AD = $$\\mathrm{i} \\overline{\\mathrm{b}} \\times \\overline{\\mathrm{B}}$$ acting upwards along the axis of suspension\nForce on arm BC = $$\\mathrm{i} \\overline{\\mathrm{b}} \\times \\overline{\\mathrm{B}}$$ acting downwards along the axis of suspension\nHence these two forces cancel.\n\nForce on arm AB = ilB acting perpendicular to the plane as shown.\nForce on arm CD = ilB acting perpendicular to the plane as shown.\nThese two forces constitute a couple on the coil.\nMoment of the couple = (Force) \u00d7 (Perpendicular distance between the forces) = ilB (PQ sin \u03b8)\nTorque = ilB b sin\u03b8\nBut l \u00d7 b = Area of coil\n\u2234 Torque = iAB sin \u03b8\nIf the loop has \u2018n\u2019 turns the torque on the coil\n\u03c4 = n i AB sin \u03b8\nIf \u2018\u03a6\u2019 is the deflection of the coil, that is the angle between the plane of the coil and magnetic field B\n\u03c4 = n i AB cos \u03a6\n\nMoving coil galvanometer:\nPrinciple : When a current carrying coil is placed in the uniform magnetic field, it experiences a torque.\nConstruction :\n\n1. It consists of a coil wound on a non metallic frame.\n2. A rectangular coil is suspended between two concave shaped magnetic poles with the help of phosphour Bronze wire.\n3. The lower portion of the coil is connected to a spring.\n4. A small plane mirror M is fixed to the phosphour Bronze wire to measure the deflection of the coil.\n5. A small soft iron cylinder is placed within the coil without touching the coil. The soft iron cylinder increases the induction field strength.\n6. The concave shaped magnetic poles render the field radial. So maximum torque acting on it.\n7. The whole of the apparatus is kept inside a brass case provided with a glass window.\n\nTheory:\nConsider a rectangular coil of length l and breadth b and carrying current i suspended in the induction field strength B.\nDeflecting torque (\u03c4) = B i A N \u2026\u2026\u2026\u2026\u2026.. (5)\nwhere A = Area of the coil\nN = Total number of turns.\nThe restoring torque developed in the suspension = C \u03b8 \u2026\u2026\u2026\u2026\u2026.. (2)\nWhere C is the couple per unit twist and 9 is the deflection made by the coil.\nWhen the coil is in equilibrium position\nDeflecting torque = Restoring torque\nB i A N = C\u03b8\ni = $$\\left(\\frac{\\mathrm{C}}{\\mathrm{BAN}}\\right) \\theta$$\nWhere K = $$\\frac{\\mathrm{C}}{\\mathrm{BAN}}$$ = Galvanometer constant.\ni = K \u03b8 \u2026\u2026\u2026\u2026\u2026\u2026 (3)\ni \u221d \u03b8\nThus deflection of the coil is directly proportional to the current flowing through it. The deflection in the coil is measured using lamp and scale arrangement.\n\nQuestion 3.\nHow can a galvanometer be converted to an ammeter ? Why is the parallel resistance smaller that the galvanometer resistance ? A moving coil galvanometer can measure a current of 10-6 A. What is the resistance of the shunt required if it is to measure 1A ?\nConversion of Galvanometer into Ammeter :\nGalvanometer is converted into an ammeter by connecting a suitable resistance is parallel to it:\n\nThis arrangement decreases the effective resistance.\n\nAmmeter is used for measuring the current in an electric circuit and it is connected in series in circuit. The inclusion of the ammeter in the circuit should not alter the current or total resistance of the circuit so it has very low resistance.\n\nThe resistance of An ideal Ammeter is zero.\nLet G and S be the Galvanometer and shunt resistances respectively.\nLet \u2018i\u2019 be the total current, divided at A into ig and is as shown in fig.\nFrom Kirchhoffs Ist law, i = ig + is\nAs \u2018G\u2019 and \u2018S\u2019 are parallel P.D. across\nGalvanometer = P.D. across shunt\nigG = isS\nS = $$\\frac{\\mathrm{i}_{\\mathrm{g}}}{\\mathrm{i}_{\\mathrm{s}}} \\mathrm{G}$$\n= $$\\frac{\\mathrm{Gi}_{\\mathrm{g}}}{\\mathrm{i}-\\mathrm{i}_{\\mathrm{g}}}$$ [\u2235 is = i \u2013 ig]\nS = $$\\frac{\\mathrm{G}}{\\frac{\\mathrm{i}}{\\mathrm{i}_{\\mathrm{g}}}-1}$$\nIf $$\\frac{\\mathrm{i}}{\\mathrm{i}_{\\mathrm{g}}}$$ = n \u21d2 ig = $$\\frac{\\mathrm{i}}{\\mathrm{n}}$$\n\u2234 The current flowing through the galvanometer be $$\\left(\\frac{1}{n}\\right)^{\\text {th }}$$ of total current.\n\u2234 S = $$\\frac{\\mathrm{G}}{\\mathrm{n}-1}$$\nIf \u2018R\u2019 is the effective resistance between points \u2018A\u2019 and \u2018B\u2019 then\n\nHence current through galvanometer is proportional to the total current. Since \u2018S\u2019 is small major portion of the current flows through it and a small portion of current flows through G. So shunt protects the galvanometer from high currents. Parallel resistance is smaller than Galvanometer resistance because to protect the Galvanometer from high (large) current (or) to pass. Large currents through shunt and small current passes through the galvanometer.\nSolution for the problem : Current in the circuit i = 1A;\nCurrent through the galvanometer, ig = 10-6A\nShunt resistance, S = $$\\frac{G}{n-1}=\\frac{G}{\\frac{i}{i_g}-1}=\\frac{G}{10^6-1}=\\frac{G}{99.999} \\Omega$$\n\nQuestion 4.\nHow can a galvanometer be converted to a voltmeter ? Why is the series resistance greater that the galvanometer resistance ? A moving coil galvanometer of resistance 5\u2126 can measure a current of 15mA. What is the series resistance required if it is to measure 1.5V ?\nConversion of Galvanometer into Voltmeter : A galvanometer is converted into voltmeter by connecting a high resistance (R) in series with it. Voltmeter is used to measure the P.D. between any two points in circuit and it is connected in parallel to the component of the circuit.\n\nLet \u2018V\u2019 be the potential difference to be measured between the points \u2018A\u2019 and \u2018B\u2019.\n\u2234 V = (R + G) ig [\u2234 V = iR]\nig = Current passing through the galvanometer\n$$\\frac{\\mathrm{V}}{\\mathrm{i}_{\\mathrm{g}}}$$ = R + G\nR = $$\\frac{\\mathrm{V}}{\\mathrm{i}_{\\mathrm{g}}}$$ \u2013 G \u2026\u2026\u2026\u2026\u2026. (1)\nThe value of \u2018R\u2019 can be calculated by using the above formula. If Vg is the maximum P.D. across the galvanometer then Vg = ig G\n\u2234 ig = $$\\frac{V_g}{G}$$ \u2026\u2026\u2026\u2026\u2026.. (2)\nSubstitute \u2018ig\u2018 in Equ (1)\nR = $$\\frac{V_G}{V_g}$$ \u2013 G = $$\\left(\\frac{V}{V_g}-1\\right)$$\nIf $$\\frac{V}{V_g}$$ = n \u21d2 R = G(n \u2013 1)\nNote : n = $$\\frac{V}{V_g}$$ is the ratio of maximum voltage to be measured to the maximum voltage across the galvanometer.\n\nSeries resistance is greater than galvanometer resistance because the current in external resistance and potential difference will be decreased and to increase the resistance of the galvanometer.\nSolution for the problem:\n\nProblems\n\nQuestion 1.\nTwo long and parallel straight wires A and B canying currents of 8.0 A and 5.0 A in the same direction are separated by a distance of 4.0 cm. Estimate the force on a 10 cm section of wire A.\nSolution:\nGiven I1 = 8A, I2 = 5A and r = 4 cm = 0.4m\nF = $$\\frac{\\mu_0}{4 \\pi} \\cdot \\frac{2 \\mathrm{I}_1 \\mathrm{I}_2}{\\mathrm{r}}=\\frac{10^{-7} \\times 2 \\times 8 \\times 5}{0.04}$$ = 2 \u00d7 10-4 N\nThe force on A of length 10 cm is F1 = F \u00d7 0.1 (\u2235 1 m = 100 cm)\nF1 = 2 \u00d7 10-4 \u00d7 0.1\nF1 = 2 \u00d7 10-5 N.\n\nQuestion 2.\nA current of 10A passes through two very long wires held parallel to each other and separated by a distance of 1m. What is the force per unit length between them ? [A.P. & T.S. Mar. 15]\ni1 = i2 = 10A\nr = 1m\n$$\\frac{\\mathrm{F}}{l}=\\frac{\\mu_0 \\mathrm{i}_1 \\mathrm{i}_2}{2 \\pi \\mathrm{r}}$$\n= $$\\frac{4 \\pi \\times 10^{-7} \\times 10 \\times 10}{2 \\pi \\times 1}$$\n$$\\frac{\\mathrm{F}}{l}$$ = 2 \u00d7 10-5 Nm-1.\n\nQuestion 3.\nA straight wire of mass 200 g and length 1.5 m carries a current of 2 A. It is suspended in mid-air by a uniform horizontal magnetic field B (Fig.). What is the magnitude of the magnetic field ?\n\nSolution:\nFrom Eq F = Il \u00d7 B we find that there is an upward force F, of magnitude IlB,. For mid-air suspension, this must be balanced by the force due to gravity.\nm g = I lB mg\nB = $$\\frac{\\mathrm{mg}}{\\mathrm{I} l}$$\n= $$\\frac{0.2 \\times 9.8}{2 \\times 1.5}$$ = 0.65 T\nNote that it would have been sufficient to specify mll, the mass per unit length of the wire. The earth\u2019s magnetic field is approximately 4 \u00d7 10-5 T and we have ignored it.\n\nQuestion 4.\nThe horizontal component of the earth\u2019s magnetic field at a certain place is 3.0 \u00d7 10-5 T and the direction of the field is from the geographic south to the geographic north. A very long straight conductor is carrying a steady current of 1 A. What is the force per unit length on it when it is placed on a horizontal table and the direction of the current is\n(a) east to west;\n(b) south to north ?\nSolution:\nF = Il \u00d7 B\nF = IlB sin \u03b8\nThe force per unit length is\nf = F\/l = IB sin\u03b8\na) When the current is flowing from east to west,\n\u03b8 = 90\u00b0\nHence,\nf = IB\n= 1 \u00d7 3 \u00d7 10-5 = 3 \u00d7 10-5 Nm-1\nThis is larger than the value 2 \u00d7 10-7 Nm-1 quoted in the definition of the ampere. Hence it is important to eliminate the effect of the earth\u2019s magnetic field and other stray fields while standardising the ampere.\nThe direction of the force is downwards. This direction may be obtained by the directional property of cross product of vectors.\n\nb) When the current is flowing from south to north, .\n\u03b8 = 0\u00b0\nf = 0\nHence there is no force on the conductor.\n\nTextual Examples\n\nQuestion 1.\nA straight wire of mass 200 g and length 1.5 m carries a current of 2 A. It is suspended in mid-air by a uniform horizontal niagnetic field B (Fig.). What is the magnitude of the magnetic field ?\n\nSolution:\nFrom Eq F = Il \u00d7 B we find that there is an upward force F, of magnitude IlB,. For mid-air suspension, this must be balanced by the force due to gravity, m g = I lB .\nB = $$\\frac{\\mathrm{mg}}{\\mathrm{I} l}$$\n= $$\\frac{0.2 \\times 9.8}{2 \\times 1.5}$$ = 0.65 T\nNote that it would have been sufficient to specify m\/l, the mass per unit length of the wire. The earth\u2019s magnetic field is approximately 4 \u00d7 10-5 T and we have ignored it.\n\nQuestion 2.\nIf the magnetic field is parallel to the positive y-axis and the charged particle is moving along the positive x-axis (Fig.), which way would the Lorentz force be for (a) an electron (negative charge), (b) a proton (positive charge).\n\nSolution:\nThe velocity v of particle is along the x-axis, while B, the magnetic field is along the y-axis, so v \u00d7 B is along the z-axis (screw rule or right-hand thumb rule). So, (a) for electron it will be along -z axis, (b) for a positive charge (proton) the force is along +z axis.\n\nQuestion 3.\nWhat is the radius of the path of ah electron (mass 9 \u00d7 10-31 kg and charge 1.6 \u00d7 10-19 C) moving at a speed of 3 \u00d7 107 m\/s in a magnetic field of 6 \u00d7 10-4 T perpendicular to it ? What is its frequency ? Calculate its energy in keV. (1 eV = 1.6 \u00d7 10-19 J).\nSolution:\nUsing Eq. r = m\u03c5\/qb we find\nr = m\u03c5\/(qB) = 9 \u00d7 10-31 kg \u00d7 3 \u00d7 107 m s-1 \/ (1.6 \u00d7 10-19 C \u00d7 6 \u00d7 10-4 T)\n= 26 \u00d7 10-2 m = 26 cm\nv = \u03c5 \/ (2 \u03c0r) = 2 \u00d7 106 s-1 = 2 \u00d7 106 Hz = 2MHz.\nE = (1\/2)m\u03c52 = (1\/2) 9 \u00d7 10-31 kg \u00d7 9 \u00d7 1014 m2\/s = 40.5 \u00d7 10-17 J\n\u2248 4 \u00d7 10-16 J = 2.5 keV.\n\nQuestion 4.\nA cyclotron\u2019s oscillator frequency is 10 MHz. What should be the operating magnetic field for accelerating protons ? If the radius of its does is 60 cm, what is the kinetic energy (in MeV) of the proton beam produced by the accelerator.\n(e = 1.60 \u00d7 10-19 C, mp = 1.67 \u00d7 10-27 kg, 1 MeV = 1.6 \u00d7 10-13 J).\nSolution:\nThe oscillator frequency should be same as proton\u2019s cyclotron frequency.\nUsing Eqs. r = m\u03c5\/qb and \u03c9 = 2\u03c0\u03c5 = $$\\frac{\\mathrm{qB}}{\\mathrm{M}}$$ we have\nB = 2\u03c0 m \u03c5\/q = 6.3 \u00d7 1.67 \u00d7 10-27 \u00d7 107 \/ (1.6 \u00d7 10-19) = 0.66 T\nFinal velocity of protons is\n\u03c5 = r \u00d7 2\u03c0 v = 0.6 m \u00d7 6.3 \u00d7 107 = 3.78 \u00d7 107 m\/s.\nE = 1\/2 mv2 = 1.67 \u00d7 10-27 \u00d7 14.3 \u00d7 1014\/ (2 \u00d7 1.6 \u00d7 10-13) = 7 MeV\n\nQuestion 5.\nelement \u22061 = \u2206x$$\\hat{\\mathrm{i}}$$ is placed at the origin and carries a large current I = 10 A (Fig.). Wat is the magnetic field on the y-axis at a distance of 0.5 m. \u2206x = 1 cm.\n\nSolution:\n\|dB\| = $$\\frac{\\mu_0}{4 \\pi} \\frac{I \\mathrm{dl} \\sin \\theta}{\\mathrm{r}^2}$$\ndl = \u2206x = 10-2 m, I = 10 A, r = 0.5 m = y, \u03bc0\/4\u03c0 = 10-7 $$\\frac{\\mathrm{Tm}}{\\mathrm{A}}$$\n\u03b8 = 90\u00b0; sin \u03b8 = 1\n\|dB\| = $$\\frac{10^{-7} \\times 10 \\times 10^{-2}}{25 \\times 10^{-2}}$$ = 4 \u00d7 10-8 T\nThe direction of the field is in the +z-direction. This is so since,\ndl \u00d7 r = $$\\Delta \\mathrm{x} \\hat{\\mathrm{i}} \\times \\mathrm{y} \\hat{\\mathrm{j}}=\\mathrm{y} \\Delta \\mathrm{x}(\\hat{\\mathrm{i}} \\times \\hat{\\mathrm{j}}) \\mathrm{y} \\Delta \\mathrm{x} \\hat{\\mathrm{k}}$$\nWe remind you of the following cyclic property of cross-products,\n$$\\hat{\\mathrm{i}} \\times \\hat{\\mathrm{j}}=\\mathrm{k} ; \\hat{\\mathrm{j}} \\times \\hat{\\mathrm{k}}=\\hat{\\mathrm{i}} ; \\hat{\\mathrm{k}} \\times \\hat{\\mathrm{i}}=\\hat{\\mathrm{j}}$$\nNote that the field is small in magnitude.\n\nQuestion 6.\nA straight wire carrying a current of 12 A is bent into a semi-circular arc of radius 2.0 cm as shown in Fig. Consider the magnetic field B at the centre of the arc. (a) What is the magnetic field due to the straight segments ? (b) In what way the contribution to B from the semicircle differs from that of a circular loop and in what way does it resemble ? (c) Would your answer be different if the wire were bent into a semi-circular arc of the same radius but in the opposite way as shown in Fig. (b) ?\n\nSolution:\na) dl and r for each element of the straight segments are parallel. Therefore, dl \u00d7 r = 0. Straight segments do not contribute to \|B\|.\n\nb) For all segments of the semicircular arc, dl \u00d7 r are all parallel to each other (into the plane of the paper). All such contributions add up in magnitude. Hence direction of B for a semicircular arc is given by the right-hand rule and magnitude is half that of a circular loop. Thus B is 1.9 \u00d7 10-4 T normal to the plane of the paper going into it.\n\nc) Same magnitude of B but opposite in direction to that in (b).\n\nQuestion 7.\nConsider a tightly wound 100 turn coil of radius 10 cm, carrying a current of 1 A. What is the magnitude of the magnetic field at the centre of the coil?\nSolution:\nSince the coil is tightly wound we may take each circular element to have the same radius R = 10 cm = 0.1 m. The number of turns N = 100. The magnitude of the magnetic field is (From Eq.),\nB0 = $$\\frac{\\mu_0 \\mathrm{I}}{2 \\mathrm{R}} \\hat{\\mathrm{i}}$$\nB = $$\\frac{\\mu_0 \\mathrm{NI}}{2 \\mathrm{R}}=\\frac{4 \\pi \\times 10^{-7} \\times 10^2 \\times 1}{2 \\times 10^{-1}}$$ = 2\u03c0 \u00d7 10-4 = 6.25 \u00d7 10-4 T\n\nQuestion 8.\nMagnetic field due to a long current-carrying wire Oersted\u2019s experiments showed that there is a magnetic field around a current-carrying wire. We determine the magnitude of magnetic field at some distance from a long striaght wire carrying a current I.\nSolution:\nThe direction of the field is given by the right hand rule. The figure shows an element dl of the current-carrying wire. The point P, where the field is to be determined is at a perpendicular distance \u2018S\u2019 from the wire. The position vector of P from dl is r.\n\nThe magnitude dB of the magnetic field due to dl is given by Biot-Savart law to be\n\nnow from the figure S = r cos\u03b8 which gives l\/r2 = cos2\u03b8\/s2\nand l\u2019 = S tan\u03b8 which gives dl\u2019 = S sec2\u03b8 d\u03b8 = S d\u03b8\/cos2\u03b8\nthus dB = $$\\frac{\\mu_0 I \\cos \\theta}{4 \\pi S}$$ d\u03b8\nwe integrate this to get B at P If the wire is very long then the limits for 0 would be -\u03c0\/2 to \u03c0\/2\nthus B = $$\\frac{\\mu_0 l}{2 \\pi S}$$ (emerging from the paper at P)\n\nQuestion 9.\nFind $$\\oint$$ B . dl for the paths shown in (a) and (b)\n\nSolution:\na) Going around theKpath in the anticlockwise direction, I1 is taken as positive while I3 is negative. Currents I2 and I4 do not matter as they are NOT enclosed by the path.\n$$\\oint$$ B . dl = \u03bc0(I1 \u2013 I3)\nNote : Currents I2 and I4 create magnetic fields all around them and B due to them on any element of the path would be non-zero. However, the sum B.dZ due to them would be zero, b) Calculation of B. dl for the entire path can be broken up into two separate calculations, one covering all contributions from an anti-clockwise traversal around I1 and the other covering all contributions from a clockwise traversal around I3. Thus\n$$\\int_1 \\mathrm{~B} . \\mathrm{d} l$$ = \u03bc0I1 for all elements around I1 traversed in an anti-clockwise direction\n$$\\int_2 \\mathrm{~B} . \\mathrm{d} l$$ = \u03bc0I3 for all elements around I3 traversed in a clockwise direction; I3 taken as positive because it is flowing into the plane. Thus the total $$\\oint$$ B.dl = \u03bc0 (I1 \u2013 I3)\n\nQuestion 10.\nFigure shows the circular cross-section of a long straight wire of radius a carrying steady current I. The current I is uniformly distributed across this cross-section. Calculate the magnetic field in the region r < a (dashed inner circle) and r > a (dashed outer circle).\n\nSolution:\na) Consider the case r > a. The Amperian loop, labelled 2, is a circle concentric with the cross-section. For this loop,\nL = 2\u03c0r\nIe = Current enclosed by the loop = I\nThe result is the familiar expression for a long straight wire B(2\u03c0r) = \u03bc0I\nB = $$\\frac{\\mu_0 I}{2 \\pi \\mathrm{r}}$$ \u2026\u2026\u2026\u2026\u2026\u2026 (1)\nb) Consider the case r < a. The Amperian loop is a circle labelled 1 . For this loop, taking the radius of the circle to be r,\nL = 2 \u03c0 r\nNow the current enclosed Ie is not I (because r < a), but is less than this value. Since the current distribution is uniform, the current enclosed is,\n\nFigure shows a plot of the magnitude of B with distance r from the centre (axis) of the wire. The direction of the field is tangential to the respective circular loop (1 or 2) and given by the right-hand rule described earlier in this section.\nThis example possesses the required symmetry so that Ampere\u2019s law can be applied readily.\n\nQuestion 11.\nA solenoid of length 0.5 m has a radius of 1 cm and is made up of 500 turns. It carries a current of 5 A. What is the magnitude of the magnetic field inside the solenoid ?\nSolution:\nThe number of turns per unit length is,\nn = $$\\frac{500}{0.5}$$ = 1000 turns \/ m\nThe length l = 0.5m and radius r = 0.01 m. Thus, l\/a = 50 i.e., l > >a.\nHence, we can use the long solenoid formula, namely, Eq. (B = \u03bc0nI)\nB = \u03bc0 n I\n= 4\u03c0 \u00d7 10-7 \u00d7 103 \u00d7 5 = 6.28 \u00d7 10-3 T\n\nQuestion 12.\nThe horizontal componet of the earth\u2019s magnetic field at a certain place is 3.0 \u00d7 10-5 T and the direction of the field is from the geographic south to the geographic north. A very long straight conductor is carrying a steady current of 1A. What is the force per unit length on it when it is placed on a horizontal table and the direction of the current is\n(a) east to west;\n(b) south to north ?\nSolution:\nF = Il \u00d7 B\nF = IlB sin \u03b8\nThe force per unit length is\nf = F\/l = IB sin\u03b8\na) When the current is flowing from east to west,\n\u03b8 = 90\u00b0\nHence,\nf = IB\n= 1 \u00d7 3 \u00d7 10-5 = 3 \u00d7 10-5 Nm-1\nThis is larger than the value 2 \u00d7 10-7 Nm-1 quoted in the definition of the ampere. Hence it is important to eliminate the effect of the earth\u2019s magnetic field and other stray fields while standardising the ampere.\nThe direction of the force is downwards. This direction may be obtained by the directional property of cross product of vectors.\n\nb) When the current is flowing from south to north,\n\u03b8 = 0\u00b0\nf = 0\nHence there is no force on the conductor.\n\nQuestion 13.\nA 100 turn closely wound circular coil of radius 10 cm carries a current of 3.2A. (a) What is the field at the centre of the coil ? (b) What is the magnetic moment of this coil ?\nThe coil is placed in a vertical plane and is free to rotate about a horizontal axis which coincides with its diameter. A uniform magnetic field of 2T in the horizontal direction exists such that initially the axis of the coil is in the direction of the field. The coil rotates through an angle of 90\u00b0 under the influence of the magnetic field, (c) What are the magnitudes of the torques on the coil in the initial and final position ? (d) What is the angular speed acquired by the coil when it has rotated by 90\u00b0 ? The moment of inertia of the coil is 0.1 kg m2. [A.P. Mar. 19]\nSolution:\na) From B = $$\\frac{\\mu_0 \\mathrm{NI}}{2 \\mathrm{R}}$$\nHere, N = 100; I = 3.2 A, and R = 0.1 m. Hence,\nB = $$\\frac{4 \\pi \\times 10^{-7} \\times 10^2 \\times 3.2}{2 \\times 10^{-1}}=\\frac{4 \\times 10^{-5} \\times 10}{2 \\times 10^{-1}}$$ (using \u03c0 \u00d7 3.2 = 10)\n= 2 \u00d7 10-3 T\nThe direction is given by the right-hand thumb rule.\n\nb) The magnetic moment is given by\nm = N I A = N I \u03c0 r2 = 100 \u00d7 3.2 \u00d7 3.14 \u00d7 10-2 = 10 A m2\nThe direction is once again given by the right hand thumb rule.\n\nc) \u03c4 = \|m \u00d7 B\|\n= mBsin \u03b8\nInitially, \u03b8 = 0. Thus initial torque \u03c4i = 0. Finally, \u03b8 = \u03c0\/2 (or 90\u00b0).\nThus, final torque \u03c4f = m B = 10 \u00d7 2 = 20 N m.\n\nd) From Newton\u2019s second law.\nI$$\\frac{\\mathrm{d} \\omega}{\\mathrm{dt}}$$ = mBsin \u03b8\nwhere I is the moment of inertia of the coil. From chain rule,\n$$\\frac{\\mathrm{d} \\omega}{\\mathrm{dt}}=\\frac{\\mathrm{d} \\omega}{\\mathrm{d} \\theta} \\frac{\\mathrm{d} \\theta}{\\mathrm{dt}}=\\frac{\\mathrm{d} \\omega}{\\mathrm{d} \\theta} \\omega$$\nUsing this,\nI\u03c9 d\u03c9 = m B sin\u03b8 d\u03b8\nIntegrating from \u03b8 = 0 to \u03b8 = \u03c0\/2,\n$$\\mathrm{I} \\int_0^{\\omega \\mathrm{I}} \\omega \\mathrm{d} \\omega=\\mathrm{mB} \\int_0^{\\pi \/ 2} \\sin \\theta d \\theta$$\n$$\\mathrm{I} \\frac{\\omega_{\\mathrm{I}}^2}{2}=-\\left.\\mathrm{mB}[\\cos \\theta]\\right\|_0 ^{\\pi \/ 2}=\\mathrm{mB}$$\n\u03c9f = $$\\left(\\frac{2 \\mathrm{mB}}{\\mathrm{I}}\\right)^{1 \/ 2}=\\left(\\frac{2 \\times 20}{10^{-1}}\\right)^{1 \/ 2}$$ = 20 s-1\n\nQuestion 14.\na) A current-carrying circular loop lies on a smooth horizontal plane. Can a uniform magnetic field be set up in such a manner that the loop turns around it self (i.e. turns about the vertical axis).\nSolution:\nNo, because that would require \u03c4 to the in the vertical direction. But \u03c4 = I A \u00d7 B, and since A of the horizontal loop is in the vertical direction, \u03c4 would be in the plane of the loop for any B.\n\nb) A current-carrying circular loop is located in a uniform external magnetic field. If the loop is free to turn, what is its. orientation of stable equilibrium ? Show that in this orientation, the flux of the total field (external field + field produced by the loop) is maximum.\nSolution:\nOrientation of stable equilibrium is one where the area vector A of the loop is in the direction of external magnetic field. In this orientation, the magnetic field produced by the loop is in the same direction as external field, both normal to the plane of the loop, thus giving rise to maximum flux of the total field.\n\nc) A loop of irregular shape carrying current is located in an external magnetic field. If the wire is flexible, why does it change to a circular shape ? What could be the sense of current in the loop and the direction of magnetic field ?\nSolution:\nIt assumes circular shape with its plane normal to the field to maximize flux, since for a given perimeter, a circle encloses greater area than any other shape.\n\nQuestion 15.\nIn the circuit (Fig.) the current is to be measured. What is the value of the current if the ammeter shown (a) is a galvanometer with a resistance RG = 60.00 \u2126; (b) is a galvanometer described in (a) but converted to an ammeter by a shunt resistance rs = 0.02 \u2126; (c) is an ideal ammeter with zero resistance ?\n\nSolution:\na) Total resistance in the circuit is,\nRG + 3 = 63 \u2126. Hence I = 3\/63 = 0.048 A.\n\nb) Resistance of the galvanometer converted to an ammeter is,\n$$\\frac{\\mathrm{R}_{\\mathrm{G}} \\mathrm{r}_{\\mathrm{s}}}{\\mathrm{R}_{\\mathrm{G}}+\\mathrm{r}_{\\mathrm{s}}}=\\frac{60 \\Omega \\times 0.02 \\Omega}{(60+0.02) \\Omega}$$ = 0.02 \u2126\nTotal resistance in the circuit is,\n0.02 \u2126 + 3 \u2126 = 3.02 \u2126. Hence I = 3\/3.02 = 0.99 A.\n\nc) For the ideal ammeter with zero resistance,\n1 = 3\/3 = 1.00 A","date":"2023-03-21 22:58:51","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7256501317024231, \"perplexity\": 897.1693055342402}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2023-14\/segments\/1679296943747.51\/warc\/CC-MAIN-20230321225117-20230322015117-00238.warc.gz\"}"}	null	null
\section{Introduction} The {\bf O}bservatory survey at {\bf H}igh {\bf AN}gular resolution of {\bf A}ctive OB stars (OHANA) combines high spectral with high spatial resolution across the Br$\gamma$ and He{\sc i}$\lambda$2.056 lines to characterize the dynamics of winds and disks. It is carried out by the VLTI group at the Paranal observatory with the three-beam combining instrument AMBER \citep{2007A&A...464....1P}. The survey was designed to make use of the observing time not requested by other programs, usually due to bad weather or unsuitable local sidereal time slots. \section{Observations and Data Reduction} The survey targets consist of twelve bright Be stars, thirteen O and B type supergiants, and one interacting binary (see {Table~1}). Almost 300 observations were obtained. By design, namely targeting quantities relative to the adjacent continuum, no calibrators were observed. However, in some nights calibrators, taken for technical purpose or other programs using the same setup, are available. These have been added to the database. Basic data reduction was performed with amdlib, v3.0.6 \citep{2007A&A...464...29T,2009A&A...502..705C}, and then processed further with idl. In particular: \begin{itemize} \item The pixel shifts between the spectral channels were a matter of concern, and seem not to be entirely stable. Whether this is a real effect or a consequence of noise affecting the determination of the shift is under investigation. \item Since the program aims for relative quantities, which do not suffer from degradation of absolute visibility, 100\% of the frames were selected for display in this work. However, the final reduction includes several lower selection ratios as well. \item In the case of continuous observations of more than 30 minutes, ($u,v$) points were merged into 30 minute bins. \item Intensity spectra were extracted, and the absolute wavelength scale corrected using telluric lines. The flux continuum was normalized to unity. \item Visibilities in the continuum were normalized to unity, phases in the continuum to zero. If calibrators were taken, these were used to check for and eventually remove instrumental ripples. \item RMS in the continuum was measured for each quantity to estimate data quality. \end{itemize} The raw data have become public immediately, and the results of the final reduction of the Br$\gamma$ observations will be made public as soon as they are complete. The reduction of the He{\sc i}$\lambda$2.056 observations is pending. \begin{table} \begin{center} \caption{Observed targets, spectral types, and data obtained. For each spectral line, the number of observations on the {\bf s}mall, {\bf i}ntermediate, and {\bf l}arge telescope configurations (s--i--l) are given.} \label{Rivinius_OHANA_tab1} \begin{tabular}{llccllcc} Target & Sp.~type & Br$\gamma$ & He{\sc i}$\lambda$2.056& Target & Sp.~type & Br$\gamma$ & He{\sc i}$\lambda$2.056\\ & & s--i--l & s--i--l & & & s--i--l & s--i--l \\ \hline\\[-2ex] \multicolumn{4}{c}{\bf Be Stars}\smallskip & \multicolumn{4}{c}{\bf OBA Supergiants} \\ $\mu$\,Cen & B2\,Vnpe & 2--5--3 & 0--1--0 & $\eta$\,Car & LBV & 22--16--5 & 3--1--0\\ $\chi$\,Oph & B2\,Vne & 0--0--1 & 0--0--0 & HR\,Car & LBV & 4--4--1 & 2--0--0\\ $\zeta$\,Tau & B2\,IVe-sh & 2--1--0 & 1--0--0& $\zeta$\,Pup & O4\,If & 4--6--1 & 1--2--2\\ $\delta$\,Cen & B2\,IVne & 3--5--2 & 1--1--1& $\iota$\,Ori & O9\,III & 1--2--0 & 1--0--0\\ $\epsilon$\,Cap & B3\,Ve-sh& 1--5--4 & 0--2--0& $\zeta$\,Ori & O9.7\,Iab& 2--1--2 & 1--0--1\\ $\beta^1$\,Mon\,A & B3\,Ve & 6--8--0 & 2--1--0& $\epsilon$\,Ori & B0\,Iab & 1--1--0 & 0--0--0\\ $\beta^1$\,Mon\,B & B3\,ne & 2--1--0 & 0--0--0& $\kappa$\,Ori & B0\,Iab & 3--2--0 & 2--0--0\\ $\beta^1$\,Mon\,C & B3\,e & 2--1--0 & 0--0--0& $\zeta^1$\,Sco & B0.5\,Ia+& 0--1--3 & 0--0--1\\ P\,Car & B4\,Vne & 6--5--2 & 2--3--1& $\gamma$\,Ara & B1\,Ib & 0--1--0 & 0--1--0\\ $\beta$\,Psc & B6\,Ve & 1--4--4 & 0--2--0& HR\,6142 & B1\,Ia & 0--0--1 & 0--0--1\\ $\eta$\,Tau & B7\,IIIe & 0--0--0 & 1--0--0& $\epsilon$\,CMa & B2\,Iab & 4--3--1 & 1--1--1\\ Electra & B8\,IIIe & 0--0--0 & 1--0--0& HD\,53\,138 & B3\,Ia & 11--16--3 & 2--5--1\\[.5ex] \multicolumn{4}{c}{\bf Interacting Binary}\smallskip & V533\,Car & A6\,Iae & 3--5--2 & 1--1--1\\ SS\,Lep & A1\,V\,+\,M6\,II & 7--1--2 & 1--1--2 & &&&\\ \hline\\[-2ex] \end{tabular}\smallskip \end{center} \end{table} \section{Data Description and First Impressions} Due to the snapshot/backup/filler nature of the program, the data quality is inhomogeneous. Typical values for a good data set are an uncertainty of the visibility (normalized to unity) of about $\pm0.05$, and of the phase $\pm 2^\circ$, at a SNR of the combined spectrum of above 100. Selected data sets of the target stars are shown in Figs.~\ref{Rivinius_OHANA_fig1} and \ref{Rivinius_OHANA_fig2}. For each of the four targets, four baselines are shown, taken from two observations. The uppermost panels for each target show the flux spectra, then subpanels a-d show visibility and phase (upper and lower resp.\ profiles), while the centered panel show the ($u,v$) plane covered by the four baselines shown. \subsection{Be Stars} Visual inspection of the Be star observations shows them to be {compatible with the canonical picture}, namely a cicumstellar decretion disk. The targets span all inclinations (equatorial to pole-on) and spectral subtypes. For some of the brighter stars the disk is already well resolved in the intermediate configuration (typical baseline lengths 30--70m), and overly resolved in the large configuration (typical baseline lengths 80--130m) Data for {$\beta^1$\,Mon and $\mu$\,Cen are shown in Fig.~\ref{Rivinius_OHANA_fig1}}. $\mu$\,Cen shows a broad shallow ramp-type wing in the line, which is reflected in the phase. This may be the signature of freshly ejected material closer to the star than the bulk of the disk. \begin{figure}[t] \begin{center} \parbox{0.5\textwidth}{\centerline{$\mu$\,Cen (B2\,Vnpe)}}% \parbox{0.5\textwidth}{\centerline{$\beta^1$\,Mon (B3\,Ve)}}% \includegraphics[width=0.5\textwidth]{muCen_intf.pdf}% \includegraphics[width=0.5\textwidth]{betMon_intf.pdf}% \caption{Example of OHANA data for the Be stars $\mu$\,Cen and $\beta^1$\,Mon.} \label{Rivinius_OHANA_fig1} \end{center} \end{figure} \begin{figure}[t] \begin{center} \parbox{0.5\textwidth}{\centerline{$\zeta^1$\,Sco (B0.5\,Ia+)}}% \parbox{0.5\textwidth}{\centerline{HD\,53\,138 (B3\,Ia)}}% \includegraphics[width=0.5\textwidth]{zetSco_intf.pdf}% \includegraphics[width=0.5\textwidth]{HD53138_intf.pdf}% \caption{Example of OHANA data for the B-type supergiants $\zeta^1$\,Sco and HD\,53\,138.} \label{Rivinius_OHANA_fig2} \end{center} \end{figure} \subsection{OB Supergiants} The OBA supergiants can be divided into three distinct sets, namely LBVs and the remaining ones along the wind bi-stability at about $T_{\rm eff}=22\,000$\,K. For the LBVs $\eta$\,Car and HR\,Car, dedicated contributions to this volume are presented by Mehner et al.\ and Rivinius et al. The {O- and early B-supergiants} do not show any obvious signature in visibility or phase, meaning their winds are too small to detect. In turn, the {later B- and A-type supergiants} do show such signatures in visibility, but again very little in phase. This is obvious for the hypergiant $\zeta^1$Sco, indicating an extended, but largely symmetric wind (Fig.~\ref{Rivinius_OHANA_fig2}, left). For HD\,53\,138 this is less obvious in Fig.~\ref{Rivinius_OHANA_fig2}, right, but comparison with calibrator data shows the visibility signature to be real, not instrumental. For HD\,53\,138 spectral emission variability goes together with a changing visibility and phase signature, which may indicate a variable, asymmetric wind. Further analysis of the data at hand may provide {constraints on the size and clumping of these winds}, while further observations may be able to {trace variability}, in particular for the slower winds with flow times of up to several weeks. \subsection{Interacting Binaries} The only observed interacting binary was SS\,Lep, with barely any interferometric signature. Small wiggles seen in the visibility of some longer baselines need to be verified. \section{Conclusions} The OHANA survey provided interferometric data of the circumstellar environments of Be stars and OBA supergiants. The raw data is publicly available, the reduced data will become so as soon as the final reduction has passed quality control tests. The reduced data will be made available from {\tt http://activebstars.iag.usp.br/index.php/34-ohana}. \bibliographystyle{iau307}	{ "redpajama_set_name": "RedPajamaArXiv" }	6,584
Patriotic Front may refer to: Patriotic Front (Austria) Patriotic Front (Bulgaria) Patriotic Front (Cyprus) Patriotic Front (Trinidad and Tobago) Patriotic Front (Zambia) Patriotic Front (Zimbabwe) Zimbabwe African National Union - Patriotic Front Patriotic Front for Political Action (UK) Rwandese Patriotic Front Manuel Rodríguez Patriotic Front, a Marxist-Leninist paramilitary organization in Chile	{ "redpajama_set_name": "RedPajamaWikipedia" }	8,343
The National Memorial Arch is dedicated "to the officers and private soldiers of the Continental Army December 19, 1777 June 19, 1778". The Arch is situated at the top of a hill at the intersection of Gulph Road and Outer Line Drive in Valley Forge National Historical Park, Chester County, Pennsylvania. The Arch was erected in 1910 by an act of the 61st Congress. It is modeled on the Arch of Titus in Rome. The architect in charge of the arch was Paul Philippe Cret. This description uses material from the Wikipedia article on National Memorial Arch and is licensed under the Creative Commons Attribution-ShareAlike License (view authors).	{ "redpajama_set_name": "RedPajamaC4" }	2,337
Der Air-France-Flug 358 (AF 358) war ein Passagierflug der Air France am 2. August 2005 vom Flughafen Paris-Charles de Gaulle (CDG) zum Toronto Pearson International Airport (YYZ). Die Maschine verließ Paris um 11:15 Uhr UTC (13:15 Uhr Ortszeit) und landete in Toronto um 20:02 Uhr UTC (16:02 Uhr Ortszeit). Bei der Landung auf dem kanadischen Flughafen schoss das Flugzeug über die Landebahn hinaus, stürzte in einen Graben und ging in Flammen auf. An Bord des Airbus 340-313X befanden sich 309 Personen (297 Passagiere und 12 Crewmitglieder), Kapitän war der 54-Jährige Alain Rosaye und Kopilot der 42-Jährige Frédéric Naud. Da der Unfall keine Todesopfer und nur einige Leichtverletzte forderte, wird auch vom Wunder von Toronto gesprochen. Die Maschine brannte vollständig aus. Daraufhin wurden alle geplanten Landungen auf andere Flughäfen umgeleitet, die größte Aktion nach der Operation Yellow Ribbon, bei der nach den Terroranschlägen in den USA am 11. September 2001 255 Flüge zu 15 verschiedenen kanadischen Flughäfen umgeleitet wurden. Ablauf Der Unfall geschah am 2. August 2005 um 16:02 Uhr Ortszeit. Zu diesem Zeitpunkt herrschte über dem Flughafen ein starkes Gewitter mit heftigen Niederschlägen und böigem Wind. Die Maschine setzte erst 1160 Meter (3800 Fuß) hinter dem Anfang der Landebahn 24 auf, also deutlich zu spät und wurde mittels der Fahrwerksbremsen mit voller Kraft gebremst. Allerdings wurde die Schubumkehr erst 12,8 Sekunden nach der Landung eingeleitet und hatte erst 16,4 Sekunden nach der Landung volle Kraft erreicht. Der Bremsweg reichte nicht mehr aus. Die Maschine rollte 300 Meter über das Ende der Bahn hinaus und kam zum Stehen, nachdem sie 12 Meter tiefer in eine Baumgruppe bis unmittelbar vor einen kleinen Bach rutschte, wo das Leitwerk am Heck abbrach und das Flugzeug Feuer fing. In der Mitte der Maschine brach Feuer aus und blockierte einige Notausgänge, außerdem versagten zwei Notrutschen. Trotzdem gelang die Evakuierung des Flugzeugs innerhalb von zwei Minuten nach der Bruchlandung, wobei sich einige Insassen Verletzungen zuzogen. Der Copilot verließ das Wrack als letzter. Die Passagiere liefen zum Highway, der parallel zur Landepiste verläuft, wo die Peel Regional Police sie in Empfang nahm. Einige Verletzte, darunter der Kapitän, wurden von Autofahrern mitgenommen und in naheliegende Krankenhäuser gefahren. Das Flugzeug brannte innerhalb von zwei Stunden völlig aus, die endgültige Löschung wurde um 18:00 Uhr gemeldet. Der Unfall wurde von einer Webcam gefilmt, das Material wurde anschließend beispielsweise auf CNN und n-tv ausgestrahlt. Bei der sofort angelaufenen Ermittlung konnte der von einigen Augenzeugen gemeldete Blitzeinschlag nicht bestätigt werden. Passagiere Fluggerät Bei der verunglückten Maschine handelte es sich um einen Airbus A340-313, der 1999 seinen Erstflug absolviert hatte. Das Flugzeug mit dem Luftfahrzeugkennzeichen F-GLZQ war mit vier CFM56-5C4-Triebwerken ausgestattet, die es auf eine maximale Geschwindigkeit von Mach 0,86 bringen konnten. Die letzte Überprüfung des Flugzeuges war am 5. Juli 2005 durchgeführt worden. Untersuchung Die Flugunfalluntersuchung wurde von der kanadischen Behörde für Transportsicherheit, (TSB, Transportation Safety Board of Canada) in Zusammenarbeit mit weiteren Organisationen durchgeführt: Transport Canada – Ministerial observer for Minister of Transport (Canada) Airbus Air France GE-Aviation United States National Transportation Safety Board (NTSB) Vermutungen kanadischer Ermittler im Vorfeld der Untersuchung Kanadische Ermittler erhoben im Vorfeld der Untersuchung gegen beide Piloten des Airbus Vorwürfe. Sie kritisierten insbesondere das Verhalten des ersten Offiziers, der das Flugzeug zum Unfallzeitpunkt führte. Er habe das Flugzeug erst "weit hinter der normalen Aufsetzzone" und damit deutlich zu spät auf der Start- und Landebahn aufsetzen lassen und dadurch die sichere Zone der 2800 Meter langen Landebahn verfehlt. Die Piloten hätten zwar, nachdem sie den Fehler bemerkt hatten, noch eine Notbremsung eingeleitet, trotzdem habe sich das Flugzeug auf dem unbefestigten Terrain nach dem Ende der Piste noch mit etwa 150 km/h bewegt. Eine Behauptung, der erste Offizier habe versucht, durchzustarten, konnte nicht bestätigt werden. Verzögertes Auslösen der Schubumkehr Die bei einer Landung zwingend und unverzüglich einzuleitende Schubumkehr (auch Umkehrschub genannt) erfolgte erst 17 Sekunden nach dem Aufsetzen der Maschine und damit viel zu spät. Der Kapitän erklärte hierzu später, dass der erste Offizier beim Aufsetzen der Maschine die Steuerorgane stark verkrampft hielt, und er selbst daher erst nach einigen Sekunden den Umkehrschub aktivieren konnte. Die Ermittler nehmen an, dass ohne diese Verzögerung auch das verbleibende Landebahn-Teilstück von 1500 m ausgereicht hätte, um das Flugzeug sicher zum Stillstand zu bringen. Downburst als mögliche Erklärung für das Verhalten des Flugzeugs Die Auswertung des Bodenradars durch die Ermittler ergab, dass sich die Geschwindigkeit des Flugzeugs auf der Landebahn zunächst erhöhte, anstatt sich zu verringern. Angesichts der Wetterbedingungen zum Zeitpunkt der Landung ist eine zumindest plausible Erklärung hierfür, dass ein Downburst hinter dem landenden Flugzeug niederging und die am Boden aufschlagende Böenwalze das Flugzeug von hinten erfasste. Das Flugzeug wäre von diesem rasch fortlaufenden Rotor angehoben worden und hätte wenige Meter über Grund beschleunigt, ohne dass die Piloten der Beschleunigung wirksam begegnen konnten. Die Bremsen wären wirkungslos geblieben, da das Fahrwerk keinen Bodenkontakt mehr hatte. Mit dieser Erklärung sind auch Zeugenaussagen von Passagieren in Einklang zu bringen; sie hätten gespürt, wie das Flugzeug wieder beschleunigte. Auch die Funktionen des Flugzeugs zur automatischen Landung konnten den Unfall wegen der zu kurzen Rest-Landebahnlänge nicht verhindern. Bei einer von Hand gesteuerten Landung bei Starkniederschlägen (wet downburst) wäre erschwerend die sogenannte Wasserglätte (Aquaplaning) hinzugekommen, die den Bremsweg weiter verlängert hätte. Fehlende Warneinrichtungen am Flughafen Auf dem Flughafen Toronto war kein sog. Windshear Radar (NEXRAD – next generation radar (engl.)) vorhanden. Das auf dem Doppler-Effekt beruhende Radar NEXRAD soll Flughafen und Piloten vor plötzlichen Böen und einem Downburst warnen. In Kanada ist bisher kein Flughafen mit dem NEXRAD ausgestattet, in den Vereinigten Staaten hingegen gehört es bereits zum Standard für Flughäfen. Ob der Flugsicherung und dem diensttuenden Flugmeteorologen online Satellitenaufnahmen von geostationären Satelliten zur Verfügung standen, aus denen klar die gefährliche meteorologische Entwicklung zu entnehmen war, klärte auch der endgültige Untersuchungsbericht des TSB nicht. Den Piloten standen diese bildlichen Wetter-Informationen jedenfalls nicht zur Verfügung, sie folgten strikt der Landeanweisung des Towers. Air-France-Chef Jean-Cyril Spinetta erklärte, die Flughafenaufsicht hätte in dieser widrigen Wetter-Situation von einer Landung dringend abraten müssen. Die Ermittler hingegen erklärten, der Kapitän trage die volle Verantwortung für die Entscheidung zur Landung. Abschlussbericht des TSB Der Abschlussbericht wurde am 16. Oktober 2007 zur Veröffentlichung freigegeben. Das TSB kommt im Wesentlichen zu dem Ergebnis, der Unfall sei auf eine Verkettung von widrigen, wetterbedingten Ereignissen zurückzuführen. Für einen Blitzschlag gab es keine Indizien. Die Piloten hätten – für sie nicht erkennbar – nicht alle nötigen Informationen gehabt; sie hätten die Schubumkehr der Triebwerke, die möglicherweise das Überschießen über das Landebahnende vermieden hätte, verzögert eingeleitet und auch die aktuell erforderliche Landebahnlänge trotz Gewitterwarnung nicht berechnet. Zudem hätten die vorgeschriebenen Verfahren das Risiko von Fehlern erhöht. Die Entscheidung der Crew, die Landung durchzuführen, wurde unter den gegebenen Umständen als den Vorgaben entsprechend eingestuft. Am Flughafen sei das Gelände ab 150 m nach dem Ende der Landebahn topografisch ungünstig gestaltet gewesen und habe zur Beschädigung des Flugzeugs beigetragen. Der Ablauf der Evakuierung sei nicht optimal gewesen, da die Ausstiegsrutschen wegen unzureichender Kennzeichnung nur einbahnig benutzt wurden, obwohl sie zweibahnig waren. Zudem habe fast die Hälfte der Passagiere das Handgepäck mitgenommen. Der Unfall zeigt nach Auffassung des TSB, dass Piloten generell insbesondere die direkten Wirkungen konvektiver Ereignisse, wie z. B. lokaler Gewitter, gefährlicher Scherwinde und Downbursts im Zusammenhang mit Starkregen bei Starts und Landungen immer noch unterschätzen. Einige der ausgelesenen Daten des Flugdatenschreibers sind im Anhang des Abschlussberichtes dokumentiert. Konsequenzen Wie nach den meisten Flugunfällen wurde die Nummer des Linienfluges von Paris nach Toronto zunächst geändert. Nach dem 1. April 2009 wurden jedoch wieder Flüge unter der Nummer 358 durchgeführt, laut der Internetseite FlightAware beispielsweise im Jahr 2013 Flüge von Réunion nach Paris Orly. Die Untersuchung des TSB stellte fest, dass die "Runway Safety Areas" am Ende der Start- und Landebahnen kanadischer Flughäfen die internationalen Standards nicht erfüllen und verbessert werden müssen. Das TSB schlug auch Vorsichtsmaßnahmen vor, die Fluggesellschaft und Flughafenbetreiber ergreifen sollen, wenn Landungen unter schlechten Wetterbedingungen erfolgen. Kapitän Alain Rosaye schied nach dem Unfall freiwillig aus dem Dienst der Air France aus. Er hat seit dem Unfall weder ein Luftfahrzeug der Air France noch ein anderes Luftfahrzeug geführt. Er leidet nach wie vor unter der psychischen Belastung und den Verletzungsfolgen. Der erste Offizier Frédéric Naud wurde während der Ermittlungen für drei Monate beurlaubt und fliegt seit Anfang 2006 wieder für Air France. Weblinks Bericht der kanadischen Transportsicherheitsbehörde (TSB) (engl.) Bilder eines Wettersatelliten zum Absturz AF-358 mit Animationen (engl.) Einzelnachweise Flugunfall in Kanada Flug 0358 Geschichte (Toronto) Flugunfall 2005 Geschichte der Luftfahrt (Frankreich) Luftverkehr (Toronto) Airbus A340	{ "redpajama_set_name": "RedPajamaWikipedia" }	3,720
Q: Total number of count in entire data frame I have a pandas data frame with 10*5, as shown in the fig the numbers in this vary from 1-10 I need to count the total number of occurrences of each number. Please note that it should find the entire data frame, not just an individual column Eg: number (1) appears : 3 times number (2) appears : 7 times number (3) appears : 5 times number (4) appears : 0 times number (5) appears : 6 times number (6) appears : 8 times number (7) appears : 7 times number (8) appears : 5 times number (9) appears : 6 times number (10) appears : 3 times Note: Data frame shown here is just an example, numbers may vary to from 1 to 30. Please guide me. Many thanks in advance. I just started coding in python and using pandas on my own and I admit I am a bit lost. Thanks for reading all this and thanks in advance for any suggestions and feedback. ! If further information is required , please leave your comment A: Use DataFrame.stack for Series and then count values by Series.value_counts with Series.reindex for add also missing values, last for custom ouput is possible use loop with print: np.random.seed(123) df = pd.DataFrame(np.random.randint(10, size=(5,5))) s = df.stack() out = s.value_counts().reindex(range(0, 11), fill_value=0) print (out) 0 5 1 4 2 3 3 3 4 3 5 0 6 2 7 2 8 0 9 3 10 0 dtype: int64 for k, v in out.items(): print(f'number ({k}) appears : {v} times') number (0) appears : 5 times number (1) appears : 4 times number (2) appears : 3 times number (3) appears : 3 times number (4) appears : 3 times number (5) appears : 0 times number (6) appears : 2 times number (7) appears : 2 times number (8) appears : 0 times number (9) appears : 3 times number (10) appears : 0 times Or: print (out.reset_index().apply(lambda x: f'number ({x["index"]}) appears : {x[0]} times', axis=1)) 0 number (0) appears : 5 times 1 number (1) appears : 4 times 2 number (2) appears : 3 times 3 number (3) appears : 3 times 4 number (4) appears : 3 times 5 number (5) appears : 0 times 6 number (6) appears : 2 times 7 number (7) appears : 2 times 8 number (8) appears : 0 times 9 number (9) appears : 3 times 10 number (10) appears : 0 times dtype: object	{ "redpajama_set_name": "RedPajamaStackExchange" }	2,165
package numeric import ( "github.com/ready-steady/linear/matrix" ) // Compute calculates the temperature profile corresponding to a power profile. // // The power profile is specified by a function func(time float64, power // []float64) evaluating the power dissipation at an arbitrary time moment. The // time moments for which the temperature profile is computed are specified by // the time array; see the corresponding ODE solver for further details. // // http://godoc.org/github.com/ready-steady/ode#Integrator func (self Temperature) Compute(power func(float64, []float64), time []float64) ([]float64, []float64, error) { nc, nn := self.nc, self.nn A, B := self.system.A, self.system.B P := make([]float64, nc) dSdt := func(self float64, S, dSdt []float64) { matrix.Multiply(A, S, dSdt, nn, nn, 1) power(self, P) for i := uint(0); i < nc; i++ { dSdt[i] += B[i] P[i] } } S, time, err := self.integrator.Compute(dSdt, make([]float64, nn), time) if err != nil { return nil, nil, err } ns := uint(len(time)) Q, Qamb := make([]float64, nsnc), self.system.Qamb for i := uint(0); i < nc; i++ { for j := uint(0); j < ns; j++ { Q[jnc+i] = S[j*nn+i] + Qamb } } return Q, time, nil }	{ "redpajama_set_name": "RedPajamaGithub" }	2,167
{"url":"https:\/\/authorea.com\/users\/3537\/articles\/3612-unearthing-the-contributions-and-ecology-of-uncultured-soil-bacteria-to-the-metabolism-of-xylose-and-cellulose-in-soil\/_show_article","text":"05\/12\/2016\nAbstract\n\n# Introductory Paragraph\n\nWe explored the microbial contributions to decomposition using a sophisticated approach to DNA Stable Isotope Probing (SIP). Our experiment evaluated the dynamics and ecological characteristics of functionally defined microbial groups that metabolize labile and structural C in soils. We added to soil a complex amendment representing plant derived organic matter substituted with either $$^{13}$$C-xylose or $$^{13}$$C-cellulose to represent labile and structural C pools derived from abundant components of plant biomass. We found evidence for $$^{13}$$C-incorporation into DNA from $$^{13}$$C-xylose and $$^{13}$$C-cellulose in\u00a049 and\u00a063 operational taxonomic units (OTUs), respectively. The types of microorganisms that assimilated $$^{13}$$C in the $$^{13}$$C-xylose treatment changed over time being predominantly Firmicutes at day\u00a01 followed by Bacteroidetes at day\u00a03 and then Actinobacteria at day\u00a07. These $$^{13}$$C-labeling dynamics suggest labile C traveled through different trophic levels. In contrast, microorganisms generally metabolized cellulose-C after 14 days and did not change to the same extent in phylogenetic composition over time. Microorganisms that metabolized cellulose-C belonged to poorly characterized but cosmopolitan soil lineages including Verrucomicrobia, Chloroflexi and Planctomycetes.\n\n# Significance\n\nSoil microorganisms drive C flux through the terrestrial biosphere, and models that predict terrestrial C flux can benefit by accounting for microbial ecophysiology in soils. However, characterizing the ecophysiology of microbes that mediate C decomposition in soil has proven difficult due to their overwhelming diversity. We characterized microbial C metabolism in soil and show that different types of C have distinct decomposition dynamics governed by different microbial lineages. For example, we found that uncharacterized microbial taxa, which are cosmopolitan in soils, assimilated cellulose-C into DNA. These microbes may drive cellulose decomposition on a global scale. We identify microbial lineages engaging in labile and structural C decomposition and explore their ecological properties.\n\n# Introduction\n\nSoils worldwide contain 2,300 Pg of carbon (C) which accounts for nearly\u00a080% of the C present in the terrestrial biosphere (Amundson, 2001; Batjes, 1996). Soil microorganisms drive C flux through the terrestrial biosphere and C respiration by soil microorganisms produces annually tenfold more CO$$_{2}$$ than fossil fuel emissions (Chapin, 2002). Despite the contribution of microorganisms to global C flux, many global C models ignore the diversity of microbial physiology (Allison et al., 2010; Six et al., 2006; Treseder et al., 2011) and we still know little about the ecophysiology of soil microorganisms. Characterizing the ecophysiology of microbes that mediate C decomposition in soil has proven difficult due to their overwhelming diversity. Such knowledge should assist the development and refinement of global C models (Bradford et al., 2008; Neff et al., 2001; McGuire et al., 2010; Wieder et al., 2013).\n\nThough microorganisms mediate 80-90% of the soil C-cycle (Coleman et al., 1996; Nannipieri et al., 2003), and microbial community composition can account for significant variation in C mineralization (Strickland et al., 2009), terrestrial C-cycle models rarely consider the community composition of soils (Zak et al., 2006; Reed et al., 2007). Variation in microbial community composition can be linked effectively to rates of soil processes when diagnostic genes for specific functions are available (e.g. nitrogen fixation (Hsu et al., 2009)). However, the lack of diagnostic genes for describing soil-C transformations has limited progress in characterizing the contributions of individual microorganisms to decomposition. Remarkably, we still lack basic information on the physiology and ecology of the majority of organisms that live in soils. For example, contributions to soil processes remain uncharacterized for cosmopolitan bacterial phyla in soil such as Acidobacteria, Chloroflexi, Planctomycetes, and Verrucomicrobia. These phyla combined can comprise 32% of soil microbial communities (based on surveys of the SSU rRNA genes in soil) (Janssen, ???; Buckley et al., 2002).\n\nTo predict whether and how biogeochemical processes vary in response to microbial community structure, it is necessary to characterize functional niches within soil communities. Functional niches defined on the basis of microbial physiological characteristics have been successfully incorporated into biogeochemical process models (E.g. (Wieder et al., 2013; Kaiser et al., 2014)). In some C-cycle models physiological parameters such as growth rate and substrate specificity are used to define functional niche behavior (Wieder et al., 2013). However, it is challenging to establish the phylogenetic breadth of functional traits. Functional traits are often inferred from the distribution of diagnostic genes across genomes (Berlemont et al., 2013) or from the physiology of isolates cultured on laboratory media (Martiny et al., 2013). For instance, the wide distribution of the glycolysis operon in microbial genomes is interpreted as evidence that many soil microorganisms participate in glucose turnover (McGuire et al., 2010). However, the functional niche may depend less on the distribution of diagnostic genes across genomes and more on life history traits that allow organisms to compete for a given substrate as it occurs in the environment. For instance, rapid resuscitation and fast growth are traits that may allow microorganisms to compete effectively for glucose in environments that exhibit high temporal variability. Alternatively, metabolic efficiency and slow growth rates may be traits that allow microbes to compete effectively for glucose in environments characterized by low temporal variability in glucose supply. These different competitive strategies would not be apparent from genome analysis, or when strains are grown in isolation. Hence, life history traits, rather than genomic capacity for a given pathway, are likely to constrain the diversity of microbes that metabolize a given C source in the soil under a given set of conditions. Therefore, to generate an understanding of functional niche as it relates to biogeochemical processes in soils it is important to characterize microbial functional traits as they occur in situ or in microcosm experiments.\n\nNucleic acid stable-isotope probing (SIP) links genetic identity and activity without the need diagnostic genetic markers or cultivation and has expanded our knowledge of microbial processes (Chen et al., 2010). Nucleic acid SIP has notable complications, however, including the need to add large amounts of labeled substrate (Radajewski et al., 2000), label dilution resulting in partial labeling of nucleic acids (Radajewski et al., 2000), the potential for cross-feeding and secondary label incorporation (DeRito et al., 2005), and variation in genome G$$+$$C content (Buckley et al., 2007). As a result, most applications of SIP have targeted specialized microorganisms (for instance, methylotrophs (Lueders et al., 2004), syntrophs (Lueders et al., 2004a), or microorganisms that target pollutants (DeRito et al., 2005)). Exploring the soil-C cycle with SIP has proven to be more challenging because SIP has lacked the resolution necessary to characterize the specific contributions of individual microbial groups to the decomposition of plant biomass. High throughput DNA sequencing technology, however, improves the resolving power of SIP (Aoyagi et al., 2015). It is now possible to use far less isotopically labeled substrate resulting in more environmentally realistic experimental conditions. It is also possible to sequence rRNA genes from numerous density gradient fractions across multiple samples thereby increasing the resolution of a typical nucleic acid SIP experiment (Verastegui et al., 2014). With this improved resolution the activity of more soil microorganisms can be assessed. Further, since microbial activities can be more comprehensively assessed, we can begin to determine the ecological properties of functional groups defined by a specific activity in a DNA-SIP experiment. We have employed such a high resolution DNA stable isotope probing approach to explore the assimilation of both xylose and cellulose into bacterial DNA in an agricultural soil.\n\nWe added to soil a complex amendment representative of organic matter derived from fresh plant biomass. All treatments received the same amendment but the identity of isotopically labeled substrates was varied between treatments. Specifically, we set up a control treatment where all components were unlabeled, a treatment with $$^{13}$$C-xylose instead of unlabeled xylose, and a treatment with $$^{13}$$C-cellulose instead of unlabeled cellulose. Soil was sampled at days\u00a01,\u00a03,\u00a07,\u00a014,\u00a0and\u00a030 and we identified microorganisms that assimilated $$^{13}$$C into DNA at each point in time. We designed the experiment to test of the degradative succession hypothesis as it applies to soil bacteria, to identify soil bacteria that metabolize xylose and cellulose, and to characterize temporal dynamics of xylose and cellulose metabolism in soil.\n\n# Results\n\nAfter adding the organic matter amendment to soil, we tracked the flow of $$^{13}$$C from $$^{13}$$C-xylose or $$^{13}$$C-cellulose into microbial DNA over time using DNA-SIP (Figure\u00a0\\ref{fig:setup}). The amendment consisted of compounds found in of plant biomass including cellulose, lignin, sugars found in hemicellulose, amino acids, and inorganic nutrients (see Supplemental Information (SI)). The amendment was added at\u00a02.9 mg C g$$^{-1}$$ soil dry weight (d.w.), and this comprised 19% of the total C in the soil. The cellulose-C (0.88 mg C g$$^{-1}$$ soil d.w.) and xylose-C (0.42 mg C g$$^{-1}$$ soil d.w.) in the amendment comprised 6% and 3% of the total C in the soil, respectively. The soil microbial community respired 65% of the xylose within one day and 29% of the added xylose remained in the soil at day\u00a030 (Figure\u00a0\\ref{fig:13C}). In contrast, cellulose-C declined at a rate of approximately 18 $$\\mu$$g C d $$^{-1}$$ g\u2005$$^{-1}$$ soil d.w. and 40% of added cellulose-C remained in the soil at day\u00a030 (Figure\u00a0\\ref{fig:13C}).\n\n## Community-level signal of $$^{13}$$C-assimilation in relation to substrate and time\n\nWe assessed assimilation of $$^{13}$$C into microbial DNA by comparing the SSU rRNA gene sequence composition of SIP density gradient fractions between $$^{13}$$C treatments and the unlabeled control (see Methods and SI). Our main focus is to identify evidence of isotope incorporation into the DNA of specific OTUs (as described below), but it is instructive to begin by observing overall patterns of variance in the SSU rRNA gene sequence composition of gradient fractions. In the unlabeled control treatment, fraction density represented the majority of the variance in SSU rRNA gene composition (Figure\u00a0\\ref{fig:ord}). This result is expected because Genome G$$+$$C content correlates positively with DNA buoyant density and influences SSU rRNA gene composition in gradient fractions (Buckley et al., 2007). In contrast, isotope assimilation into DNA will cause variation in gene sequence composition between corresponding density fractions from controls and labeled treatments. For example, the SSU rRNA gene composition in gradient fractions from the $$^{13}$$C-cellulose treatment deviated from corresponding control fractions on days\u00a014 and\u00a030 and this difference was observed only in the high density fractions ($$>$$1.7125 g mL$$^{-1}$$, Figure\u00a0\\ref{fig:ord}). Likewise, SSU rRNA gene composition in gradient fractions from the $$^{13}$$C-xylose treatment also deviated from corresponding control fractions but on days\u00a01,\u00a03,\u00a0and\u00a07 as opposed to 14 and 30 (Figure\u00a0\\ref{fig:ord}). The $$^{13}$$C-cellulose and $$^{13}$$C-xylose treatments also differed from each other in corresponding high density gradient fractions indicating that different microorganisms were labeled across time these treatments (Figure\u00a0\\ref{fig:ord}). These results are generally consistent with predictions of the degradative succession hypothesis.\n\nWe can observe further differences in the pattern of isotope incorporation over time for each treatment. For example the SSU rRNA gene sequence composition in the $$^{13}$$C-cellulose treatment was similar on days 14 and 30 in corresponding high density fractions indicating similar patterns of isotope incorporation into DNA on the days. In contrast, in the $$^{13}$$C-xylose treatment, the SSU rRNA gene composition varied between days\u00a01,\u00a03,\u00a0and\u00a07 in corresponding high density fractions indicating different patterns of isotope incorporation into DNA on these days. In the $$^{13}$$C-xylose treatment on days 14 and 40 the SSU gene composition was similar to control on days\u00a014\u00a0and\u00a030 for corresponding high density fractions (Figure\u00a0\\ref{fig:ord}) indicating that $$^{13}$$C was no longer detectable in bacterial DNA on these days for this treatment. These results show that the dynamics of isotope incorporation into DNA varied considerably for organisms that assimilated C from either xylose or cellulose.\n\n## Temporal dynamics of OTU relative abundance in non-fractionated DNA from soil\n\nWe monitored the soil microbial community over the course of the experiment by surveying SSU rRNA genes in non-fractionated DNA from the soil. The SSU rRNA gene composition of the non-fractionated DNA changed with time (Figure\u00a0\\ref{fig:bulk_ord}, P-value\u00a0$$=$$\u00a00.023, R$$^{2}$$ $$=$$\u00a00.63, Adonis test (Anderson, 2001)). In contrast, the microbial community could not be shown to change with treatment (P-value\u00a00.23, Adonis test) (Figure\u00a0\\ref{fig:bulk_ord}). The latter result demonstrates the substitution of $$^{13}$$C-labeled substrates for unlabeled equivalents could not be shown to alter the soil microbial community composition. Twenty-nine OTUs exhibited sufficient statistical evidence (adjusted P-value $$<$$\u20040.10, Wald test) to conclude they changed in relative abundance in the non-fractionated DNA over the course of the experiment (Figure\u00a0\\ref{fig:time}). When SSU rRNA gene abundances were combined at the taxonomic rank of \u201cclass\u201d, the classes that changed in abundance (adjusted P-value\u00a0 $$<$$\u00a00.10, Wald test) were the Bacilli (decreased), Flavobacteria (decreased), Gammaproteobacteria (decreased), and Herpetosiphonales (increased) (Figure\u00a0\\ref{fig:time_class}). Of the\u00a029 OTUs that changed in relative abundance over time, 14 putatively incorporated $$^{13}$$C into DNA (see below and Figure\u00a0\\ref{fig:time}). OTUs that likely assimilated $$^{13}$$C from $$^{13}$$C-cellulose tended to increase in relative abundance with time whereas OTUs that assimilated $$^{13}$$C from $$^{13}$$C-xylose tended to decrease (Figure\u00a0\\ref{fig:babund}). OTUs that responded to both substrates did not exhibit a consistent relative abundance response over time as a group (Figure\u00a0\\ref{fig:time}\u00a0and\u00a0\\ref{fig:babund}).\n\n## Changes in the phylogenetic composition of $$^{13}$$C-labeled OTUs with substrate and time\n\nIf an OTU exhibited strong evidence for assimilating $$^{13}$$C into DNA, we refer to that OTU as a \u201cresponder\u201d (see Methods and SI for our operational definition of \u201cresponder\u201d). The SSU rRNA gene sequences produced in this study were binned into 5,940 OTUs and we assessed evidence of $$^{13}$$C-labeling from both $$^{13}$$C-cellulose and $$^{13}$$C-xylose for each OTU. Forty-one OTUs responded to $$^{13}$$C-xylose,\u00a055 OTUs responded to $$^{13}$$C-cellulose, and 8 OTUs responded to both xylose and cellulose (Figure\u00a0\\ref{fig:l2fc}, Figure\u00a0\\ref{fig:tiledtree}, Figure\u00a0\\ref{fig:genspec}, Table\u00a0\\ref{tab:xyl}, and Table\u00a0\\ref{tab:cell}). The number of xylose responders peaked at days\u00a01 and\u00a03 and declined with time. In contrast, the number of cellulose responders increased with time peaking at days\u00a014 and\u00a030 (Figure\u00a0\\ref{fig:rspndr_count}).\n\nThe phylogenetic composition of xylose responders changed with time (Figure\u00a0\\ref{fig:l2fc}\u00a0and\u00a0Figure\u00a0\\ref{fig:xyl_count}) and 86% of xylose responders shared $$>$$ 97% SSU rRNA gene sequence identity with bacteria cultured in isolation (Table\u00a0\\ref{tab:xyl}). On day 1, Bacilli OTUs represented 84% of xylose responders (Figure\u00a0\\ref{fig:xyl_count}) and the majority of these OTUs were closely related to cultured representatives of the genus Paenibacillus (Table\u00a0\\ref{tab:xyl}, Figure\u00a0\\ref{fig:tiledtree}). For example, \u201cOTU.57\u201d (Table\u00a0\\ref{tab:xyl}), annotated as Paenibacillus, had a strong signal of $$^{13}$$C-labeling at day\u00a01 coinciding with its maximum relative abundance in non-fractionated DNA. The relative abundance of \u201cOTU.57\u201d declined until day 14 and \u201cOTU.57\u201d did not appear to be $$^{13}$$C-labeled after day\u00a01 (Figure\u00a0\\ref{fig:example}). On day\u00a03, Bacteroidetes OTUs comprised 63% of xylose responders (Figure\u00a0\\ref{fig:xyl_count}) and these OTUs were closely related to cultured representatives of the Flavobacteriales and Sphingobacteriales (Table\u00a0\\ref{tab:xyl}, Figure\u00a0\\ref{fig:tiledtree}). For example, \u201cOTU.14\u201d, annotated as a flavobacterium, had a strong signal for $$^{13}$$C-labeling in the $$^{13}$$C-xylose treatment at days 1 and 3 coinciding with its maximum relative abundance in non-fractionated DNA. The relative abundance of \u201cOTU.14\u201d then declined until day 14 and did not show evidence of $$^{13}$$C-labeling beyond day\u00a03 (Figure\u00a0\\ref{fig:example}). Finally, on day\u00a07, Actinobacteria OTUs represented 53% of the xylose responders (Figure\u00a0\\ref{fig:xyl_count}) and these OTUs were closely related to cultured representatives of Micrococcales (Table\u00a0\\ref{tab:xyl}, Figure\u00a0\\ref{fig:tiledtree}). For example, \u201cOTU.4\u201d, annotated as Agromyces, had signal for $$^{13}$$C-labeling in the $$^{13}$$C-xylose treatment on days\u00a01,\u00a03\u00a0and\u00a07 with the strongest evidence of $$^{13}$$C-labeling at day\u00a07 and did not appear $$^{13}$$C-labeled at days\u00a014 and\u00a030. The relative abundance of \u201cOTU.4\u201d in non-fractionated DNA increased until day\u00a03 and then declined until day\u00a030 (Figure\u00a0\\ref{fig:example}). Proteobacteria were also common among xylose responders at day\u00a07 where they comprised 40% of xylose responder OTUs. Notably, Proteobacteria represented the majority (6 of 8) of OTUs that responded to both cellulose and xylose (Figure\u00a0\\ref{fig:genspec}).\n\nThe phylogenetic composition of cellulose responders did not change with time to the same extent as the xylose responders. Also, in contrast to xylose responders, cellulose responders often were not closely related ($$<$$ 97% SSU rRNA gene sequence identity) to cultured isolates. Both the relative abundance and the number of cellulose responders increased over time peaking at days 14 and 30 (Figure\u00a0\\ref{fig:l2fc}, Figure\u00a0\\ref{fig:rspndr_count}, and Figure\u00a0\\ref{fig:babund}). Cellulose responders belonged to the Proteobacteria (46%), Verrucomicrobia (16%), Planctomycetes (16%), Chloroflexi (8%), Bacteroidetes (8%), Actinobacteria (3%), and Melainabacteria (1 OTU) (Table\u00a0\\ref{tab:cell}).\n\nThe majority (85%) of cellulose responders outside of the Proteobacteria shared $$<$$ 97% SSU rRNA gene sequence identity to bacteria cultured in isolation. For example, 70% of the Verrucomicrobia cellulose responders fell within unidentified Spartobacteria clades (Figure\u00a0\\ref{fig:tiledtree}), and these shared $$<$$ 85% SSU rRNA gene sequence identity to any characterized isolate. The Spartobacteria OTU \u201cOTU.2192\u201d exemplified many cellulose responders (Table\u00a0\\ref{tab:cell}, Figure\u00a0\\ref{fig:example}). \u201cOTU.2192\u201d increased in non-fractionated DNA relative abundance with time and evidence for $$^{13}$$C-labeling of \u201cOTU.2192\u201d in the $$^{13}$$C-cellulose treatment increased over time with the strongest evidence at days\u00a014 and\u00a030 (Figure\u00a0\\ref{fig:example}). Most Chloroflexi cellulose responders belonged to an unidentified clade within the Herpetosiphonales (Figure\u00a0\\ref{fig:tiledtree}) and they shared $$<$$ 89% SSU rRNA gene sequence identity to any characterized isolate. Characteristic of Chloroflexi cellulose responders, \u201cOTU.64\u201d increased in relative abundance over 30 days and evidence for $$^{13}$$C-labeling of \u201cOTU.64\u201d in the $$^{13}$$C-cellulose treatment peaked days 14 and\u00a030 (Figure\u00a0\\ref{fig:example}). Bacteroidetes cellulose responders fell within the Cytophagales in contrast with Bacteroidetes xylose responders that belonged instead to the Flavobacteriales or Sphingobacteriales (Figure\u00a0\\ref{fig:tiledtree}). Bacteroidetes cellulose responders included one OTU that shared 100% SSU rRNA gene sequence identity to a Sporocytophaga species, a genus known to include cellulose degraders. The majority (86%) of cellulose responders in the Proteobacteria were closely related ($$>$$ 97% identity) to bacteria cultured in isolation, including representatives of the genera: Cellvibrio, Devosia, Rhizobium, and Sorangium, which are all known for their ability to degrade cellulose (Table\u00a0\\ref{tab:cell}). Proteobacterial cellulose responders belonged to Alpha (13\u00a0OTUs), Beta (4\u00a0OTUs), Gamma (5\u00a0OTUs), and Delta-proteobacteria (6\u00a0OTUs).\n\n## Characteristics of cellulose and xylose responders\n\nCellulose responders, relative to xylose responders, tended to have lower relative abundance in non-fractionated DNA, demonstrated signal consistent with higher atom % $$^{13}$$C in labeled DNA, and had lower estimated rrn copy number (Figure\u00a0\\ref{fig:shift}). OTUs that assimilated C from either cellulose or xylose were also clustered phylogenetically (see below) indicating that these traits were not dispersed randomly across bacterial species.\n\nIn the non-fractionated DNA, cellulose responders had lower relative abundance (1.2 x 10$$^{-3}$$ (s.d. 3.8 x 10$$^{-3}$$)) than xylose responders (3.5 x 10$$^{-3}$$ (s.d. 5.2 x 10$$^{-3}$$)) (Figure\u00a0\\ref{fig:xyl_count}, P-value\u00a0$$=$$\u00a01.12 x 10$$^{-5}$$, Wilcoxon Rank Sum test). Six of the ten most common OTUs observed in the non-fractionated DNA responded to xylose, and, seven of the ten most abundant responders to xylose or cellulose in the non-fractionated DNA were xylose responders.\n\nDNA buoyant density (BD) increases in proportion to atom % $$^{13}$$C. Hence, the extent of $$^{13}$$C incorporation into DNA can be evaluated by the difference in BD between $$^{13}$$C-labeled and unlabeled DNA. We calculated for each OTU its mean BD weighted by relative abundance to determine its \u201ccenter of mass\u201d within a given density gradient. We then quantified for each OTU the difference in center of mass between control gradients and gradients from $$^{13}$$C-xylose or $$^{13}$$C-cellulose treatments (see SI for the detailed calculation, Figure\u00a0\\ref{fig:c1}). We refer to the change in center of mass position for an OTU in response to $$^{13}$$C-labeling as $$\\Delta\\hat{BD}$$. This value can be used to compare relative differences in $$^{13}$$C-labeling between OTUs. $$\\Delta\\hat{BD}$$ values, however, are not comparable to the BD changes observed for DNA from pure cultures both because they are based on relative abundance in density gradient fractions (and not DNA concentration) and because isolated strains grown in uniform conditions generate uniformly labeled molecules while OTUs composed of heterogeneous strains in complex environmental samples do not. Cellulose responder $$\\Delta\\hat{BD}$$ (0.0163 g mL$$^{-1}$$ (s.d.\u00a00.0094)) was greater than that of xylose responders (0.0097 g mL$$^{-1}$$ (s.d.\u00a00.0094)) (Figure\u00a0\\ref{fig:shift}, P-value\u00a0$$=$$\u00a01.8610 x 10$$^{-6}$$, Wilcoxon Rank Sum test).\n\nWe predicted the rrn gene copy number for responders as described (Kembel et al., 2012). The ability to proliferate after rapid nutrient influx correlates positively to a microorganism\u2019s rrn copy number (Klappenbach et al., 2000). Cellulose responders possessed fewer estimated rrn copy numbers (2.7\u00a0(1.2\u00a0s.d.)) than xylose responders (6.2\u00a0(3.4\u00a0s.d.)) ( P\u00a0=\u00a01.878 x 10$$^{-9}$$, Wilcoxon Rank Sum test, Figure\u00a0\\ref{fig:shift} and Figure\u00a0\\ref{fig:copy}). Furthermore, the estimated rrn gene copy number for xylose responders was inversely related to the day of first response (P\u00a0=\u00a02.02 x 10$$^{-15}$$, Wilcoxon Rank Sum test, Figure\u00a0\\ref{fig:copy},Figure\u00a0\\ref{fig:shift}).\n\nWe assessed phylogenetic clustering of $$^{13}$$C-responsive OTUs with the Nearest Taxon Index (NTI) and the Net Relatedness Index (NRI) (Webb, 2000). We also quantified the average clade depth of cellulose and xylose responders with the consenTRAIT metric (Martiny et al., 2013). Briefly, the NRI and NTI evaluate phylogenetic clustering against a null model for the distribution of a trait in a phylogeny. The NRI and NTI values are z-scores or standard deviations from the mean and thus the greater the magnitude of the NRI\/NTI, the stronger the evidence for clustering (positive values) or overdispersion (negative values). NRI assesses overall clustering whereas the NTI assesses terminal clustering (Evans et al., 2014). The consenTRAIT metric is a measure of the average clade depth for a trait in a phylogenetic tree. NRI values indicate that cellulose responders clustered overall and at the tips of the phylogeny (NRI:\u00a04.49, NTI:\u00a01.43) while xylose responders clustered terminally (NRI:\u00a0-1.33, NTI:\u00a02.69). The consenTRAIT clade depth for xylose and cellulose responders was\u00a00.012 and\u00a00.028 SSU rRNA gene sequence dissimilarity, respectively. As reference, the average clade depth as inferred from genomic analyses or growth in culture is approximately\u00a00.017,\u00a00.013 and\u00a00.034 SSU rRNA gene sequence dissimilarity for arabinase (arabinose like xylose is a five C sugar found in hemicellulose), glucosidase and cellulase, respectively (Martiny et al., 2013; Berlemont et al., 2013). These results indicate xylose responders form terminal clusters dispersed throughout the phylogeny while cellulose responders form deep clades of terminally clustered OTUs.\n\n# Discussion\n\nWe highlight two key results with implications for understanding structure-function relationships in soils, and for applying DNA-SIP in future studies of the soil-C cycle. First, cellulose responders were members of physiologically undescribed taxonomic groups with few exceptions. This suggests that we have much to learn about the diversity of structural-C decomposers in soil before we can begin to assess how they are affected by climate change and land management. Second, the response to xylose was characterized by a succession in activity from Paenibacillus OTUs (day 1) to Bacteroidetes (day 3) and finally Micrococcales (day 7). Notably, Paenibacillus have been previously shown by DNA-SIP to metabolize glucose (Verastegui et al., 2014), also a common sugar in plant biomass. This activity succession was mirrored by relative abundance profiles and may mark trophic-C exchange between these groups. While trophic exchange has been observed previously in DNA-SIP studies (Lueders et al., 2004) most applications of DNA-SIP focus on proximal use of labeled substrates. However, with increased sensitivity, DNA-SIP is well suited to tracking C flows throughout microbial communities over time and is not limited only to observing the entry point for a given substrate into the soil C-cycle. Trophic interactions will critically influence how the global soil-C reservoir will respond to climate change (Crowther et al., 2015) but we know little of biological interactions among soil bacteria. Often bacteria are cast as a single trophic level (Moore et al., 1988) but it may be appropriate to investigate the soil food web at greater granularity. Additionally, our results show that DNA-SIP results can change dramatically over time suggesting that multiple time points are necessary to rigorously and comprehensively describe which microorganisms consume $$^{13}$$C-labeled substrates in nucleic acid SIP incubations.\n\nBacteria that consumed $$^{13}$$C-cellulose were seldom related closely to any physiologically characterized cultured isolates but were members of cosmopolitan phylogenetic groups in soil including Spartobacteria, Planctomycetes, and Chloroflexi. Often cellulose responders were less than 90% related to their closest cultured relatives showing that we can infer little, if anything at all, of their physiology from culture-based studies. Notably, many Spartobacteria were among the cellulose responder OTUs. This is particularly interesting as Spartobacteria are globally distributed and found in a variety of soil types (Bergmann et al., 2011). These lineages may play important roles in global cellulose turnover (please see SI note 1 for further discussion of the phylogenetic affiliation of cellulose responders).\n\nThe turnover of cellulose and plant-derived sugars in soil has been studied previously using DNA-SIP (e.g. (Verastegui et al., 2014)). Similar to our study, phylotypes among the Chloroflexi, Bacteroidetes and Planctomycetes have all been previously implicated in soil cellulose degradation (Schellenberger et al., 2010). Additionally, functional metagenomics enabled by DNA-SIP has identified glycoside hydrolases putatively belonging to Cellvibrio and Spartobacteria further suggesting a role for these organisms in cellulose breakdown in soils (Verastegui et al., 2014). Fungi undoubtedly also contribute to the decomposition of cellulose in soils (Boer et al., 2005), but they are not a focus of this experiment. It should be noted that longstanding hypotheses that delineate the life history strategies of fungi and bacteria on the basis of substrate preference have been recently questioned (Rousk et al., 2015). The approach we describe is also suitable for observing the activity of fungi (by targeting genetic markers in fungi with fungal specific PCR primers) and should prove useful in testing hypotheses that explain the functional traits of both bacteria and fungi as they occur in soils.\n\nIn addition to taxonomic identity, we quantified four ecological properties of microorganisms that were actively engaged in labile and structural C decomposition in our experiment: (1) time of activity, (2) estimated rrn gene copy number, (3) phylogenetic clustering, and (4) density shift in response to $$^{13}$$C-labeling. Labile C was consumed before structural C and these substrates were consumed by different microorganisms (Figure\u00a0\\ref{fig:ord}). This was expected and is consistent with the degradative succession hypothesis. Consumers of labile C had higher estimated rrn gene copy number than structural C consumers (Figure\u00a0\\ref{fig:shift}). rrn copy number is positively correlated with the ability to resuscitate quickly in response to nutrient influx (Klappenbach et al., 2000) which may be the advantage that enabled xylose responders to rapidly consume xylose. Both xylose and cellulose responders were terminally clustered phylogenetically suggesting that the ability to use these substrates was phylogenetically constrained. Although labile C consumption is generally considered to be mediated by a diverse set of microorganisms, we found that xylose responders at day 1 were mainly members of one genus, Paenibacillus. Our results suggests that life-history traits such as the ability to resuscitate quickly and\/or grow rapidly may be more important in determining the diversity of microorganisms that actually mediate a given process than the genomic potential for substrate utilization (see SI note 2 for further discussion with respect to soil-C modelling). And last, labile C consumers, in contrast to structural C consumers, had lower $$\\Delta\\hat{BD}$$ in response to $$^{13}$$C-labeling. This result suggests that labile C consumers were generalists, assimilating C from a variety of sources both labeled and unlabeled, while structural C consumers were more likely to be specialists and more closely associated with C from a single source.\n\nWe propose that the temporal fluctuations in $$^{13}$$C-labeling in the $$^{13}$$C-xylose treatment are due to trophic exchange of $$^{13}$$C. Alternatively, the temporal dynamics could be caused by microorganisms tuned to different substrate concentrations and\/or cross-feeding. However, trophic exchange would explain well the precipitous drop in abundance of Paenibacillus after day 1 with subsequent $$^{13}$$C-labeling of Bacteroidetes at day 3 as well as the precipitous drop in abundance of Bacteroidetes at day 3 followed by $$^{13}$$C-labeling of Micrococcales at day 7. Trophic exchange could be enabled by mother cell lysis (in the case of spore formers such as Paenibacillus), viral lysis, and\/or the direct indirect effects of predation. Bacteroidetes types have been shown to become $$^{13}$$C-labeled after the addition of live $$^{13}$$C-labeled Escherichia coli to soil (Lueders et al., 2006) indicating their ability to assimilate C from microbial biomass. In addition, the dominant OTU labeled in the $$^{13}$$C-xylose treatment from the Micrococcales shares 100% SSU rRNA gene sequence identity to Agromyces ramosus a known predator that feeds upon on many microorganisms including yeast and Micrococcus luteus (Casida, 1983). Agromyces are abundant microorganisms in many soils and Agromyces ramosus was the most abundant xylose responder in our experiment \u2013 the fourth most abundant OTU in our dataset. It is notable however, that if Agromyces ramosus is acting as a predator in our experiment, the organism remains unlabeled in response to $$^{13}$$C-cellulose which suggests that its activity may be specific for certain prey or for certain environmental conditions (see SI note 3 for further discussion of trophic C exchange). Climate change is expected to diminish bottom-up controls on microbial growth increasing the importance on top-down biological interactions for mitigating positive climate change feedbacks (Crowther et al., 2015). Currently the extent of bacterial predatory activity in soil, and its consequences for the soil C-cycle and carbon use efficiency is largely unknown. Elucidating the identities of bacterial predators in soil will assist in assessing the implications of climate change on global soil-C storage.\n\n## Conclusion\n\nMicroorganisms govern C-transformations in soil and thereby influence global climate but still we do not know the specific identities of microorganisms that carry out critical C transformations. In this experiment microorganisms from physiologically uncharacterized but cosmopolitan soil lineages participated in cellulose decomposition. Cellulose responders included members of the Verrucomicrobia (Spartobacteria), Chloroflexi, Bacteroidetes and Planctomycetes. Spartobacteria in particular are globally cosmopolitan soil microorganisms and are often the most abundant Verrucomicrobia order in soil (Bergmann et al., 2011). Fast-growing aerobic spore formers from Firmicutes assimilated labile C in the form of xylose. Xylose responders within the Bacteroidetes and Actinobacteria likely became labeled by consuming $$^{13}$$C-labeled constituents of microbial biomass either by saprotrophy or predation. Our results suggest that cosmopolitan Spartobacteria may degrade cellulose on a global scale, decomposition of labile plant C may initiate trophic transfer within the bacterial food web, and life history traits may act as a filter constraining the diversity of active microorganisms relative to those with the genomic potential for a given metabolism.\n\n# Methods\n\nAll code to take raw SSU rRNA gene sequencing reads to final publication figures and through all presented analyses is located at the following URL:\nhttps:\/\/github.com\/chuckpr\/CSIP_succession_data_analysis.\nDNA sequences are deposited on MG-RAST (Accession XXXXXXX).\n\nTwelve soil cores (5 cm diameter x 10 cm depth) were collected from six sampling locations within an organically managed agricultural field in Penn Yan, New York. Soils were sieved (2 mm), homogenized, distributed into flasks (10 g in each 250 ml flask, n = 36) and equilibrated for 2 weeks. The soil type was Honeoye previously measured to be approximately neutral pH (for a thorough description of the site see Berthrong et al. (2013)). We amended soils with a mixture containing 2.9 mg C g$$^{-1}$$ soil dry weight (d.w.) and brought soil to 50% water holding capacity. By mass the amendment contained 38% cellulose, 23% lignin, 20% xylose, 3% arabinose, 1% galactose, 1% glucose, and 0.5% mannose. 10.6% amino acids (made in house based on Teknova C9795 formulation) and 2.9% Murashige Skoog basal salt mixture which contains macro and micro-nutrients that are associated with plant biomass (Sigma Aldrich M5524). This mixture approximates the molecular composition of switchgrass biomass with hemicellulose replaced by its constituent monomers (Schneckenberger et al., 2008). We set up three parallel treatments varying the isotopically labeled component in each treatment. The treatments were (1) a control treatment with all unlabeled components, (2) a treatment with $$^{13}$$C-cellulose instead of unlabeled cellulose (synthesized as described in SI), and (3) a treatment with $$^{13}$$C-xylose (98 atom% $$^{13}$$C, Sigma Aldrich) instead of unlabeled xylose. Other details relating to substrate addition can be found in SI. Microcosms were sampled destructively at days\u00a01 (control and xylose only),\u00a03,\u00a07,\u00a014, and\u00a030 and soils were stored at -80\u2005$$^{\\circ}$$C until nucleic acid extraction. The abbreviation \u201c13CXPS\u201d refers to the $$^{13}$$C-xylose treatment ($$^{13}$$C Xylose Plant Simulant), \u201c13CCPS\u201d refers to the $$^{13}$$C-cellulose treatment, and \u201c12CCPS\u201d refers to the control treatment.\n\nWe used DESeq2 (R package), an RNA-Seq differential expression statistical framework (Love et al., 2014), to identify OTUs that were enriched in high density gradient fractions from $$^{13}$$C-treatments relative to corresponding gradient fractions from control treatments (for review of RNA-Seq differential expression statistics applied to microbiome OTU count data see (McMurdie et al., 2014)). We define \u201chigh density gradient fractions\u201d as gradient fractions whose density falls between 1.7125 and 1.755 g ml$$^{-1}$$. For each OTU, we calculates logarithmic fold change (LFC) and corresponding standard error for enrichment in high density fractions of $$^{13}$$C treatments relative to control. Subsequently, a one-sided Wald test was used to assess the statistical significance of LFC values with the null hypothesis that LFC was less than one standard deviation above the mean of all LFC values. We independently filtered OTUs prior to multiple comparison corrections on the basis of sparsity eliminating OTUs that failed to appear in at least 45% of high density fractions for a given comparison. P-values were adjusted for multiple comparisons using the Benjamini and Hochberg method (Benjamini et al., 1995). We selected a false discovery rate of 10% to denote statistical significance.\n\nSee SI for additional information on experimental and analytical methods.\n\n## Acknowledgements\n\nThe authors would like to acknowledge the assistance of John Christian Gaby and Mallory Choudoir in developing the method used to produce $$^{13}$$C-labeled cellulose. We would also like to thank Ruth Ley, Steve Zinder, Nelson Hairston, and Nick Youngblut for providing comments that were helpful in the development of this manuscript. Sander Hunter assisted with the microcosm set up. This material is based upon work supported by the Department of Energy Office of Science, Office of Biological & Environmental Research Genomic Science Program under Award Numbers DE-SC0004486 and DE-SC0010558. Manuscript preparation by Ashley N. Campbell was performed under the auspices of the U.S. Department of Energy by LLNL under Contract DE-AC52-07NA27344.\n\nChange in non-fractionated DNA relative abundance versus time (expressed as LFC) for OTUs that changed significantly over time (P-value $$<$$ 0.10, Wald test). Each panel shows one phylum (labeled on the right). The taxonomic class is indicated on the left. OTUs that responded to just xylose are shown in green, just cellulose in blue, and both xylose and cellulose in red.\n\nRelative abundance in non-fractionated DNA versus time for classes that changed significantly. Samples from different treatments are labeled with different colors as indicated in the scale. Statistical analysis is presented in main text.\n\nNMDS ordination of SSU rRNA gene sequence composition in gradient fractions shows that variation between fractions is correlated with fraction density, isotopic labeling, and time. Dissimilarity in SSU rRNA gene sequence composition was quantified using the weighted UniFrac metric. SSU rRNA gene sequences were surveyed in twenty gradient fractions at each sampling point for each treatment (Figure\u00a0S1). $$^{13}$$C-labeling of DNA is apparent because the SSU rRNA gene sequence composition of gradient fractions from $$^{13}$$C and control treatments differ at high density. Each point on the NMDS plot represents one gradient fraction. SSU rRNA gene sequence composition differences between gradient fractions were quantified by the weighted Unifrac metric. The size of each point is positively correlated with density and colors indicate the treatment (A) or day (B).\n\nEnrichment of OTUs in either $$^{13}$$C-cellulose (13CCPS, upper panels) or $$^{13}$$C-xylose (13CXPS, bottom panels) treatments relative to control, expressed as LFC (see Methods). Each point indicates the LFC for a single OTU. High enrichment values indicate an OTU is likely $$^{13}$$C-labeled. Different colors represent different phyla and different panels represent different days. The final column shows the frequency distribution of LFC values in each row. Within each panel, shaded areas are used to indicate one standard deviation (dark shading) or two standard deviations (light shading) about the mean of all LFC values.\n\nThe metabolization of $$^{13}$$C-xylose and $$^{13}$$C-cellulose is indicated by the percentage of the added $$^{13}$$C that remains in soil over time. Soils were pooled (three samples per time point per treatment) prior to measuring $$^{13}$$C-content.\n\nXylose reponders in the Actinobacteria, Bacteroidetes, Firmicutes exhibit distinct temporal dynamics of $$^{13}$$C-labeling. The left column shows counts of $$^{13}$$C-xylose responders in the Actinobacteria, Bacteroidetes, Firmicutes and Proteobacteria at days 1, 3, 7 and 30. The right panel shows OTU enrichment in high density gradient fractions (gray points, expressed as fold change) for responders as well as a boxplot for the distribution of fold change values (The box extends one interquartile range, whiskers extend 1.5 times the IR, and small dots are outliers (i.e. beyond 1.5 times the IR)). Each day in the right column shows all responders (i.e. OTUs that responded to xylose at any point in time). High enrichment values indicates OTU DNA is likely $$^{13}$$C-labeled.\n\nCharacteristics of xylose responders (green) and cellulose responders (blue) based on estimated rrn copy number (A), $$\\Delta\\hat{BD}$$ (B), and relative abundance in non-fractionated DNA (C). The estimated rrn copy number of all responders is shown versus time (A). Kernel density histogram of $$\\Delta\\hat{BD}$$ values shows cellulose responders had higher average $$\\Delta\\hat{BD}$$ than xylose responders indicating higher average atom % $$^{13}$$C in OTU DNA (B). The final panel indicates the rank relative abundance of all OTUs observed in the non-fractionated DNA (C) where rank was determined at day 1 (bold line) and relative abundance for each OTU is indicated for all days by colored lines (see legend). Xylose responders (green ticks) have higher relative abundance in non-fractionated DNA than cellulose responders (green ticks). All ticks are based on day 1 relative abundance.\n\nEstimated rrn copy number for xylose and cellulose responders. The leftmost panel contrasts estimated rrn copy number for cellulose (13CCPS) and xylose (13CXPS) responders. The right panel shows estimated rrn copy number versus time of first response for xylose responders. Colors denote the phylum of the OTUs (see legend).\n\nCounts of xylose responders and cellulose responders over time.\n\nNMDS analysis of SSU rRNA gene composition in non-fractionated DNA (colored points) indicates that isotopic labelling does not alter overall microbial community composition, microbial community composition in the soil microcosms changes over time, and variance in non-fractionated DNA is smaller than variance in fractionated DNA (black points). SSU rRNA gene sequences were determined for non-fractionated DNA from the unlabeled control, $$^{13}$$C-xylose, and $$^{13}$$C-cellulose treatments over time (colors indicate time, different symbols used for different treatments). Distance in SSU rRNA gene composition was quantified with the UniFrac metric. The leftmost panel indicates NMDS of data from both non-fractionated and fractionated samples. The rightmost panel indicates NMDS of data only from non-fractionated DNA. Statistical analysis is presented in main text. Samples not represented in the ordination did not sequence successfully and constitute missing data (e.g. \u201c12CCPS\u201d day 7).\n\nChange in relative abundance in non-fractionated DNA over time for xylose responders (13CXPS) and cellulose responders (13CCPS). Each panel represents a responders to the indicated substrate (i.e. cellulose (13CCPS) or xylose (13CXPS)) within the indicated phylum except for the lower right panel which shows all reponders to both xylose and celluose. The abbreviations Proteo., Verruco., and Plancto., correspond to Proteobacteria, Verrucomicrobia, and Planctomycetes, respectively.\n\nDensity profile for a single cellulose responder in the $$^{13}$$C-cellulose treatment (blue) and control (orange). Vertical lines show center of mass for each density profile and the arrow denotes the magnitude and direction of $$\\Delta\\hat{BD}$$. Right panel shows relative abundance values in the high density fractions (The boxplot line is the median value. The box spans one interquartile range (IR) about the median, whiskers extend 1.5 times the IR.\n\nDensity profile for a single non-responder OTU. The $$^{13}$$C-cellulose treatment is in blue and the control treatment is in orange. The vertical line shows where high density fractions begin as defined in our analysis. The right panel shows relative abundance values in the high density fractions for each gradient (The boxplot line is the median value. The box spans one interquartile range (IR) about the median, whiskers extend 1.5 times the IR.\n\nMaximum enrichment at any point in time in high density fractions of $$^{13}$$C-treatments relative to control (expressed as LFC) shown for $$^{13}$$C-cellulose versus $$^{13}$$C-xylose treatments. Each point represents an OTU. Blue points are cellulose responders, green xylose responders, red are responders to both xylose and cellulose, and gray points are OTUs that did not respond to either substrate. Line indicates a slope of one.\n\nPhylogenetic position of cellulose responders and xylose responders in the context of all OTUs that passed sparsity independent filtering criteria (see Methods). Only those phyla that contain responders are shown. Colored dots are used to identify xylose responders (green) and cellulose responders (blue). The heatmaps indicate enrichment in high density fractions relative to control (represented as LFC) for each OTU in response to both $$^{13}$$C-cellulose (13CCPS, leftmost heatmap) and $$^{13}$$C-xylose (13CXPS, rightmost heatmap) with values for different days in each heatmap column. High enrichment values (represented as LFC) provide evidence of $$^{13}$$C-labeled DNA.\n\nWe added a carbon mixture that contained inorganic salts and amino acids (not shown here) to each soil microcosm where the only difference between treatments was the $$^{13}$$C-labeled isotope (in red). At days 1, 3, 7, 14, and 30 replicate microcosms were destructively harvested for downstream molecular applications. DNA from each treatment and time (n = 14) was subjected to CsCl density gradient centrifugation and density gradients were fractionated (orange tubes wherein each arrow represents a fraction from the density gradient). SSU rRNA genes from each gradient fraction were PCR amplified and sequenced. In addition, SSU rRNA genes were also PCR amplified and sequenced from non-fractionated DNA to represent the soil microbial community.\n\nRaw data from individual responders highlighted in the main text (see Results). The left column shows OTU relative abundance in density gradient fractions for the indicated treatment pair at each sampling point. Time is indicated by the line color (see legend). Gradient profiles are shaded to represent the different treatments where orange represents \u201ccontrol\u201d, blue \u201c$$^{13}$$C-cellulose\u201d, and green \u201c$$^{13}$$C-xylose.\u201d The right column shows the relative abundance of each OTU in non-fractionated DNA. Enrichment in the high density fractions of $$^{13}$$C-treatments indicates an OTU likely has $$^{13}$$C-labeled DNA.\n\n### References\n\n1. Ronald Amundson. The carbon budget in soils. Annu Rev Earth Planet Sci 29, 535-562 Annual Reviews, 2001. Link\n\n2. N. H. Batjes. Total carbon and nitrogen in the soils of the world. Eur J Soil Sci 47, 151-163 Wiley Blackwell (Blackwell Publishing), 1996. Link\n\n3. F Chapin. Principles of terrestrial ecosystem ecology. Springer, 2002.\n\n4. Steven D. Allison, Matthew D. Wallenstein, Mark A. Bradford. Soil-carbon response to warming dependent on microbial physiology. Nat Geosci 3, 336\u2013340 (2010). Link\n\n5. J. Six, S. D. Frey, R. K. Thiet, K. M. Batten. 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Copyright © 2017 by Bruce Kading All rights reserved First edition Published by Academy Chicago Publishers An imprint of Chicago Review Press Incorporated 814 North Franklin Street Chicago, Illinois 60610 ISBN 978-1-61373-628-9 Library of Congress Cataloging-in-Publication Data Names: Kading, Bruce, author. Title: Miguel's gift / Bruce Kading. Description: Chicago: Chicago Review Press Incorporated, 2017. Identifiers: LCCN 2016029766 (print) \| LCCN 2016036244 (ebook) \| ISBN 9781613736258 (pbk.: alk. paper) \| ISBN 9781613736272 (pdf) \| ISBN 9781613736289 (epub) \| ISBN 9781613736265 (kindle) Subjects: LCSH: United States. Immigration and Naturalization Service—Employees—Fiction. \| Homicide investigation—Fiction. \| Illegal aliens—Fiction. \| Fraud investigation—Fiction. \| United States—Emigration and immigration—Fiction. \| GSAFD: Mystery fiction. Classification: LCC PS3611.A3285 M54 2017 (print) \| LCC PS3611. A3285 (ebook) \| DDC 813/.6—dc23 LC record available at <https://lccn.loc.gov/2016029766> Cover design: Rebecca Lown Cover image: Shutterstock/IVASHstudio Typesetting: Nord Compo Printed in the United States of America 5 4 3 2 1 _This digital document has been produced byNord Compo_. _Whoso would be a man must be a nonconformist_. —Ralph Waldo Emerson # CONTENTS Title Page Copyright Page Prologue Part I Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Part II Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Part III Chapter 16 Chapter 17 Chapter 18 Chapter 19 Acknowledgments # PROLOGUE _Chicago, 1974_ Dusk came early that day. The clouds had rolled in, cloaking the streets in a wintry gloom. Alarmed by a forecast of snow, commuters fled the city like an army in retreat. Agent Michael Landau pulled into heavy traffic on North Clark Street while his partner, Frank Kelso, casually scanned the pedestrians who hurried along, their shoulders hunched against the cold, damp air. Landau checked his rearview mirror as they crossed Foster Avenue. "We just lost Tatum at the light," he said evenly. "It's OK. He knows where we're going," replied Kelso. "You said mainly Peruvians at this place?" "Yeah, the foreman's Peruvian. Takes care of his own." They drove on silently for a few moments, and then Kelso said, "Hey, pull over. That guy's wet." He was looking at a scruffy young man wearing a faded leather jacket, who was leaning with his back against the brick facade of a bookstore. The man had long, unruly blond hair, and there was a sullen, almost angry look on his face. Landau edged the car over and studied the man. "Looks like an addict. What makes you think he's illegal?" "I'm not sure," said Kelso, already stepping out of the car. "Tell Buck." Landau grabbed the mic. "Buck, we're going to talk to a guy—half a block north of Foster, east side." "Be right there," said Tatum, shaking his head. It was vintage Kelso—never willing to ignore a suspected illegal, even if it was inconvenient. When the light changed, Tatum accelerated briefly and then slowed. There was Kelso, talking to a man whose glazed eyes were darting in every direction, looking for a way out. This could be trouble, thought Tatum. As he slid the transmission into park, a quick movement caught his eye—Kelso and the man now struggling, Landau running toward them. Tatum flew out of the car and reached for the handcuffs on his belt. Sharp commands and curses echoed down the street, a tangle of three bodies pitching back and forth, the glint of metal at the center of desperately flexed arms and hands. Tatum dropped the cuffs and pulled the .357 revolver from his shoulder holster—too late. A flash of orange and the dry crack of gunfire. Kelso letting out a deep, wavering moan and falling away. Tatum leaned forward, his arms extended, elbows locked, and fired. At such close range the shot smoked a ring of black powder into the man's forehead, the hollow-point bullet expanding like a grenade on contact—a deadly explosion into vital brain tissue. The man instantly crumpled against the brick wall, his head falling limply to his shoulder, eyes open but lifeless. As they waited for the ambulance, Landau held Kelso around his shoulders and tried to comfort him. A nearby shopkeeper offered a towel, and Landau used it to slow the blood surging from Kelso's chest. Tatum stood over them, waving onlookers away and repeating over and over, "Yer gonna be fine, Frank." But Tatum couldn't pull his eyes away from the young man he'd fatally shot. Though he couldn't place it, the face was hauntingly familiar. Frank Kelso lost consciousness and died before the ambulance arrived, just five minutes after the bullet pierced his heart—a bullet fired from his own gun. # Part I # 1 _Chicago, 1987_ They were to meet outside the pawnshop on the south edge of the Loop. "I'll pick you up early, around five thirty," Willis had grumbled. "I'm not gonna wait around if you're not there." Nick Hayden stood alone in the darkness, feeling a bit lopsided from the unfamiliar weight of the .38-caliber Smith & Wesson revolver on his right hip. Wearing a sport coat and tie, he held his arms across his chest against the cool morning air and listened to the city—the echo of traffic, the squeak and clatter of the elevated train. A patrol car rolled by, shined its spotlight on him, and continued on. Now and then a shabbily clad wino would stumble in or out of the three-story flophouse next to the pawnshop and look Nick over suspiciously. Glancing at his watch, he saw that it was nearly six o'clock and was seized by a moment of panic—perhaps he'd gotten the location wrong. Seconds later a battered green van, its tailpipe coughing a trail of black smoke, came to a stop at the curb. Hayden at first ignored it—no way could that wreck be an official Immigration Service vehicle—but the loud honks got his attention. He stepped closer and could make out the stern visage of Joe Willis behind the wheel, puffing a cigarette. Nick slid into the passenger seat. "Morning, sir," he said. Saying nothing, Willis jerked away from the curb, took a sharp right turn at the corner, and pulled into the four-lane westbound expressway. The van shuddered and teetered from side to side, while Hayden gripped the armrest for support. A crosshatched metal screen separated the front seats from the cargo area, where wooden bench seats ran the length of each side. Peering through the screen, Nick spotted a reddish stain on the metal floor, but in the faint light he couldn't tell if it was dried blood, vomit, or salsa. He sniffed the air, thick with the fetid vapors of sweaty prisoners who'd ridden there. "You'll get used to the smell," Willis said. "The openings in the screen are the real problem. Last month one of the wets pissed all over a detention officer's shoulder." Willis wore a brown polyester suit with leather patches on the elbows. His head was completely bald, and his nose was covered with an intricate network of blue and scarlet veins. Thirty years of unfiltered Lucky Strikes had taken their toll: his voice was gravelly, his teeth heavily stained. Though he appeared older than his fifty-four years, a feral energy pulsed through his wiry frame. "Sometimes we cram twenty wets in there and they're pressed up against the screen," said Willis. "Farting, belching, upchucking huevos rancheros—you name it." "You always drive this vehicle?" asked Hayden. "No, but detention claimed they were shorthanded today. Been happening more and more lately." Willis took a final drag on the Lucky, flicked it through the open window, and glanced at his sandy-haired new partner. Though Hayden appeared physically capable, Willis saw callowness in the young man's brown eyes. "I hear you didn't go through the Patrol," said Willis. "No." "Figures. Those geniuses at headquarters don't have a fucking clue." The sun rose in a dramatic burst, unfurling like an amber carpet over the city. Willis weaved through the traffic, cutting off several vehicles as he skipped from lane to lane. Whenever they honked or flashed their lights in protest, he let out a chuckle, as if provoking a reaction was cause for celebration. They soon passed the city's tightly packed office and apartment buildings, exited the expressway, and entered a vast, partially developed industrial park, where most of the warehouses were two-story brick structures separated by fields of prairie grass. The fuzzy snap of the police radio came through the speaker on the floorboard, followed by the amused voice of Sam Payton. "We're almost there, Joe. Seems like we had a little problem last time." Willis grabbed the mic from under the dash. "You've got a gift for understatement, Payton. I've still got boot prints on my face. Maybe you can do better this time." "If thirty wets come at us, it's gonna be the same thing," said Payton. "We'll do what we can." Nick listened intently, hoping to glean something useful. He still had no clear idea what to expect during this, his first field operation, or how to respond if things went awry. Though he'd been given a badge and assigned to area control—the unit responsible for rounding up illegals in the Chicago area—he'd not yet gone to the academy for training. The day before, after a fifteen-minute orientation session with the district firearms officer and half an hour of firing off practice rounds in the basement range, he'd somehow managed to shoot a qualifying score and been issued a .38-caliber revolver. Journeymen officers who, like Willis, had started their INS careers as Border Patrol agents had offered a frosty reception, many of them barely willing to acknowledge Hayden's presence. Now he was hoping his crusty partner would fill him in on what to expect, but Willis's attitude toward Hayden seemed to fluctuate between indifference and outright hostility. "This is my first field operation, Mr. Willis," Hayden finally ventured. "What do you want me to do?" "You'd like that, wouldn't you? For me to tell you exactly what to do, so you don't have to think for yourself. Well, it doesn't work that way. In this job you have to think on your feet, and there's no book that tells you how to do it." There were a few moments of stony silence before Willis spoke again: "How many sets of cuffs they give you?" he asked, softening his tone a bit. "They said you'd have some." Willis grunted and pulled his jacket back to reveal five sets on his belt. "Here, you can have two of mine. Just start grabbing bodies when they take off and wet 'em down." "Wet 'em down?" "Get 'em to admit they're illegal—mostly Mexicans at this place." "What if—" he began, but Willis cut him off. "It's the place with the loading dock in front," he said, pointing to a warehouse about a hundred yards away. Seconds later a dozen or more brown-skinned men wearing T-shirts could be seen running from the rear of the building into the surrounding fields. "Shit, somebody saw us and called the plant," hissed Willis. He grabbed the mic. "Payton, head off the wets flying out the back!" As Willis brought the van to a skidding stop beneath the front loading dock, a large metal door opened and about ten men exploded from inside, jumping from the dock to the pavement. One of them sailed from the dock onto the top of the van, clomped across the roof, and jumped off the back. Willis swung his door open as a runner was passing by, striking the man's arm and sending him flying to the ground. His heart pounding, Nick leaped from the van in pursuit of two panic-stricken young men racing toward an adjoining field. They were slender and fast but were soon slowed by the tall, wet grass. One peeled off to the right, but Hayden stayed locked on the other. The Mexican thrashed desperately through the waist-high grass and cattails, while Hayden steadily gained ground until they both sank into a shallow, muddy ditch. Holding him by the shirt, Nick clumsily pulled out his badge. " _Soy de Inmigración. ¿Tiene papeles_?" Hayden gasped. "You got papers?" The Mexican, winded and disheveled, shook his head and looked down at the mud covering his shoes and pants. Hayden took a moment to catch his breath before cuffing the man's wrists together. He then walked him back to the parking lot, pleased that he wasn't returning empty-handed. Willis and the other agents were gathered next to the van with a dozen handcuffed Mexicans. "When I told you to wet 'em down, I didn't mean throw him into a fucking lagoon," crowed Willis. The other agents laughed but not with the relish of Joe Willis. Hayden managed a sheepish grin, knowing he'd passed a minor test. "All right, get 'em into the van. Let's get outa here," said Willis. The van hung low under the weight of the prisoners as it sped toward the office. The Mexicans laughed and talked cheerfully among themselves as though nothing much had happened. Surprised that the Spanish he'd learned in school and while traveling abroad was holding up pretty well, Hayden listened as one of the Mexicans regaled the others with stories of his previous arrests along the border and in Chicago. Ten minutes later they pulled into the basement of the Federal Building, where agents were transferring prisoners to green-uniformed detention officers. The Mexicans found themselves dwarfed by fourteen burly Poles, arrested at a construction site. Hayden and a detention officer escorted the illegals into an elevator equipped with a large compartment behind metal bars and another smaller space for the accompanying officers. It was quiet except for the sound of breathing and a low mechanical hum as they were whisked up to the third floor. The tight quarters and metal bars had sobered the prisoners, and there was a palpable feeling of defeat among them, their plans and dreams at least temporarily obliterated. They stared at Hayden with looks of resignation, sadness, and something else—a measure of respect, the kind of respect that borders on fear. Nobody had ever looked at him that way before. A curiously pleasant feeling of power swept over him. A steady procession of vehicles continued through the morning, agents unloading their prisoners like fishermen unloading their catch. * * * The atmosphere of the area control squad room was grim but functional. Thirty gunmetal-gray desks were arranged in tight rows, each with a vintage Smith-Corona typewriter and a straight-backed chair. There were no dividers for privacy, no family photos or other personal items, and no wall decorations. Even when sunlight penetrated the grime on the floor-to-ceiling windows, the room had a dingy, impersonal feel that was vaguely depressing. Black metal filing cabinets lined the pale green walls and an earthy scent, reminiscent of a men's locker room, permeated the air. A corpulent young woman, smacking gum and looking bored, listened to the scratchy radio transmissions from agents announcing their arrest totals, destinations, and estimated times of arrival. In response, she repeatedly muttered "ten-four" into the desktop microphone, while making entries on a log sheet. Hayden led the young Mexican he'd arrested toward an empty desk next to Willis amid the chatter of typewriters and buzz of conversations. Several agents interviewed a group of young men from Pakistan, who had entered the country as students and were found working as cabdrivers. The "Pakis" were dark-skinned and thin, their eyes roaming nervously around the room. The Mexicans sat quietly, their hands folded between their legs, responding softly to agents' questions. Standing out like flashing neon signs were five transvestites from Central and South America, arrested the night before at a club where they did impersonations of well-known female entertainers. They all had fake eyelashes, flaming red lipstick, and long, brightly colored nails. The hulking Poles on the opposite side of the room grunted terse responses via interpreters and stared at the transvestites, as if trying to decide whether they were repelled or attracted by them. There was a sense of urgency in the air because buses would be leaving that night with those Mexicans who could be persuaded to sign "voluntary departure" agreements. A Greyhound bus destined for Juárez was already waiting in the basement. Hayden rolled the standard report form into the typewriter and began collecting biographical information, but he found the pandemonium distracting. Willis, unfazed, methodically rapped out the forms using his index fingers, hardly acknowledging the silent figure seated next to him. After thousands of arrests and interviews, there was little need for talk. He already knew the answers. Willis noticed that Nick had stopped typing and was watching the little dramas playing out around him. "We don't have all day, Hayden," he snapped. "Get moving." "Yes, sir." "And don't call me 'sir.' I'm not a supervisor, thank God." Only a few of the agents noticed that Lou Moretti's door had swung open at the far corner of the room. Moretti, chief of area control, had a thin layer of oily hair combed over his large head and a red, alcohol-ravaged nose. He wore a cheap, snap-on tie, and his shirtsleeves were rolled up to his elbows. Moretti, who rarely left his office when things were going well, stalked out with an angry gleam in his eyes. "OK. Everybody stop what you're doing," he roared, and the room fell instantly silent. Moretti began pacing back and forth like a sentry guarding a checkpoint. "I don't care if the wets hear this. They can be my witnesses if the shit hits the fan. I've got a list here with eighteen names on it." He lifted a pair of glasses to his eyes. "We've got Nigerians, Jamaicans, Guatemalans, Colombians, Chinese, a Laotian . . . all arrested early yesterday. But what _else_ do you suppose they have in common?" He continued pacing, knowing nobody would answer. "They all pose a threat to _my_ financial well-being because they've been sitting in lockup for twenty-three hours and haven't been served with a formal notice as to why they're being deported. This presents a bit of a problem because the ACL fucking U would love nothing more than to sue the shit out of . . . guess who?" Moretti stopped pacing and faced his audience. He paused for emphasis, then bent forward and spoke with exaggerated gentleness, as if addressing schoolchildren. "Yeah, _me_ , that's who. And anybody else they can shake down. They're going for personal assets these days, ladies and gentlemen, not just the government's. They have this crazy idea that I am somehow responsible for everything you guys do. And I find that very frightening." He straightened and his voice deepened. "So whichever of you is responsible, I want something on my desk within the hour." There were several moments of silence as Moretti scanned the room with tired, cynical eyes. He stopped when he noticed one of the prettier transvestites and the agent sitting next to her in the middle of the room. "Wickberg, I don't care if you bring in fake women, as long as they're deportable," he said. "But there's no reason to take two hours to process each one. People are starting to talk." Leticia Boyer, the Hispanic Judy Garland, fluttered her fake eyelashes at agent Adam Wickberg. "Adam, I didn't know you took more time with us. That's so cute," cooed Boyer as she reached over to pat his hand. Wickberg's face turned crimson as the squad room erupted in laughter. Moretti rolled his eyes and shook his head. "OK, OK. Remember, I want that paperwork within the hour." The office buzz quickly resumed. Hayden turned to the Mexican sitting next to him. "Bad luck today, no?" he asked in Spanish. "Yes, sir. You run very fast," said the Mexican. "The mud slowed you down." Willis observed the exchange with visible irritation. "What the hell are you doing, Hayden?" "Just trying to be civil," Hayden responded. "We don't have time for fuckin' civility," said Willis. "This guy ran you through a mud pit, remember? Collect the information and ship his ass." At that moment a tall, heavyset man in a tweed jacket appeared next to Hayden's desk. Charlie McCloud had wavy brown hair, his eyebrows and mustache flecked with hints of red. "You upset again, Joe?" said McCloud with a patient smile. "Let your blood pressure skyrocket and you won't make retirement." "Mind your own business. Besides, I don't wanna retire," Willis said, with a wearied look, as if he'd been through this before with McCloud. "Young fella was just exercising his Spanish a little," said McCloud. "No harm in that, is there?" "We don't have time for idle chitchat," said Willis sharply, getting up from his desk. "I'm going for coffee. Watch my guy, Hayden." McCloud chuckled softly and turned to Hayden. "Nick Hayden?" "Yes, sir," said Hayden. He stood and shook McCloud's hand. "Charlie McCloud, your training officer. I've been out of the office for a few days. How things going so far?" There was a trace of sympathy in McCloud's eyes. "OK. I'm sure I can learn a lot from Mr. Willis." "Yeah, Joe's been around—knows the street. Listen, when you get a break here, stop by my office. No rush—I'll be in all afternoon." After Nick finished the paperwork, he interviewed and processed two more of the Mexicans they'd captured outside the factory. Willis had caustically informed him that the only way to remove dozens of illegals in a single day was to convince them to give up their right to a deportation hearing and return voluntarily to their homeland. The court system would collapse if they all demanded a hearing before an immigration judge, and it would delay their departures for several days. But each of the three Mexicans Hayden interviewed had readily agreed to return to his country immediately. Altogether, fifty-eight Mexicans had been arrested that day by area control units in Chicago, and almost all of them would be on the bus headed for Juárez later that night. After being released on the other side of the border, many would quickly return, often to the same jobs they'd left behind. Clearly, the merry-go-round of capture, removal, and reentry satisfied everybody, even those temporarily caught in the net. Delays orchestrated by the bureaucracy were a relatively small price to pay. It was late afternoon before things quieted down and Willis allowed Hayden to leave the unit. Nick stopped in the washroom on his way to McCloud's office. Tired but exhilarated, he splashed cold water on his face and took a moment to reflect. This was going to be more of a challenge than he'd anticipated—thrown into the fire without formal training and partnered with a guy who seemed like a character out of a Dickens novel. He could see that the job's physical and emotional demands were such that his clandestine mission could not be his top priority, at least for now. Still, he was confident that in time he would find answers to the questions that had been preying on his mind all these years. Keep your eyes and ears open and trust nobody, he told himself. He patted his face dry, brushed the remaining bits of dried mud from the sleeves of his sport coat, and began the short walk to McCloud's office. * * * Charlie McCloud picked his way through Nick Hayden's personnel file with growing interest. Hayden had earned a degree in English literature from the University of Illinois and spent almost two years traveling and working odd jobs in Spain and Germany. Then he'd successfully completed a year of law school before dropping out and signing on with INS—a rather curious sequence of events, McCloud thought. Why would he give up the prospect of a lucrative career as a lawyer in favor of employment with a relatively obscure federal agency? McCloud had arrived at the INS Investigations Division in Chicago by a more traditional route. Born and raised in central Michigan, he'd been hired by the Border Patrol upon graduation from college and been dispatched, along with his young wife, to Yuma, Arizona. But after two years on the job he'd begun to find the work tedious; and his wife, never excited about her husband's career choice, felt marooned in the heat, wind, and isolation of the desert. Encouraged by his wife, McCloud had applied and been accepted into the graduate program in political science at UCLA. Almost simultaneously he'd been selected for a criminal investigator position at the Chicago INS office, a job he'd applied for on a whim. He ultimately convinced his wife that the job would pay for his education and he could attend night school at DePaul University. The job would be temporary, he'd told her, until he could transition into the world of academia. On reporting for duty at his new post, McCloud was assigned to area control but was soon transferred into the fraud investigations unit where he began working criminal cases—setting up complex undercover operations that targeted organizers of immigration fraud schemes and traffickers in counterfeit green cards, social security cards, visas, and birth certificates. In the process, McCloud discovered that life as an investigator in a large city, particularly one as riddled with crime as Chicago, was far more interesting than tracking illegals in the desert. McCloud was soon hooked. The cases were like novels crammed with vivid characters, and _he_ was orchestrating the storyline. Within a few years he'd posted more convictions than anybody else in the office and had become an acknowledged expert in the immigration fraud cases that abounded in the Chicago area. Prosecuting attorneys could rely on McCloud to deliver cases that were so well documented that there was little or no question about their outcome. And when the defendants received prison sentences, nothing could match the feeling of accomplishment—knowing that he'd helped bring at least a small measure of justice to society. To his wife's chagrin, he'd never gotten around to enrolling at DePaul, and she began to observe unwelcome changes in her now remote and distracted husband. His warm, vulnerable side seemed to have disappeared, and he'd developed a blunt, condescending way of communicating that made her feel cut off and alone. Five years after their move to Chicago, and feeling as though she was living with a stranger, she took their two girls and left him. On reflection years later, McCloud couldn't blame her. For reasons he didn't grasp at the time, he'd become self-absorbed, begun drinking heavily, and devoted most of his energy to his beloved investigations. Only in retrospect was he able to see that in his zeal to succeed professionally, people had become as impersonal to him as chess pieces on a board. Perhaps unavoidably, it had spilled over into his personal life. Finally, after more than nineteen years on the job, his forays into criminal investigations began to lack the urgency that had sustained him for so long. He lived in a small one-bedroom apartment and did his best to hide the fact that he was very lonely. He put in long hours at the office, hoping a new case would reignite the old magic, and secretly feared what appeared to be the barren landscape of retirement. When the training officer position opened up, McCloud jumped on it, keenly aware that if he didn't take the job, some young, ambitious agent hoping to pad his résumé would happily parrot the company line to new agents, who had no idea of what they were getting into. McCloud knew things—not just how to conduct investigations—and he wanted to share them. McCloud worked out of a small, windowless room—"the bunker," he called it—the walls lined with bookcases. When Hayden arrived, the door was open, and McCloud had him take a seat while he finished reviewing his file. Hayden noticed that among the manuals and law books on the shelves were several volumes by Steinbeck and Hemingway. "Everybody knows the first year of law school is the hardest," said McCloud finally, peering at Hayden over reading glasses that sat on the tip of his nose. "You made it through and then walked away. That's pretty unusual." "I was tired of school and wasn't looking forward to two more years," said Hayden. "Besides, this job sounded fascinating—being around people from other cultures . . . a different kind of learning opportunity." McCloud raised his eyebrows. "That sounds pretty esoteric, Hayden. This isn't some human laboratory where you go around in a white coat and make notes on a clipboard. If you keep talking like that, they'll call you 'the professor.' And that ain't good." McCloud nodded toward the squad room down the hall. "They want you to be good backup, not a student of local anthropology." "No, of course not," Hayden replied stiffly. "Most of these guys aren't impressed with degrees or higher education. In fact, having a degree can work against you and create suspicion. It's like in Cambodia when the Commies took over—Pol Pot wanted to kill anybody who wore glasses because he thought they were intellectuals and couldn't be trusted. Your law school experience won't help. If anything, it'll create distrust." "I never expected it to give me any special status," said Hayden. "Well, don't get me wrong. I think it's good that we're hiring guys who are educated and creative, because the cases we're working in other units are becoming more complex." "What kind of cases?" "Smuggling, counterfeit documents, fraud schemes to get papers. There are great cases out there, hanging like ripe fruit. But for now, as a trainee, area control is the best place to learn the street." "How long will I be there?" "At least two or three years. Area control is the equivalent of being a uniformed beat cop but without the uniform. Eventually you'll get a chance to work criminal cases in another unit, which is like being promoted to detective." "I don't have any problem with picking up illegals for a couple years." "Good, because you have no say in it. You go where they want you to go and do what they want you to do." McCloud paused momentarily for a reaction. Hayden nodded respectfully. "You'll go to the academy in a couple of weeks," McCloud continued. "Then we'll have training classes for you and other guys who are in their first couple of years on the job. You'll have to go before the retention panel after a year to find out if you've made it through probation." "Yes, they told me." "I'm surprised with your background you didn't go with one of the pretty-boy agencies—the FBI or Secret Service. They would have taken you." "This opened up first and . . . it looked like a good opportunity." McCloud leaned back, webbed his hands behind his head, and studied Hayden for a moment. "I don't know if anybody's mentioned it, but the bosses have decided to be aggressive again in picking up wets, at least for a while, so things can get pretty dicey in area control. When you're arresting hundreds of people every week there are going to be some bad apples in the mix, so be prepared for anything. Stay alert. And regardless of what Willis or anybody else tells you, don't forget that you're dealing with human beings out there. You have a lot of power in this job, and even though you have to enforce the law and arrest people, they deserve respect. It's part of being a true professional. Some of these guys have forgotten about that." "Yes, sir. I'll remember that," said Hayden. McCloud seemed to have finished, but his penetrating stare made Hayden uneasy. Nick nodded toward the bookcase. "I see you like Hemingway. I've read almost everything he's written." "The short stories in particular are great," said McCloud. "Hemingway's books are even more interesting after you've read his biographies." McCloud gazed distractedly at the bookcase for a moment. "He was a genius, but he wouldn't have been any good at this job." "Why's that?" "Because he was an artist, and artists are looking for transcendent truths. Where could he find that around here? Plus, he had internal demons and was always trying to prove something. That can be dangerous in this line of work. Hell of a writer though." McCloud paused briefly. "Anyway, we're done here for the moment. I'll let you know about your training schedule in the next few days." "OK." Hayden stood up to leave and was reaching for the door when McCloud thought of something. "You know, the name Hayden sounds kind of familiar. Can't place it, but I know I've heard it before." "It's a pretty common name. Everybody's run into a Hayden at some point, I guess." With a grimace and shake of his head, McCloud shoved the file into his desk drawer. "OK, I'm here if you need anything." "Thank you, sir." Hayden closed the door and stood in the hallway, his heart galloping. He drew a deep breath and let it out slowly. Perhaps McCloud had come across some other Hayden and his curiosity meant nothing. But Nick had known all along that he was vulnerable, that it was entirely possible that McCloud or another veteran agent could make the connection. It was as if he were straddling the rim of a deep canyon. Even a small gust of wind could send him tumbling off the edge. * * * Tom Kane drove the Plymouth Fury through the bright morning sunshine that streamed between abandoned warehouses on South Halsted Street. Many of their large windows had been shattered by vandals' rocks, and flocks of sparrows soared through the openings like fleets of tiny warplanes. The sweet aroma of bread from a commercial bakery filled the air. As Hayden took in the scenery from the passenger seat, they entered an area of decaying apartment buildings and small businesses, some of which were boarded up. "Ten years ago this area was thriving," said Kane, playing the role of tour guide. "A lot of the businesses moved to the suburbs where it's safer. But there are still a lot of wets down here in these roach-infested buildings." Kane waved dismissively toward a bus stop where several Hispanic-looking men were huddled. "Hell, we shouldn't even bother with factories. We could fill up our cars right here." Kane was wearing his usual charcoal-colored suit, the elbows shiny from wear, a narrow black tie over a white shirt, and dark sunglasses. If you gave him a black fedora, he could pass for one of the Blues Brothers. Kane had a rangy, powerful build and thick, dark brown hair that flowed over the tops of his ears. When he flashed one of his infrequent smiles, it came off anywhere from mischievous to menacing. Though women considered him handsome, they also found him gruff, remote, and a bit frightening. Kane had never thought that growing up in a working-class Irish family on the southwest side of Chicago had prepared him for much of anything. But sharing close quarters with five brothers and four sisters in an atmosphere of nonstop bedlam seemed to have girded him for his future profession. From the start, he brought to his work an almost manic energy and an instinct for taking charge of fast-moving events in the field. His confidence, often drifting into arrogance, sent a warning to anybody who might challenge him and kept most people on the defensive. He thought of the job as his salvation, a crusade that filled the emptiness, though he never spoke of it in those terms. Instead, he adopted the more typical agent's pose of the grim and bemused cynic. Kane was apprehensive when told he'd be partnered for the day with Hayden, who had been to the academy for training and was now four months into his first year. Though Kane, like Hayden, had not come through the Patrol, he sensed the new guy was a "thinker." Too much thinking and analyzing, the theory went, creates confusion, hesitation. Hayden also had an independent streak, and unlike most young agents who sought the approval of senior officers like obedient lapdogs, he didn't follow his superiors to their favorite watering holes at the end of the day, keeping his distance as if he didn't want anybody to get to know him. Aside from being irritated with having to buy their own drinks, Kane and many of the journeymen resented what they saw as aloofness. Still, Hayden had shown that he was equal to the physical challenges of the job. Most recently he'd sprinted a quarter mile to chase down a massive Greek ship-jumper, who'd thrown an agent off a tannery loading dock and fled with a wild look on his face. Hayden had used a wrestling technique he'd picked up in high school to drop the man to the ground with a dramatic thud and, after a struggle, had somehow been able to get cuffs around the Greek's huge wrists before backup arrived. As the Greek outweighed Hayden by seventy pounds, it had meant something to Kane and the other agents. They continued south on Halsted Street, the heavy, boatlike Fury rising and dipping as though absorbing swells on Lake Michigan. "It would be easier to just pick them off the street than going to the job sites," said Hayden, nodding at yet another bus stop cubicle filled with young Hispanic men. "Yeah, but headquarters wants us to go to factories so we can show we're opening up jobs for Americans. Most of the wets on the street are working someplace, though, so in reality it doesn't make any difference," said Kane. "The whole enforcement program is a mess." "What would you do to fix it?" "Simple. You need to prevent them from getting jobs by making them produce valid immigration documents—not the phony ones they use now. The law passed last year requires employers to check the documents of their employees, but it _doesn't_ require verification. If the documents and numbers are checked through INS before they're hired, there'd be no way for them to work, and bingo!—the game's over. If you cut off the jobs, you cut off the wets. They wouldn't come. But the powers that be won't do it because they know it would work. They want everybody to think it's really complicated and almost impossible to resolve. The Republicans want cheap labor, and the Dems want the votes of the tonks who will eventually vote Democratic. All the new law did was lay the groundwork for a booming counterfeit document industry that everybody ignores. We're stuck in the middle—you, me, and the tonks." "What about the argument that they only take jobs nobody else wants?" "That's bullshit. Sure, the restaurant workers, but look at the people we pick up. Meat-cutters and drywall workers are making good money. They get jobs in the trades—teamsters, construction workers. The wets are easier to control than American workers." Judy Svoboda, one of only two female agents at the Chicago office, was leading this morning's raid of a furniture factory on the South Side. Kane, following Svoboda and four other vehicles, turned off Halsted Street into an area of small, dreary-looking factories. A smoky discharge clouded the sky, and the pungent odor of industrial chemicals came through the car window. Kane grabbed the transmitter off the dash. "Where do you want us, Judy?" "Cover the back parking lot and the alley," she said. Kane pointed up the street to an old brick warehouse. "That's the place—usually loaded with Jamaicans." As Svoboda and the other units pulled in front of the building, Kane drove through a side alley and parked in the nearly empty rear lot, where they could clearly view the only door at the back of the building. It was quiet, and the summer air was hot and gritty. "We'll give them a few minutes," said Kane. "They usually dig in here instead of trying to leave the premises." Hayden was just as wary of working with Kane as the other way around. Like Willis, Kane had a giant chip on his shoulder, which Nick assumed was a defensive measure designed to conceal vulnerability. In fact, it seemed to him that many of his new colleagues had insecurities they chose to bury because it would be devastating to acknowledge doubts or inner turmoil that might be construed as weakness, and weakness could not be tolerated in this line of work. "How long have you been in this unit?" asked Hayden. "Four years. They like me here because I produce. But I wouldn't mind a permanent assignment to Stark's unit." Hayden had heard a lot about Richard Stark's fraud investigations unit, considered the most prestigious in investigations. The agents in fraud and the antismuggling unit were often seen moving purposefully through the hallway in sweatshirts and jeans, some of them sporting beards and long hair. They worked undercover criminal cases, using informants and sting operations to set up their targets. Almost all agents aspired to join the unit, if only to position themselves for a higher grade. But it was difficult to break into the unit because senior agents filled most of the positions. "You married?" asked Hayden. "Nope. You almost can't be married and do the job right. You try to do both and you'll be like a wad of silly putty—stretched in every direction. If you look at the real producers, they're all single, or they're headed in that direction. Better just to have girlfriends and don't get trapped." Kane spoke in a clipped staccato as if reciting indisputable facts. They sat quietly for several moments, and then Kane spoke. "Judy is probably going through the song and dance with the manager. He always stalls around to give the Jamaicans a chance to dig in. Let's go." He yanked the keys from the ignition. "Don't we need to wait for her to give us the OK?" Kane glanced at Hayden with a playful look in his eye. "We saw a guy come out, see us, and run back inside. He was wearing braids to his shoulders and a T-shirt that said I LOVE JAMAICA. There's our probable cause." They left the vehicle and advanced toward the building. Kane opened the back door, looked inside, and motioned with his head for Hayden to follow. Hayden went in, shut the door behind him, and engaged the heavy chain lock. The two agents found themselves in a large room with brick walls, which was connected to the rest of the warehouse by an open gangway. The room was lit softly by lights high in the rafters and appeared to have been suddenly deserted, as music was playing on a portable radio at a large table and several workstations were strewn with tools and wrapping materials. Kane turned off the radio, and it became eerily quiet. Set back from the table were rows of cardboard boxes on pallets, stacked about fifteen feet high. "They're probably hiding inside the boxes at the top," said Kane, heading down one of the aisles. "I've found them here before." He pulled a long, black metal flashlight from his belt. Hayden went down another aisle and began climbing a column of boxes, using the openings in the pallets as a ladder. He had almost reached the top when he heard a crash, the clatter of the flashlight, and Kane cursing loudly. Hayden jumped to the ground, raced toward Kane's voice, and saw a black man with dreadlocks, clad in a blue work shirt and jeans, dashing toward the rear exit. The man had just disengaged the door's chain lock when Hayden took hold of his shirt collar and pulled him back. "I want no trouble, man," the Jamaican shouted. He held his hands out in front of him to show that he had no weapon. "OK, just get your hands up on the wall," said Hayden, gripping the man's arm. Before the man could turn around, the large hand of Tom Kane was pushing Hayden aside to grab the Jamaican by the throat. He flung the man against the brick wall and drove his fist into the man's mouth. The back of the Jamaican's head struck the wall, and he let out a groan. Hayden instinctively grabbed Kane's arm and shoved him, sending him backpedaling awkwardly. "What the hell are you doing?" shouted Hayden, and then caught himself. He was on probation and had openly defied a senior officer. Kane quickly righted himself and was glaring at the exit door, which now stood open, a mild wind blowing through it—the Jamaican nowhere in sight. Hayden ran outside into the parking lot and scanned the area, but there was no sign of the man. He ran to the edge of the building and looked down the alley, but all was quiet there as well. He stood silently for several seconds, hoping to see or hear something that would give away the Jamaican's escape route, but there was nothing. Finally Hayden turned back toward the factory door to find Kane leaning his elbow against the doorway, still breathing heavily. "Nice going, Chief," said Kane, his eyes aflame. "The guy was scared. He wasn't going anywhere," said Hayden calmly. "He knocked me to the floor and you're worried about _him_?" Kane clenched his fists and strode toward Hayden. Just then Charlie McCloud appeared in the doorway behind Kane. "You guys all right out here?" asked McCloud. Kane stopped and spun toward McCloud. "Yeah, we're fine," said Hayden, who relaxed his defensive posture. "We just lost a runner, that's all," said Kane, whose rumpled shirt was pulled out in front over his belt. McCloud paused and looked at them, waiting for the real story, but neither spoke. "OK," he said finally, "we could use your help inside. They've got eleven Jamaicans in the lunchroom." "Sure, Charlie," said Hayden, walking past McCloud and through the door. McCloud, who was familiar with Kane's unorthodox methods, looked at him suspiciously. "I'll pull our car around front," Kane said. "Yeah, you do that," said McCloud. As Kane turned toward his car, McCloud shook his head and walked back into the factory. * * * It was a cool autumn morning, still a bit dark outside the Polish restaurant. Willis sat rigidly at the table, coffee cup in hand, engrossed in the newspaper. Hayden perused the sports page and looked up the aisle whenever the waitress with nice legs rushed by. Occasionally he would check on Willis, observing him as a person might watch a tropical fish, more a curiosity than a threat. All the senior agents had plenty of Joe Willis stories, like the time Willis "arrested" a new agent, Arturo Santos, who'd been sitting innocently in area control on his first day on the job. Willis had unceremoniously thrown Santos into the crowded lockup, ignoring Santos's claim that he had not yet been issued a badge and identification. When the truth emerged, instead of apologizing, Willis excoriated local management for not warning everybody that they'd hired a new agent who looked wet. "They should have put his mug shot on the damn bulletin board," he declared angrily. Though Willis was entertaining in his way, Hayden had hoped for a new partner when he returned from the academy. Unfortunately, nobody other than a trainee would put up with Willis, so they were stuck with each other for the time being. "This so-called war on drugs is a loser," muttered Willis, staring down at a _Chicago Tribune_ story about the mountains of federal money spent to fight drug lords. "I suppose it can't really be controlled," Hayden offered blandly. "You want to legalize drugs, is that it?" grumbled Willis, without looking up from the paper. "What a charming idea." It didn't matter how hard Hayden tried. Willis seemed to enjoy twisting anything Nick said to spark an argument or emphasize the gulf between them. Hayden knew it wasn't really personal, that he would give _any_ trainee a hard time, especially one who hadn't been in the Patrol. Willis himself had gone through rough times when he'd started with the Patrol thirty years earlier in Brownsville, Texas. Born and raised in a lower-middle-class suburb of Chicago, Willis, with his strange accent and fast-talking intensity, had been treated as an outsider, especially during his first year on the border. If _he'd_ had to go through it, so should everybody else. After finishing his fifth cup of coffee, Willis looked at his watch, winked at the waitress, and threw a dollar bill on the table. "Let's go to work, trainee," he said coolly. Willis pulled sunglasses from the pocket of his sport coat and marched into the emerging sunshine as if he didn't care whether Hayden followed him or not. As Hayden pulled the Ford Torino onto the Stevenson Expressway, Willis rifled through the glove compartment as though looking for something to read, wiped an undetectable layer of grime from the inside of the front windshield, and spent several minutes on the radio making important-sounding but thoroughly unnecessary calls to other agents involved in the day's operation. Finally he settled down and began a lecture on the true merits of various federal law enforcement agencies as opposed to their public images. Hayden had already heard several versions of this narrative from Willis, and his mind drifted. Peering out the window, he wondered whether the white cloud that hung over the sleepy town of McCook was mist rising from the nearby canal or pollution from smokestacks that stood inelegantly in the distance. He recalled playing a baseball game in McCook as a teenager and losing a fly ball in the opaque, misty sky. His mind fell deeper into the past, until a name jolted him like a strong whiff of ammonia. "Buck Tatum," declared Willis, who tilted his head up as if scouring his memory for an image of Tatum. "Only federal agent in Chicago to smoke a guy in the last fifteen years. FBI in Chicago hasn't in years, even with thirty times the number of agents we have. The average citizen thinks FBI agents are out there risking life and limb on a daily basis. Hell, most of 'em never make arrests. How can you develop any street smarts if you're not out there making arrests and getting into fights and all the shit we have to do?" "So Tatum was an immigration agent?" "Yeah—an INS agent, not FBI, not DEA," sputtered Willis. "Were you there when it went down—the shooting?" "No, I wasn't there. But we lost a good man because of the trainee." "What happened?" Willis sighed and paused a moment to pull up the details in his mind. "Well, a guy named Frank Kelso was working with this rookie . . . Landau, I think was his name. Smart kid, but not cut out for police work—had no Patrol experience. Kelso and the trainee were riding together somewhere on the North Side, Tatum following them." Willis picked bits of lint from his polyester slacks as he continued. "Kelso had a great nose for wets—could pick 'em out of a crowd as well as anybody I ever knew. He sees a guy who looks suspicious—a big guy from Argentina it turned out. So Kelso jumps out of the car and he's talking to him, but before he can cuff him, the guy starts fighting." Joe lit a fresh Lucky and cracked the window open. Hayden had become rigid behind the wheel. "So they're both struggling with the wet, trying to get him under control. But the wet goes for Kelso's gun and manages to fire a round—right into Kelso's heart. He's dead, or will be in a few minutes. Tatum shoots the guy in the head, killing him. But Landau never gets a shot off—never even gets his gun out. If he'd reacted like he should have, Kelso would still be here. Guess he didn't have it in him to kill a guy, even when his partner's life was threatened." "Is that what Tatum said?" "Tatum was pretty closemouthed about it. Whole thing upset him—wouldn't talk to anyone. But they did an investigation and that's what came out." "What kind of a guy was Buck Tatum?" "He was in the Patrol for sixteen years. Good man, until the shooting. Then he was different." Willis took a long drag from the cigarette and sent a billow of smoke out the window. "Different how?" "Shooting seemed to hollow him out—walked around like a fucking ghost. He retired about a year later. Disappeared. Might be dead, for all I know." Willis paused a moment and then turned toward Hayden. "Why you so interested in Tatum?" Hayden had to concentrate to prevent a shake in his voice. "It's not Tatum. It's the shooting. You don't hear about stuff like that very often. Maybe I can learn something from it." Willis spit out a piece of loose tobacco. "One thing you can learn is if your partner's life is threatened, you act without hesitation." "Right," said Hayden. His heart was thumping and perspiration covered his forehead. He was grateful when a garbled radio transmission came through the speaker. Willis grabbed the mic and bent over to listen to the scratchy voice—somebody asking for their location and ETA. Hayden used the distraction to take a deep breath and wipe the sweat from his forehead. Willis gave a lengthy response and put the microphone back in its holder on the dash. "To get back to my point, the bureau would have us believe that Efrem Zimbalist Jr., who shot a guy every week on television, is a realistic portrait. That's what they tell them at Quantico, and like a bunch of Boy Scouts, they believe it." By now they had left the scented mist over McCook behind and the sky had cleared, but Hayden had retreated deep into his thoughts and was oblivious of his surroundings. Though Willis spoke with authority about the shooting, how reliable was his account, no doubt tainted by personal prejudice and the passage of time? Willis had seen nothing himself, so anything he said was suspect, and crucial details were missing. That calmed Nick a bit. He took another deep breath and tried to push it from his mind. He had no choice. In a few minutes, they would begin another roundup of wets. # 2 He often shambled down Twenty-Sixth Street, smiling at everybody as if he were running for political office. Standing six feet two and weighing over two hundred and fifty pounds, Marcos Ortega was a commanding presence. His large, round face was dominated by a hooked nose and a thick, black mustache that curved around his mouth bandito-style. Some were drawn to him by his sunny disposition; others were intimidated by his size. Mesmerized by stories of unlimited opportunities in America, Marcos had left his remote Mexican village at the age of twenty-five, slipped across the Rio Grande, and headed straight to Chicago, where he'd been welcomed into his uncle's home in the largely Hispanic Pilsen area on the South Side. Ambitious by nature, he'd taken an English course for Spanish-speaking immigrants, augmenting what he'd already learned at his Catholic school in Mexico. Without legal papers or connections, he'd not been averse to starting at the bottom of the economic ladder, and took a job as a dishwasher at a busy Mexican restaurant on Eighteenth Street. There he'd met a waitress by the name of Connie Salinas. Connie was so quiet and efficient that she was seldom noticed amid the noise and bustle of the restaurant. She kept her dull, black hair pulled back in a ponytail, wore no makeup, and had a pudgy figure that was virtually devoid of feminine curves. Connie was not pretty and had never thought of herself as pretty, but she was a superb waitress, driven by fear of a complaint or a look of disapproval—the lingering effect of a demanding and temperamental father. She didn't live so much as react, meekly following the path of least resistance. Aside from a perfunctory nod or greeting as they passed in the kitchen, Marcos paid no attention to her. One day Marcos was unloading dishes into a basin of hot water, steam rising all around, when he looked up to find Connie standing at the far end of the kitchen staring at him. "Is first time I see you without stack of plates," said Marcos, flashing a big smile. He spoke English clearly but with an accent. "You are always busy, no?" Connie froze. She nervously pushed away strands of hair that had fallen across her eyes. "Oh, yes. It is very busy," she mumbled. "Come see me if you get break. Is lonely back here," said Marcos, instantly recognizing the possibilities. Though ostensibly a Catholic, he saw his faith less as a deterrent to committing sinful acts than as a means for absolving them. "Yes, well . . . I better get back to work," said Connie with a shaky smile, grateful she'd been able to speak at all. Two days later Marcos asked her to go out with him. Connie was so surprised that she lost her grip on a plate of chicken mole and it crashed noisily on the kitchen floor. Omar Garcia, the restaurant owner, rushed back from the cash register. "I'm so sorry, Señor Garcia," Connie said, dropping to the floor to clean up the mess. "Hey, you," Garcia shouted angrily at Marcos, "get back to your dishes and don't be bothering the waitresses." When the dust settled, Connie was smiling and conversing with customers as though a new person had been born. Connie lived with her parents in a small bungalow in the Pilsen neighborhood. Her father, Ray Salinas, who had worked for twenty-three years at an auto repair shop on Ashland Avenue, had forbidden her to date until she was eighteen, and then only if he approved. He saw all men as predatory by nature and was therefore fiercely protective. Ray was a short, stocky man with massive forearms and hands that had grown incredibly strong from his work at the shop. Over the years, he'd been arrested many times for instigating liquor-fueled brawls at the local bar. Though Connie was now nineteen, she knew her father would be suspicious of Marcos, so she told her parents that she was going out with "a friend from work." They had dinner at an unpretentious little restaurant on Damen Avenue. Marcos chose a table in a quiet corner and ordered a bottle of inexpensive wine to go with their steak burritos. He said little, listened respectfully to everything Connie said, and treated her with great courtesy. She felt comfortable talking with him and thought this was quite remarkable—an indication of a special relationship. Marcos provided Connie with few details of his past, but that was how her father was, and apparently the way most men were. He was too shy, she thought, to kiss her on their first date or the next one. But on the evening of their third date, as they were standing outside a movie theater on Cermak Road, Marcos placed his hands gently on her shoulders and looked at her very seriously. "Connie, would you do me honor of being my wife?" Shocked but overjoyed, she threw her arms around his neck and kissed him. Marcos smiled down at her as one smiles when giving a child a birthday present. "Of course I'll marry you! We'll have the most beautiful wedding!" "But not yet, my dear. That cost money, and I no want to go to your father until I have better job. I hear about your father. We go to city hall to get married first. Later I tell your parents, and we plan big wedding. We no live together or say anything now. Is important we no say nothing." She, too, feared her father's reaction to the news, so agreed to keep it a secret for the moment. Connie and Marcos applied for a license and were married at city hall by a judge who absently muttered the vows. It wasn't the wedding she'd dreamed of, but there was something romantic about doing it secretly, and she consoled herself with thoughts of the real wedding to come. In lieu of a honeymoon, they went out to lunch at a greasy spoon, where Marcos told her they should say nothing to Omar or anybody else at the restaurant for fear word would get back to her parents. He again stated that he didn't want to present himself to her father as a mere dishwasher and that her parents would be hurt and angry for not having been invited to the marriage ceremony. The surprising news emerged at the end of their meal. "I almost forget," Marcos said. "We must go to immigration office. I no can go to your father unless I have green card." Connie was momentarily speechless. She'd assumed he was a legal immigrant. He spoke English so well and carried himself with ease and confidence, unlike the other illegal Mexicans at the restaurant, who rarely spoke and were almost invisible. "Why didn't you say anything about that?" she asked softly. "I thought you know this—from others at restaurant." He paused. "I no do this for the papers. You must no think this, my dear." "No, of course not," she said with a nervous smile. "We have wedding in church in few months," he declared. "I save money so we have nice apartment." As Marcos talked enthusiastically about their plans, Connie felt somewhat reassured, though it was now even more important that her father not learn of the relationship until her husband had secured his immigration papers. Two days later they submitted a petition at the INS office and were told they would be called in for an interview. In the weeks that followed, Connie's life resumed its old rhythm—as if she weren't married at all. Marcos had made it clear that he took his Catholic faith seriously, and they could not consummate the marriage or live together until it was sanctified by a church ceremony. She would continue to live with her parents and Marcos with his uncle. Connie, like Marcos, had been raised Catholic and, though she was burning with sexual passion, was grateful that her husband was a man of faith. They would wait for everything to be right in the eyes of God. Connie had begun to run out of patience when, eight weeks after they married, Marcos told her that he had good news. "I get new job at tortilla factory. I will be foreman and make more money. And we have interview at immigration office next week and if goes well, I get green card." On a cold December morning they appeared at the INS office and were interviewed by a young man wearing wire-rimmed glasses. Since Marcos claimed to have entered the country on a temporary visa at a border crossing, he was eligible to obtain permanent status without returning to Mexico. The examiner asked a few questions about how they met and seemed impressed with the couple's apparent happiness about being newly married. With numerous other couples waiting to be interviewed, the officer stamped the application APPROVED and informed Marcos he would receive his green card in the mail within a month or so. He was now a legal resident and was given a piece of paper emblazoned with a stamp to prove it. When they left the building, Marcos was so pleased that he kissed Connie with a passion he'd not shown before. "I start at tortilla factory day after tomorrow," said Marcos. "Then we tell your parents our plans. No say anything now. We surprise them together. Tomorrow will be last day at restaurant." But Connie's elation over this news was short lived as Marcos did not show up at the restaurant the next day. She repeatedly called his uncle's house, but there was no answer. That evening, after distractedly eating dinner with her parents, she hurried through the dark streets to the uncle's house, about a mile away. But the lights weren't on, there was no response when she rang the doorbell, and Marcos's car was nowhere to be seen in the neighborhood. She returned home but was barely able to sleep that night. At the restaurant the next morning, she found that Marcos had been replaced by a short Mexican who blended seamlessly into the background. After her shift, she took the bus to Twenty-Sixth Street to inquire at the tortilla factory. Encouraged to see Marcos's car parked outside, she went into the office and asked to speak to her husband. The receptionist looked at her curiously and said the workers could not be disturbed during working hours, but agreed to deliver a message. Connie scratched out a note saying she was worried about him and asking him to call her. But Marcos did not call, and the cold reality began to set in. She had been duped—abandoned by her husband before they had even spent a minute together in the same house. There was no question in her mind that this had been his intention from the beginning. He had used her and discarded her like a piece of trash. That night, tears welled up in Connie's eyes as she lay in bed, staring at the ceiling, embarrassed and ashamed for having been so easily taken advantage of. After she'd had a long cry, she began to feel something unfamiliar: a deep-seated loathing of another human being. A few days later she went back to the INS office to tell them of Marcos's misdeeds and was referred to the same man who had conducted their interview. She immediately informed him that she wanted to withdraw the petition she had filed for her husband. "No, it's too late for that," he said, explaining that the petition had already been approved—that Marcos had been accorded legal status. He listened gloomily as Connie told him of Marcos's deception. "Well, even if I can't withdraw the petition, you can deport him, can't you?" "No, it's not that simple." "After what he did, you can't deport him?" She'd been rather calm up to that moment but now felt a surge of anger. "Why not?" "We would have to revoke his legal status first. It's a very difficult process, and the courts have ruled that living together or consummating the relationship is not really required. Once he receives permanent status, the burden of proof shifts dramatically. You two dated before getting married, so there was a relationship of some kind. It is highly unlikely we could prove that from the beginning he only married you to get his card. He'll just say you had a fight and realized you weren't right for each other." Connie stared at him in disbelief. "It's what we call a one-sided fraud," he offered feebly. "They're very hard to prove, and we have limited resources." Before leaving the building, Connie took a seat in the reception area and tried to gather herself. The realization that Marcos had deceived her had already been emotionally devastating. Now the shock set in that he was going to get away with it. She looked around at couples waiting to be interviewed and wondered how many of the women were being victimized, their worlds about to fall apart. After a few minutes she staggered out and made her way down State Street. Though the temperature was below freezing, the city was adorned with brilliant sunlight. It was the week before Christmas, and crowds of people bustled happily past Salvation Army bell-ringers and colorful decorations. But Connie found the gaiety intolerable. She trudged heavily down the steps into the darkness of the subway. As she arrived at the platform a train was pulling away, its red lights growing smaller as it disappeared in the tunnel. Alone in the cold, dimly lit station, Connie waited for the next train home. * * * Marcos, bored and distracted, watched his crew of illegal Mexicans bag warm tortillas on the line, mulling the risks and rewards of his latest idea. Aside from the tedium and endless paperwork of his job, he knew it would never provide him with the financial independence he desired. The only way to make serious money, he'd concluded, was to run his own business—something he could manage without giving up the steady income and respectability of his job. When a newly hired worker walked by, Marcos reached out and playfully spun him around by the shoulder. "Let me see that card of yours, my friend—the one I made a copy of this morning," said Marcos in Spanish. When the young man looked up suspiciously, Marcos quickly reassured him. "I know they're all phony. Do you think I give a damn?" The man fumbled through his wallet, removed the laminated card, and handed it to Marcos. "How much you pay for this?" inquired Marcos. "Two hundred fifty, for that and the social security," said the man, looking around nervously. Hair-netted Mexican workers were watching tortillas coming at them along a perforated stainless steel assembly line. Several of them turned to look but couldn't hear the exchange because of the drone of the machinery. "You got it from one of those _cholos_ at a bar?" The man nodded and looked away. Marcos pulled his own card from his wallet, the good one given to him for marrying Connie Salinas, and examined them both. The man's card looked bad by comparison, the printing not as sharp, but it was good enough to serve its purpose. "OK, get back to work," Marcos said, returning the card and patting the man on the shoulder. Marcos headed to his office in a state of building excitement. For the love of God, why hadn't he thought of it earlier? Marcos always made a great show of cooperating when INS agents arrived to check the workforce at the tortilla plant. One of the lead agents, a funny, bald-headed man named Willis, even seemed to view him as a partner in weeding out illegals. During his last visit, Willis had commented about the problem of counterfeit documents. "Nobody is working those cases. Not a high-enough priority with the front office or the clowns at headquarters," Willis had said casually, after finding almost all of the workers at the tortilla factory in possession of counterfeits. "I can't remember the last time anybody got busted for selling phony documents. It's a damn outrage. I'm not even allowed to tell you how to detect one." "Yes, it is shame, Mr. Willis," Marcos had replied sympathetically. "I not know they were bad cards. What can I do? They all look good to me." A week later, Marcos talked it over with Sixto Montoya, a truck driver who made regular deliveries of flour to the tortilla plant. Like Marcos, Sixto had secured legal status through a sham marriage to an unsuspecting woman. The two men had become friends, Sixto often lingering in Marcos's dusty little office over coffee and donuts. Physically, they were a study in contrasts. Sixto, thin and wiry, had sharp features and a permanently serious facial expression. The men spoke in their native Spanish. "We are sitting on top of a gold mine, my friend," said Marcos with a coy grin. "What are you talking about?" "Let me show you something." Marcos opened his desk drawer and pulled out a manila folder. He removed a single sheet of paper on which an image of a green card had been copied. He pushed the copy across his desk. Sixto surveyed the page. "Yes, I've seen plenty of these. What about it?" He spoke quickly, spitting the words out as if they were bitter in his mouth. "I've got forty of those in this folder from just the past two weeks. I always have to make a copy to prove we checked documents before hiring to comply with the new law. But they are all phony. And we don't even have to check them through the government to see if they're good." "Yes, I've heard about it," said Sixto. "There's no need to show a good document, so they all want the fake ones. It's a joke." "Yes, a joke with a big payoff! Look at those who sell the documents—drunks, drug users, and lowlifes who hang around the bars. They get arrested, go on binges. Whoever brings order to it will make a lot of money." Sixto was looking past Marcos, thinking it through. His eyes shifted back to Marcos. "What do you have in mind?" "The key is buying in quantity and selling at a reasonable price. We could drive the small operators out of business in a very short time. I can get some money from my uncle. The blank cards can be purchased cheaply across the border in Tijuana. That's where the printing presses are. My uncle even has a contact there. The Mexican cops let them operate freely because of bribes. I'm taking a trip down there. When I get back I'll need somebody to take control of things in your area on the North Side. I'll take care of things on the South Side. I thought you might be interested." "Of course I'm interested," said Sixto, who lived in an area thick with immigrants of every nationality. He pulled a cigarette from the open pack in his shirt pocket and held it between his fingers. "What sort of profit could we expect?" "The blank documents can be purchased for very little, a few dollars per document—green cards and social securities. They can be sold easily on the street for at least a hundred fifty for a set. The equipment needed to put the cards together is very cheap. We can be the wholesalers and sell to the guys who will work the street and make the cards. The more vendors we have, the more we make. We'll have them do business quietly, behind the scenes. I'll give you a good price on the blanks, and you'll be free to distribute them as you see fit." Sixto lit his cigarette and dropped the match to the cement floor. "This is risky, no? What about the feds?" "That's the beauty of it. I have spoken with an immigration official. He tells me they don't have the manpower to go after the counterfeiters. They're leaving it wide open." Sixto blew out a long cloud of smoke before speaking. "I'm sure I could find people to help us on the North Side. It should not be difficult." "I'm leaving for Tijuana on Friday. Just be careful who you talk to about this." "Yes, of course," said Sixto. Though making decent money at the factory, Marcos had begun to feel pressure to develop other income. He had already paid for a divorce from Connie, who had gone along with it on the promise that he would pay her two thousand dollars within the next few months, though he knew there was little chance he would make good on that. Now that the divorce was final, he would have to go through the charade of remarrying his young wife in Mexico so that he could file the necessary papers for her and their two children. It would look suspicious, but he would claim they had lived together common-law and never married. To prove otherwise, _la migra_ would have to find the tiny church in the remote Mexican countryside and dig up the marriage certificate. It seemed clear that they didn't have the resources to check such things. Even if they did, he knew people in Durango—records could be destroyed. * * * The restaurant was quiet, aside from the distant clinking of glasses in the kitchen. The lunchtime customers had cleared out, except for an old man, who sat in a booth nursing a bottle of Corona. Two waitresses sat at the counter lazily counting tips. The owner, Felix Vasquez, a thin, nervous Panamanian, sat in a rear booth, staring at the entrance. Marcos lumbered into the restaurant and stood heavily inside the door, like a gunslinger entering a saloon. He was wearing a short-sleeved, embroidered white shirt that hung down over his belt, and a pair of cowboy boots, so that he appeared even more imposing than usual. Marcos smiled at the waitresses, nodded at the old man, and did a visual sweep of the restaurant, his eyes stopping to admire the colorful paintings of bullfighters that lined the walls. Vasquez, speaking Spanish, greeted him as if he were royalty, escorted him to a booth in the back, and had a waitress deliver coffee. "My friend should be here shortly, Mr. Ortega. In the meantime, can I offer you something to eat?" "Perhaps some of your delicious flan," said Marcos with a smile and a twinkle in his eye. "Of course," said Vasquez, who snapped his fingers and gestured to one of the waitresses. "Rita, some flan over here right away." Marcos was amused by the hubbub his arrival had caused. His status in the community had clearly grown over the past six months, particularly with small business owners whose employees were illegals and needed phony identification. Through subtle intimidation and by offering lower prices, Marcos had already succeeded in driving most of his competitors out of business. "I should come by more often," he said. "Everybody knows you have the best enchiladas in the barrio." He stirred several teaspoons of sugar into his coffee, and the waitress delivered a dish of flan covered with caramel sauce. Marcos divided the flan into two pieces and shoveled one of them into his mouth. He winked at Vasquez appreciatively, sipped the coffee, and set the cup down. "When you called, you said this friend of yours could be of service to me in some way." "Yes, perhaps he can," Vasquez began. "He arrived two weeks ago from Panama. You understand how it is, getting started here. He is living on the North Side. I think he would be good at this kind of work . . . with the documents. It could mean more money for you, Mr. Ortega." Marcos's face hardened. "I'm busy enough as it is," he said coldly. He didn't care to have Vasquez giving him business advice. "Most of my people start by working regular jobs. I don't like them depending on this to get by. Even I keep a regular job at the tortilla plant." Vasquez, realizing he'd been inept, tried to repair the damage. "You know better than I about such things. I'm sure he will find other work, as you suggest. He is an intelligent man and would do as you say if you took him on." "Of course he would do as I say," said Marcos indignantly. "What sort of business do you think I'm running?" Vasquez was momentarily speechless—searching for words that would placate his irritable guest—when Salvador Rico entered the restaurant. "Here he is!" said Vasquez. A solidly built man of medium height, Rico was wearing drab, loose-fitting work clothes. He stepped up to the table, a tight smile on his face, and held out his hand to Marcos. Vasquez made the introductions. "It is an honor to meet you, sir," said Rico. Saying nothing, Marcos remained seated and reluctantly shook Rico's hand. He nodded curtly for Rico to sit next to Vasquez and absently punched little creases into the flan with his spoon. "So, Felix tells me you arrived not long ago from Panama," said Marcos. "Yes, we are from the same neighborhood in the capital," said Rico, who had small eyes with lids that looked almost oriental and a wide, flat nose. A scar cut across his upper lip, upsetting the normal curve of his mouth. But Marcos could see nothing remarkable, nothing particularly revealing of character. His manner was respectful. "You are not working yet?" he asked. "No, but I talked to a man yesterday about working in his photo shop." Marcos sipped his coffee and thought it over. Although he was initially unreceptive, what would it hurt to take on another vendor? This Rico would be in Sixto's area on the North Side, so he wouldn't have to deal with him. It would make Vasquez look like a man of influence and he would be indebted to Marcos—more complimentary flan and free meals. He motioned with his spoon toward Vasquez. "It is only because of this man that I will allow you to work for me. Don't forget that you owe him a debt of gratitude." "Yes, of course I am very grateful," said Rico, with a quick nod at Vasquez. "You will need other income and a legitimate job as cover," said Marcos, and he slid the remaining half of the flan down his throat like a pelican swallowing a fish. "I have a man up on the North Side—Sixto Montoya. Give me a phone number and he will call. If he tells you to do something, imagine it is me talking. He will give you an area—show you what equipment is needed to get started. You will have to buy the equipment and documents yourself." "Of course. That will be no problem." "Sixto will show you the ropes," continued Marcos. "We don't charge more than a hundred and fifty dollars for both the green card and social security card. It would be easy to take advantage because many of them don't have any idea what a fair price is. We make money, but we don't gouge them. If I hear of any vendors charging more, they are cut off. Do you understand?" There was a resonant edge to his voice, suggesting that anyone who defied him would be dealt with harshly. "Of course, Mr. Ortega," said Rico softly. "You can count on me to do as you wish." # 3 It was cold, and a thin layer of new snow powdered the streets. Though the snow provided faint illumination, it was still quite dark. The cars advanced like a slow-moving funeral procession, the snow absorbing their sounds. Hayden could see the GETTY'S MEATS sign at the top of the three-story brick building and soft yellow light through hazy windows. The odor of freshly slaughtered meat was seeping in through the partially open car window. "Hey, Joe, buy your pork chops at the store like everybody else," said Sam Payton over the radio. During their last visit, he'd spotted Willis stuffing a bag of freshly cut ribs into his coat pocket and had been needling him ever since. "They were throwin' 'em out," barked Willis. "Mind your own business, Payton." It was one of the few remaining slaughterhouses on the South Side of Chicago. The pigs, fatted to bursting, were trucked in, emptied into a large pen, and then, squealing mightily, herded into a narrow chute that led them to workers who would stun the animals with an electronic prod. They were then hoisted onto a hook that sent them toward an army of butchers—men dressed in blood-spattered white coats and plastic helmets, who would slit the pigs' throats and carve them into parts. Wielding long, razor-sharp knives, the men were strong and had large, powerful hands. They did their work without speaking, without thinking, concentrating only on the relentless parade of flesh and bone. Most of them were from Poland, many having entered the States on tourist visas before melting into the vast Polish community in Chicago. As several tan Plymouths pulled into the parking lot and others took up positions around the perimeter of the building, the secretary, sitting near the front window, immediately recognized them. She called back to her boss, who was in the adjoining office with his door open. "Mr. Getty, it's those jerks from INS again." Without hesitation, George Getty, a rotund, middle-aged man with dark bushy hair, picked up the phone and pushed the speaker button that sent his voice out to the plant. He said simply: "INS is here." While the agents were still getting out of their cars, the reaction inside the plant was immediate and well rehearsed. Eighty percent of the workers dropped their knives and left their workstations. Getty knew he could legally refuse to allow INS to enter, but that could lead to a search warrant operation that would shut the plant down for several hours and likely generate a blizzard of unfavorable publicity, as INS would sometimes bring the press and TV media along to spotlight the problem of undocumented workers. Hoping that some of his Polish workers would hide while he stalled, Getty spent five minutes in a half-hearted effort to reach his attorney before allowing the agents to enter the plant. Once inside, the agents split into pairs and spread out. One of them, Milos Jankowicz, who spoke Polish fluently, would assist other agents in interviews as needed. The question of their alien status was usually answered, however, by the fact that they were fleeing or hiding. Hayden went with Judy Svoboda to search the third floor. They found it deserted, but there was a thin metal stairway leading to a skylight that opened to the roof. Svoboda climbed up to check it out. The skylight was not properly latched, and there was moisture on the steps at the top of the stairway. "Looks like they've been up here," she said. She pushed open the skylight, and a block of cold air came through, along with a sprinkling of dry snow. She poked her head above roof level and looked around. There was enough light reflecting off the snow to see the area clearly. Observing no movement, she stepped up onto the roof, Hayden behind her. They stood next to the skylight, listening. About thirty feet away, a massive gray metal generator produced a deep hum and belched out plumes of steam. Svoboda pointed to footprints in the snow leading away from the skylight toward the edge of the roof. They followed the footprints to a fire escape ladder that curved over the tile parapet. Hayden looked over the edge at Agent Tim Reynolds, who was standing in the alley below. "Hey, Tim, any activity from up here?" Hayden called out. "I heard something up there a few minutes ago," said Reynolds. "But some guy ran out through the dock in front, so I wasn't here for a while. Looks like somebody came down here while I was gone." Reynolds was peering at the snow and a line of messy footprints that indicated that at least one person had escaped down the alley. Hayden looked at the snow on the roof. There was another fresh path between the parapet and the generator, but it was impossible to tell from the muddled footprints whether somebody had come to the parapet from that direction or the other way around. Hayden gestured for Svoboda to follow him, and they walked toward the generator. As they drew near he noticed a suspicious puff of condensation drift skyward from around the corner. "OK, buddy, let's go," said Hayden as he turned the corner. Hayden saw the flash of the carving knife and instinctively reached up with both hands to grab a wrist the size of his own arm. He swung it away, twisting the man's arm and shoulder at such a severe angle that the knife slipped from his grasp and the Pole cried out in pain, both of them tumbling to the snow-covered roof. Svoboda dropped her knee into the man's back so that he was splayed out on his stomach. As Hayden stood up, he could see him better—a stocky young man wearing a long white butcher's coat. Hayden kicked the knife away through the snow, grabbed a set of cuffs from his belt, and pulled the man's arms behind his back, as Svoboda continued to apply pressure. The man was weeping and spewing Polish but made no effort to resist Hayden, who quickly closed the cuffs on his massive wrists. "Are you crazy?" cried Svoboda at the Pole. She then glanced up at Hayden and registered a look of concern. Hayden felt the coolness on his forehead but not the line of blood that flowed past his ear and down his jaw. He could see from Svoboda's expression that something must look bad, and he reached his hand up to feel the wetness. Seeing the blood on his hand and in the snow, he pulled a glove from his jacket pocket and pressed it against his forehead. "Let me take a look at that," said Svoboda, who reached over to lift the glove off the wound long enough to get a sense of it. "It's not as bad as I thought. Not too deep. He just grazed you." "I can go to the clinic downtown if I need a few stitches," said Hayden, breathing heavily. He looked at the Pole, who lay crying on the roof. "That was a pretty good move you put on this guy," said Svoboda, who'd retrieved the bloody carving knife. "I'll have Reynolds come up and take some photos. I'm sure they'll prosecute on this." Ten minutes later, after a dozen other Poles had been arrested and loaded into vehicles, Hayden sat in the passenger seat, looking at the snow falling and melting against the windshield. Svoboda had fished a bandage from a first-aid kit and pasted it across Hayden's forehead. If he thought about it, Nick could feel a subtle throbbing, but he knew it wasn't serious, and a strangely pleasant torpidity had swept over him, as though he'd been given a mild anesthetic. The Pole was in the backseat with Jankowicz next to him as Willis, uncharacteristically silent, pulled slowly away from the slaughterhouse and headed toward the office. The Pole was sitting forward, unable to sit comfortably because of the handcuffs behind his back. The tears had dried on his cheeks, but his eyes were shining with emotion. Every few seconds he sniffled back the discharge from his runny nose. He looked pleadingly toward Hayden, who stared vacantly out the front window. The big Pole seemed to think his fate now rested solely in Hayden's hands. Finally he could contain himself no longer and began speaking rapidly, spraying Jankowicz with foamy spit. "He says he is more sorry than he can express in words," said Jankowicz, who translated in a dry monotone. "He says he has never done anything like this before—that he panicked with the thought of having to go back to Poland so soon after coming here. He just arrived two weeks ago. He says he's not a criminal, has no criminal record. He is here only for his family, to take care of them." Hayden felt numb and was barely listening. It was too complicated, he thought, trying to discern who was a threat and who wasn't. This man had a story to explain it, of course. Everybody had reasons or excuses, even for committing acts of violence. Maybe the Pole was telling the truth. Then again, maybe he'd murdered his wife, fled Poland, and this explained his desperation. Either way, it didn't matter. They were all threats, and they were everywhere. It was the only way to think about it if you were going to survive. He felt neither hatred nor empathy, just a weary recognition of how things were. The Pole was muttering quietly to Jankowicz. "He says he wants to know if you can forgive him for what he has done today. He will always be ashamed of this," said Jankowicz. "Tell him to shut up," said Willis. "We've heard enough." There was silence as Hayden gazed out the window. The Pole was leaning forward, tensed, waiting for some response, but Hayden said nothing. After a moment Jankowicz raised his hand and shook his head at the Pole, who leaned back awkwardly, his shoulder blades pressed low against the seat back. It was very quiet as the vehicle rolled smoothly through the snow. * * * "Other people punch their time card and go to work," said McCloud. "You punch in and walk into the middle of a tornado. And that's why you like it." In contrast to the bedlam that reigned every afternoon on the third floor in area control, it was serenely quiet on the twenty-second floor. The small conference room, just across the hall from a US District Court, offered expansive views of the Chicago skyline. As he spoke, McCloud paced slowly in front of the floor-to-ceiling windows. Hayden and the two other agents attending the lecture, who were both in their second year on the job, were intrigued with this departure from the ordinary curriculum, which was usually a discussion of some tedious aspect of immigration law or procedure. "By his third year on the job, the typical agent in Chicago has arrested over a thousand illegals. You're dealing with people en masse _—_ moving them like herds of cattle. Over time you can't help but think of them as objects—cargo to be processed and shipped. It all happens gradually so you don't notice it, but inevitably the awareness of your impact on other human beings begins to deteriorate. Psychologists call it 'emotional erosion'—when the daily requirements and stress of the job force you to erect a firewall around your emotions. And when that happens you're in danger of falling into what I call the 'gladiator syndrome.' "The gladiator, caught up in his heroic mission, sees that the problem of illegal immigration is huge and his ability to deal with it is very limited. It's not just the countless wets, but the criminal activity that inevitably follows. His powers of recognition have sharpened to the point where he can detect wets and criminal activity everywhere. Since he takes his job seriously, this creates intense frustration and imposes a psychological burden. So the gladiator tries to level the playing field by overstepping his legal authority. And initially he gets away with stuff, whether it's an illegal search, manufacturing probable cause, whatever. Naturally, this strengthens a false sense of invulnerability. He thinks he's Superman and doesn't know there's kryptonite out there. "Out on the street doing the job, he's dynamic, in control, ordering people around, and taking charge. People listen to him and usually defer to his authority. When he gets home, he puts his gun away, but the armor remains. Other people's feelings and thoughts have begun to splatter like insects on a windshield. Not surprisingly, the wife or girlfriend isn't going to like this new attitude. And as the gulf between them grows, he gradually spends less time at home. The tavern becomes his refuge—a place where he can be himself and commiserate with other agents. "Believe me, this gladiator syndrome is unsustainable. Reality will eventually intervene and knock him off his pedestal. He will take risks on the job that are foolish, and outside of work he'll push people away so that he becomes more and more isolated. A bunker mentality takes over. "But it doesn't have to reach that point. When you see the warning signs, you need to pull back and put some emotional distance between yourself and the job. You can choose to be a philosopher instead of a gladiator. You won't see things in such black-and-white terms. A more mature, thoughtful attitude will emerge, so you won't take your job or yourself so seriously. And that's a _good_ thing." McCloud paused a moment before continuing. "You may even develop a vague sort of kinship with the wets because they're caught up in the same mess you are." * * * Seven months into his first year, Nick Hayden caught a break. An extra car became available, and Willis, due to his seniority, was allowed to ride alone. Hayden was more than a little relieved, as dealing with his partner's mood swings and autocratic style was emotionally draining, and though Hayden had performed well, Willis still hadn't fully accepted him. Nick realized it wasn't personal—that Willis had difficulty getting along with everyone, particularly trainees who hadn't been in the Border Patrol. Though eccentric, Joe was a competent, dedicated agent whose world had become defined by the job's physical and emotional demands—a kind of low-level warfare he'd grown to cherish. Chicago, a city of gruff characters, patiently tolerated him, as did his professional colleagues. As they drove toward the office on their last day together, Hayden made a final peace offering: "Thanks for putting up with me, Joe. I learned a lot from you." This caught Willis off guard, and he seemed at a loss for how to respond. Finally, he said, "Well, buttering me up ain't going to do you no good. You've still got plenty to learn." Hayden smiled. What else could he have expected from Willis? Hayden's next partner was Vince Kozlowski. Born and raised on the southwest side of Chicago, Kozlowski had a lopsided nose, a wry smile, and a calm manner that instantly put others at ease. Though tough and capable, Kozlowski didn't have a nasty bone in his body, nor did he lust for higher office. Kozlowski hadn't been in the Patrol and was far more accepting of Hayden than most of the other journeymen agents. He was in many ways Joe Willis's opposite—free of ego, not taking anything personally, and wanting only to get the job done so he could go home to the domestic bliss he shared with his wife and three young children. Having grown up amid the corruption and inefficiencies that were a normal part of life in Chicago, Vince was patient with government policies, no matter how incoherent or perverse. Resistance to these forces was, in his mind, both futile and self-destructive. Whenever Hayden voiced frustrations over the disarray of immigration policy, Vince would gently chide him. "Look at it this way," Kozlowski would say with a knowing smile. "It's great job security. There will never be a shortage of wets. If the government wanted to stop illegal immigration, they'd make employers check the phony documents the wets use to get work. But they don't wanna do that because it would work. Obviously, if the wets don't think they can get jobs, they won't come—and we'd be out of a job. Just go along with it, take your paycheck, and try to enjoy life." Earlier than most of his colleagues, Kozlowski had embraced the "philosopher" mindset. Hayden thought he was one of the most uncomplicated and emotionally healthy people he'd ever met. Meanwhile, it was a wild time out in the field. Under pressure from headquarters, Moretti ordered agents to keep hitting businesses until they'd corralled at least a hundred illegals every day. "Don't bother coming into the office until your cars are fully loaded," he warned. Setting out before dawn in caravans of up to twenty vehicles and a detention van or two following along, they invaded one factory after another, many of them housed in crumbling warehouses that violated every city code imaginable. Agents grew accustomed to working around physical hazards: asbestos hanging from warehouse pipes, open vats of foul-smelling toxic waste, and assembly lines choked with smoke and deafening noise. The agents' arrival typically led to pandemonium—large segments of the workforce scattering in every direction. Fights and altercations of one kind or another became daily occurrences. Among the notable injuries sustained by agents that spring, Al Winfield was struck in the back of the head by a Nicaraguan, who came out of a tool shed wielding a long piece of metal tubing as if it were a samurai sword. At the office it was discovered that the Nicaraguan had been deported three times before, had assaulted an INS agent in Newark, and was wanted for armed robbery. Jack Hibbert got into a brawl with a Mexican on the roof of a factory. The Mexican slashed Hibbert in the arm with a switchblade but was captured when he jumped off the roof and broke his ankle. Coming to the aid of a fellow agent outside a scrap yard, Judy Svoboda was attacked by a snarling Doberman and had to shoot it down. The same day a group of El Salvadorans fled a factory and ran onto a nearby freeway, dodging high-speed traffic. A car skidded into one young man, sending him flying onto an embankment, breaking both of his legs. If apprehensions were running low, agents would pretend to have information on whatever business they happened to be passing. Those were often the most productive operations. Agents were very adept at implying that owners had no choice but to allow them to take over their properties and interrogate the entire workforce. Confronted with a team of ten or more federal officers glaring at them with righteous indignation, few had the temerity to turn them away. The more daring illegals would resist the flight instinct during raids, hiding in plain sight, but their poses of casual indifference were often dead giveaways. When questioned, some would claim to have been born in Texas or California, but they had difficulty explaining why they could speak no English. Others, insisting they were born in Puerto Rico, had no idea where the island was or knew nothing about its history or customs. Nevertheless, agents were keenly aware that arresting someone who turned out to be a citizen would lead to lawsuits and depositions, so they proceeded with caution. The mere presence of the INS caravans in ethnic neighborhoods aroused fear and panic, as immigrants of all nationalities had become familiar with the INS fleet, most of them clunky, tan Plymouth Furies with antennas poking from their roofs. Fleeing illegals scurried in front of traffic and down side streets, and the Furies would roar off in pursuit. The chases often led to enclaves of illegals in stores or apartment buildings, and the backseats of the Furies steadily filled up. Agents made so many arrests every day that pat-downs got sloppy, and sometimes weapons weren't found until illegals were admitted into lockup. Moretti would dump a boxful of undetected knives and switchblades on a table in the middle of the squad room. "This is what you guys are missing," he'd bellow. "I won't tolerate an agent being killed on my watch because of negligence. When you throw your borders open, some bad people are going to come in with the average wet who is just looking for work to support his family. Do I have to remind you of the agents we've already lost around the country?" Amid the stress of field operations, personal animosities between agents sometimes came to a boil. Once that summer, Hayden entered a parking lot outside a factory to find two men grappling on the oily ground. He jumped in to assist in the anticipated arrest, only to find they were both journeymen agents, pummeling each other over some perceived slight. As illegals often concealed themselves in the dirtiest and most remote sections of warehouses, agents frequently ended the day covered with layers of soot and grime. Yet the dress code required a jacket and tie, so each agent had a collection that was frayed and soiled. McGinty's Tavern, just around the corner from the office, became a decompression chamber at the conclusion of the day's field operations. Agents, especially the older ones, would pause to fortify themselves with beers and shots of Irish. Then they would grab a sandwich and head up to the office for the hectic drudgery of writing up illegals for deportation, which often took all afternoon and well into the evening. Hayden found that he thrived on the excitement, challenges, and unpredictability of field work. While some agents would lose their composure amid the chaos, he would often arrive at a state of inner calm, particularly when things were spinning most out of control. Eventually his coolness under pressure drew quiet compliments from senior agents. Meanwhile, twelve-hour workdays left little time for outside activities. Hayden usually returned exhausted to his spare studio apartment near DePaul University. He sometimes forced himself to go for a short run before wolfing down a dinner of pizza or canned soup. If he had any energy left, he would study immigration law manuals in preparation for the written exams he would have to pass. Then he would sleep hard and get up early. It was a demanding schedule, but he didn't mind because it was more interesting than anything he'd ever done in his life, and he was convinced it was important work. Still, knowing he could be fired without cause during the first year, Hayden was apprehensive about his upcoming appearance before the probationary review panel. Despite having earned a reputation as a hard worker and doing well academically, he felt like an outsider—tolerated, perhaps, but not embraced by his colleagues. He wondered whether the incident with Tom Kane and the Jamaican had something to do with it. But the issue that caused the greatest concern was his reason for taking the job in the first place. If it were discovered, he would certainly be fired. He'd asked senior agents a lot of questions about the shooting, and that may have raised suspicions. McCloud had been curious about his name, and though they'd since developed a good relationship, he could have referred the matter to the regional office for further investigation. Anything seemed possible. When Hayden found out that the head of investigations at the Minneapolis field office would be part of the panel, he had a sinking feeling. Victor Bolton, a hardliner with an enormous ego, didn't like agents hired "off the street." A number of probationers at the Minneapolis office who hadn't been in the Border Patrol had been fired in recent years for no legitimate reason, and Bolton had purportedly enjoyed letting the guillotine fall. Then there was Jack Connelly, director of investigations at the Chicago office. With his carefully combed white hair, pencil mustache, frequent scowl, and horn-rimmed glasses, Connelly was a distant figure, not one to engage personally with the younger agents, and he tended to shift with the wind, which could be dangerous. Connelly would be in charge of the panel, and his opinion would be crucial. It would be Connelly, Bolton, and somebody from the regional office to render final judgment. On the morning of the hearing, Hayden sat at his desk in the empty squad room and tried to remain calm as he waited to be called into Connelly's office. He was wearing the only suit he had that hadn't been torn or otherwise damaged during a field operation—a gray pinstripe, crisply pressed, accompanied by a white shirt and a red silk tie. He hadn't slept well the night before and noticed in the office lavatory that he had dark circles under his eyes. The suit at least made him look respectable, he told himself. Moretti had earlier informed him that Earl Fasco, a regional investigator, had been selected as the third person on the panel, and that Fasco had spent most of his career doing internal investigations, cases in which agents had taken bribes or engaged in other improper conduct. Nick suddenly felt they _had_ to know something. He had been told to be ready at nine o'clock. It was already ten, and still they hadn't sent for him. Feeling edgy, he took a stroll down the hall past Connelly's office to the drinking fountain. Through the frosted glass windows, he could see three blurry figures sitting behind Connelly's desk and a fourth in a chair in the middle of the room facing them. That had to be Lou Moretti. It was normal for them to talk to his supervisors, but why for so long? A few moments later, Moretti emerged from Connelly's office and approached Hayden. "They want you in there now," said Moretti. Hayden studied Moretti's face, but his eyes were flat and expressionless. Hayden buttoned the jacket of his coat, took a deep breath, and walked into Connelly's office. All three of the men were sitting rigidly behind Connelly's large desk, glaring suspiciously at Hayden. Connelly was in the middle. Without standing, he introduced Fasco and Bolton. Hayden stepped forward to shake their hands. Bolton shook his hand with exaggerated firmness and offered an icy smile. Fasco, a swarthy man of about fifty, leaned forward, allowed a weak shake, and sank back into his chair, looking down at the file materials in front of him. Hayden glanced at the papers and could make out what looked like his original application for employment, which sent his mind racing. Why would Fasco be studying a document that had nothing to do with his performance during the past year? Hayden sat in the chair vacated by Moretti. The room felt stuffy and warm. All three of the men were now silently looking down at the papers in front of them and occasionally glanced up at Hayden as if to reconcile what they had read with the person sitting before them. This went on for what seemed like several minutes, while Hayden's temperature rose around his shirt collar. Then Bolton, a square-jawed, middle-aged man with a receding hairline and a deadly serious manner, plunged forward before Connelly had a chance to say anything—a clear breach of protocol. "Hayden, we've reviewed your evaluations and your academic record. Is there anything you want to tell us that you think is important to this proceeding?" said Bolton in a deep, sonorous voice. Though now certain they knew something, Hayden decided there was no point in admitting anything. He wasn't going to break, not without being confronted with specific evidence. "No. I'm willing to let the record speak for itself." He was pleased that his voice sounded calm and steady. Bolton was sitting with his large hands folded in front of him on the desk, looking at Hayden intently, as though he could look through his eyes and into his soul. He examined Hayden silently for several moments in an apparent effort to unsettle him. Nick noted an impish grin on the face of Jack Connelly, apparently amused by Bolton and the situation. He didn't know what to make of that, but took minor comfort from the fact that Earl Fasco looked utterly bored. "I see you weren't in the Patrol," said Bolton, who made it sound like an accusation. "No, I wasn't." "That's unfortunate." Bolton paused before continuing. "You know, a number of years ago an agent from this office was killed—shot dead by an illegal alien. Were you aware of that?" Though growing increasingly nervous, Hayden maintained his surface composure. "Yes, I've heard about it." "It was found that an officer, a trainee like you, didn't have what it took to shoot a man before that man killed his partner," said Bolton, who let the statement hang in the air. Hayden said nothing, and Bolton continued. "It ended up costing the life of a good agent. I knew the agent who was killed, Frank Kelso. He was a fine man. So I'm going to ask you an important question." Hayden noticed that Fasco and Connelly were now fully engaged in the exchange, staring at him as though they knew what was coming. Bolton continued: "If you had to pull that trigger to save yourself or your partner, would you hesitate?" "No, of course not," said Nick, as Bolton studied him doubtfully. Hayden was still girding himself for an extended interrogation when, to his surprise, Jack Connelly stepped in. "Well, Hayden, you have done quite well in your first year. All your supervisors say so. I don't see any reason to prolong this line of questioning. Everything indicates that you have a bright future here." Hayden was shocked. He had a sense that Connelly was being more kind than normal as a counterpoint to Bolton, who had clumsily taken over Connelly's preeminent position on the panel. That's what the grin was about. He'd allowed Bolton to continue and then taken delight in pulling the rug out from under him. Bolton was sitting back in his chair looking deflated. Apparently he'd been trying to rattle Nick and plant some seeds of doubt about an agent who hadn't come from the Patrol. They knew nothing after all. Fasco followed up with a couple of innocuous questions about what types of investigations Hayden most enjoyed. Then Connelly resumed control and, without asking the others if they had further questions, congratulated Hayden on successfully completing probation and dismissed him from the room. Bolton, his face flushed, shot a baleful glance at Connelly. As Hayden closed the door behind him, an enormous sense of relief swept over him. He felt he was gliding inches off the floor as he walked back to area control. * * * The day after his probation hearing, Hayden, curious about what he'd accomplished in his first year, leafed through the leather-bound logbook that recorded all of the unit's arrests and deportations. He counted over five hundred illegal immigrants arrested during the past year with his name next to theirs, which meant that he'd done the paperwork on them and, in many cases, personally arrested them. In all, the Chicago office had been responsible for removing or placing in deportation proceedings some ten thousand illegal aliens during that year. Considering the logistics of moving around that many people, it was a remarkably efficient operation. Yet politicians, activists, and pundits regularly pillaged INS, in no small part _because_ of its efficiency. Agents were accused of insensitivity, brutality, and racism, even though cases of outright cruelty or abuse were extremely rare. Hayden had been struck by how meticulous agents were in making certain that the children of illegals were not left unattended when one or both of the parents were arrested. While agents from the FBI or any number of other federal agencies were routinely glorified and thought of as heroic, INS agents fought a lonely and unheralded battle, more often objects of derision than praise. * * * The small studio apartment where Hayden had been living for the past year was on the North Side of the city in a vibrant area of businesses—restaurants, bars, and small shops—intermixed with apartment buildings and three-flats. After work he sometimes played basketball at a nearby field house—pickup games with anyone who showed up. It was a good way to blow off steam and got him away from the habit of stopping at McGinty's to trade war stories with his colleagues, which always left him feeling empty. There were many attractive single women in his neighborhood, and it wasn't difficult to meet them. Some were obviously turned off by his gritty line of work, while others found it intriguing. Either way, he was so consumed with the job that he hadn't the time or energy to be drawn into anything beyond brief liaisons. His most meaningful personal encounters took place at the Veterans Hospital in Maywood, just west of the city. He'd noticed an article in the paper that mentioned a need for volunteers to visit bedridden veterans, particularly those without families, who would often fall into intense boredom and depression. Most were older men, many of them World War II or Korean War veterans, who enjoyed talking about their war experiences and were fascinated with Hayden's INS work. Hayden tried to get there once a week, usually on the weekends. Though the men were appreciative of his visits, he often thought _he_ was getting more from the experience than the patients. The shooting of Frank Kelso and its aftermath had deeply affected Hayden, as he had lost the most important and supportive relationship in his life. From the beginning, the circumstances surrounding that terrible event had been vague, and he'd formulated countless theories to fill in the blurry picture; but without solid evidence they would remain nothing more than speculation. Though Willis had provided only a general description of the incident, Buck Tatum's extreme reaction suggested that the situation might not have been as straightforward as Willis seemed to believe. Hayden had hoped more facts would emerge after talking to agents who had worked with Kelso, Landau, and Tatum, but none of them had direct personal knowledge, and they seemed to accept the results of the investigation conducted at the time. His unusual curiosity could raise suspicion, potentially costing him his job. He'd passed the first professional hurdle by making it through probation. Now he was determined to sharpen his investigative skills and try to earn a position in one of the units that worked the more challenging criminal cases. He would have to be patient and wait for the right moment to make further inquiries about the shooting. * * * Hayden usually didn't remember his dreams and made little effort to do so. To him they were mere flights of the imagination, not to be taken seriously. But there was one dream he'd begun to have almost every week, and it disturbed him. It would always begin in a desert, the sun blazing through a cloudless sky—the peaks of dry, craggy mountains looming hazily in the distance. Several figures dressed in brown hooded robes, like those of Franciscan monks, shuffled slowly along a sandy path. The hoods hung loosely over their heads so that he couldn't make out their faces. It was a peaceful scene, the figures blending with the washed-out earth tones of the desert. They plodded along, a methodical purpose to their gait, as if they had traveled this path before and knew exactly where they were going. Nick, from a distance, would call out to get their attention, but they couldn't hear him. His voice had no strength behind it and always vanished into the air. # 4 It was a windless day in the city of Guadalajara, the air thick and humid. A vast cloud of exhaust fumes filled the sky, diffusing the sunlight. On the Calle de Leon there were no trees or landscaping—nothing but concrete pavement and a long line of buildings with little or no space between them. A pack of bony dogs sniffed through garbage that lay next to a toppled metal container. The dogs scattered when a pickup truck pulled in front of the decaying six-story apartment building. Miguel Chavez stepped out of the passenger side and looked up at a third-floor window where his son, Paco, was leaning over the windowsill. "Papa!" the boy shouted happily, his voice echoing down the street. Miguel, dressed in loose-fitting jeans, work boots, and a tan shirt with the sleeves rolled up, waved and walked toward the building, carrying his metal lunchbox. He had straight black hair combed cleanly back from his forehead. Broad-shouldered and thick at the waist, he moved with the unhurried ease of a man older than his thirty-six years. Miguel went inside and climbed the sagging stairs. He had barely closed the apartment door behind him when Paco, ten years old and small for his age, began excitedly searching his father's pockets. "Where is it, Papa?" he cried in Spanish. Carmen was watching from the kitchen. "Let your father breathe, Paco. He didn't promise. He only said he _might_ have something." She looked at Miguel's face for some sign but could tell nothing from his placid expression. Finding nothing, Paco stepped back and looked sadly at the floor. "Here, son, take this to your mother," said Miguel, handing over his lunchbox. Paco cradled it in his arms and marched slowly toward the kitchen. "You might want to open it," Miguel murmured softly. Paco's face lit up as he placed the box on the kitchen table, fumbled with the metal latch, and flung it open. He pulled out a bright blue Chicago Cubs cap, the red letter _C_ on the front. Beaming with delight, he ran to his father and hugged him around his waist. "The Cubs are my favorite team, Papa!" "Yes, why do you think I got that one?" Miguel laughed and stroked the boy's hair. "Go show Luis your new cap. I saw him out on the landing." Paco smiled and raced out the front door. Carmen, with a restrained smile, looked at the basket on the kitchen counter where their two-month-old daughter, Maria, slept peacefully, undisturbed by the commotion. "This one will sleep through anything," Carmen said. Miguel kissed his wife's forehead and looked down at Maria, his expression now solemn. "What's wrong?" Carmen asked. "They won't need me for at least a week, probably more. Before long we'll have to find an apartment where the rent is lower, and it will probably make this place look like a palace." Carmen looked away, afraid of what was coming. "We're moving backwards," Miguel said pleadingly. "Something has to change. We have to consider the jobs in Chicago my cousin has written about. I've been praying . . . waiting for an answer." Carmen, with worry in her large, brown eyes, looked out the kitchen window and then back at Miguel. "But they don't want us there." "Then why do they let so many without papers live and work there? What they do is more important than what they say, and they don't seem to do much to stop anybody from getting jobs. They must want us." She could feel her resistance beginning to crumble. "I can go first," said Miguel. "You can stay with my parents until I send for you." Carmen let out a deep sigh and rested her head gently against Miguel's chest. Perhaps he was right. Perhaps they _were_ wanted north of the border. Thinking of it that way made it seem more reasonable. * * * Miguel crouched next to a shack on a rock-strewn hilltop in Juárez. He carried no clothing or other possessions except a wallet with the eighty dollars he had scraped together. It was hot—the late afternoon sun shining brightly. He peered down at the river, all that separated Mexico from the United States, yet here the Rio Grande was no more than a ribbon of brown water that cut through the valley. Women from the Mexican side went down to the river with buckets to capture the water and then returned to a cluster of small huts made of scrap metal, plywood, and tar paper. On the other side of the river, a steep, rocky hillside crested to a busy highway. Miguel watched as two men waded across the river, climbed the hill, and hopped into a waiting truck. To his surprise, there was no sign of the Border Patrol on the Texas side of the river. Mostly it was quiet, with an occasional gust of wind rappelling through the canyon. When the sun disappeared and dusk set in, Miguel made his move—still fearing that sirens and spotlights would greet him. He descended the slope, sloshed across the knee-high river, and scrambled up the steep embankment, his feet crunching through dried branches and mesquite. He was sweating heavily and his heart was pounding when he reached the top. He walked briskly along the shoulder of the highway toward the tall buildings in the center of El Paso, less than a mile away, as cars and trucks roared past him. Where were the border agents? Don't think about them, he told himself. Just keep moving and follow the instructions. As it grew steadily darker, he relaxed a little, figuring he was less likely to be noticed. He made his way to the bus depot in the downtown area and boarded a bus for Las Cruces, New Mexico, about fifty miles to the north. There were several others on the bus who looked around nervously and appeared to be in the same situation, but he didn't speak to them. As they waited for the bus to depart, he looked out the window and for the first time saw a green-and-white Border Patrol vehicle parked at the curb just twenty-five feet away, but the agents inside were looking down, apparently doing paperwork. He could make out the heads of two prisoners in the backseat of the vehicle. The bus left without incident, and he got off an hour later in Las Cruces. Following the directions he'd been given, Miguel made his way to a large park, which had thick bushes and a small grove of trees at one corner. He lay down beneath the canopy of trees, but his mind was racing and he couldn't sleep. At the first light of dawn, he got up and walked straight to the restaurant parking lot where he'd been told a man named Carlos would be waiting. * * * They had been driving for nineteen hours when they arrived at the outskirts of Chicago. It was Saturday morning, so the traffic was relatively light as the pickup truck traveled at just below the speed limit, heading east toward the heart of the city. Carlos, a stoic, expressionless man of sixty, had insisted on driving the entire distance, turning away offers from Miguel and the other passenger, a seventeen-year-old Mexican boy who sat between them, his head propped sleepily against Miguel's shoulder. Carlos explained that he had driven this distance many times, and since they didn't have valid driver's licenses, it was safer this way. They passed swiftly through the outlying neighborhoods—endless rows of apartments and businesses separated by faded green lawns and trees filled with colorful autumn leaves. Miguel peered at the distant skyscrapers, backlit by the emerging sun. The buildings had a surreal, bluish quality, lacking dimension, as though painted onto the horizon. Carlos grunted tiredly and nodded toward the skyline. "Chicago," he said, with a faint smile. " _Qué bonita_ ," said the boy, his eyes now shining with hope and fascination. Suddenly there was a loud, wailing siren behind them. They all stiffened as two police cars, their blue lights rotating, sailed past them and quickly disappeared. Carlos turned off the highway into the shadows of a seedy, neglected neighborhood. They passed an assortment of abandoned commercial buildings, dilapidated apartments, refuse-strewn alleys, and shabbily clad men—many of them standing in doorways, grasping bottles covered by paper bags. A pungent, rotting odor hung in the air—the smell of something burning. Within minutes, they'd entered another neighborhood, this one not so impoverished and, judging by the people and the signs on the shops, populated mainly by Hispanics. They turned off busy Eighteenth Street onto a quiet, tree-lined street with small houses and two-flats on one side and a brick elementary school on the other. Carlos pulled in front of a narrow, brick two-flat covered with faded maroon paint. It was very close to the sidewalk, so there was no front yard. "Here it is," Carlos said. Miguel had armed himself with such limited expectations that this simple dwelling looked surprisingly attractive. "Are you sure?" he asked. "I have been here before. The owner uses the first floor for storage. You are on the second floor. The key is under the mat." "Do I owe you anything more?" "No, your cousin has taken care of it. Good luck to you." "Thank you," said Miguel, shaking both their hands. He stood on the street as they pulled away, his legs heavy from lack of movement. Carlos waved his large hand in a kind of salute and Miguel waved back. He watched as the pickup turned off the street and disappeared. Suddenly alone, he looked up at the building and then down the block, getting his bearings. The sky was gloriously blue, and a velvety breeze moved softly through the elm trees along the narrow parkway. Miguel whispered a prayer of thanks as he shuffled slowly up the short walk to the front steps. The bottoms of his jeans, dried stiff from the muddy waters of the Rio Grande, rubbed together at his ankles as he walked. * * * Miguel stepped inside the dimly lit tavern. It was a gloomy little place—faded wood floors, a few small tables in the shadows, circular bar stools bolted to the floor—a place where people came to drink, not socialize. The aroma of stale beer and cigarettes hung in the air. A large overhead fan cut through cigarette smoke that drifted up from a scruffily dressed old woman sitting alone at the bar. The voice of Frank Sinatra singing "Summer Wind" filled the air, the tune's polished orchestration and upbeat rhythm contrasting sharply with the bleak mood of the tavern. Chacon, a middle-aged man with a black goatee, sat at the end of the bar reading a newspaper as Miguel stepped up. Chacon looked at him with tired eyes and addressed him in Spanish. "What can I get for you?" "I look for the man called Rico." Chacon nodded toward a man sitting in the dark shadows opposite the bar. He was leaning back with his head against the wall and his eyes closed. Miguel sat down in front of Salvador Rico and waited quietly, not wanting to startle him from his sleep. Something in the man's facial features made Miguel think he was not a Mexican, and a lip wound gave him a look of quiet menace. Miguel would tread lightly. For the moment, he needed this man. The Sinatra tape ended and the silence stirred Rico, who opened his eyes and looked into the passive face of Miguel Chavez. "What do you want?" asked Rico gruffly in Spanish, pulling himself erect. "The documents." "Who sent you?" "A man. I don't know his name." Drowsy and hungover from a night of much tequila, Rico considered him for a moment through blurry eyes. "Come back tomorrow," he said finally. "This is not a good time." "I can't wait that long," said Miguel evenly. "I need them to get work, for tomorrow morning." "Eager to work, eh? You Mexicans. Well, it will cost you more on a Sunday," said Rico grumpily. "How much?" "Three hundred dollars for the green card and social security card." "I don't have that much." "How much _do_ you have?" Miguel smiled as if it wasn't a serious question. "I will do you a favor," said Rico. "Two fifty." They studied each other for several moments. Miguel knew he had no leverage, especially if he wanted them today. He'd heard that Monday was the big hiring day at the local factories, and he needed a job now. There was no way around it—it was just how things worked here, like paying off a cop in Mexico, even when you'd done nothing wrong. Fortunately, his cousin had left some money for him at the flat. "All right," Miguel said. "Give me the money." "I will pay when you give me the documents." There was no edge to Miguel's voice; he spoke calmly, looking straight into Rico's eyes. Rico glared silently at Miguel, getting the measure of him, and then he smiled. He was impressed. This Mexican was not docile and unsure like many others. "You'll get your documents," said Rico indignantly. He pulled a small notebook from the inside of his black nylon jacket, took a pen from his front shirt pocket, and began writing. "Do you have a social security number you want to use?" "No." "OK, we'll make one up. It takes years for them to figure it out, and by then you can get a good number." Rico tore a page from the notepad and handed it to Miguel. "Here, take this over to the photo shop around the corner. Knock on the back door and give the man this note. He will take your picture and give you the documents." "I pay _him_?" asked Miguel. "No, you pay me. That note will tell him I've been paid." When Miguel looked at him suspiciously, Rico grinned and called out toward the bar, "Am I good for it?" Chacon didn't look up from his newspaper. "He's good for it." Miguel counted the bills and placed them in a neat stack on the table. He now had only thirty dollars left in his wallet and a few dollars in coins back at the apartment. "You are sure he is there now?" Miguel asked. "Of course. I pay him to be there," said Rico, stuffing the bills into his shirt pocket. "Very well. You are Rico, no?" "No more questions. Just go where I told you." After Miguel left, Rico leaned back against the wall, swung his legs up on a chair, and looked lazily around the bar. "Draw me a short one, would you?" he called out. Chacon drew the beer from the tap into a small glass, marched over to Rico, and set it down in front of him. Rico looked at the beer as if it displeased him. Returning to the bar, Chacon flipped over the tape and Sinatra came back, this time belting out "My Kind of Town." It was a bit too energetic for a quiet Sunday morning and mildly irritating to Rico, still struggling to come fully awake. He took a sip of beer and closed his eyes. * * * The foreman at the Poindexter Tube Company looked through the receptionist's window at three Hispanic men seated in plastic chairs. They appeared ready for work, dressed in jeans, work boots, and heavy-duty cotton shirts. One, considerably older than the other two, glanced up and just as quickly looked down. Staring was not his way. They would speak little or no English, but the foreman knew they would have the necessary documents, probably counterfeits like most of the others. More important, they would be good workers, respectful of their bosses, and do their jobs quietly and efficiently. He knocked on the window to get their attention and gestured them forward. As soon as he opened the heavy door to the shop area, they were greeted by a wall of musty heat, a sharp metallic odor, and overwhelming noise: churning machinery, buzzing forklifts, and workers yelling to be heard over the din. The sound rose up to the cavernous rafters of the plant and came back down in a cascade of colliding echoes. With windows mounted high on the walls, you could see only the sky and nothing of the surrounding community, making the shop seem like a world unto itself. Miguel peered up at the dirty haze and copper sunlight that streamed through the windows. It reminded him of Guadalajara. The foreman led them to a huge, oblong machine that, at the moment, stood idle. He called over to a flaxen-haired young man who was using a hand-operated forklift to move a pallet of metal tubes. "Russell, show these guys what they're getting into, would you?" Russell walked over and pushed a black button on the side of the old machine. A vibration shuddered through it, and dozens of tubes hanging from a track at one-foot intervals began moving into a large opening. Thirty seconds later the tubes reappeared through an opening at the opposite end. Dull and gray before, they were now glistening silver. Russell hit a red button and everything stopped. After removing the treated tubes he stepped over to a box of untreated tubes and demonstrated how to fasten them to the metal prongs hanging from the track. This would be their job: place the tubes on the prongs, run them through the coating machine, remove and stack the treated tubes on pallets for later shipping, and keep the machine supplied with paint solutions. After Russell had demonstrated each part of the job, the foreman led them back into his tiny office. He made copies of their counterfeit documents and told them they would make $4.50 an hour. Ten minutes later, the three of them were back inside the plant, working the tube coating machine. They'd been hired. The two younger men were good workers and deferred to Miguel, who instantly became their de facto foreman. Within two hours they'd become comfortable with the system and were already joking with one another as if they'd been processing tubes for weeks. Satisfied that the new job was going to work out and that the other two could handle things for a few minutes, Miguel excused himself. As he walked to the washroom there were glances from other workers interested in the new face, and he nodded and smiled at them. In his head he calculated that he'd be earning over five times what he'd made in Guadalajara. He flashed on his family, now so far away but depending on him. They had no idea that their lives had just undergone a dramatic shift of fortune. He was grateful to find that nobody was in the large, dingy washroom. Miguel stepped into the nearest stall and latched the door behind him. It was quiet except for the muted din of the plant machinery. He removed a handkerchief from his pants pocket and mopped the moisture from his face. Taking a deep breath, he braced himself against the walls with both hands and whispered a prayer of thanks. A wave of emotion shook through him. It was powerful and gained strength—like a deep, vibrating volcano. Tears began pouring down his cheeks. He held his handkerchief close to his mouth to muffle the sobs. What would they think if they were to find him here—crying like a child when he was supposed to be working? He blew his nose and dabbed the moisture from his eyes and cheeks. It took a minute to pull himself together. Miguel couldn't stop smiling as he stepped back into the glorious, symphonic racket of the Poindexter Tube Company. # 5 Marcos Ortega was curious about the shake in Sixto's voice and his reluctance to discuss the matter over the phone, but he wasn't worried. After all, Sixto was a bit high strung and tended to overreact to small problems. It was probably a minor issue with one of his vendors—the kind that came up from time to time. They'd agreed to meet at the Fullerton Lanes, a bowling alley on the North Side. With pins clattering and bowlers shouting, it was a good place to talk and not be overheard. It was also far from Marcos's home, so they weren't likely to run into his friends or acquaintances. The bowling alley was housed in an old brick building that covered several acres near the banks of the Chicago River. Inside were fifty lanes, a restaurant, bar, and poolroom. In the evening hours, it was crowded and there was often a party-like atmosphere. A cloud of cigarette smoke hung over the bowlers' heads, its odor mingling with that of popcorn, hotdogs, and pizza. Marcos arrived early and ordered a large basket of French fries and two bottles of Corona. He took a table at the end of the dimly lit mezzanine in front of lane fifty, far from the other spectators. By the time Sixto arrived, Marcos had inhaled the fries and was relaxing like a well-fed cat with his legs stretched out, sipping his beer while watching a group of giggling young women roll gutter balls. He flashed a big smile when his friend stepped up to the table, but Sixto responded with only a sullen nod. "I love this place," said Marcos breezily. "Best fries in town. Do you want a basket?" "No. I don't like French fries," said Sixto. "Anyway, I'm not hungry." "Well, I got you a beer," said Marcos, shoving the bottle across the table, a bit irritated with Sixto's grim mood. Sixto took a few sips of beer and stared distractedly at the lanes. They sat silently for a minute. "So, what is it this time?" asked Marcos finally. "You sounded worried." Sixto took a long swallow of beer and set it on the table. "It's Salvador Rico," he said. "Ah, the Panamanian." "Yes. I wanted to get as much information as I could before bothering you with it. I wanted to take care of it myself. But I'm afraid you will have to deal with Rico." "What exactly is the problem?" "As you know, I told him the rules and gave him an area. He set up shop in the back of a photo studio and was working like any of our other guys for the first few months. Then I found out he's been hanging around Sheridan and Broadway, working the streets like a drug dealer. It was getting people's attention." "Did you talk to him?" "Yes, of course. I told him we want a low-key operation. He said he understood, that he would do as I said. That was three weeks ago, but then one of my guys saw him over by Kedzie and Diversey doing business on the street again—way out of his area. I made his boundaries very clear, so there was no confusion about it." Marcos grunted and shook his head. "Now I find out he's hired vendors of his own," said Sixto. "He's got a guy assembling the cards for him in the back of that photo studio. He funnels business to his vendors from a bar called El Palacio on Sheridan—owned by a Cuban guy who lets Rico use his place for business and probably gets a cut." Marcos listened calmly, though there was now a clear, hard look in his eyes. Sixto continued. "He's charging two-fifty for a green card and social security card, sometimes more, depending on who he's dealing with. His guys are even hanging around the Devon area—going after the Indians and Pakistanis. He's overcharging and has no respect for boundaries." Marcos glared coldly at the lanes, thinking about his conversation with Salvador Rico at the restaurant. It had gone against his instincts to take on a non-Mexican, even on a trial basis—his first serious blunder since starting the business. Though the air-conditioned bowling alley was cool, Sixto's face was flushed and beads of sweat were popping out on his forehead. He grabbed a napkin from a canister on the table and wiped it across his face. "He's trouble, this guy," he said. "I went to talk to him again a couple of days ago. He acts like he doesn't know what I'm talking about. Finally, he doesn't deny it and says if Marcos has a problem with it, you should talk to him. He threw me out of the bar. I was lying there on the curb!" Sixto took a moment to gulp what was left of the beer and looked nervously out at the bowlers, apparently hesitant to continue. "There must be something else," said Marcos. "Yes, and you're not going to like it." Sixto paused before continuing. "He's sending his boys down to work the mall on Twenty-Sixth Street." Marcos's eyes flamed, and he slammed his huge fist on the table, sending both beer bottles flying to the carpeted floor, along with the empty basket. Sixto sprang from his chair and stepped back from the table. "Why have you not told me of this earlier?" bellowed Marcos, leaning over the table. "This termite invades my territory, and you say nothing?" Sixto scanned the surrounding area. The noise from the lanes had absorbed the outburst, and nobody seemed to have noticed. He retrieved the bottles and basket, and cautiously returned to his chair. "I'm telling you now. I just found out yesterday about the guy at the mall," said Sixto unsteadily. "But this Rico is not going to listen to me." Marcos ran his hand back through his hair, took a deep breath, and looked out at the bowling lanes for a few moments. Suddenly, a sheepish grin crossed his face. "I am sorry, my friend," said Marcos. "You have done nothing wrong. It is I who made the mistake when I agreed to take him on." He reached across the table and patted Sixto on the shoulder. "Don't worry. I will take care of Rico. You wait and see." * * * When lunch hour arrived the next day, Marcos left the tortilla plant, and drove slowly down Twenty-Sixth Street and into the parking lot of the mall—a large, white building that housed small shops selling an endless variety of imported Mexican pots and trinkets, leather goods, and clothing. Shoppers could get a decent Mexican meal at one of the stands, where they cooked food on small burners. Prices were low, and thousands of people passed through every day. The music of a mariachi band blared out from loudspeakers mounted on the roof of the building. Marcos bought a steak burrito wrapped in aluminum foil and returned to his car. Scanning the parking lot, he noticed a tall young man wearing bell-bottom jeans standing at the farthest corner of the lot in front of a coin laundry. He was wearing a T-shirt with the sleeves cut off and a Boston Red Sox baseball cap. The man gestured at a pickup truck to pull up close, and he leaned inside the open window. After a brief conversation, the truck pulled away. The man stuffed something into his pants pocket and counted the bills he'd just received. Moments later the young man heard feet on the pavement and looked up at the massive figure of Marcos Ortega closing in on him. Before he could react, Marcos spun him around, grabbed him by the shoulder and seat of his pants, and flung him violently against a wooden fence that ran along the alley. The baseball cap went flying. The young man was on the ground, wedged against the bottom of the fence, looking terrified. "Listen to me carefully, young fellow," said Marcos in Spanish. "You will not sell anything on the street again. Not here, not anywhere in this city. I am not a violent man, but nobody sells the documents around here without my permission. Do you understand me?" "Yes, of course." "Give me the money and the documents." The young man, hands shaking, handed over a wad of cash, two small facial photos, and several counterfeit green cards and social security cards. "So, you are working for Salvador Rico?" asked Marcos. After a brief hesitation, the man spoke in a trembling voice: "Yes, he sells the cards to us and tells us where to go." "Tell Salvador Rico that Marcos Ortega wishes to speak to him. He has twenty-four hours. Now get out of here and don't forget what I told you." The young Mexican nodded meekly and began to pick himself up off the ground. Marcos let out a soft chuckle, turned away, and returned to his car. He drove slowly to the tortilla factory, certain that the matter would now be quickly resolved. Did Rico think he could just brush Sixto aside with no consequences? Even worse was sending vendors across town into _his_ territory—a very personal provocation. So be it. Salvador Rico would be made to understand very clearly who was in charge of the counterfeit document trade in Chicago. * * * Wind swept through cottonwood trees along the river, the leaves rustling together like fine sandpaper. There was a quarter moon on the eastern horizon and a scattering of stars overhead. Below, the Chicago River moved like black ink, so narrow here that it seemed no more than a large, gurgling creek. Marcos pulled off Fullerton Avenue onto a narrow road that wound through a grove of trees and descended into a clearing that served as the bowling alley's parking lot. The gravel lot offered privacy, as it was well below the street and was obscured by the trees. To his surprise, Fullerton Lanes was closed that Sunday night—the parking lot unlit and, so far as he could tell, completely empty. The darkened building, vaguely ominous, stood outlined against the sky like a huge ship at sea. Had he known the lanes were closed, he would have suggested a different location. Still, he'd agreed to meet in the lot, not inside. He turned his brights on and drove in a tight circle to illuminate every part of the lot. Seeing nothing, he backed the car up to the bushes lining the banks of the river, turned the lights off, and shut off the engine. A wave of foul air from the river passed through the open window. He rolled his window up halfway and waited uneasily, expecting to see another pair of headlights at any moment. His watch said it was ten minutes past the meeting time of eleven o'clock. He thought about what he would say. A few minutes passed. Then he could make out the faint sound of boots on gravel, obscured at first by the wind and rustling leaves, but it grew louder, a rhythmic scraping. Marcos looked to his left and could see an indistinct black form walking swiftly toward him in the darkness. A shaft of light from across the river flashed through the trees and for an instant fell on sharp-pointed cowboy boots with silver tips. He jumped out of the car and walked a few steps toward the advancing figure. "What's going on?" he shouted into the wind. "Where's your car?" The only reply was a bolt of orange and an explosion from a gun's muzzle. The .38-caliber bullet pierced Marcos's skull, and he felt a flame of intense heat. Staggering back, he caromed against the rear of his car and rolled heavily over a small stand of cottonwood saplings along the riverbank, coming to rest, facedown, over the embankment. For a moment there was only the sound of the wind in the trees. The shooter slowly stepped over to the body. There was just enough light from across the river to see that Marcos was no longer moving. Two minutes later a car emerged from behind the bowling alley and stopped momentarily, its headlights aimed across Marcos's motionless body. Apparently satisfied, the driver pulled slowly out of the parking lot. * * * The manager of Fullerton Lanes discovered the empty vehicle and Ortega's dead body the next morning. Detectives from the Belmont district were pessimistic, having little to work with—no witnesses, no other tire marks near the car, and no empty shell casings. The wind had apparently muffled the gunshot, as there had been no reports of disturbance in the area. Footprints could not be lifted from the hard-packed gravel, and five hundred dollars in cash was left untouched in his wallet, which seemed to eliminate robbery as a motive. The coroner reported that the slug had entered the left side of Marcos's forehead at a slight angle and was fatal within seconds. The police made the usual inquiries: talking to his family and close friends, his boss, and a few coworkers at the tortilla factory. His young wife, who had only recently arrived from Mexico with their children, knew very little of her husband's illegal business and chose to say nothing about it to the police, nor did his friends, none of whom wished to become entangled in a police investigation. Sixto Montoya assumed Rico was responsible, but he decided that the safest course of action was to get out of the document business and stay clear of both Rico and the police. Weeks passed with no new leads, and the police closed the case. "Marcos respected us," declared Joe Willis to a gathering of agents at McGinty's. "He told me once he wouldn't mind going into politics. Maybe it was some politician who had him knocked off—saw him as competition, a rising star. Hell, we'll probably never know." Willis lifted his glass in a toast. "Anyway, here's to Marcos Ortega, one of the few tonks who tried to make our job easier. I'll miss the big son of a bitch." They were the most sentimental words anybody had heard from Willis in years. In a city where hundreds of homicides occurred every year, the violent death of Marcos Ortega faded quickly from memory. # Part II # 6 She was picked up at Marshall Field's for shoplifting and turned over to INS by the store security guards, who found the Colombian passport she had carelessly left in her purse. The visa in the passport showed that she had entered the country as a tourist for thirty days—but that was in 1987, and it was now the fall of 1990. Young and very pretty, she had almond eyes, radiant black hair, and smooth, cinnamon-colored skin. She was dressed casually but expensively in tight-fitting designer jeans and a white, sleeveless blouse that highlighted her beautifully tanned shoulders. "I like older men," she whispered to Joe Willis, her eyelids falling seductively. "Find my bald head attractive, do you?" snapped Willis, who had seen agents fired for yielding to this sort of temptation. As he continued typing, the girl became visibly nervous and produced a business card of DEA agent Ike Torres. "He is friend of mine," she said, with a touch of defiance. "I'll bet he is," said Willis, whose eyes lit up as he examined the card. "How does he like it? With you on top or is he into something a little more kinky?" "Is not like that," she said bitterly. "You call him and find out." "He said he would protect you from INS, didn't he?" Taken aback by Willis's fierce glare, she was momentarily speechless. Willis persisted. "That's what he told you, didn't he?" "He is important federal agent, no?" "He's a lying piece of shit. As far as I'm concerned he's a criminal for harboring illegals." Willis flashed his crocodile smile as the woman eyed him nervously and shifted in her chair. As the time of his age-forced retirement grew more imminent, Willis, realizing opportunities for revenge were dwindling, had developed a list of enemies. He'd let slip to Payton just a few days earlier that Ike Torres was number three on the list. "A list of enemies? Who the hell do you think you are—Richard Nixon?" said Payton with a shake of his head. The seeds of Willis's hatred for Ike Torres had been planted months earlier, when he encountered a Mexican who admitted he was illegal but claimed he was "working for the government" and should therefore not be arrested. Willis had ignored the comment and grabbed him by the arm, whereupon the Mexican punched Willis in the nose, drawing a small amount of blood. There'd been a brief scuffle before Willis was able to handcuff him. Determined to charge the Mexican with assaulting a federal officer, Willis transported him to the office and threw him into lockup. The Mexican promptly called Torres, who had told him that he would protect him from INS, as long as he supplied useful drug information. Though he had no authority for it, this procedure had become routine for Torres. Ike Torres, learning of the Mexican's predicament, had spoken to the DEA chief in Chicago, who, in turn, called INS district director Jerome Farber to ask that the "misunderstanding" be overlooked and the man be released so that he could continue working on a case that had the "highest priority." Farber, more concerned with avoiding interagency strife than the fate of one illegal alien, had not bothered to inquire with Moretti or Willis before ordering the release. So Torres and Farber were added to the enemies list, though Farber was farther down as Willis made allowances for the predictable betrayals of politicians and high-level bureaucrats. Now this young woman, who desperately wanted to remain in the United States, presented a rare opportunity. Convinced that Willis now controlled her destiny, she provided detailed information on two Colombian brothers, the Padillas—both illegal—who were possibly holding several kilos of cocaine in their apartment. One of the brothers had boasted just yesterday about the drugs. But was it only a boast to impress her? She said she hadn't yet told Torres about the Padilla brothers as she was still collecting information. Willis doubted that she _ever_ planned to tell Torres, but it made no difference. It was _his_ case now. If it checked out, Willis assured her, he would see to it that she was released and given a year to depart the country on her own, which they both understood meant that she'd be allowed to disappear. On his way out of lockup, Willis told the detention officers to make sure she was given no access to a telephone or visitors, particularly any government agents such as Ike Torres. Willis wasted no time in gathering a team to meet the next day before dawn. He located a file on Francisco Padilla showing he had been deported two years earlier. In a brief meeting with the agents, Willis distributed mug shots of Padilla. The agents couldn't get a search warrant because the US Attorney would find the probable cause weak and insist on bringing the DEA and Ike Torres in on the case, so they would have to be creative. The plan was simple: get into the damned apartment by whatever means necessary and find the cocaine without the assistance or knowledge of Ike Torres or anybody from the DEA. * * * It was a diverse neighborhood on the far north side of the city, dense with apartment buildings, small houses, and three-flats with tiny yards or no yards at all. A bit of gentrification was in evidence, with an occasional rehabbed graystone next to a dilapidated high-rise, but it remained a relatively high-crime area. As agents took up their positions, the first glimmers of light emerged, softly brushing the street with color. Hayden had eagerly accepted Willis's invitation to participate in what sounded like an interesting criminal case, but he hadn't counted on being partnered with Tom Kane. It had been three years since their altercation over the fleeing Jamaican, and though Nick had always been curious about why there had been no repercussions from the incident, he'd thought it wiser to let the issue fade. Since they were both in area control, a complete lack of contact had been impossible, but the branch was big enough—some forty agents—that he'd managed to quietly avoid Kane. They sat in Kane's Fury, one of several INS vehicles scattered throughout the neighborhood, watching for any sign of the Padilla brothers entering or leaving the apartment building. It was quiet except for occasional bulletins from Willis, always happy to fill dead airspace. Hayden decided the lull was an opportunity to clear the air. "I've been meaning to ask you something." "What's that?" asked Kane. "You never told anybody about that problem we had with the Jamaican when I was a trainee, did you?" "If I'd said anything, the ex–Border Patrol guys might've seen an opening. As I recall, you were partnered with Joe Willis, who hates all trainees. Once those guys get a bad feeling about somebody, it's all over. Anyway, you'd just started and didn't have a chance to figure things out." "I was pretty naive back then," said Hayden. "The way I look at it now, if they come here illegally, they're not entitled to be treated like everybody else. If they don't like it, they can go back where they came from. I have zero sympathy for them." "Everybody changes on this job," said Kane. "You have to, otherwise you get steamrolled." "Well, I owe you one for not saying anything to Willis and the others." "That's ancient history. Forget about it." Despite their earlier confrontation, Nick had come to respect Kane, who had a solid work ethic and didn't play political games. "You still want out of area control?" asked Hayden. "Yeah, but they never want to move you if you're producing. I've done OK on short assignments to the fraud unit, so maybe I'll eventually get a shot at staying there." Willis's voice came over the radio, this time with more urgency. A man wearing a black leather jacket and a Yankees cap had left the apartment building and was walking swiftly toward Kane's vehicle. It could be one of the Padillas, Willis said, but he couldn't be sure. If it was Francisco or his brother, Enrico, they were to take him down out of sight of the apartment building. "Not just a doper, a Yankees fan," said Kane, who could see, through his rearview mirror, a figure walking toward them, about twenty-five yards away. "Here he comes, on your side." In his side-view mirror, Hayden saw the man looking suspiciously over his shoulder. Perhaps he had spotted one of the other surveillance vehicles. More likely he was just paranoid, especially if they were holding several kilos of cocaine in that apartment. Nick feared the man would spot two guys in the vehicle, assume they were cops, and take off. "I better grab him," said Hayden, stepping out of the car. In the faint light, he stood face-to-face with a startled man who had close-set eyes and a wide nose: Francisco Padilla. The Colombian spotted the gold shield on Hayden's belt and pivoted away, but Hayden grabbed him by the shoulder and thrust him savagely into the brick stairway of a two-flat apartment just off the sidewalk. Padilla gasped in pain as his knees slammed off the pointed edges of the bricks. Hayden pushed him into a prone position against the steps, pulled his hands behind his back, and quickly slid a pair of handcuffs around Padilla's wrists. Hayden thrust his right hand into the man's pants pocket, dug around, pulled out a ring of keys, and threw them to Kane, who had just arrived. "What is wrong? Why you do this?" Francisco sputtered in heavily accented English, a gash on his nose leaking droplets of blood. Kane pulled the man's shoulder back to view his face. "Yeah, this appears to be Francisco." Hayden felt something metallic pressed between Padilla's belt and abdomen, and a clip attached to the belt. "Hey, what do we have here?" he chirped. It was a black leather holster holding a nickel-plated .38-caliber revolver. He handed it back to Kane, who was now standing at Padilla's feet. Kane looked up and down the street while Hayden continued his search, pushing his hand into the inside pocket of the leather jacket. He pulled out a small glass vial of white powder and passed it to Kane. "You have any papers, Francisco?" asked Hayden. "What papers?" asked Padilla. "Immigration papers, you idiot. Do you have permission to be here or not?" demanded Hayden, as Kane pulled Padilla to a standing position next to the steps. Padilla stared defiantly at Hayden. "I'll take that as a no," said Hayden. "That means you're going back to Colombia. But first, let's make sure you have your passport and all your belongings. We wouldn't want to send you back there without your personal stuff. We know how important that is to you." "I no need anything. I no have passport." "Let's get him into the car for this," said Kane. They each grabbed one of Padilla's arms and shoved him into the backseat of the Fury, Hayden climbing in beside him. "Five-fourteen to Kane and Hayden," said Willis over the radio. "We've got him, Joe. It's Francisco," said Kane. "Good. Any trouble?" asked Willis. "No. He had a gun and a small vial of powder. Give us a minute to talk to him." Hayden knew as soon as they'd arrested Padilla how they would do it. He leaned forward over the seat. "Tell him Francisco wants to get his belongings at the apartment." "I no live around here," sputtered Padilla. "I guarantee the apartment key is on that ring," said Hayden. "And he's going to give us permission to go into that apartment." "I no give permission!" cried Padilla. Kane, a bit startled that Hayden would hatch such a scheme, paused for a moment before an impish grin came over his face and he lifted the mic. "He wants to get his stuff before being shipped, Joe." "I think we can accommodate him on that," said Willis sarcastically. Two agents were stationed in the alley beneath the second-floor apartment. Inside the dim hallway, six agents with guns drawn were poised just outside Padilla's apartment door as Willis inserted the key. Francisco Padilla stood at the end of the row of agents, cuffed behind his back. To keep him from calling out a warning, Kane wrapped his hands around Francisco's mouth from behind. Willis turned the key, and the bolt slid away from the doorjamb. He kicked the door open and, seeing nobody inside, waved the others to follow. The tension of anticipation released, the agents stampeded through the apartment like a herd of elephants. Willis and another agent charged into the first bedroom off the hallway to find Enrico Padilla next to the bed pulling on his pants. He looked up, a mixture of fear and defiance in his eyes. "Let me see your papers if you have any," said Willis, showing his badge. "You no have right," Enrico blurted, standing unclothed from the waist up. "Call the ACLU," barked Willis, already pulling Enrico's arms behind his back to cuff him. He looked a lot like his brother, short but muscular, with a barrel chest and a wide nose with flaring nostrils. It took only minutes to check the obvious places where several kilos of cocaine might be stashed: closets, dressers, mattresses, appliances, kitchen cupboards. Al Winfield even unscrewed the grilles on the heating vents, but to no avail. All they found was a loaded .357 revolver and the men's Colombian passports under Enrico's mattress. It was a spare, clean apartment and, given the absence of personal clutter that tends to accumulate over time, appeared not to have been occupied very long. The Padilla brothers were sitting on the couch in the living room, handcuffed behind their backs, when Hayden marched in from the hallway. "What do you do for work . . . to make a living?" asked Hayden. Francisco glowered, while Enrico hung his head and looked at the floor. Hayden thought there were too many reasons to believe the girl—the guns, the vial of cocaine, Francisco's jumpy and belligerent reaction. He decided to give Francisco's bedroom a second look. The room had old hardwood floors that had recently been refinished with a fresh coat of polyurethane. He pulled up an imitation Oriental rug that was lying alongside the bed, and he was about to move on when he noticed an unusual configuration in the oak boards. At first glance the smooth finishing obscured the variation, but now he could see that a number of boards had been shortened to end at the same place, the edges forming an almost perfect square. "Anybody got a flathead screwdriver?" he called out. In the living room, Francisco exploded. "You have no right for search! I want lawyer," he bellowed angrily, rising to his feet. Kane shoved him back onto the couch. Winfield pulled a screwdriver from his belt tool holder and walked past the Padillas to deliver it to Hayden, whereupon Francisco became even more animated. "Is illegal search!" he cried. "You guys must be getting close," Kane shouted toward the bedroom. "Francisco's a human Geiger counter." Hayden worked the screwdriver along the edges of the suspicious square until it came loose. The hollowed-out cavity beneath the square was only a few inches deep, but it widened beneath the floor, and they could see a number of packages wrapped in brown tape. "We hit the jackpot!" said Willis excitedly. "Better get some photos. We need fingerprints, so nobody touch the bags without rubber gloves." Winfield came in with a 35 mm camera and took several photos of the opening and packages. Slipping on rubber gloves, Hayden removed the packages—seven kilos altogether—and stacked them on the floor. He used a pocketknife to create a tiny slit in the wrapping of one, revealing a sparkling white powder. He looked up at the hovering Willis. "Looks like good coke," he said. "Good work, Hayden," said Willis. "Damn fine work. I'll take the dope in. You and Kane can take Francisco in, if you don't mind. I'll have other guys take Enrico." Hayden couldn't believe Joe Willis would ever say "if you don't mind" without a touch of sarcasm. That alone was worth more than whatever accolades might come from his supervisors. In the car, a scowling Francisco Padilla sat awkwardly in the backseat with his hands cuffed behind him. "Nice job, Nick," said Kane, pulling the car away from the curb. "We got lucky," said Hayden, unable to restrain a smile. It wasn't false modesty. He knew it hadn't taken any great skill. But everything was different now. The key had been his willingness to do something he wouldn't have considered a year earlier—sidestepping laws that seemed to him designed to thwart legitimate efforts to get criminals off the streets. In so doing he was reaping tangible benefits: a major seizure of drugs and the admiration of his colleagues, even Willis. He'd finally penetrated an invisible wall that had separated them. They sped down Lake Shore Drive beneath a clear indigo sky, everything glowing in the morning sunshine. On Lake Michigan, rolling waves broke smoothly near the shoreline. Beyond the waves the lake spread out, flat and shimmering, appearing as vast as an ocean. Buoyed by an unfamiliar sense of belonging, Hayden felt something close to euphoria. * * * The cocaine had a street value of over a million dollars. The story was on the front pages of the Chicago papers and among the lead stories on television. District Director Farber was delighted to answer questions from the media that were, for a change, not about some perceived gaffe or violation of policy, and Jack Connelly received a congratulatory call from a top INS official at headquarters. It was good for morale; even agents not involved in the bust seemed to carry themselves with a bit more swagger. Joe Willis took great pleasure in letting Ike Torres know that his unauthorized "informant" had supplied the tip that led to the seizure. Though he feigned indifference, Torres was furious. Fingerprint analysis would seal the fate of the Padilla brothers. The slick tape on the kilo-sized packages proved to be an excellent surface from which to lift fingerprints. The brothers couldn't plausibly claim that they'd known nothing about the seven kilos found in their apartment because their prints were all over them. Still, their attorneys declared the search illegal, and this led to a suppression hearing at which Hayden and Kane were called upon to testify. They looked like young bankers in their dark suits, and testified almost identically: Francisco had provided a key to the apartment and given them permission to search it, which led to the discovery of the cocaine. According to them, it was all very straightforward. Then the defense attorneys pounced. Why hadn't the agents obtained written consent to search? There was no legal requirement for it, said Hayden correctly, and there had been a witness to the verbal consent. "If Mr. Padilla was giving his voluntary consent, why was it necessary for one of the agents to cover his mouth in the hallway?" inquired Francisco's lawyer. "You never know if a person will panic and decide to warn someone inside the apartment. It was just a precaution. He never gave any indication he was withdrawing permission to conduct the search." "Are you familiar with the crime of perjury, Agent Hayden?" "Yes, of course," he replied calmly. The defense attorney asked several more questions about the search, getting nowhere, and the judge instructed him to move on. Francisco Padilla did not make a good witness. His testimony was emotional and defensive, in stark contrast to the agents' professional presentation. The judge, a tired, cynical man of sixty-five who had grown bored with the drug cases that flooded his docket, looked down at the Colombians with unconcealed disdain and ruled there was insufficient evidence to find the search illegal. Having no reasonable expectation of success at trial, the attorneys quickly negotiated a plea agreement resulting in a sentence of ten years in prison, followed by deportation to Colombia. The word from Willis's female informant was that certain Cali cartel members would be waiting for the brothers, who owed them several hundred thousand dollars. Charlie McCloud's response was muted. Watching events from afar, he was as pleased as anybody about the Padilla bust. It sent a message to the DEA and the FBI who, by routinely stealing informants and eliciting information with no thought of returning the favor, had not endeared themselves to INS agents. But McCloud was skeptical about how Hayden and Kane had obtained entry into Padilla's apartment. Colombian dope dealers, McCloud knew, weren't in the habit of leading a team of agents into their stash house voluntarily. The Colombians' vehement denials of having done so raised suspicions that were confirmed when McCloud was having a drink at McGinty's. The Padilla bust came up in conversation with agents Al Winfield and Tim Reynolds, both of whom had participated in the seizure. "That was a nice bust you guys pulled off," said McCloud. "Yeah, about time we got some good publicity," said Winfield. "Sounds like Padilla made it easy to do the search," McCloud offered mildly between sips of beer. A furtive glance passed between Winfield and Reynolds before Winfield said, "Yeah. The Colombians were stupid." He then looked away and changed the subject a little too quickly. That was enough to confirm it for McCloud. Having observed the gladiator syndrome in other agents, and even in himself earlier in his career, he could see that it had arrived in force for Nick Hayden. McCloud was now troubled by what he perceived as Hayden's metamorphosis from a smart, thoughtful agent to one diminished in stature, though the conventional wisdom in the office was that Hayden was one of the rising stars. During Hayden's first year, he and McCloud had frequently gone out to lunch to discuss whatever minor problems Nick was having in area control, and how to prepare for exams he would have to pass as part of his training regimen. Their conversations had often veered into other areas of mutual interest, such as politics or literature. They had always had a similar code of ethics, but that appeared to have changed, and the relationship had become a bit strained. McCloud suspected that Hayden had come to think of his former training officer as being from the "old school," disconnected from the realities and challenges of modern-day law enforcement. Hayden was well aware of his own evolution—his life was now almost completely consumed and defined by work. Confident in his abilities as an investigator and driven by a clear sense of purpose, he often worked late into the night, reviewing leads and planning operations. Outside interests had faded. It had been over a year since he'd been to the Veterans Hospital in Maywood. His romantic relationships were still limited to brief liaisons that never progressed to a more meaningful level. The city itself was his most steadfast companion, offering endless diversions. Though he'd assumed he would eventually finish law school, the thought of being an attorney had lost its appeal. Compared to this job, the work of lawyers appeared stuffy and tedious. The action was on the street, not in the courtroom; attorneys were there mainly to sort out the mundane details. Though the Kelso shooting still came to mind periodically, he knew that if he made further inquiries, aside from raising suspicion that could cost him his job, he might not get the answers he wanted. * * * Hayden hadn't noticed McCloud's door partly open as he strode down the hallway. "Hey, Nick, you got a minute?" Hayden stopped just past the door. "I'm kind of busy, Charlie." "It'll only take a minute," said McCloud. Hayden walked into the room and stood rigidly behind a chair in front of the paper-strewn desk. "It's been a hectic time, Charlie. You know . . . the Padilla bust and all. I've got a lot to do." "Sure, we all have a lot to do," said McCloud, leaning back in his chair. "Interesting piece of work, the Padilla thing." "Yeah, it worked out well." "You might not be so lucky next time." Nick was momentarily taken aback. "What's that supposed to mean?" "Have a seat, Nick." McCloud motioned toward the chair. "We need to talk." "I'm not a trainee anymore, Charlie." "Shut the door, would you? I've got something to say," said McCloud bluntly. Hayden considered walking away but instead turned and closed the door. This conversation was inevitable; he might as well get it over with. "What's bothering you, Charlie? Afraid we bent the rules a little to do something good?" "Sounds like you did a little more than just bend them." "Who said that?" "Nobody said it. I've been around long enough to put two and two together." "Come on, Charlie, I—" "Look, guys like Stark and the front office—they might encourage you to take these kinds of risks, but if you get caught, they'll throw you to the wolves." "I'm not doing it for them. It's what _I_ want." He reluctantly sat down. "Things might be a little different than when you were on the street." "You've been doing this stuff for four years, and you're going to tell _me_ what it's like on the street?" said McCloud with a sardonic grin. "It's a game, Charlie, and it's gotten worse. There are wets on every street corner now, and they're not afraid of us. A lot of them are involved in stuff like these Colombians, and we're supposed to just sit back and let them do whatever they want? You try to win the game—however you can." "So perjury is part of the game?" "Come on. It's not like they're innocent." "And the end justifies the means? You're supposed to be above that sort of thing." "You're giving me textbook stuff, Charlie. It doesn't hold up in the real world." "That's been said by every gladiator cop who was too lazy and full of himself to do things professionally," said McCloud. "I hear you were working with Kane. He doesn't know where to draw the line." "I can handle Kane. He has no influence on me. Besides, what we did with the Colombians was my idea." McCloud held up his hands in a gesture of mild exasperation. "OK, but remember—when things are crystal clear in this business, you're in trouble. I told you this gladiator syndrome is full of land mines. You start thinking you're indestructible." They stared coolly at one another for several moments, but each knew the other wouldn't yield. "I'm only telling you for your own good," McCloud said with a tone of weary resignation. "But you're right—you're not a trainee. So go ahead. You'll find out the hard way. Do whatever you want." "That's good advice, Charlie. I _will_ do what I want." Hayden went out, closed the door behind him, and stood in the hallway for a few moments. Then, with a disgusted wave toward McCloud's door, he turned away. * * * Sam Payton was retiring and moving back to San Antonio. They'd already had a retirement dinner with his wife and family in attendance, but at the end of his last day his colleagues gathered at McGinty's for a more casual send-off. When Hayden and Kane arrived, they found a circle of agents at a table in the corner. Payton, a heavyset, steady man, had an affable way about him that had made him one of the more popular agents in the office. He was now regaling his colleagues with stories about the old days in the Patrol and investigations, recalling the colorful characters he'd worked with. When the laughing subsided for a moment, somebody asked why Willis wasn't there. "I saw him in the office putting in a request to stay past age fifty-seven," said Payton. "That's only two weeks away. They never grant those requests, but he says he's got nothing to lose. He's coming over later." They all seemed to contemplate Willis for a few moments before Al Winfield posed a question: "Sam, what was the worst thing that happened during your time here?" "What kind of thing is that to ask on his last day?" said Kane, shaking his head. "No, that's OK," said Payton. "Let me think it over a second." He took a sip of beer, as the others waited quietly. "I'd have to say the shooting of Frank Kelso," Payton began. "Kelso was a nice fella—everybody liked him. And it did something to Buck Tatum. He wouldn't talk to anybody about it—even me, and I was pretty close to him. When he retired, Tatum wouldn't keep in touch with anybody. He left the area, and his wife didn't want to go with him—divorced him. It was strange, his reaction. Cut himself off and went into hiding. And the trainee, Landau—he got fired and committed suicide a year later, right around the time Tatum retired and disappeared." Payton's eyes narrowed, deep in recollection. "Connelly asked me to pick up a copy of the police report and photos the day after the shooting," Payton continued. "I don't know how Kelso made the guy as a wet. He was from Argentina, but he looked like a typical, long-haired American guy. The report said he had blue eyes. Anyway, I always thought there was something that never came out—the way Tatum clammed up. And it never seemed right that Landau took all the blame. It was like a piece of the puzzle was missing—maybe more than just _one_ piece. It's a gut feeling. But I guess we'll never know . . . just part of this business." After a brief pause, somebody asked Payton to tell his favorite Joe Willis story before Joe arrived, and the gathering again turned lighthearted and jovial. But Hayden had backed away from the table. He quietly slipped out the door and into the night without saying a word to Kane, who watched him curiously. Hayden felt dazed as he walked slowly to the parking garage. He got into his car and drove through the Loop into light evening traffic on Lake Shore Drive, the lake looming dark and silent to one side, the city lights on the other. Though he had more than enough to deal with already, the uneasy feeling sent a clear message. He'd kept it all buried but now realized it was simmering just beneath the surface. With Payton's suspicions about the shooting arousing such a visceral reaction, he knew he had no choice but to resume his search for the truth—even if it meant losing a job he'd grown to love. # 7 The tiny Peruvian walked stiffly through the cold, swirling wind. When he reached the corner, he glanced sideways down Sheridan Road and noticed the door to El Palacio slightly ajar, even though it was only ten o'clock in the morning. He'd bought his share of drinks there over the last couple of years. Perhaps that would count for something with Chacon. Hernan Garza was covered in layers of clothing so that, like a cat with long fur, he appeared larger than he really was—five feet two and a hundred and twenty pounds. Sweaters and shirts were covered by an overcoat that fell to the tips of his black gym shoes. The coat was threadbare and badly frayed. With a blue knit cap covering his ears, he looked like a merchant seaman. He clapped his hands against the cold, stuffed them into his pockets, and headed toward the bar. Garza slipped inside, hoping to drift unnoticed into a darkened corner, but the door's creak pierced the quiet. Chacon and Salvador Rico were standing at the bar, staring at him. Garza could tell from Chacon's sour expression that he wouldn't be welcome unless he were a paying customer. He pulled the scarf away from his face and addressed Rico in Spanish. "Mr. Rico, would you have a minute, sir? I would like to discuss something important with you." Though he had never spoken with Salvador Rico, he'd heard plenty—a leader of sorts, and ruthless. There was talk of the killing of a rival in the document trade. "Important? Important to who?" asked Rico sharply. "Please, just a minute of your time, sir," Garza pleaded. Rico had seen Garza at the bar—heard that he was a heavy user of alcohol and cocaine who eked out a meager existence as a small-time dealer. Had Rico been busy he would have dismissed him, but he found Garza to be an amusing, almost cartoonlike character. "Come," said Rico, pointing to his favorite table in the corner. They sat down, Rico with his back against the wall. Garza pulled his cap off to reveal a matted shock of graying hair. He elaborately unraveled the scarf from around his neck and used it to wipe the melting icicles from his mustache. Rico sat watching him, captivated by his every move. Though he was only forty-one years old, Garza could have been mistaken for sixty. His florid cheeks were weather-beaten and pockmarked, his teeth riddled with brown stains. Garza laid the hat and scarf on the table and looked up earnestly, like a man eager to confide in his lawyer. "I have been hoping to meet you, Mr. Rico. My name is Hernan Garza," he declared in surprisingly crisp Spanish as he held out his hand. Rico looked at it for a moment, then reached across the table and reluctantly gave it a quick shake. "Yes, I have seen you. So what did you wish to discuss?" "I know you sometimes hire people, those who are familiar with the street . . . those who can help you. I am very discreet. I see and hear many things. Perhaps I could be of service to you," said Garza, his glassy eyes taking on a hopeful glitter. Though it was an idea improvised to purchase a few moments of warmth, he suddenly realized it might have merit. He knew Rico had plenty of money. Rico studied him. Garza was not lacking in intelligence, though drugs and alcohol had obviously taken their toll. While Rico had no interest in a business relationship, he sensed that Garza, ubiquitous on local streets, possessed a wealth of information. Perhaps he could glean something useful. "You were working with Mario Duran, no? Before he got busted?" inquired Rico. Duran, also from Peru, had been a familiar presence at El Palacio until he'd been arrested a week earlier by the DEA for possession of two kilos of cocaine. The mention of Duran sparked an immediate reaction in Garza. "I did work with Mario, yes, but don't believe everything you hear, Mr. Rico. There are men who lie for their own purposes." Garza's eyes were suddenly brimming with emotion. "You heard it was _me_ who informed on Duran, didn't you? It's that filthy Colombian, Bautista, I tell you! He puts the word out that it was me, but Mario knows better—he knows I would never do such a thing." "I did hear something about it," Rico lied. "Bautista works both sides. He sells drugs and is an informant for the DEA and the state police. They protect him. Bautista made at least two thousand dollars for ratting out Duran. Plus he gets rid of a competitor." Garza's hands were desperately gripping the edge of the table. "How do you know this?" Garza turned and looked nervously around the bar, still empty except for Chacon. He then spoke in a whisper. "Bautista was the only one who knew about the two kilos besides me, but then he tells people it was _me_ who ratted. He set me up!" "How do you know the federal agents pay that much for information?" "It came out in court last year. The FBI paid six thousand to an informant after they got six kilos of cocaine. Do I look like I've got thousands of dollars in my pocket?" Garza leaned closer and smiled, revealing several gaps where teeth were missing. His reeking breath arrived in a sudden wave, prompting Rico to back away from the table. "I don't want dirty money from ratting," Garza continued frantically. "Bautista is holed up in his apartment with a lot of 'coca' right now. But even on Bautista I won't squeal!" Rico listened intently, yet betrayed no more than casual interest. "Do you want a drink?" he asked. "Yes, perhaps a shot of whiskey." Garza smiled appreciatively and began to salivate in anticipation. "Bring over a shot of whiskey for my friend," Rico called out to Chacon. He looked back at Garza. "So, Bautista was working with the feds, eh?" "Yes, of course. I had to defend myself . . . tell people it was Bautista and not me. Now nobody wants to deal with _him_ either. That is why he is holed up. People are afraid to deal with him." "I see. Now I understand your side of the story." Garza's face broke into a smile at this apparent breakthrough. "If I wanted to make easy money, I would go to the cops about Bautista. But I have too much integrity to do that, even though he lies about me." "Yes, I can see that—a man of integrity." Chacon arrived with the whiskey and set it in front of Garza, who grabbed the glass with a trembling hand and immediately tossed the amber liquid to the back of his throat. His eyes twinkled, and he let out a pleasurable sigh. He took a moment to admire the empty glass and set it down on the table. "Listen, Hernan," said Rico, "I don't believe what they say about you. And I will let you know if I need you." Rico dug into a back pocket of his slacks, pulled out a wad of bills, and peeled off a fifty. He reached across the table and stuffed it into Garza's hand. "Here, take this," he said. "But don't tell anybody we talked. If you do, I will not be pleased." "Yes, I understand," said Garza gleefully, stashing the bill into the inside pocket of his wool coat. "I say nothing." "And don't come in here again," said Rico, a firm edge to his voice. "If you need to talk to me, get word to one of my people." "Of course. I know how to do things properly." "I think you'd better leave now." Rico had gotten what he wanted and was no longer interested in Garza. "Yes, Mr. Rico. Thank you for your time." Garza stood up, pulled his knit cap over his ears, and wrapped the scarf around his neck. He nodded toward Rico and marched toward the door. Though he desperately wanted another shot of whiskey, he wouldn't spend any of his fifty dollars here—to hell with Chacon! Garza went out the door into the freezing air, convinced that his visit had been a complete success. He had not only escaped the cold but also gotten a free whiskey and made fifty dollars! It was quiet again in the bar. Rico sat in the corner and mulled over how to best utilize the windfall of information he'd just received. He chuckled softly at the image of Hernan Garza. It was his good fortune that the little Peruvian had stumbled into El Palacio. * * * Hernan Garza sat in the corner of a donut shop on Lincoln Avenue and slurped a hot cup of coffee. It was another frigid, gray February morning. He looked out the window at cars plowing through a fresh layer of snow and contemplated his dilemma. With Duran in jail, his brief career as a dealer of small bags of cocaine was over. He was almost broke, having spent most of the fifty dollars Rico had given him a week ago. The thought of robbing a liquor store passed through his mind. He'd noticed an inviting target on Pulaski Road, though he knew he had to consider getting a regular job. The thought depressed him. He looked down at a _Chicago Tribune_ somebody had left on the table and was about to page through to the classifieds, when the headline near the bottom of the front page caught his attention: COCAINE BUST NETS TWELVE KILOS. The name jumped out: Raul Bautista! His nemesis, Bautista, had been arrested by the FBI for possession of twelve kilos of high-quality, uncut cocaine. Garza's head felt like it was on fire. He knew he was now in grave danger. His instincts told him that it had to be Salvador Rico who was responsible for Bautista's arrest. Rico was the only one he'd told about the Colombian holding the cocaine and that the FBI would pay thousands for the information. To protect himself, Rico had probably already spread the word that Garza was the rat. Bautista and his friends, having every reason to believe this story, would seek violent revenge. Suddenly, every passing vehicle and person was a threat. How incredibly foolish he had been—all for fifty dollars and a bit of warmth on a frigid morning. He tried to calm himself and think it through clearly. He didn't have enough money to relocate to another city, yet it was too dangerous now to stay in Chicago. His mind worked feverishly for several minutes before it came to him—a route to safety that would cost him nothing. Garza had been sleeping nights in the utility room of a three-flat in the Humboldt Park area on the West Side. With the furnace rumbling and pipes dripping overhead, he'd made a home of sorts, paying the building custodian a small amount each month to allow him to use the space. There was an industrial sink in one corner and a toilet in the adjoining supply room. Reasonably certain that the Colombians didn't know of his hideout, he decided to risk one last visit. After checking the street and alley for signs of the Colombians, Garza darted down the cement stairs and through the basement door. He took time only to take the loose brick from the wall and remove the passport from the space he'd carved out. He left the .22-caliber revolver and the half-full bottle of Wild Turkey and replaced the brick. He then fled, pulling the collar of his wool coat up to hide his face and protect it from the freezing wind. He jumped out of the train when it reached Jackson Boulevard and felt great relief when he passed through a revolving glass door and into the warmth of the Federal Building. Garza strode quickly along the marble floor to a stainless steel elevator that whisked him up to the third floor reception area of the INS office. He told the deportation officer he had no papers and had been unable to find work. Life was too hard here, he confided sadly, and he hadn't sufficient funds to go back to Peru on his own. The INS office was always looking to pad their apprehensions of OTMs—"Other Than Mexicans"—if only to deflect charges that they discriminated by targeting Mexicans. Whether illegals were arrested or came in voluntarily, they all counted on the department's monthly tally sheet. Garza waived a deportation hearing, and they had sufficient funds on hand for airfare to Lima, so he would be allowed to return voluntarily at government expense. Garza felt safe in jail. Ironically, he would do time in the same jail (the Metropolitan Correctional Center) as Raul Bautista. But Garza would be placed in the minimum-security area, several floors below Bautista and other high-flight-risk prisoners. Deportation officers would need time to get clearance from the Peruvian Consulate and to make travel arrangements, so it would be several days before his departure via jet from Chicago to Lima. That was fine with Garza. He liked the warmth of the jail. He liked the three regular meals a day and watching television on a big screen. He liked talking to other prisoners, trading stories and ideas on the best places to cross the border. Still, as the days passed behind bars, Garza's thoughts drifted to Salvador Rico. And when the self-recriminations subsided, a loose plan for revenge began to emerge. # 8 _Six Months Later_ Francisco Campos shuffled through the marble-floored pavilion of the Federal Building, pushed his way into a crowded elevator, and hit the button for the fourth floor. A short, chunky man with a thick mustache, Campos had the manner of a struggling, small-time businessman. A look of anguish seemed permanently etched on his face, as though he had just caught a whiff of old cheese. Nobody recognized him as an alderman, the elected representative for Chicago's Twenty-Fifth Ward. Despite Campos's frequent public criticisms of the Chicago INS office, District Director Farber respected the feisty alderman. After years of being stabbed like a human piñata, Farber had developed the hide of an alligator and didn't take the attacks personally. Besides, he knew he couldn't refuse to meet with a member of the city council. It would only provide grist for another INS-bashing news conference. Farber had his secretary usher the alderman into his office. Campos declined the offer of coffee and donuts and sank into the burgundy leather chair in front of Farber's desk. He folded his hands together on his lap—his face creased with worry. Farber, a portly but elegant man who favored expensive three-piece suits, smiled cautiously and settled into his chair. He passed a soft hand lightly over his wavy hair and sighed, girding himself for the next crisis. "Well, now. How can I help you, Alderman?" "There is a problem, Mr. Director," said Campos ominously. "Yes, of course. There are always problems." "Certain unsavory individuals have taken control of the counterfeit document business," Campos murmured dryly. "You mean those who controlled it in the past were _not_ unsavory?" asked Farber with a playful grin. Having little sense of humor, Campos ignored the comment. "The vendors are now working openly on the streets," he said. "They used to work behind the scenes. Now they are becoming a nuisance, flagging people down, getting in the way of ordinary shoppers, especially on Cermak and Twenty-Sixth Street. Alderman Baez is equally concerned." "What about the police?" asked Farber. "Can't they get rid of them?" "They say it is an INS problem. There is the mayoral decree that prevents them from cooperating with INS enforcement efforts. Most of the vendors are undocumented, and city workers aren't supposed to assist in arresting them. Besides, they don't have the manpower to continually pick up people for misdemeanors like vagrancy." "You supported that mayoral decree, Alderman. In fact, you were one of those who initiated it." "Yes, but I don't agree with their interpretation of it in this case." "I see." "Perhaps a modest allocation of manpower would return things to normal, Mr. Director." Farber considered Campos and the situation for a moment before speaking. "Need I remind you, Alderman, of the conversation we had three years ago? You complained that having agents working counterfeit document cases was a waste of time. I agreed and ordered that ordinary document cases not be worked—only cases on major distributors. You seem to have changed your mind." "It's different now. Before, they were operating reasonably. Now they are doing business openly. The businessmen are complaining about them." "Ah, of course . . . the businessmen." Farber smiled knowingly. "Yes. We must do something about it." "Get them to 'operate reasonably.' That's how you put it?" said Farber. "Yes, not so visibly." "Who _are_ these people who have taken over?" "They are organized, but I don't know who is behind it. The leaders are not Mexicans, from what I hear. Perhaps a couple of your better agents can look into it." "If I do as you wish, what do I get in return?" "Well, if you do nothing, I would have to get the media involved. And I can assure you it would be very embarrassing," said Campos evenly. There was a silence as he let Farber think it over. The alderman knew he was holding the cards. He looked toward the wall at a collection of photographs of Farber and various dignitaries; then his eyes slowly drifted back to Farber. "In the end, you will have to do something. If you wait, it will appear you are only reacting to pressure. If you do it now, bad publicity can be avoided, and you appear to be in control." Farber considered the irony of Campos as political counselor and sudden advocate of INS enforcement. He sifted through likely scenarios—television crews filming vendors on the street, front-page news stories charging INS with incompetence. He knew how little it took to get them started. They would have no sympathy for excuses about manpower. That never worked. The accusatory interviews would put him on the defensive, and the news would find its way to region and headquarters. If things were as flagrant as Campos suggested, there was a possibility of national media exposure. It wouldn't matter to officials at headquarters that they had intentionally ignored the problem of counterfeit documents. _He_ would be blamed. Where the hell was Jack Connelly? It was his job to stay on top of things like this. But Connelly was burned out and ready to retire, so disengaged that Francisco Campos was more diligent in rooting out violators than his own director of investigations. Farber knew that he was trapped and had no real choice. "I'll see what I can do, Alderman. I may need a month or two." "Yes, of course, but the sooner the better. I can't guarantee the press won't pick up on it before you are able to act." Campos always knew the right buttons to push. "No, I suppose not," said Farber. "Please contact me before you bring in the media." "Certainly. And it is to our mutual benefit that the substance of this meeting should never be discussed, don't you agree?" Farber smiled. "We have only been discussing how to improve community relations." "You are always a very reasonable man, Mr. Director." Given Campos's past public criticisms, it seemed a ludicrous statement, yet he appeared to be completely serious. "I would appreciate it if you would pass those sentiments along to your friends in the media, Alderman." For the first time there was a hint of a smile in Campos's eyes. "You know, Mr. Director, I can only go so far." "Of course," said Farber. "I understand very well." * * * Hayden and Kane, having no idea why they'd been called in, took seats facing the two supervisors. Lou Moretti, looking depressed, peered through reading glasses at a roster of agents, trying to figure out how to make up for the loss in production. "Well, boys, the big time is calling," he said, smiling beneath flat, joyless eyes. He looked like the weary manager of a minor-league team about to lose his best players to the majors. Richard Stark, standing behind Moretti's desk and casually leaning against a filing cabinet, chuckled at Moretti's implied compliment. Or _was_ it a compliment? He was never quite sure if Moretti was being sincere or sarcastic. Stark was a tall, lanky man in his early forties with small gray eyes that shifted restlessly beneath bushy eyebrows. As a field agent, Stark had managed to garner outstanding performance evaluations, not through hard work but by fawning over his supervisors, dressing well, and carefully avoiding the controversies that seemed to dog his more productive colleagues. His ambition was so transparent, however, that he had no real friends, only temporary allies. Everything was going according to plan for Stark. He'd been promoted to first-line supervisor and a year later to his current position as chief of fraud investigations. Now he desperately wanted to succeed Jack Connelly as Chicago's director of investigations. Looking around the office, Stark found only one serious competitor—Ed Gleason, a solid field agent in his day, a competent supervisor for twelve years and, at least on paper, the most qualified to take over for Connelly. With Connelly retiring in three months, Stark knew he didn't have much time to position himself ahead of Gleason. He saw the counterfeit document task force ordered by Farber as a vehicle to push him over the top, but because fraud had become a low priority, he found himself supervising slow-moving dinosaurs who were mainly killing time before retirement. The obvious solution was to poach a couple of young, ambitious agents from another section. With Farber's directive applying the needed pressure, Jack Connelly agreed to Stark's request for Moretti's best agents: Tom Kane and Nick Hayden. "We thought you two might be interested in working criminal cases in our shop," said Stark. "I want somebody to work counterfeit documents again. Vendors are now dealing out in the open. I've been trying to convince the front office for some time that we can no longer ignore it." Moretti rolled his eyes, recalling that the day before he had seen Alderman Campos on the fourth floor. Now it all made sense. Stark continued. "No dress code. You can wear jeans and gym shoes. It would be a two-month detail; then we'll see where we are. As you know, a number of guys detailed to fraud from area control have ended up with permanent assignments." Hayden and Kane looked at Moretti, who said nothing, feigning indifference. Stark, following their eyes, rushed to fill the void: "Of course, Lou fully supports this." "Yeah, we'd be interested," said Kane. "At least, I would be." All eyes shifted to Hayden. Nick was surprised he wasn't more excited about the offer. From the beginning, the fraud investigations unit had been the most attractive. Yet there was something in Stark's demeanor that made him hesitate. "So we'd be partners, Tom and I?" he asked. "Right," said Stark. "Normally I'd want you working with a journeyman, but everybody is tied up with other cases at the moment. You've both already spent time on details in fraud and gone through the usual training. Two months is plenty of time to clear the vendors off the street and take a crack at the guys behind it. I think you can handle it. Naturally, I'll be there for guidance along the way." Moretti grimaced. Guidance? The only thing Stark would be able to instruct them in would be how to skillfully caress the posteriors of superiors at the district and regional offices. And the only thing the old-timers in fraud were "tied up with" was happy hour at McGinty's. The bullshit had grown too intense. Moretti pretended he was wearing thick earmuffs, swiveled in his chair, and peered out the window, trying to spot an attractive female on the street below. "When would we report?" asked Hayden, who knew he couldn't pass up the opportunity. "Next week. But you guys can start moving your stuff down any time now. There are a couple of desks in back," said Stark. "I've also arranged for two seized vehicles to be at your disposal, a Camaro and a Firebird. Good for surveillance." Hayden again glanced at Moretti, knowing it was bad form to eagerly accept a detail out of the unit without his tacit approval. But he could immediately tell his concern was misplaced. Moretti was now staring out the window, his gaze fastened on a young woman in a leather miniskirt and high heels making her way poetically down the street. Moretti wished Stark would get the hell out of his office so he could lock the door, get out his binoculars, and peer down Jackson Boulevard in peace. * * * Kane and Hayden had both reached a point where their jobs and identities had merged into one—it had become very personal. Those who violated the immigration laws or committed crimes that fell within their statutory authority were a threat, not just to the rule of law but to their very identities. Though they'd never spoken of it, they observed the same messianic fire burning in the other and thought it could be the basis of an effective working relationship. A few days after the meeting in Moretti's office, they sat in Kane's Camaro, just off Twenty-Sixth Street. It was the center of commercial activity in the largely Hispanic Little Village area, featuring a long line of small but thriving businesses: restaurants, clothing stores, and other retail shops. The buildings were old, two-story brick structures, each with unique architectural details, unlike the generic strip malls that had sprung up more recently. Thousands of pedestrians flocked to the area every day, and police cars rolled by slowly every half hour or so. The popular Mexican import mall was just a few blocks away. The two agents watched as a car pulled into a parking spot on Twenty-Sixth and a man in an orange shirt and a straw cowboy hat walked up and stuck his head inside the passenger window. He and the driver appeared to be negotiating a deal. Looking farther up the street, Kane and Hayden could see at least two other vendors, one at an intersection about half a block away, and the other working from the doorway of an apartment building. The men engaged almost any pedestrian indiscriminately. To passing vehicles they flashed a sign with their thumb and forefinger in the rectangular shape of a card. "It's an open market," observed Hayden. "Yeah, like shooting fish in a barrel," Kane agreed. "We could go after these guys and flip them against their boss or supplier. Most of them have to be wet." "Right," said Hayden, lifting the binoculars to his eyes, "but if they don't cooperate and word gets back to the boss that we're onto him, he gets nervous and closes down until our detail is over. If they're just low-level vendors like these guys, they know they won't get much jail time, so there's not enough pressure to get them to flip on the boss." The man in the cowboy hat walked to the curb, stuffing bills into his pocket, and the car proceeded down the street. "I wonder how many orders he takes before delivering them to the pad where they make the cards," said Hayden. "We've got less than two months," Kane responded. "And we don't have teams of surveillance units or manpower for wiretaps." "No, but if we can get somebody to go undercover, we have a shot at making a really good case, not just taking foot soldiers off the street. They're getting sloppy because they don't think anybody's working these cases. We have to take a shot at whoever's behind all this. These clowns couldn't organize a one-man parade. _Look_ at him!" Hayden was pointing at the cowboy-hatted vendor, who had spotted several girls in a car and swiveled his hips seductively as if dancing with them. Kane couldn't help grinning at the street performer. "I guess we have a little time," he conceded. "These guys aren't going anywhere. They're having too much fun." # 9 Hayden left the office, walked swiftly through the fading sunlight on Jackson Boulevard, and turned down a narrow street that was shadowed by tall office buildings. The stores at street level were closed, but the purple neon sign of McGinty's cast an inviting glow. Glancing through the tavern's window, he recognized the bearlike shape of Charlie McCloud hunched over the bar, apparently lost in some inner conversation. It had been several weeks since their tense encounter in Charlie's office, and the casual setting of the bar seemed like a good place not only to clear the air but also to ask an important favor of McCloud. McGinty's had a long mahogany bar, dark wood tables and chairs, and soft lighting. The atmosphere was heavy and masculine—a comfortable refuge for federal agents, many of whose offices were located nearby. It was Wednesday, so the bar was relatively quiet. Tony Bennett crooned softly in the background, enveloping the place in a sort of timeless, sleepy warmth. Hayden recognized a couple of IRS agents at the far end of the bar and a familiar collection of secretaries from the DEA and the US Attorney's office huddled in a corner. Nick leaned against the bar just inches from McCloud and swung a shoe onto the brass foot rail, giving off a metallic ring, but McCloud was so preoccupied he didn't react. "A wise training officer once told me drinking alone can be dangerous," whispered Hayden into Charlie's ear. McCloud was momentarily startled—then smiled in recognition and gestured toward the empty stool next to him. "I was picturing myself retired. It used to seem like heaven. But now that it's closer . . ." His voice trailed off, and he quaffed deeply from his mug of beer. Hayden noticed an empty shot glass in front of McCloud. "I would think you'd be relieved to get out." "Everybody thinks that when they're young." McCloud paused and, knowing Hayden wouldn't understand, decided to change the subject. "So, you and Kane making any progress?" "It's only been a few days. We're getting our bearings. We could take down some vendors on the street right away and work it from the bottom up, but we have a little time." "You'll need a good informant," said McCloud, who signaled with his hand to the bartender to bring a beer for Hayden. "You know of any we could use?" asked Hayden. "Well, I'd be happy to give you one of my old ones. They're good, but they've gone to seed a bit—they've got families and jobs. They'd be going in cold. You're better off looking for one who's arrived in the last couple of years. They would know who the current players are—maybe even had contact with them." "We're looking through leads for somebody like that." "Good—you're better off developing your own informants, unlike the FBI or DEA. They say they'll borrow—then they steal them." "So I've heard." McCloud could tell Hayden was distracted and ill at ease. "What's on your mind, Nick?" "I owe you an apology, Charlie. The conversation in your office—I know you were trying to help." McCloud smiled. "It's OK. You're a gladiator, right? I was there at one time. Now I'm an over-the-hill pussy who's afraid of his own shadow. When you're a gladiator, nobody can tell you shit." McCloud sipped his beer before continuing. "Some never come out of it. Those guys implode and break into a million pieces." Hayden was surprised that McCloud wasn't softening his earlier comments. Not wishing to reignite that debate, Nick steered the conversation to a recent incident involving a DEA agent who'd killed a drug dealer in self-defense in an alley off Howard Street. The agent, who was shot in the neck, was now doing better. It was the first use of deadly force by a federal agent in Chicago since the Kelso shooting, and a useful pretext for where Hayden wanted to go. They sipped their beers for a moment. Nick had never asked Charlie about the Kelso shooting because of McCloud's curiosity about the name Hayden when he'd first reported for duty. But now he felt he had to risk it. "By the way, Charlie, what do you know about the shooting in '74 when Frank Kelso got killed?" "I had no direct knowledge—just heard the story that went around the office." "Payton said something didn't smell right about it, like something got buried." "Something _always_ gets buried. I wasn't in area control at the time so I wasn't as familiar with the details as Payton and some others." "It's frustrating that nobody seems to know the details of how it all went down." Hayden paused briefly. "You know, I wouldn't mind seeing a copy of the report on the shooting." "How you gonna do that?" "Since you're a training officer, maybe you could justify getting it for training purposes." "Ah," said McCloud with a wry smile. "You want _me_ to get it for you." "Only if you can do it without any trouble. It's not worth sticking your neck out." "Why so much interest?" inquired McCloud. "Partly because of what Payton said. An agent died—I'm just interested in what happened." There was a hint of defensiveness in the shrug of his shoulders and his voice, suggesting that McCloud ought to understand without further explanation. McCloud watched him through the mirror behind the bar, but Hayden just sipped his beer and offered nothing more. "Well, it was obviously tough on everyone involved," said McCloud. "Kelso dies. The wet dies. Trainee lost his job over it. And Buck Tatum . . . poor guy was never the same again." He paused a moment before continuing. "I don't blame you for not taking what Willis says at face value." "It's vague," said Hayden. "And apparently Tatum wouldn't talk about it." "Clamming up isn't unusual after the trauma of a shooting. I guess nobody wanted to push him. The trainee, Landau, was smart but not one of the guys. It was pretty tough down there in area control. If you hadn't been in the Patrol, there wasn't much room for error. He'd been a social worker or something—that didn't help with that crew." "Maybe they pinned the shooting on him to dump him." "I don't know about that, but whatever Landau had to say at the time wouldn't have been given much weight. A lot of it had to come down to what Tatum said, because I don't think there were any other witnesses." McCloud took a swallow of beer and wiped the foam from his mustache. "I assume Tatum had to talk to the investigators about it," said Hayden. "Yeah, they would have gotten a statement." McCloud paused. He suddenly remembered something. "You heard what happened to Landau after he was fired, didn't you?" "Yeah, Payton mentioned it." "I don't know if it had anything to do with the shooting." "Couldn't have helped." "So, Kelso and the wet die, Tatum is an emotional wreck, and Landau ends up losing his job and killing himself. Not a pretty picture. I was so absorbed in my own cases, I don't even know who did the shooting investigation." McCloud paused briefly. "That was around the time my wife left me, so my head was spinning." "That's understandable," said Hayden. He could feel McCloud's eyes studying him. "OK, I'll see what I can do about getting the report," said McCloud finally. "I'll have to find the right person up at the regional office. They live to deny requests like this." Hayden took a final swallow of beer and laid money on the bar for McCloud's next round. "I'll let you know when I get the file," said McCloud. "Thanks, Charlie," said Nick as he stepped away. McCloud watched as Nick went out the door and disappeared into the shadows. He had to admit that something about the Kelso shooting didn't add up. Just as intriguing, he had a feeling that Hayden was hiding something. * * * Charlie McCloud's old friend Hank Balsam had done a five-year stint in the Chicago INS office of investigations and then, in a life-altering pivot, accepted a higher-grade staff position at the regional office in Minneapolis. Soon after arriving, however, he realized that he'd entered a world of surreal, Kafkaesque logic that made sense only to the most jaded, hard-core bureaucrats. Much of his time was now spent reviewing vacancy announcements and planning his escape with the desperate vigor of a soldier tunneling from a prison camp. Balsam whispered into the telephone: "If you stay up here too long, you become one of them, Charlie—the hollow eyes, the zombielike devotion to screwing people in the field offices. I feel like I've been abducted by freakin' Martians. It's frightening." "I warned you, Hank." "Don't remind me. And listen, I'm still using you as a reference on my applications, OK?" "Of course, Hank. Anything I can do to help," said McCloud sympathetically. Balsam didn't think twice about McCloud's request for the file on the Kelso shooting. Not wanting to take the time to copy the whole file, and not willing to let a secretary in on the conspiracy, Balsam personally packaged and mailed the original. McCloud's curious mind was finally zeroing in on the case. Any shooting would be traumatic, but why had Buck Tatum's response been so extreme? He'd completely cut off contact with anybody from INS, been divorced by his wife of twenty years, and, if still alive, was squirreled away somewhere in self-exile, though nobody knew where. Landau was dead . . . now Hayden's peculiar interest. McCloud received the file on Monday, shoved it into his top desk drawer, and waited until early evening so there would be no calls or distractions while reviewing it. After picking up a cup of coffee from the shop across the street, he returned to the deserted office. He then shut off the fluorescent lights in his room, turned on the green-shaded desk lamp, which was easier on his eyes, and removed the file from his desk drawer with the sense of anticipation he used to feel when searching out evidence on a good criminal case. CONFIDENTIAL had been stamped diagonally in large black letters across its cover, and a metal-rimmed label identified it as KELSO SHOOTING FILE, CHI 50/001.1974. McCloud started with the supporting documents and exhibits on the left side of the file. It was an old habit—reviewing the physical evidence first and then comparing his analysis of it with that of the case agent, whose report would be on the right side. The first item was a copy of a report dated March 9, 1974, from the Chicago police officer who responded to the shooting, scribbled out in longhand and barely readable. McCloud moved his finger down the blocks of information. _OFFENDER : ANTONIO CANO. Date of birth: 4/20/49. Nationality: Argentina. Residence address: unknown._ _VICTIM : FRANK KELSO. Date of birth: 7/11/34. INS agent, c/o INS office, 219 S. Dearborn St., Chicago, Illinois._ _WITNESSES : MICHAEL LANDAU and WILLIAM TATUM, INS agents, c/o INS office, 219 S. Dearborn St., Chicago, Illinois._ There was a brief description of the shootings, followed by a statement that the homicide division had taken photos and handled the preliminary evidence collection, but that federal authorities would conduct a thorough follow-up investigation. Next in the file was a yellow property envelope containing a stack of black-and-white photos—good quality, six-by-eight-inch images. The first in the stack were of Cano, a young man with high cheekbones and long, blond hair. His body was wedged into a sitting position against a brick wall, his hair matted with streaks of drying blood. There were several photos from different angles, then the close-up photos of Cano's face, showing a single perforation just above the nose, gunpowder burns on the forehead, and a line of dried blood running along his nose and through his mustache. It appeared to be a direct frontal shot through Cano's forehead. His pale eyes were half open and glistened from the flash of the camera. The photos of Frank Kelso sent a wave of nausea through McCloud. Kelso had been the sort of happy-go-lucky guy who'd clearly found his niche in life. He was often smiling, rarely complained, and drove his partners to frustration with a work ethic that was unmatched by anybody in area control. He had a remarkable knack for ferreting out illegals in a crowd—often able to identify their nationalities based on factors so subtle that even _he_ couldn't always articulate them. In this case, it would have been difficult to distinguish Cano from any young American with long hair. One photo showed Kelso lying flat on his back on the pavement with arms spread straight out, his legs close together, as in a crucifixion pose. His sport coat was unbuttoned, and the shirt beneath it was completely saturated with blood. There was a sharp tear in the shirt's fabric at the bottom center of his chest, which was swollen—the flesh pressed against the shirt. His black hair, streaked with gray, had fallen in front to his eyebrows and his eyes were shut. The slightest upturn at the corners of his lips added an odd, lighthearted quality to the image, as though Kelso was only playing at being dead. McCloud carefully examined a photo of Kelso taken from several feet away that showed the full length of his body. Along Kelso's left hip, where the open sport coat had fallen away, McCloud could see Kelso's empty black holster fastened to his belt. He must have been left-handed, thought McCloud. He didn't remember that about Kelso. Then, looking closely at the shape of the holster, he realized it was backwards—the side facing forward bowed out to enclose the trigger guard. This meant that Kelso was right-handed but had been wearing his gun in a "cross-draw" fashion on his left hip—prohibited because it would take longer to reach in an emergency. Even more important, an assailant could more easily grab the pistol, because the handle would stick out invitingly. McCloud had known a couple of older agents who insisted on wearing their guns that way because they felt it was easier to pull the gun out across their bodies. He wondered how such a crucial piece of information could _not_ have been widely known throughout the office in the wake of Kelso's death, and it made him curious about who had conducted the investigation. The coroner's report indicated Cano had traces of heroin in his bloodstream and a series of needle marks on his left arm. The .357-caliber, hollow-point bullet had exploded in Cano's brain, causing extensive and irreversible damage—his death quick and relatively painless. Kelso had not been so fortunate. He would have been partially conscious for several horrible minutes. As McCloud had expected, and the coroner's report confirmed, the heart had been pierced by the .38-caliber bullet, and the main coronary artery had been severed, causing massive internal and external bleeding. Kelso had literally felt his life fading away as he lay on the pavement. McCloud leaned back in his chair and pictured the scene on Clark Street. Two bodies lay dead or dying on the cold cement, blood covering the sidewalk, a crowd quickly gathering. Landau and Tatum had no doubt called for an ambulance and were ministering to the fallen Kelso. A police squad car or two would have arrived to establish order and sort things out. And then, after the street had been cleared, those first quiet moments for Tatum and Landau to consider what had happened—measuring their degree of guilt or responsibility. The images would be seared permanently into their minds—life forever divided into two eras: _before_ and _after_ the shooting. McCloud left the photos scattered on his desk and moved to the next item—an FBI rap sheet that summarized Cano's known criminal history in the United States: _March 1969: Armed Robbery; New York City Police Dept.; no disposition_ _December 1969: Solicitation of Prostitution; Chicago Police Dept.; dismissed_ _January 1972: Armed Robbery; Chicago Police Dept.; TOT INS_ _March 1972: INS warrant for deportation issued; Chicago INS office; no disposition_ McCloud had seen countless rap sheets like this one and knew how to read between the lines. INS in New York hadn't been contacted following Cano's first arrest, and he skated free on the robbery charge. He came to Chicago, where he got caught in a prostitution sting and was released, the police again not delving into his immigration status. The charge was later dismissed. Then he was arrested for another armed robbery. This time somebody checked his alien status, and he was turned over to INS. The cops would get credit for a felony collar without the paperwork and would hand him over to INS for what they thought would be immediate deportation. But McCloud knew it didn't work that way. Prompt removal for non-Mexicans was a relatively unusual event. All they had to do was request a deportation hearing, and soft-hearted judges could be counted on to lower the bond to as little as five hundred dollars, or release the alien on his own recognizance, even if he had an arrest record. Once released, the delays could be endless. A deportation hearing could be scheduled a year or more after the initial arrest, and attorneys could get delays of many months or years after that. Cano had been released, probably after posting a nominal bond, and hadn't shown up for his deportation hearing. A warrant would have been issued, and the file would have been sent to investigations to locate and arrest him. There were several large file cabinets in area control containing hundreds of these cases, which were supposed to be worked by agents when they had time between daily field operations. McCloud scratched Cano's eight-digit file number on a notepad. He'd check on it later. Beneath the rap sheet, McCloud found another property envelope, this one filled with the investigator's notes scribbled on the backs of business cards and scraps of paper. The handwriting had a distinctive quality—small, precise lettering with sharpness at the corners that suggested rigidity. It was vaguely familiar. He tried to match the writing with a name, but all he could summon was the unpleasant essence of somebody from the past. McCloud looked at the pink sheet on the right side of the file. INVESTIGATOR'S REPORT had been stamped across it in large black letters. He flipped past it to the administrative page. There, in the middle of the page, was the author's typed name: WILLARD SMITH. "Oh no, not that son of a bitch," he said aloud. Willard Smith had come to the Chicago office from Texas in 1967—about the same time as McCloud. They were soon followed by Joe Willis, Buck Tatum, and Sam Payton, among other Border Patrol agents—the agency's belated response to the presence of vast and growing communities of illegals in America's big cities. Some, like Smith, who had left the Patrol for higher grade plainclothes positions, had spent their lives in the rural Southwest and now became immigrants themselves, as disoriented in a sprawling metropolis as the illegals they pursued. Images of Willard Smith flooded McCloud's mind. Six feet tall, the rugged Smith exuded an air of confidence, though he found the noise, size, and diversity of Chicago intimidating. Smith, never timid about expressing his opinions, frequently lashed out at Chicago and other large cities as fostering the "moral decay" of America. McCloud was initially partnered with Smith—an awkward pairing to say the least. The two of them patrolled the South Side of Chicago, picking up illegal Mexicans at bus stops or looking for ship-jumpers who had fled foreign vessels docked at Calumet Harbor, south of the city. Smith would drive slowly to their destination, defying the rush of the city while chain smoking Camels, his eyes shielded by mirrored sunglasses. Wearing polyester slacks that were too short, a bolo tie, and cowboy boots, Smith was uncomfortable around McCloud, who was considered an intellectual by other agents. "Why'd a smart boy like you wanna go down to the border in the first place?" Smith had asked one morning as they cruised down Damen Avenue. "That's where the work was." "Didn't care for it down there, did ya?" "It was fine. I got along OK," McCloud had replied, refusing to take the bait. Smith and most of his former Border Patrol colleagues had been adamantly opposed to hiring investigators "off the street"—those who hadn't first passed through the Border Patrol gauntlet. When the agency began doing so a couple of years after Smith arrived in Chicago, the policy shift represented a challenge to the Border Patrol's preeminent position within the enforcement hierarchy. Smith and other former Border Patrol agents felt slighted by the perceived disrespect to the Patrol and threatened by the new recruits, most of whom had college degrees and more contemporary views of society. Several trainees had been dismissed on specious grounds at the conclusion of their one-year probationary period. Meanwhile, former Border Patrol agents who came north had been welcomed with open arms. Tolerance and flexibility had no place in Smith's emotional universe, McCloud had observed. He was instinctively opposed to change or anything that did not reinforce his prejudices and narrow worldview. As the country moved through the turbulent 1960s, the status quo had to be fiercely defended, and Smith had been determined to do his small part. In 1972 Willard Smith had moved on to the regional office in Minneapolis for a higher grade, survived two tedious years there, retired, and returned to Texas at the end of 1974. A month later, he had dropped dead from a heart attack. Shortly before retiring, however, he had been tapped to conduct the Kelso shooting investigation. It had evidently not occurred to regional officials that Smith's previous assignment at the Chicago office created a rather obvious conflict of interest. McCloud flipped to the synopsis page and began reading Smith's summary: _On March 9, 1974, Criminal Investigators Kelso, Tatum, and Landau attempted to arrest Antonio Cano, an illegal alien from Argentina. Cano violently resisted, disarmed Investigator Kelso, and shot Investigator Kelso in the chest with Kelso's service-issued, .38-caliber Smith & Wesson revolver. Investigator Tatum, in justified self-defense, shot Cano in the head. Investigator Kelso and Cano both died at the scene._ It was the second paragraph that had spelled the end of Michael Landau's career with INS: _Investigator Tatum used an appropriate level of force, and the use of his revolver to subdue the offender was fully justified. The shooting of Investigator Kelso might have been prevented if Investigator Landau had taken more positive and forceful action._ McCloud cringed. Smith had stated an opinion as though it were fact. Any opinion, if necessary at all, was reserved for a clearly labeled investigator's comments section. It had no legitimate place on the synopsis page, which was supposed to be purely factual. McCloud gulped what was left of the coffee and flung the paper cup into the wastebasket. He folded the synopsis page back and started in on the details section of the report. Smith, with the help of a Chicago homicide detective, had put together a series of diagrams showing the positions of the individuals involved in the shooting in relation to physical landmarks such as the street and nearby businesses. He had attached and summarized the coroner's report to establish Cano's and Kelso's causes of death. Finally, there was Smith's description of the shooting itself: _Investigator Kelso encountered Cano near Cleo's Vintage Books in the 5300 block of North Clark Street at approximately 5:45 PM. As he attempted to place the subject under arrest, Cano resisted and was able to remove Investigator Kelso's .38-caliber Smith & Wesson revolver from his waistband holster. A struggle followed during which Investigator Landau attempted to restrain Cano but, without the use of deadly force, was not able to prevent the shooting of Investigator Kelso. Cano fired one deadly shot into Investigator Kelso's heart. Investigator William "Buck" Tatum then used his .357-caliber Smith & Wesson revolver to fire one deadly shot to Cano's head. Both Investigator Kelso and Cano died at the scene before medical personnel arrived._ McCloud was shocked and disgusted. Smith had compressed an enormously complex event into a one-paragraph summary without details provided by Landau and Tatum. As a result, there was no way to visualize, except in a general way, what had actually happened that night. Nor was it possible to examine discrepancies between their accounts or to reconcile those discrepancies with the physical evidence. There was no indication that Smith had attempted to locate other witnesses to the shooting, nor was there mention of the position of Kelso's holster on his left hip. McCloud's eyes fell to the next short paragraph: _The interviews of Investigators Tatum and Landau concerning this incident were tape-recorded by this investigator. No other persons were present during the interviews. The cassette tapes are attached in a property envelope in this file._ McCloud flipped the page over to the last item in the file, a mustard-colored property envelope. Willard's distinctive handwriting was at the bottom: TAPES OF INTERVIEWS WITH TATUM AND LANDAU. McCloud lifted the envelope from the bottom but could see it was empty and completely flat, without the creases usually formed over time by the edges of a tape or tape case. Unless the tapes could be located, it wouldn't be easy to piece together what actually happened that night. A search of Smith's notes revealed nothing concerning his interviews with Tatum or Landau. That, too, was odd, even if the interviews had been recorded. McCloud realized his shirt was damp with sweat. He felt trapped in his small office, bombarded with visions of the unsavory Willard Smith and gripped by a sense that something had gone terribly wrong in the wake of the shooting. He suddenly felt the need to get out of there and breathe fresh air. It was past ten o'clock when he stepped away from the building, the night air cool and bracing against his face. He noticed the huge American flag on the plaza across the street hadn't been taken down and was whipping in the wind. A clasp on the flag's rope clanged loudly against the metal pole—a discordant note on an otherwise quiet evening. * * * The next day McCloud called Balsam to inform him that the tapes were missing from the shooting file. "There's an envelope for them, but it's empty. I need you to look for the tapes up there, Hank." Balsam quickly checked the regional evidence locker and found nothing. He then conducted a thorough search of the filing cabinet where the shooting file had been stored to make sure nothing related to Smith's investigation had been misfiled, but again found nothing. McCloud could think of only one other place where the tapes might turn up. "Hank, I need Landau's personnel file. They may have needed the tapes for the probation hearing and left them in his file." "I'll check the file and if the tapes are there, I'll send them to you." "No, I need to see the personnel file." There was a moment of silence before McCloud continued. "Look, I'm very suspicious about how Smith handled this investigation. I don't even know exactly what I'm looking for, but I want to see every piece of paper connected to this thing." "We both know a personnel file is even more sensitive. What's my cover for sending it to you?" "Chicago's training officer requested it. I'll take full responsibility if there are any questions." There was only a brief hesitation before Balsam spoke: "What the hell—maybe I'll have a better chance of getting out of here if I piss them off. OK, I'll send it." A large, yellow envelope appeared on Charlie McCloud's desk three days later. He immediately tore it open and found the pale green personnel file of Michael Landau. He laid the file flat on his desk and went through both sides, not pausing to read anything, just looking for a property envelope that might contain the tapes. But there were no tapes to be found and no indication they had ever been there. Though disappointed, McCloud began a more thorough examination of the file's contents. On the very top was a clipping from the obituary section of a Portland newspaper that reported the death of Michael Landau. There was no photo. It was the kind of lean article one would expect to see for a skid row bum. Beneath the news clipping, McCloud found a form that documented Landau's dismissal on May 25, 1974. PROBATIONARY NONRETENTION had been typed into one of the blocks. The review panel recommendation form was next. McCloud's eyes fell to the signature blocks at the bottom of the form for the three review panel members. To his amazement he found the signature of the suddenly ubiquitous Willard Smith. Even after Smith's damning report on the shooting, somebody had allowed him to be on the panel that would decide Landau's fate. Next to Smith's signature was an X in the square indicating recommendation for nonretention. The next signature was that of Thomas Reilly, the head of investigations at the Chicago office at the time of Landau's hearing. Reilly would certainly not have resisted Willard Smith's recommendation, especially if he'd believed that Landau couldn't be relied upon in difficult situations. The third and final signature was that of the head of investigations for the Detroit office. All had recommended nonretention. On the second page of the review panel recommendation form, one sentence was scrawled in the hand of Thomas Reilly: _Although Agent Landau received acceptable performance ratings his first year, his actions in the shooting death of Agent Frank Kelso, as outlined in the report by Willard Smith, cast doubt on his ability to use deadly force._ That had made it clear. The entire hearing would have been perfunctory at best. McCloud flipped through the remaining documents in the file. There was a copy of Smith's report, along with evaluations by journeyman agents who had worked with Landau. He had done extremely well on written examinations and had finished second in his class at the academy. Then, a final document, buried at the very bottom: Landau's original application for employment, the standard government form SF-171, which included personal biographic information. McCloud scanned the blocks. Landau was born in 1940 in Hinsdale, Illinois; graduated with honors from the University of Illinois; received bachelor's and master's degrees in social work; was hired by the Veterans Administration in 1965. This guy was even more of a misfit than I'd imagined, thought McCloud. It reminded him of Hayden, or the way Hayden had once been. He moved down the page to the section for dependents and relatives. Michael Landau's spouse, Joyce Landau, then her maiden name: Hayden. In the space for the couple's children, there was one entry: Nicolas, age eleven years. * * * Hayden spent two hours alone in McCloud's office combing through every piece of paper in the shooting file. Even the smallest details held a lurid fascination for him. But when he was finished, he felt empty. He'd hoped he could fit the pieces together into something coherent and conclusive, but that hadn't happened. He now had more information, but the crucial question—whether his father had acted appropriately under the circumstances—remained unanswered. Hayden knew that if his father had not used deadly force when it was necessary to save the life of another agent—if he'd been unable to respond appropriately—his dismissal was justified. But that case hadn't been made by Willard Smith, and the tapes that might have provided some clarity were missing. There was a glaring absence of detail about what had happened in the moments before the shooting. Though he was trying to keep an open mind about his father's conduct, he couldn't help feeling resentful toward Smith for what appeared to be a lack of thoroughness and for improperly stating opinions instead of simply presenting facts. The report suggested that Smith was either inept or biased against his father. As a result, Nick was left with a picture that was far from complete, and it appeared Buck Tatum was the only potential source of additional information—if he was still alive. When McCloud returned to his office, Nick, careful to conceal his emotions, offered his observations about the position of Kelso's holster and what appeared to be unorthodox liberties taken by the report's author. "We still don't know what really happened, Charlie." "Yeah, there's definitely something missing here, and the principals aren't around to clear things up—except maybe Tatum. Even if Smith were alive, you couldn't trust anything he'd say. I worked with him here in Chicago. He was a horrible investigator—driven by animosities and prejudices. He thought the Border Patrol was the only worthwhile part of INS. Anything he said in that report is suspect." McCloud paused. "By the way, I found Cano's file. The judge set bond at five hundred dollars, so he had no trouble making it, and he never showed up at his deportation hearing—ordered deported in absentia. Only thing that seemed strange was that there's no indication the file was sent to investigations to locate him. Maybe the court screwed up and it was sent to the file room by mistake." Silence lingered for several moments until Hayden became aware that McCloud was looking at him differently. He wasn't sure if it was sympathy or suspicion, but it was now McCloud who was hiding something. "You know, don't you?" Hayden asked softly. McCloud nodded. "Yeah, I know." * * * Though Hayden had concealed his relationship with former INS agent Michael Landau, McCloud wasn't angry, only curious about what else might have been covered up. He assured Nick that he hadn't yet told anybody in the office but would need more details before deciding what to do. They agreed to meet after work in a side room at McGinty's that was usually deserted and fairly quiet, except for the muffled sound of traffic on Dearborn. Nick busied himself with paperwork for the rest of the afternoon and arrived early. He wanted to be as clear-headed as possible, so he ordered a Coke instead of a beer and waited anxiously at one of the tables. McCloud soon came in and set his mug of beer down across from Hayden. "I've got plenty of time, Nick, so don't feel rushed," he said, draping his coat over the back of a chair and taking a seat. "I hope you didn't have to rearrange your schedule," said Hayden. "No. It's not like I have a thriving social life. Besides, this is important." McCloud paused and fixed Nick with a sober stare. "Listen, I don't want to be blindsided, so I need you to be straight and not hold anything back, OK?" "Sure. You can trust me to tell you everything." "I thought I could. Just relax and tell it at your own pace." "OK, I appreciate it, Charlie." "After we talked I pulled your personnel file and saw that on your application you identified Michael 'Hayden' as your father, and you didn't mention that he ever worked for the federal government." "I was pretty sure that if they'd known I was the son of a federal agent, they would have checked into his background and I wouldn't have been hired." "That's a reasonable assumption." "So I had to say that I had no relatives who had been employed by the federal government, except my mother. I knew they would interview her as part of the background investigation, and she agreed not to mention that my father had worked for INS if they didn't bring it up and, fortunately, they didn't. She thought I was crazy for wanting to do this work, and I couldn't tell her the truth—that I had to find out what really happened—because I didn't want her to know how it haunted me. But I couldn't see any way to get the job without concealing his connection to INS." "They could charge you with making a false statement on the application, though I doubt it would come to that," said McCloud evenly. "Your dismissal would probably be sufficient." "Yeah, they'd have to fire me." Hayden searched McCloud's passive face a moment before continuing. "Anyway, I knew there was a risk that you or somebody else would find out once I started digging into it . . . and I know you're in an awkward position. If you feel you need to tell somebody, I'll understand." "I'll let you know if I need to do that . . . after I hear more." Nick looked out the window for a moment to collect his thoughts. "Well, I guess it all started with my mother. She's the one who wanted my father to take the job with INS. He was working as a social worker at the Veterans Administration Hospital in Maywood, and she was a secretary at the DEA down here in the Loop. She heard about the job openings at INS, and I think she liked the idea of my father being in law enforcement. She seemed to be impressed with the DEA agents she worked with and thought his job as a social worker sounded dull, though I don't know that he ever complained about it. He had a master's degree in social work, so it was what he was trained for, and I have a feeling he was pretty good at it. But the INS job paid more because of overtime, and my mother was always concerned about money. So he took the job at least partially to please her. I have to say I've wondered how my parents ended up together in the first place. My dad was more of a thinker and did a lot of reading. Maybe it was physical attraction they took for love, because they didn't seem to have much in common. "Anyway, things were going along well enough between them as far as I could tell until that night in March. I think I was twelve at the time. I had gone to bed already, but I heard a car pull up and looked out the window from the second floor. It was snowing a little, and somebody was dropping off my dad. I knew he was working a late shift that day, and I didn't think much about it. So he comes in the back way, and I had my door open upstairs and I hear him talking to my mother in the kitchen. And he says, 'Joyce, something terrible has happened.' They sat down, and he talked kind of low so I couldn't hear everything, but I remember him saying an agent and another guy had been shot and killed. The name Buck Tatum was mentioned as one of the agents involved. For some reason that name stuck in my mind. Anyway, after he told her what happened, it got real quiet and Dad said, 'Well, I did the best I could do. I wish I could have done more,' and I was waiting to hear something comforting from my mother, but I don't think she said anything. There was just an awkward silence. "The next day I asked him about it, and he seemed surprised that I'd heard them talking. And he told me that an arrest got out of control, that an agent had been killed, and Buck Tatum had shot and killed a guy from Argentina. He said something like, 'It was a terrible thing, but it sometimes happens in this line of work. You just have to deal with it as best you can.' That was about all he said. "But starting from that point, everything was different between my parents. They seemed to stop talking to each other, and my mother became very quiet and withdrawn. It was like she was ashamed of him. My dad wasn't the same either, although at first he seemed to be OK, and then gradually he became more distant, probably because he was worried about losing his job, which he did about two months later." "So you were an only child?" asked McCloud. "Yes. Much later I asked my mother why they didn't have more kids, and she said my father wanted more, but she wasn't ready, which is not surprising because I always had the feeling that she didn't really enjoy being a mother. "So my father was suddenly out of work, and I remember that he talked about it as if he was better off doing something else. Nobody ever said that he was fired from the job, but even though I was young I could tell what happened. Pretty quickly he got a job unloading trucks, which was hard work but the pay was OK, and my mother was still working for the DEA. But within a couple of months he told me he was moving out; that he and my mother had to live apart for a while. He asked me if I wanted to live with him, and I was a little surprised that my mother would be OK with that. But she wanted to be alone, so I moved in with Dad, which was fine because my father was just a warmer and more supportive person by nature. We were living in Forest Park at the time, and he got a small apartment only a couple miles away so I could stay in the same school. "But my dad was having a tough time. He got home from work exhausted, and he tried to hide it, but he seemed depressed . . . kind of emotionally fragile. I think his confidence had been shattered—first the shooting and losing his job, then my mother wanting the separation. It got worse when my mother asked for a divorce. After that, he just seemed completely dispirited. But I still wanted to live there with him instead of with my mother. Then one weekend there was a series of phone calls between them. I couldn't hear what was said, though my father raised his voice a couple of times, which was unusual. The next day, out of nowhere, he told me that he wanted to scout things out in Portland, Oregon. For some reason he thought it was a good place to get a fresh start, and he said that if I wanted to join him later out there, I could. I didn't know what to think because I'd never been there, but the idea of moving didn't seem too bad. Anyway, a few days later he dropped me off at my mother's place and said he would be in touch within a couple of weeks. "But I never talked to him again. About a week later my mother and I were sitting in the living room and the phone rang and I answered it. It was a police officer calling from Portland. Somehow I knew why he was calling. I asked him if my dad was OK, and he didn't answer—just asked to talk to my mother. I went to my bedroom, feeling sick to my stomach. And then I heard my mother crying. She eventually came into my bedroom and told me that Dad had died. Later I found out he'd hanged himself in his room at the YMCA. "My dad may not have been the strongest person around, but he was a good man, and I missed him a lot. My mother got over it quicker than I did, and that angered me . . . that it didn't seem to affect her as much. She quit her job at the DEA and started a career in real estate and did quite well. She had her occasional boyfriends, and they were nice to me in a distant sort of way. When I started high school she decided that we should both change our last names to her maiden name. I didn't want to, but she insisted, telling me that it was the perfect time to make a switch. I had the feeling that she was still somehow ashamed about her connection to Dad; like she wanted to leave him completely behind. We had a decent relationship, Mom and I. We weren't at each other's throats, but it was more like living with an aunt who had no choice but to care for an abandoned nephew. It was OK with me, though, because I was independent and pretty self-sufficient as I went through high school and college. I was lucky because I was interested in my studies, especially history and literature, and I got involved in sports, mainly baseball. Most of my friends were guys I met playing sports. "But as the years passed, I became more and more curious about where all the problems seemed to start for my father. I kept wondering—what exactly happened that night? My mother had not gone after details as far as I knew, and simply assumed when they fired him that he'd not done enough to prevent Kelso's death. At one point she said he was too gentle and civilized a person for law enforcement work. To her the fact that he'd been fired suggested he'd failed, but a 'suggestion' wasn't going to satisfy me, and I had to have as many details as possible. The name change to Hayden made it possible to get hired, and I thought being on the inside was the only way to find the truth. My plan was to stay at INS long enough to find out what really happened and then go on with my life. But when I found how much I liked the work, I came up with reasons not to look further into it. And I began to realize that I had a powerful need to prove that I could do the job well, regardless of whether my father had. That became more important for a while than learning more about the shooting . . . until Payton said a piece of the puzzle seemed to be missing. Then I _had_ to know the truth, no matter what might happen to me and my career. That's when I reached out to you to get the file, though I knew you might figure it out." Hayden paused. He felt relieved to have told somebody but was suddenly very tired. He peered out the window as a cab sped by, its red taillights sailing smoothly through the night. "That's pretty much it, Charlie," he said wearily. "I'm sorry about your father, Nick. I didn't have much contact with him, but he seemed like a good guy. I wish I'd known him better." "You two would probably have gotten along well together." "Yeah, I think so." McCloud pulled a folded piece of paper from his shirt pocket and passed it across the table. "This was all I could find," he said. "I couldn't get a street address." Hayden opened it to find a handwritten note that read, "Buck Tatum, PO Box 133, Hollins, Florida." # 10 The voice was so loud that she held the phone away from her ear. "It's about time this country stands up and doesn't take this shit anymore," the man growled. "These damn wetbacks come across the border; next thing you know they're taking good jobs from American citizens. Like this guy I just told you about." Rita Bustos, a petite, middle-aged woman with a billow of black hair and rimless reading glasses, sat in a corner of area control, her desk covered with stacks of leads she'd written up. She'd taken thousands of such calls from discontented workers over the previous ten years. "What is his job at the plant, sir?" she asked politely. "They just made him a damn foreman, for chrissakes," the man said. "Been here less than four years and already he's in management. Hell, I've been workin' there eight years. Guess I'm not the right color. I ain't black, brown, or yellow, so I ain't worth shit!" She carefully took down the information, and then remembered Hayden's request that she ask all callers what they knew about phony documents. "Does he have counterfeit documents—a green card or social security card?" "Course he does. They all do. What a laugh!" he said, letting out a bitter cackle. "I've heard about guys selling 'em in bars around here." "Do you know who sells them, sir?" "No, I don't know any _names_ ," he said. "But a couple of years ago I heard some Mexicans flappin' their jaws about this bar called the El Paladio or El Palacio or somethin' like that. I guess that's where they go for the documents. It's over on Sheridan . . . a tonk bar." "But you don't know who sells the cards at this bar?" "How would I know that? I don't go to tonk bars," he barked. "Hey, I'm calling about this one guy, is all, and you're askin' me about all this other stuff! It's _this_ guy I want picked up!" "Yes, sir, I understand. I just need to get all the information you have. It helps us do our job." "Well, I'm an American citizen. I want this damn wetback picked up and I want him picked up now!" "Can you give me your name and number so an agent can call you if there are any other questions, sir?" "You got enough information. Remember, he's driving a tan Fairlane." "Yes, I have that." "And listen, if he's not picked up damn quick, I'll call my senator and tell him you all ain't doin' your jobs down there. You hear me?" Rita said nothing. "You got it?" he demanded. "We have it. Thank you, sir." Rita placed the report on a far corner of her desk. Just before leaving that day, she walked down to fraud and left it on Nick Hayden's desk. * * * Hayden and Kane sat in the shadow of the "L" tracks, the trains thundering overhead. Between trains it was quiet, a morning breeze gently stirring a line of trees on the parkway. Kane had parked between a pair of abandoned cars about fifty yards south of the entrance to the Poindexter plant. They were watching the tan Fairlane that had been mentioned in the tip Hayden had received from Rita the day before. It was thought to belong to an illegal Mexican named Miguel Chavez, who worked at the plant as a low-level shop supervisor. The rusted-out Fairlane was parked with a few other vehicles in a makeshift lot beneath the tracks. At seven o'clock, they could hear the distant ring of the shift bell from inside the plant. Hayden, in the passenger seat, suddenly felt the presence of a figure to his right: a middle-aged man with muttonchop sideburns, wearing a knee-length overcoat and a pair of ragged construction boots. The man swayed unsteadily as he squinted to focus on the car with two men inside. "Hey, are you guys a couple of homos or what?" the man bellowed, looking around for somebody with whom to share his discovery. He staggered in short steps to the front of the vehicle to get a better look. Hayden grimaced. "Great, our guy is coming out in a few seconds and this wino shows up. I'll get rid of him." He got out of the car and advanced toward the drunk, who looked up with frightened eyes, and then tried false bravado. "Who 'n hell do ya think—" he sputtered, but Hayden had grabbed his coat at the back of the neck and was walking him to the sidewalk. The man instantly became docile. "Hey, I didn't mean nothin' by it." Hayden launched the drunk headfirst into a clump of bushes adjacent to the parking area. The man fell awkwardly into them, a pint bottle of liquor falling out of his coat pocket. Hayden kicked the bottle, and it skidded down the sidewalk. "Get the hell out of here," ordered Hayden. "If you come back, I'll take your bottle and throw you in jail." The man slowly extracted himself and began to walk away shakily. Hayden gave him a swift kick in the butt, and the man staggered down the sidewalk, muttering and casting angry glances over his shoulder. Silence returned to the street as Hayden got back in the car. "Never a dull moment," said Kane, grinning. A few minutes later a small cluster of men, some Anglo and some Hispanic, emerged from the alley next to the plant. They dispersed quickly, some climbing the stairs to the "L" platform, others retrieving cars parked on the street or beneath the tracks. Then a dark-skinned man appeared in the alley, an unhurried dignity in his gait. He made his way to the Fairlane, got in, and slowly pulled away. "Let him drive off," said Hayden. "We can keep a loose tail on him until he stops somewhere." Irritated with his partner's recent habit of issuing orders, Kane defiantly pulled the Camaro right up behind the Fairlane at a stop sign. They could see the driver looking curiously in the rearview mirror. "So much for a loose tail," said Hayden. "Now he's watching us. What's the idea?" "Just because he looks at us doesn't mean anything," said Kane coolly. They followed the car as it moved smoothly through the traffic along Montrose Avenue and then south on Ashland. Kane dropped back and another car cut in, separating them from the Fairlane. As they came to a stop at a red light, he rhythmically tapped his fingers on the steering wheel while both of them leered at two young women in short skirts waiting at a bus stop. The light changed, and they passed through the intersection. "This is kind of a long shot, isn't it?" said Kane. "All we know is this guy _might_ be wet, _might_ have phony documents, and _might_ have gotten them from somebody at a bar on Sheridan." "That's why we're out here—to find out if it's good information . . . if he cooperates. Anyway, what else have we got?" A couple of miles farther down Ashland Avenue, the Fairlane veered sharply into a grocery store parking lot. "He's trying to find out if we're tailing him," said Hayden. "Stay back unless he gets out of the vehicle. We don't want him to take off in the car." Kane smiled. He would have been delighted if the car had sped off so he could pull out the flashing light, get the siren going, and begin weaving wildly through traffic. As they entered the lot in front of the store, they watched the man pull into a parking space, hop out, and walk briskly toward a pay phone near the corner of the building. He picked up the receiver and for a moment, as they came closer, seemed to be making a call. The man glanced over his shoulder, spotted the vehicle bearing down on him, and a look of alarm crossed his face. He dropped the receiver, ran to the nearby corner of the building, and began to fight desperately through a cluster of bushes that hugged the side of the building—trying to reach the alley behind the store. Nick leaped from the car in pursuit. Kane flipped on the siren and sped out of the lot to intercept the man in the alley. Chasing people had been fun for the first year or so, but now it aroused hostility in Hayden. How dare they defy his authority? He pushed through the bushes—purple berries smearing his leather jacket. This son of a bitch was going to pay, he thought, pushing through the sharp branches with his elbows. Finally he burst free of the bushes and into the alley. To his left he saw the momentary flash of a green jacket as it disappeared through a space between the garages that lined the alley. Where the hell was Kane? Hayden darted between the squat, shingled garages and down a narrow cement walkway. Hearing footsteps, he circled the garage until he again faced the alley and a tall, crosshatched metal fence—the man climbing it frantically. "Stop right there," Hayden called out in Spanish. "Federal agent." The man had reached the top rung of the fence when Hayden grabbed his belt from behind and pulled hard, so that the man lost his grip and tumbled to the cement, sprawled out helplessly at Hayden's feet. For a moment they stared at each other, both wheezing from the run. As the man slowly raised himself, Hayden, feeling a surge of anger, thrust his elbow into the man's chin, a jarring blow that knocked him on his back. Hayden, suddenly dizzy and weak, dropped to the ground, his hands and knees on the cement. Even after thousands of arrests, many of them rough, he'd never struck a person except in legitimate self-defense, and he felt a twist of shame. He was woozy and not sure how long he'd been on his knees when he realized he was being helped to his feet by the dark-skinned man he'd struck. There was a cut and a bit of blood on the man's chin. "I sorry, sir," said the man calmly. "Is foolish to run. You are _la migra_?" Hayden needed a moment to steady himself before answering. "Yeah, Immigration," he said weakly and nodded at the man's chin. "Sorry about that." "Is not bad." "You speak good English. You're Chavez?" "Yes, Miguel Chavez," he said, holding out his hand to Hayden. After a moment's hesitation, he shook Miguel's hand. "Good to meet you," he said. It was an odd thing to say to a person he had just assaulted and arrested, but Hayden knew the man could have escaped—could easily have scrambled away instead of helping him. At that moment Tom Kane appeared breathlessly around the corner of the garage to find Chavez and Hayden facing each other. "What the hell's going on here?" said Kane, his face flushed. Not waiting for an answer, he grabbed Miguel's arm and pushed him against the side of the garage. "It's OK," said Hayden. "He's all right." "You pat him down yet?" Chavez, sensing Hayden's disorientation and Kane's impatience, placed his hands up against the garage. "Is he our guy?" asked Kane, as he checked Miguel's pockets. "Yeah . . . Miguel Chavez." Kane handed Miguel's wallet to Hayden and was about to handcuff him behind his back. "We don't need to cuff him, Tom," said Hayden, wiping sweat from his forehead with his handkerchief. "He already tried to escape," Kane said. "Now you're both covered with fucking berry stains, you're all scratched up, he's got a bloody face, and you don't want to cuff him?" "That's right," said Hayden firmly. "We won't need the cuffs." Miguel stepped between the two agents with his hands outstretched. "Is OK," he said to Hayden. "No, Miguel," said Hayden, and then to Kane, "We don't need them." Kane's expression eased, and he looked at Chavez cautiously. "Well, if we aren't going to cuff him, you'll have to sit with him in back. "OK," said Hayden, patting Kane on the back. "What happened to you, anyway?" "Damn garbage truck was blocking the alley." Hayden peered absently out the window as they drove to the office. He was replaying the incident in his mind, the elbow driving forward, Chavez falling back on the cement, then helping him up. How had it come to this? For most of his life, Nick had thought of violence, except to protect yourself or another person, as cowardly. His father had taught him that. "Nick, you OK?" Kane was looking at him through the rearview mirror. Hayden shifted in his seat and cleared his throat. "I'm fine." "You gonna check his documents?" Hayden wiped his sweaty brow with a handkerchief. He opened Miguel's wallet and pulled the contents from beneath a buttoned leather flap. There were frayed business cards and a driver's license issued nearly two years earlier with an address on Francis Street. Then the photos—a girl, perhaps three years old, in a pink dress; a boy with a baseball glove; a woman with a humble smile and black hair swept behind her ears; then the family together, the children laughing as if the photographer had made a funny face. Nick had rifled through countless wallets like this but had never paused to look at personal photos. Finally he came to the counterfeit permanent resident card—the quality of the printing quite good, but not good enough to fool an agent. It looked identical to any number of counterfeits he had come across in recent months. The social security card was also an obvious phony. Kane had been looking curiously at Hayden, who was moving at half speed, and adjusted the mirror to view Chavez, who was sitting impassively. Blood was now trickling down his swollen jaw. "How'd he cut his chin?" asked Kane. Before Hayden could speak, Chavez said, "I cut on fence." "It looks like more than a cut," said Kane. "Your whole chin is starting to swell up." Chavez shrugged and looked out the window. Hayden offered his handkerchief. "Here, Miguel, your chin is bleeding." Nick then turned to Kane: "The cards look the same as the ones we've been finding. They're all coming from the same printer." * * * Hayden leaned over the sink, splashed cold water on his face, and patted himself dry, but the nausea grew more intense. He staggered into an open stall and threw up violently into the bowl. Perspiration rose in a hot wave from his forehead as he gripped the sides of the stall. He was pulling himself together at the sink when Tom Kane entered the washroom. "Jesus, it smells like puke in here," said Kane. Hayden was wiping his hands with a paper towel and said nothing. "What the hell went on back there between you and the tonk?" demanded Kane. "He just tried to get away," said Hayden. "Did he come at you?" Hayden looked wearily at Kane through the mirror. Kane persisted: "Come on—I need to know what to expect from this guy, especially if he's going to work for us." "He didn't do anything. He's fine." Nick knew Kane wouldn't understand. Or, worse, he _would_ understand and suspect that Hayden was going soft. "Well, whatever happened, I'm gonna keep an eye on this guy," said Kane. * * * Miguel Chavez sat in a chair beneath the flat, fluorescent light and wondered whether it had all been worth it. He thought back to the trip north, finding work, arranging for his family to join him, the enormous effort of it. Now it was over. Still, he had earned more money in the past two years than he would have earned in ten years in Mexico. He had even gotten used to the precarious nature of his life. His wife and children would be terribly disappointed, of course, as they were now comfortable here. He knew of others who had lived here for years without papers and never had an encounter with INS. Eventually they were able to legalize their status. The quickest and most certain avenue was to fake a marriage to a US citizen, but he could not do that. It was one thing to cross the border without papers, quite another to enter a dishonest scheme like that. He felt a subtle pounding in his chin and ran his fingers over the cut. If he were in Mexico and had run from the police, he would likely have been severely beaten. This was nothing. Miguel hesitated briefly before answering the agents' questions about the documents, but there was no reason to protect Salvador Rico. He told them how he had met and bought documents from Rico at El Palacio, the rumors about the demise of Marcos Ortega, and how Rico had taken control of the counterfeit document trade. Though Rico told people he'd been born in Puerto Rico, there was talk that he was really from Panama. Hayden and Kane listened intently until Miguel had told them everything he knew or had heard about Rico. "You may be able to help us and yourself at the same time, Miguel," said Hayden. "How?" "If you're willing to do undercover work for us, we can let you stay here and keep your job at Poindexter," said Hayden. "You won't have to go back to Mexico. It could end up being permanent." "What you want me to do?" "You would have to meet with Rico and wear a wire," said Hayden, who reached to the far side of his desk and picked up a wire with a tiny microphone attached to its end. He held it up for Miguel to see. "You'd be buying a lot of documents this time." Miguel nodded. "And my family?" "They could stay. But you'd have to be willing to testify later, if the case against Rico goes to trial. You need to understand that," said Hayden, who noticed Kane frowning. The idea of testifying in open court wasn't normally thrown at a potential informant right away. Many were scared away, so it wasn't mentioned until later, if at all. "We stay and get the papers if I do this?" Miguel asked. "We could carry you as an informant as long as we want," said Hayden, "but you'd have to be productive. You know, help us make criminal cases. There's a possibility of getting permanent papers if you're here long enough." Miguel stared at the floor, mulling it over for several moments, and then looked at Hayden. "Is dangerous, no?" he asked. "We'll be there along the way," said Kane. "There's nothing to worry about." "There _is_ danger, of course," said Hayden. "We have to assume Rico and his buddies will be armed and dangerous. But we'll provide protection. If you come through, we'll take care of you. You can trust us to do that. In a worst-case scenario, we may have to move you to a different part of the country, but we'll protect you." Miguel wasn't so sure about the other agent, but there was something about this man that he trusted, despite their altercation. "Yes, I do this. I think the Lord wish it for my family . . . and for him also." "For who?" asked Kane. "This man . . . Salvador Rico." # 11 Kane felt like the captain of a small submarine. On his knees in the back of the van, he gripped the handles of the periscope and scanned the street in front of El Palacio. A series of lenses inside the periscope column delivered an image from a mirror on the van's roof that could be adjusted by pushing the handles left or right. The mirror was concealed by a metal cap that looked like an air vent. Parked in front of a small grocery store, the van was an inconspicuous part of the scenery along Sheridan Road. Wearing jeans and a sweat-soaked T-shirt, Kane muttered profanities at Floyd Baker, the cerebral little technician responsible for outfitting the only legitimate surveillance van in the Chicago INS fleet. Thanks to Baker there was no cooling system in the rear of the van, aside from a small fan, and almost no ventilation. This was fine during the cooler months, but now, the second week of an unusually hot and humid September, it was like a furnace. To provide cover for the van, Baker, with unintentional irony, had attached removable magnetic signs that read, FLOYD'S HEATING & AIR CONDITIONING SERVICE. A week of surveillance had revealed a pattern of sorts. Rico would arrive at El Palacio in midmorning, parking his black Volvo directly in front. At about eleven o'clock, a colorful assortment of young men would begin parading through the bar. Unlike regular customers who would come for drinks or Chacon's greasy tamales, they would remain for only five or ten minutes, just long enough to conduct business with Rico and his subordinates. Wearing gym shoes and T-shirts, some carried backpacks or thin briefcases. Though they weren't from the neighborhood, the area surrounding the bar was such a revolving farrago of pedestrians and vehicles that their comings and goings went largely unnoticed by the casual observer. Through license plate checks and photos, Hayden and Kane had identified two men as lieutenants in the Rico organization. Rosario Nieto was a large, muscle-bound Bolivian, whose arms and neck were covered with tattoos. INS records showed that he'd been deported twice. The other, Felix Pinal, was a thin, studious-looking man who had no known prior deportations but was presumed to be illegal. Both of them spent a good deal of time at El Palacio and could often be seen conversing with street vendors in front of the bar. Salvador Rico usually remained inside, hidden from view. On alternate days one of the agents, in the suffocating heat of the van, would snap photographs through a camera with a powerful telephoto lens. The other agent would conduct surveillance from a separate vehicle, parked close enough to pick up a loose tail on Rico's business associates. On this day Nick had followed one of Rico's briefcase-wielding associates to Twenty-Sixth Street and sat in his Firebird watching the young man and others ply their trade. Cars pulled up, and items were exchanged and passed to couriers, who would deliver the orders to pads where the cards were manufactured. The customers would return in a couple of hours to pick up their orders. The whole operation churned along briskly, unimpeded by authorities and ignored by almost everybody, aside from business owners, who sometimes angrily chased vendors from one sidewalk location to another. As he watched, a question began to prey on Nick's mind: Who _was_ Salvador Rico? They had done criminal checks using the name and date of birth on Rico's driver's license and come up empty. But it made no sense. A confident man in his midthirties, firmly in command of a large criminal enterprise, doesn't appear out of nowhere. Hayden's gut told him that Rico had a history, probably a bad history, and wouldn't hesitate to blow to smithereens anybody who would threaten his little empire—precisely what they were asking Miguel Chavez to do. * * * As Nick climbed the staircase to Miguel's flat, the scent of old wood gave way to the savory aroma of fried sausage and onions. A makeshift coat rack was fastened near the door—a length of plywood with several nails sticking out. A crumpled Cubs baseball cap hung on one of the nails. He rapped on the door and could hear the shuffle of feet and the muffled ebb and flow of conversation. When the door opened, Miguel and his family were standing in a row, like soldiers awaiting inspection. "Mr. Hayden," said Miguel, who was wearing a stiff white shirt with ironed creases at the shoulders. "Is great honor to welcome you. Please come in." Miguel quickly introduced his family. Paco stood rigidly beside his father, while the tiny Maria leaned against her mother's leg and smiled radiantly. Miguel's wife, Carmen, appeared shy and uncertain. Hayden was touched by their innocence and sincerity. "Thanks for inviting me, Miguel," he said, reaching out to shake his hand. Nick glanced around the flat. The hardwood floors badly needed refinishing, and the old plaster walls had a few cracks and blemishes, but the overall atmosphere was clean and warm. There were handsome moldings and baseboards, which he'd noticed were common even in modest houses built in the early 1900s. The flat was furnished with old furniture they had probably found discarded or at flea markets. "Would you like beer or soda, Mr. Hayden?" asked Miguel. "What are you having?" "Ginger ale. I no drink anymore." "Ginger ale is fine." Miguel gave him a can of soda and went into the kitchen to help Carmen, while Hayden sank into a lumpy armchair in the living room. On the wall behind the sofa was a framed image of Jesus that looked as though it had been cut out of a magazine. A white plaster-of-Paris sculpture of the Virgin Mary hung next to it. A Bible with frayed edges rested on a small end table next to the chair. Nick became aware of Paco sitting on the sofa, watching him curiously. Hayden spoke in Spanish. "Is that your cap out in the hallway, Paco?" Paco smiled, showing teeth that looked exceptionally white next to his tan cheeks. He replied in English with only a slight accent. "Yes, my father got it for me. Are you a Cubs fan, Mr. Hayden?" "Yeah, big Cubs fan. Your buddies down here on the South Side must give you grief about that—not being a White Sox fan." "What is 'grief'?" "You know, they must razz you about being a Cubs fan." "'Razz'? I don't know that word either." Hayden silently cursed his ineptitude. "It's just that . . . the Cubs aren't too popular down here." Paco smiled. "I like both teams the same." "That's a good attitude, Paco." "Do you want to see my baseball cards?" Paco had already grabbed a stack of cards from a shoebox on the sofa. "Sure, let's take a look." Paco shuffled through the stack, stopping in the middle. "This is my favorite, Ozzie Guillén," he said, standing and handing the card to Hayden. "He's a great shortstop." "No question about it," said Hayden, pleased with so quickly finding common ground. "You've got a nice collection here." Paco sifted through the deck as Hayden looked at the back of the card showing the player's career statistics. Nick had collected hundreds of baseball cards as a boy and understood their magical quality—as though possessing a player's card established a personal connection with him. From the dining room, Miguel announced that dinner was ready. "We can go through the rest after dinner, Paco," said Hayden. The Chavez family stood, politely waiting for Hayden to take his seat. A small ceiling light cast a soft glow over the table, which was covered with a freshly ironed white tablecloth. When they were all seated, Miguel said a short prayer in English and then very rapidly in Spanish, thanking God for food and blessings, and for introducing his family to Mr. Hayden. The family all crossed themselves and then quietly waited for Nick to fill his plate from the large, steaming bowls. Rich food aromas filled the room. "This is quite a feast, Carmen," said Hayden. Carmen was wearing a light green dress. Her hair was swept back, which accented the largeness of her brown eyes. She smiled, but her blank expression told Nick she didn't understand. He repeated the words in Spanish, and she nodded agreeably. "Thank you," she said softly in English. "Her English is improving," said Miguel. "Is hard because she is home all day. Paco already studies English before he comes here. Maria learns also." Maria, wearing a flowered dress, was sitting next to her mother in a high chair, staring at Hayden. "Please go ahead, Mr. Hayden," said Miguel, who began serving the others. "You have a nice family, Miguel," said Hayden. "You're a lucky man." "Yes, is true. Perhaps you someday have family. You would be good father." "I don't know about that, but thank you," said Hayden. It was one of the kindest things anybody had ever told him, but he wasn't at all sure it was true. He'd already concluded that it was unlikely he would ever get married. After dinner, Paco helped Carmen clear the table, while Miguel and Nick sat down in the living room with cups of coffee. "Have you known many guys like Rico?" asked Hayden. "Yes. I am not so different when I am younger." "That's hard to believe." "I never go so far as him, so far bad, but before I find the Lord, my life is different. I was very foolish," he said with a sheepish grin. "I not say I am smart and wise . . . just not so foolish like before." Nick looked at Miguel inquisitively, waiting for more. "I love the tequila," said Miguel finally. "And women. I live for the body, what the body wants. It was, how you say . . . shallow, very shallow life—has no meaning. I no keep any job. I live like child. One morning I wake up in alley in city of Morelos, many miles from home. I no remember how I come there. And I find wound in my stomach and was bleeding. It is long cut, right here, from knife." He motioned with his finger across his abdomen. "I get up and walk down street. I am very thirsty—my mouth feels like desert. I need water, but everything is closed. Then I come to small chapel and door is open. I go inside. I think maybe priest give me water. But there is nobody there, no priest. I am alone. I sit in back of chapel, and I look up and I feel very small. He is there up on cross and something happen. My heart come open, and He speak many things to me. He say nothing of stupid things I do, just I should trust and follow His way, and He protect me. And I feel like I am hit by . . . how you say . . . the lightning! Life is never same since that time. Men who are blind think those who follow God are weak, but is not true. I am stronger. Maybe because I am stronger, the Lord give me Carmen, the children. He let me come here—to this country. And He bring you to our family. Many good things come to me. So I am very blessed." He smiled warmly at Hayden, who was lost in the scene Miguel had described. Nick had always respected those who could sift some higher meaning and order from what often seemed the arbitrary chaos of life. "Yes," said Hayden finally. "I can see that, Miguel." A sharp knock rattled the front door. Miguel looked up with an expression of mild concern. "I take care of this," he said calmly. Carmen stepped out of the kitchen and looked nervously at Miguel. When he opened the door, Tom Kane was leaning against the wall next to the stairway. "Mr. Kane. Please, come in," said Miguel, opening the door wide. "No," said Kane coolly, staring past Miguel at Hayden, who had risen from his chair. "Something came up, Nick. We have to take care of it." "Carmen, please get Mr. Kane a beer," said Miguel. "No," said Kane. "I can't stay. We have to go right away. It's important." Hayden was now at the door beside Miguel. "What's up?" inquired Hayden. "I'll tell you about it outside," said Kane. "Mr. Kane, please, you must meet my family while you are here," said Miguel. "Maybe some other time," said Kane, already starting down the stairway. Hayden stood at the doorway, annoyed with Kane's brusque manner. "Paco, please get Mr. Hayden's jacket," said Miguel. Hayden thanked Carmen for the meal and apologized for the hasty departure. He promised Paco he would return to see more of his baseball cards and bring his glove so they could play catch. Miguel insisted on going down the stairs and outside onto the porch with Hayden. Nick again thanked him for his hospitality, while Tom Kane stood next to his car and watched, scowling. Hayden strode toward Kane, making sure Miguel had closed the door before speaking. "How'd you find me?" "I was checking things out on Twenty-Sixth, to see if Rico's guys were out on a Friday night. Saw your car when I was driving down Eighteenth Street." "So what's the emergency?" Kane glanced around the neighborhood, apparently concerned their conversation would be overheard. "We can't talk here. I'll meet you at the usual place on Cermak." The lot was nearly empty as they parked next to each other along an old railroad embankment a good distance away from the front of a large grocery store. It was darker now, and an overhead streetlight at the center of the parking lot cast a pale light that barely reached them. Hayden had spent the drive over telling himself not to jump to conclusions, but his adrenaline was pumping when he stepped out of the car and advanced toward Kane, who was casually leaning against his Camaro. "What's this all about?" demanded Hayden. "The question is, what was _that_ all about? We can't be socializing with informants," said Kane. "You know as well as I do that you can't get too close to them or—" "So that was a lie about there being something urgent—is that what you're telling me?" "Would you feel better if I told Miguel you were putting him and his family in danger?" "We need these people to trust us if we ask them to risk their lives." "That's bullshit," Kane retorted. "All we need is for them to be frightened enough to do whatever we want them to do. We're supposed to _handle_ 'em, not _coddle_ 'em." "I'll deal with him as I see fit," said Hayden sharply, his chest bumping against Kane's. Kane shoved Hayden as though he were weightless, sending him reeling awkwardly back on his heels. "He's not _your_ informant, you know," said Kane, his face red with anger. "We both arrested the son of a bitch." Hayden gathered himself and drove into Kane with his shoulder, pushing him hard against the hood of the Camaro. Kane, though off balance, quickly righted himself and pushed Nick aside with a thrust of his powerful arms. Suddenly a bright spotlight engulfed them, and there was the squeal and skid of a fast-moving car as it came to a stop. Two uniformed cops jumped out of a squad car, one grabbing Hayden, the other Kane. "OK, up against the car," said the cop who had grabbed Hayden, pushing him toward the Camaro. "Hey, guys, we're cops," shouted Kane, as he grabbed the roof of the car. "Check my inside pocket." The officer reached around Kane's back and inside the leather jacket, slipping out the shiny black credentials case, the gold badge embossed on its cover. He flipped it open and pointed his flashlight down to view the ID and photo. Hayden's cop did the same, and the two, both rangy men in their thirties, relaxed and stepped back. "So, you guys been partners too long or what?" said Kane's cop, now amused by the situation. "Just a little spat," Hayden said between deep breaths. "You know how it is." "Oh, yeah . . . we know," said the other cop with a knowing grin. "It's not unusual in our precinct, but we try to keep it out of public view." The cops were looking at Kane, the spotlight from the squad car on his face. He squinted against the light but said nothing, still catching his breath. They seemed to be waiting to hear something conciliatory so they could be on their way. "We'll be fine, guys," said Kane finally, pulling his jacket back into position. He forced a weak smile. "Sorry we caused you any concern." Kane's cop flipped the credentials back to him. "Don't make us come back, all right?" "Don't worry," said Hayden. "We know you've got better things to do." The spotlight went off, and the police car peeled out of the lot, leaving Hayden and Kane facing each other. "It's good for you those guys came along," said Kane, pushing his wildly tousled hair back into place. "You were about to go down." Hayden knew Kane could make short work of him in a real fight. Besides, it was no time for a rift that would permanently undermine the partnership, both of them being keenly aware that there were only about three weeks remaining in their detail. They leaned against the Camaro, silently looking down at their shoes when Kane remembered the six-pack of beer in the trunk. Sipping the warm beer, Kane eventually conceded that "maybe" it hadn't been wise to barge in on the Chavez family, regardless of his misgivings. It could have been discussed later. Hayden acknowledged that he'd been wrong to suggest he had sole control of Miguel and that he should have informed Kane of his plans. By the time they'd each had a couple of beers, they were trading office gossip, and the heaviness had lifted. As they prepared to leave, Hayden gave Kane a brotherly pat on the shoulder to suggest that there were no hard feelings. They got in their cars and pulled out of the parking lot but headed in opposite directions on Cermak Road. # 12 Chacon had cleared away the empty bottles of Corona and was wiping off the counter when he noticed a man standing at the bar watching him. "What can I get for you?" asked Chacon in Spanish. "I'd like to see Mr. Rico, if you don't mind," replied Miguel. "It's not like before," said Chacon impatiently. "There are people on the street that can help you. Not here anymore." "No, this is something else. I must talk with Mr. Rico, please," said Miguel firmly. "I am Luna." Though he was under orders from Rico to get rid of such people, there was a forthright, serious quality about the man that made Chacon consider him for a moment. "Wait here," said Chacon, who disappeared through a beaded curtain into a room at the end of the bar. Miguel looked around. The place seemed to have undergone a facelift since he'd been there two years before. The dusty wood floors had been replaced by black and white tiles arranged in checkerboard fashion. There were sleek-looking tables and chairs, fresh curtains, and an elevated square of parquet flooring in a corner with a stand-up microphone on it. Clearly there was more money coming into the bar these days. Chacon returned. "Through that curtain," he said curtly. Rico was sitting behind a large mahogany desk, about twenty-five feet from the door. There was an oblong banker's lamp on the desk and a single light bulb overhead that cast weak, grainy light throughout the room. Two small windows against the wall behind Rico's desk had been covered with black paint, blocking the light from outside. Miguel noticed that Rico's face was heavier, his hair expensively styled. He wore a tan blazer of thin leather over a black shirt, open at the top to reveal a heavy gold chain. "I understand you have business," said Rico gruffly in Spanish. Miguel stood inside the door, respectfully waiting for an invitation into the inner sanctum, his eyes adjusting to the frail light. There was a sofa against the wall to the left and two wooden chairs in front of Rico's desk. "Yes, Mr. Rico. That is correct," said Miguel. "Well, come closer," said Rico. He motioned toward the chairs in front of his desk. "Have a seat here." He was alert and studying Miguel intently. "We met a couple of years ago," said Miguel, sitting down. "It was out there." He gestured toward the bar. "I remember you now," said Rico softly. He paused and leaned back into his chair. There was an aura about this man that encouraged Rico to defer to him, to seek his favor. Self-conscious under Miguel's calm stare, he needlessly picked up an ashtray and set it on a stack of papers. "Well, then . . . you are Luna?" "Yes, Miguel Luna. I bought the documents. You were kind enough to help me with this." It was a reasonable statement, but directness of speech was not a desirable attribute in Rico's business. "I don't know what you are talking about," said Rico. "What sort of business do you wish to discuss?" "I am a Mexican. I know many people on the South Side. Many are afraid to buy the documents from those on the street." "Is that so? Why are they afraid?" "Some are still afraid to do these things in the open. If you give me the opportunity, I can sell many of the documents quietly and professionally." Rico considered Miguel thoughtfully. Was he wearing a wire, or was he just plainspoken by nature? Rico pointed toward the wood-paneled wall to his left and rose from his chair. "Put your hands up against that wall," he said evenly. Miguel looked at the wall and then back at Rico with the hint of a smile. "You don't have to worry about me, Mr. Rico." "Maybe not, but you're not walking out of here until I search you." Miguel paused for only a moment. "Yes, of course," he said, standing. "It is always wise to take precautions." Miguel spread his legs and placed his hands high against the wall. Rico gently patted him down. Miguel was wearing work pants and a thin nylon jacket over a long-sleeved work shirt, the type of loose-fitting clothing that could easily conceal a recorder or transmitter. Finding nothing suspicious, Rico stepped back, staring at Miguel's midsection. "OK, now take off your jacket and shirt." Miguel removed them and faced Rico. He was wearing a ribbed undershirt with narrow straps over the shoulders. There was a tattoo of a heart with an arrow through it on his upper right arm. Rico lifted the undershirt, exposing a ten-inch diagonal scar across Miguel's stomach just below the ribs. Rico looked up with a smile. "What do we have here, my friend?" "That is from an accident," said Miguel. Rico looked at him for further explanation, but Miguel offered none and pulled the shirt back over his stomach. "OK . . . unbuckle your pants," said Rico. Miguel wasn't expecting a crotch search. He looked at Rico for several moments in defiant contemplation. "Do you think I like doing this?" barked Rico. "Pull 'em down!" Slowly, Miguel released his belt buckle and dropped the pants down to his knees with one hand, revealing a pair of boxer shorts. "Turn around," ordered Rico. Miguel shuffled awkwardly in a circle, holding his pants at his knees, until he had come fully around. Rico, finally satisfied, turned away. Miguel pulled his pants up, refastened his belt, and put his shirt and jacket on. "We must be careful," said Rico triumphantly, stepping behind his desk. "Men are tempted if their circumstances are desperate." Miguel knew the word "we" represented an important shift, and that he probably had Rico where he wanted him. Rico appeared relieved as he settled back into his chair. "These federal cops don't seem to care about what we do. But that could change, and we must be ready." "Yes, I understand," said Miguel, sliding his jacket back on and returning to the chair. "Now we can talk freely," said Rico. "Do you want some coffee? A beer?" "No, thank you." "So, what do you have in mind?" "Perhaps I could buy a couple hundred documents to start—green cards and social securities. I believe I could sell them quickly." Rico could feel his reservations melting away. This fellow was a leader—no posturing or game playing. He almost felt complimented that Miguel would come to him. If this deal worked out all right, perhaps he would hire him to keep the wild Mexican vendors in line. He opened his top desk drawer and removed a copper box of cigarettes, opened the lid, and pushed them toward Miguel, who politely declined. Rico quickly lit a cigarette and exhaled a line of smoke. "Do you have the money already?" asked Rico. "How much?" "Let's say nine thousand. I'm giving you four hundred documents altogether, when you include the social securities. Those two hundred sets are worth at least thirty or forty thousand on the street if you do it right. You'll quadruple your money. But you have to stay away from where my people are working on Cermak and Twenty-Sixth Street." "As I said, I would not work openly on the street. But I was hoping the price would be a bit less," said Miguel. Rico broke into an open smile that clearly showed his deformed lip. "Where did you get that idea?" he asked. "If this becomes a regular thing, I can drop the price some." "By Wednesday of next week I will have the money. Is Thursday all right with you?" "It doesn't matter to me what day." Rico scribbled a note on a calendar that lay open on his desk. "I've put you down for ten in the morning on Thursday, September 27." "OK." "Use this number if you need to contact me." Rico pulled a business card from a plastic holder and flipped it to the front of the desk. "But don't say anything about the documents when you call. If you do anything stupid like that, the deal is off." "Of course," said Miguel, who looked briefly at the card and shoved it into his jacket pocket. "One other thing," said Rico. His small eyes had gone hard and cold as he leaned forward and clasped his hands together on the desktop. "If I ever find that you're working against me in any way, I won't hesitate to do what is necessary to you, your family, anybody close to you. Do you understand?" Miguel had no doubt that Salvador Rico meant what he said. He was looking at a man who had probably killed and would kill again. "Yes, of course," said Miguel. "I understand very well." * * * Hayden had chosen a remote section of Lincoln Park for the debriefing—down a winding, tree-lined road to a deserted parking lot. Shortly after leaving El Palacio, Miguel drove into the lot, making sure he wasn't followed, and joined Hayden and Kane in Nick's Firebird. It took him only a few minutes to report what had transpired in the meeting with Rico. Though both agents were pleased, Hayden's reaction was subdued. The prosecutor with the US Attorney's Office had requested that an undercover officer accompany Miguel to meetings with Rico, but the agents had explained that trying to involve a person Rico had never met would probably kill the deal before it got started. Fortunately, they had been able to convince him that one large purchase by Miguel would be sufficient, as long as it was tape-recorded. The agents had provided Miguel with a set of license plates that, if checked, would come back to a "Miguel Luna" at the address of a large apartment building with hundreds of residents. They had also made sure through surveillance that Miguel would find Rico alone in his office at El Palacio. Had his two subordinates been present, it would have been more difficult, if not impossible, for Miguel to establish a personal relationship. Nieto and Pinal would probably be at the next meeting, but the agents thought it was likely that Rico, now apparently comfortable with Miguel, would not allow another awkward search of a man he wanted to hire. After meeting with the agents, Miguel took the long, slow way home—west to Ashland Avenue, and then south, where he would encounter sluggish traffic and lights at every other corner. It was a pleasant day to take a leisurely drive, and he was working the graveyard shift at the plant, so there was no hurry. He rolled down the window, and a gust of warm air blew in. Although Miguel had tried to ignore it, a sense of unease was building. He had told Carmen very little, stating vaguely that he would help INS from time to time in their investigations and his identity would be protected. The agents would always be there to make sure he was safe, he'd assured her. Paco knew only that his father was friendly with the agents and that the family was allowed to stay—mainly because of Mr. Hayden. Rico's threats came as no surprise to Miguel. In his younger days, before he'd found the Lord and started a family, they wouldn't have fazed him in the least. But now he was a man with responsibilities, and everything he did had repercussions for his wife and children. In that light, threats from the lips of a person so utterly devoid of conscience were disturbing. His palms grew damp and thoughts of a hasty departure passed through his mind. They could, after all, return to Mexico and enjoy relative peace, if not prosperity. But he knew instantly that this seemingly reasonable thought had sprung out of fear. He could not allow fear to overrule whatever plan the Lord had for his life. Miguel glanced up at his rearview mirror and noticed a silver-and-black sedan driven by a swarthy man with a black beard. The man seemed to look away as soon as Miguel noticed him. Perhaps Rico was having him followed. Coincidentally, he was on the same stretch of Ashland Avenue where Hayden and Kane had followed him just weeks earlier. Then, abruptly, the suspicious man wheeled into the left lane, roared past him, and turned into the parking lot of a Middle Eastern restaurant, where several yellow cabs were parked and a small group of men had gathered. Miguel slowed and watched the man jump out of his car to greet the others. He was wearing a white sarong that hung like a skirt to his ankles. Though relieved, Miguel felt foolish. Paranoia, it seemed, was a price he would have to pay to remain in this country. He continued slowly down Ashland Avenue. People were moving purposefully all around him—workers filling potholes with fresh blacktop, masons tuck-pointing the wall of an apartment building, cab drivers ferrying passengers to their destinations. He enviously imagined their lives as uncomplicated, free of worry—anonymous players in the grind and bustle of a vibrant city. Meanwhile, _he_ was risking everything—leading his family into a potential crisis they knew nothing about, the outcome of which could be disastrous. Less than an hour earlier he had been cool and unruffled, even while meeting with a man who wouldn't hesitate to kill. Now his hand was trembling as he pulled it away from the steering wheel. He had never seen his hand shake like that, even in his heavy drinking days. Miguel had left the North Side and entered an area of public housing—scruffy bars, liquor stores, and abandoned buildings. He drove a bit faster and within minutes was back in the familiar Pilsen neighborhood. He turned onto Francis Street and pulled slowly into the shade of the elm trees in front of his home. Miguel shut off the engine, closed his eyes, and began to pray—asking forgiveness for his imperfect faith. He believed that only by God's grace had he and his family found their way here, to this secluded little street that seemed protected—an island of tranquility. He was convinced that he had been led here as part of a divine plan. As Miguel sat quietly, a feeling of deep peace gradually swept over him. # 13 Rico drove his Volvo slowly through rows of empty vehicles and pulled in a few spaces away from a black BMW. It was their usual meeting place—the parking lot of a dreary shopping center near Midway Airport. He shut off the engine and watched cars entering and exiting the lot from Cicero Avenue. He'd recently sensed that he was being followed, though he had seen nothing to give credence to his suspicions. So far, it was only a feeling. Rico left his car and strolled to the BMW. He'd removed his heavy gold chain and expensive clothing and was now wearing gym shoes, baggy pants, and a black T-shirt—a more subdued, working-class look. When he slid into the front passenger seat, Byrd muttered a cool greeting and sat stiff and silent, like a spurned lover. FBI agent Jerry Byrd wore his hair in a military-style crew cut and was dressed casually in a golf shirt and blue jeans. Although the agent was in his early forties and had been with the bureau for eleven years, to Rico he seemed naive—willing to accept at face value that Rico was no more than an ordinary, law-abiding citizen who held down a dull job as manager of El Palacio. Byrd hadn't even asked for proof of Rico's spurious claim to being born in Puerto Rico. Months earlier Rico had dropped the Bautista drug case into Byrd's lap, and the seizure of twelve kilos of cocaine had no doubt enhanced the agent's career and professional reputation, though Byrd had done little more than execute a search warrant. Rico had benefited as well, collecting a ten-thousand-dollar reward, which he promptly invested in a large purchase of counterfeit documents. Now Rico was stringing Byrd along for protection and inside information. But today something seemed to be bothering the agent. "You haven't been keeping in touch," said Byrd irritably. "I didn't _have_ to give you that much money for Bautista, you know. Part of it was like a down payment. I've been waiting to hear more . . . about your new friends." Rico was momentarily at a loss. New friends? Then he remembered he'd spoken cryptically in their last meeting of "getting close" to a group of Colombian drug dealers who frequented a bar on Montrose Avenue. "I been working on this. These guys big," said Rico. "They no deal five or ten kilos like Bautista. They sell thirty, sometime fifty." "Now we're getting somewhere," said Byrd, his mood brightening. "They competitors to Cali organization." "They have names?" "I have only nicknames—one is El Flaco. Another El Gato. But no way I get last names yet. They very careful. I try to get license plates." "Why are they willing to talk to you?" A jet roared loudly overhead. Rico, looking at the sky, waited for the noise to pass as he thought it over. Perhaps it was time to take another risk—throw a line in the water to see if Byrd was as indiscreet as he was gullible. "I help them get documents. You know, the fake documents," said Rico, pausing to observe Byrd's reaction. "I hope is not problem, OK?" Byrd didn't look away or register an unusual reaction. "I'll cover for you this time," he said. "But from now on you can't break the law unless I say it's OK in advance." "I no can be too clean. They don't trust. I only help them . . . to get close." "Don't worry about it. In the meantime, see if you can get those plate numbers and more information about them." Rico decided to probe further. "INS—they have cases on who sell the documents?" he asked, as though the thought had just occurred to him. Byrd flashed on the image of his occasional drinking buddy Lou Moretti and smiled. "No, those bozos are too busy picking up Mexicans at factories. They may get to it in the next century." "I no hear about these things," said Rico. "You don't have to worry about falling into their net because the government doesn't _want_ a net. They have a few hundred agents scattered around the country to round up millions of illegal aliens. There isn't time to look into counterfeit documents," said Byrd, who began to chuckle at what seemed the hopeless absurdity of the INS mission. Rico joined in, amused with the irony of Byrd confiding in him about the immigration mess, and relieved to hear that INS wasn't even working document cases. Jerry Byrd was convinced that Rico's new case would boost his career even more dramatically than the Bautista case had. It was now clear how to proceed. He would ignore Interpol's request for a better set of prints on Rico. What was to be gained by digging further? If it were found that Rico was wanted in another country or had lied about his place of birth, he'd not only lose a good informant but also the Bautista conviction might be reexamined. The fact that he hadn't thoroughly vetted Rico before registering him as an informant would tarnish his reputation and career prospects. And now that Rico was promising another high-profile case, there was plenty to lose in discovering anything incriminating from his past. As it grew darker outside, Byrd and Rico exchanged final pleasantries, neither paying attention to the Camaro with tinted windows at the other end of the lot. At that distance, about a hundred feet away, they couldn't see the binoculars as Tom Kane lifted them to his eyes. * * * Rico lit a cigarette and stared dully across the desk at Felix Pinal, who wore a tan safari jacket with epaulets at the shoulders, black jeans, and cowboy boots. He could have been a photographer covering a foreign war. A few months earlier, Pinal had come into El Palacio looking for a set of documents, and Rico had hired him on the spot. Pinal had attended university for a time in his native Venezuela and spoke with the smooth articulation of an educated man. He was not large—medium height and slender, clean-shaven, hardly an intimidating physical presence. But he was useful in handling administrative tasks, keeping track of the documents, and making deliveries to vendors—an obedient foot soldier. On the other side of the room Rosario Nieto was sitting on the sofa against the wall, his muscular arms closed across his chest. He was one of the largest Bolivians Rico had ever seen—well over six feet tall, with broad shoulders tapering to a thin waist. He wore a blue denim jacket, jeans, and sharply pointed, alligator-skin cowboy boots. Nieto had a classic Indian face: the skin a deep bronze, and flat, high cheekbones. Life's subtleties glided past Nieto's lethargic eyes, as though what appeared to the rest of the world in color was to him a dull monochrome. There was an absence of both joy and fear. He'd confided to Rico early on that he'd been involved in the cocaine trade in Bolivia, ended up on the wrong side of a heated drug war, and fled the country. Now he was Rico's enforcer. The death of Marcos Ortega had paved the way for Rico's alliance with a team of flamboyant street vendors. Unlike Marcos, Rico had no benevolent ideas of keeping prices down. He kept his vendors happy by allowing them to charge whatever they could get. What was the point of controlling supply if you weren't going to take advantage of it? Once he'd set up shop in a corner of El Palacio, the street traffic gave a huge boost to the bar, which had been on the brink of going broke. Rico's customers would stop for a beer or two, and word got around. It was no longer just a seedy watering hole for winos to idle away the hours. When the money started rolling in, Rico had paid for a thorough remodeling of the bar. Rico was dressed in dark colors, his silk shirt opened at the top to reveal several sparkling gold chains around his neck. He told Pinal to get on with the weekly ritual of announcing income figures for the previous week but was distracted and hardly seemed to listen. He puffed hungrily on the cigarette until the ember was burning hot. When Pinal finished, Rico opened a side drawer, pulled out a silver stainless-steel semiautomatic handgun, and placed it on the middle of the desk. "I want you to start carrying this, at least when you're around here," said Rico. "I thought that's what he was for," said Pinal, nodding toward Nieto. "He's not always here," said Rico seriously. "Besides, if somebody tries to take us down, they're not coming in with just one guy. We need all the protection we can get." Pinal picked up the gun and with his thumb pressed the release button that dropped a loaded magazine from the bottom of the handle and into his left hand. He placed the magazine on the desk and pulled back on the slide, sending the one remaining shell flying into the air. He caught the shell with his right hand, looked into the empty chamber, and blew through the cylinder. "This is almost brand new," he said admiringly. "Looks like you don't need Rosario to show you how to use it," said Rico. "No, my father had a large gun collection." Rico crushed his cigarette in the ashtray and turned toward Nieto. In the dimness of the room Nieto didn't notice the intensity in Rico's eyes. "So, how are we doing on Twenty-Sixth Street?" asked Rico. "People are coming in from Wisconsin and Michigan just to buy documents from these guys," said Nieto. "There was a gang of farm workers yesterday who came up from southern Illinois. Word has gotten around. It keeps getting better." Rico ignored what Nieto thought would please his boss. "I hear your boys are still acting up and drawing a lot of attention. I thought you were going to talk to them about that." Nieto stiffened a bit. "I did. They do what they want when I go away. They're just wild Mexican kids." "Those wild kids are supposed to be frightened of you! I hear one of our boys flashed himself to a carload of young girls last week." Rico paused and glowered at Nieto, who remained silent. "That is the kind of thing that could put us out of business." Nieto said nothing. It was the best way to handle Rico's occasional eruptions. "Anyway, I might have somebody who can help us down there," said Rico. "An older Mexican guy." Rico waited a moment for some reaction, but Nieto and Pinal remained silent. "He's coming back here next week, Thursday morning, to pick up two hundred sets of documents—green cards and social securities," said Rico. He nodded at Pinal. "Have them ready. And I want both of you here. He might be working with us, so I want you to meet him." "What do we know about this guy?" asked Nieto. "What do we know about any of them?" said Rico indignantly. "I did some business with him a couple of years ago." "Did you go to him, or did he come to you?" asked Nieto. "What's wrong? You afraid he's an informant for the government?" "We have to be careful." "Careful?" said Rico, exasperated. "I hired you, didn't I? Don't tell me about being careful. Anyway, they aren't working phony document cases. I have it on good authority. If it makes you feel any better, I checked him for a wire when he was here last week." "Maybe we should check him again Thursday," said Nieto. Rico grimaced. He knew Miguel wouldn't like it. On the other hand, what would it hurt? To hell with him if he didn't like it. "All right. We can pat him down again." After a long silence, Pinal spoke up. "We've never discussed exactly what we'd do if somebody tries to rip us off or we find out he's an informant." Nieto began laughing softly and looked toward Rico as if the question were preposterous. Rico's eyes narrowed and his mouth crinkled into a wry, contemptuous grin. "I didn't think it was _necessary_ to talk about it." # 14 It was another unseasonably hot day. Warm air that smelled vaguely of mold and sewage was being pumped through vents in the fraud unit. The building maintenance department had been contacted, but didn't seem in a hurry to address the issue. It made everybody irritable, especially Kane, who was fuming about the latest bizarre decision to come out of the Board of Immigration Appeals—as always, it seemed, destroying what remained of practical enforcement mechanisms in the immigration laws. Cursing loudly, Kane tore a copy of the decision into little pieces and tossed them into the wastebasket. Hayden tried to ignore the tirade. Three other agents in the unit, who knew that when Kane was angry he was like a gorilla on steroids, quietly slipped away. The phone ringing silenced Kane and zapped some of the tension from the room. Kane grabbed the receiver and listened, then nodded toward Hayden. "It's for you—Interpol." Though they had agreed not to put a close tail on Rico, Hayden was pleased that Kane had recognized Jerry Byrd as an FBI agent he'd met in Moretti's office a few months earlier. Byrd was part of a drug unit the bureau had recently set up, so it was assumed he was using Rico as an informant. Contacting Byrd, they agreed, was out of the question. An FBI agent couldn't be trusted to do anything but protect his own turf and wouldn't be above spiriting Rico out of town, or even trying to take over the document case and claim it as his own. But Hayden thought it possible that Byrd had checked with the Interpol office in France for outstanding warrants when registering Rico as a confidential informant. Perhaps Rico was using a different identity with Byrd. There was nothing to lose, so Nick had left a message for Interpol agent Ken Vogel, formerly with INS, requesting that he verify whether Byrd had done a record check in the past year on Salvador Rico or anybody else. "I looked into it," said Vogel. "Byrd sent in a bad set of fingerprints on Salvador Rico several months ago, so we sent them back and asked for another set, but we've received nothing so far." "My information is that Rico might be from Panama, even though he claims he was born in Puerto Rico," said Hayden. "I have no idea what his real name might be." "We don't have that many fugitive warrants out of Panama right now. About how old is Rico?" "Midthirties, I'd say." "Hang on a second. Let me see what I can pull up on our database." Vogel took a minute to search his computer before coming back on the line. "OK, I've got a couple of guys in that age bracket from Panama. Does your guy have any identifying marks or tattoos?" "He's got a slightly deformed upper lip," said Hayden. There was a brief pause as Vogel reviewed information on his screen. "Well, one of these guys, name of Liriano Solis, has what is referred to as a 'cut scar' on his lip, but it doesn't say if it's upper or lower." "Do you have a photo of Solis?" asked Hayden. "No photo, sorry. A lot of this stuff from Latin America is incomplete." "What's Solis wanted for in Panama?" "Murder and armed robbery. Looks like he and his pals knocked off a bank in Panama City about four years ago. Somebody must have gotten killed." Hayden's heart was thumping. "You still there?" asked Vogel. "Do you have any details about the bank robbery?" "No, we'd have to request reports and photos from Panama." "I guess it's still a long shot, but I could use that stuff by next Tuesday. We've got a deal planned with Rico for next Thursday." "I'll try to get our contacts in Panama to send it directly to you instead of coming through our office. That'll save a few days." "I appreciate it, Ken. Listen, I have a concern about what Byrd would do if he found out." "I'll keep it quiet," said Vogel. "Just let me know if you make an arrest." Hayden hung up the phone and glanced around the squad room, which was still deserted in the wake of Kane's outburst. Kane had left too, probably to get coffee in the cafeteria. Hayden felt an impulse to get out of the office to consider the new information alone. He could fill Kane in later about his conversation with Vogel. Nick scratched out a message saying he had something personal to take care of, placed it on Kane's desk, and made a clean getaway. Outside it was very humid, and a cloud of copper-colored exhaust fumes hung over the city. Hayden pulled out of the garage and onto the Dan Ryan Expressway, where he was immediately engulfed in a sea of fast-moving traffic: cars, trucks, and buses, all careening down the highway in the late afternoon rush hour. Feeling trapped, Hayden forced his way across two lanes of traffic, evoking honks and gestures of outrage from other drivers for not staying with the pack, and headed down the exit ramp. Relieved to escape the madness, he took a deep breath and drove slowly toward Eighteenth Street. By the time he turned the corner onto Francis Street, the haze had thinned a bit, and there were traces of blue in the sky. A breeze passed in soft waves through the elm trees on the parkway. It was so serene and quiet that it was hard to believe he was still in the heart of a throbbing metropolis. Paco was home, and the two of them played catch in the empty lot next to the house. Hayden threw balls high into the air, and Paco deftly snagged nearly all of them. Miguel soon pulled his car up slowly to the curb. As he walked toward them, his face opened into a broad smile. "What a good surprise, Mr. Hayden," he said. "You stay for dinner?" "Thanks, but I don't have time, Miguel. I need to talk to you." " _Hijo_ , go upstairs," said Miguel to Paco. "Tell your mother I come when I done talking to Mr. Hayden." Paco, disappointed, walked slowly away. "We'll play again soon, Paco," said Hayden. "I can see you're a good player." Paco smiled shyly and went inside. Hayden and Miguel settled in on the porch, facing the empty schoolyard across the street. "You should come more often, Mr. Hayden. You always welcome." "I know, Miguel. I appreciate it." "You are like hero to Paco. He knows because of you, we no hide. He is old enough that he understand." "You deserve credit for that, not me. He ought to know that." "Maybe some day he know, but not now. Even Carmen not understand all these things. Is better they not know." "I guess you're right. They'd worry, especially Carmen." They sat silently for several moments. "Is reason you come now?" Miguel finally ventured. Hayden looked at Miguel seriously. "You don't have to do it, you know." "You mean with Rico?" Nick nodded. "He won't hesitate to hurt somebody if he feels threatened. I'm not trying to scare you, but you have a right to know." "No, I do this. I know he is person who would kill. He no have respect for life," said Miguel. "Is sad thing to see—a man lose his soul." "It's not your job to reclaim his soul, Miguel." "Maybe the Lord want this." Hayden looked at Miguel as if he were naive to believe such a thing. Miguel smiled. "You not religious man." Hayden paused. "Not like you," he said finally. "I not worried about this thing we do. I have doubt before, but no more. I have faith it happen as God wish." Neither spoke for a few minutes. At the far end of the schoolyard, a few children kicked a ball around, their cheerful voices echoing off the brick walls of the school. Nick felt no more comfortable than when he'd arrived, but could see no way to stop the momentum of the case and Miguel's role in it. He told Miguel he would be in touch. * * * Within minutes of leaving Francis Street, he merged back into the noisy chaos of the city. Hayden drove over to Twenty-Sixth Street to observe the vendors, scribbled notes about their locations, and did the same on Cermak Road. As dusk set in he headed north out of the Pilsen area and stopped at a Chinese restaurant on Division Street. It was a good place for eating alone, as it was never very crowded. Smooth, synthesized music was piped in over the speaker system. American songs he had never liked seemed more innocent and appealing with the singsong intonation of the Chinese singers. The restaurant was staffed by pretty, smiling waitresses who could barely speak English and seemed not to have a care in the world as they glided past the tables with steaming plates of food. From his table, Hayden watched the Chinese cooks through the open window into the kitchen. He figured that they, too, were probably illegal, having traveled thousands of miles through God knows what sort of horrible conditions, so that they could labor in a blazing hot kitchen for little money. Yet they appeared happy. His thoughts gradually drifted to a grim reality. He was an INS agent, sitting in a restaurant staffed by illegals, in a city teeming with illegals of every conceivable nationality, looking for a way to extract Miguel, another illegal, from a looming crisis—a crisis he'd personally engineered. He now wished he'd gone along with Kane's suggestion to pick a few document vendors off the street and declare victory. But he knew his problems extended far beyond the Rico case. If he'd not allowed compulsive curiosity about his father to alter his career path—if he'd been reasonable and less emotional, he would likely be practicing law in the comfort of well-furnished offices and courtrooms. It seemed that almost everything in his professional and personal life was out of sync and out of control. He thought of Miguel's faith in a higher power, which until recently he'd dismissed as wishful thinking. Yet suddenly the idea of a random, godless world was a depressing notion to contemplate. He finished the fiery kung pao chicken, left fifteen dollars to pay the ten-dollar check, and headed back to the office. * * * As Nick had hoped, the office was deserted when he arrived at eight o'clock that evening. There was much to do in preparation for next week's operation, and it was easier to concentrate without phones ringing and other interruptions. He spread out the photos of street vendors on his desk and sketched out a crude map identifying their locations. It was now dark outside. As he looked out the window, he could see the lit-up offices in the other federal building across the street. Most of the building was unlit, but cubicles of light would snap on and off as the cleaning crew moved from one office to another. From this distance the workers were indistinct, though he could make out their powder-blue uniforms. They, too, were probably illegals, he concluded, just like the cooks at the Chinese restaurant. Wherever he went, even to government buildings, there seemed to be no escape. He tried to ignore them, recalling one of McCloud's dictums: "Looking at the big picture will drive you crazy. Just think about the case you're working on." He'd found that approach useful early in his career, but he now wondered why the hell he _shouldn't_ think about the big picture. Hayden sorted through the photographs, picking out the ones to be given to agents on the day of the operation. He pulled the desk lamp closer and was using a magnifying glass to make out the blurred face of one of the vendors, when he heard the murmur of voices and the scuffle of shoes in the hallway. " _A la derecha_ . . . in that door," said a deep male voice. The handcuffed prisoners shuffled in through the door at the far end of the room. There were six brown-skinned men, looking tired and disoriented, wearing heavily soiled work clothing. From across the room Hayden could smell the grease and sweat. He guessed they had been working on an assembly line in a manufacturing plant. Phil Denton, a tall, businesslike agent wearing a wrinkled gray suit without a tie, entered the room behind the men. As always, he sported a toupee that looked like a flattened Brillo pad. A good-natured sort, Denton took a lot of heat for the toupee, but he didn't seem to care. "You guys sit down there. _Siéntese alli_ ," he said, pointing at the metal radiator that ran along the wall. Slowly, awkwardly, the men sat down, the stainless steel cuffs clinking noisily. Four women came next, also handcuffed together. Three of them were very young, probably teenagers, and looked at Hayden shyly. They too had been sweating, and their hair had become matted and stiff as it dried in the night air. One woman, much older than the others, looked woozily at the floor with half-closed eyes. The women sat on the radiator next to the men and were followed into the room by another agent, Henry De Rosa, a short, stocky man with dark features who rarely spoke and seemed to believe that his job was to act as Denton's chauffeur and valet. He stood silently at the doorway. "I saw your light on up here, Nick," said Denton. "We picked 'em up out in Joliet about an hour ago. We could use something to eat before getting 'em to jail for the night." "Want me to watch 'em for ya?" asked Hayden. "Yeah, if you don't mind. We'll run across the street and bring something back," said Denton. As Denton and De Rosa left the room, Hayden thought it fortunate the prisoners were cuffed and tired. They weren't going anywhere, so he could return to his work. But moments later a soft voice called out in Spanish. "Excuse me, sir. Could she have some water?" It was the young man sitting closest to the older woman, who was now swaying slowly back and forth. "They'll be back in a few minutes," said Hayden in Spanish. "They'll give you water." Nick was about to go back to his work when he looked at the older woman more closely. Her eyes were closed, her mouth slack and partly open. Her swaying stopped, and she leaned heavily against the young woman next to her. She appeared close to fainting. Perhaps it was the quiet intimacy of the office at night. There was none of the usual office noise and activity that created an invisible barrier. Hayden studied the whole group, one by one. On the surface, they appeared no different from any of the thousands that had come before. Yet they _were_ different now. Hayden picked up the cup of lukewarm coffee from his desk and walked over to them. "You're all from Mexico?" he asked, looking at the man who had called out. "Yes, Mexico," said the young man with a smile that revealed several missing teeth. The outer edges of his two front teeth were lined with thin bands of gold. "When they took us, we had no break for four hours, and it was very hot in the factory. They let us go to the bathroom before we left, but we had nothing to eat or drink." The older woman seemed unaware that Hayden was standing in front of her. He knelt down and held her left shoulder to steady her. Her eyes came partly open, and she said something in slurred words that he couldn't understand. "Here, drink some of this," said Hayden, lifting the cup of coffee to the woman's mouth. She took a sip, then eagerly took hold of the cup with both hands and tilted it to drain the remaining coffee. It seemed to revive her a bit, and she looked up gratefully at Hayden. Nick stepped into the hallway and went to the drinking fountain to fill the empty coffee cup with water. When he returned he gave the cup to the woman and she drank it eagerly, some spilling down her chin and onto the floor. She handed the cup back to Hayden and glanced at the water on the floor. "I sorry," she said, and dropped to the floor on her knees. She wiped the wet tiles with the shirtsleeve of her unshackled hand and smiled weakly. "That's OK," said Hayden. "Don't worry about it." Hayden made several trips to the hallway drinking fountain and was filling the cup again when he heard the elevator bell and the low voices of Denton and De Rosa. When Denton turned the corner, he saw Hayden at the fountain and was instantly concerned about his untended prisoners. "What's going on, Nick?" he asked. The two were carrying white bags, and the aroma of hamburgers and fries filled the hallway. "They're all a little dehydrated," he said. Denton and De Rosa walked around him into the squad room but offered no comment. When Hayden returned, the two agents were sitting at a desk, munching away silently. Hayden brought the cup of water to the last Mexican in line, a middle-aged man who sat looking at the agents, his face weathered and sad. The agents watched Hayden curiously as he handed the cup to the man, and an awkward silence enveloped the room. Hayden knew what Denton and De Rosa were thinking. He'd intervened in something that, according to accepted protocol, was none of his business. He thought of Denton as a good professional, not remarkable in any way, but a solid, reliable agent. He was neither overly aggressive nor too soft. If Denton had been aware of the woman's condition, he too would have provided assistance. Yet he no doubt found Nick's concern and involvement excessive. It took so little to arouse suspicion. "They won't give them anything to eat at the jail until morning, but water will help a little," said Hayden. There was a silent pause as Denton and De Rosa looked at Hayden and kept eating. "One of the women here almost passed out after you guys left." Denton grunted disgustedly at what he took as implied criticism. "The women always want special attention," he said. "They play games." Hayden let the remark pass. He'd said exactly the same thing himself when dealing with women detainees. He returned to his desk with an empty cup and tried to go back to work but couldn't keep his eyes off the Mexicans, who now seemed as interested in Hayden as he was in them. They could feel the unspoken tension between Hayden and the other agents. Finally, Denton and De Rosa finished eating and rose from their chairs. "OK, let's go," said Denton. The Mexicans stood up, their handcuffs clinking together, and began trudging toward the door. It reminded Hayden of his recurring dream of faceless people in the desert. But unlike the dream, he could see these people clearly, their eyes, their expressions—each a distinct, individual presence. He felt a subtle shift, as though a ray of penetrating sunlight had awakened something deep inside him. As they staggered out, the older woman looked back at Hayden, smiled feebly, and gave a short wave of her hand. Hayden nodded and lifted a hand in response. As the Mexicans disappeared out the door, Denton and De Rosa both glanced curiously back at Hayden. He listened to them make their way down the hallway and into the elevator. Alone again, Hayden peered out the window at the cubicles of light and the blue-clad figures methodically going about their work. # 15 A large envelope covered with bright yellow Panamanian stamps was on Hayden's desk when he arrived on Tuesday morning. He removed the contents: a report on the bank robbery, a two-page rap sheet, and mug shots of Liriano Solis. Hayden had seen Rico only once during surveillance from at least thirty yards away, but Kane had taken photos of him. Nick spread them out on the desk, along with a copy of Rico's driver's license, which had a blurry photo. There was no question: the rounded features, thick eyebrows, and small, flat eyes. Especially telling was the curvature of the upper lip. He wasn't surprised. It made perfect sense that Rico would have a criminal past, though confirming it certainly raised the stakes. He flipped back to the rap sheet and found that Solis had been arrested for numerous petty thefts, armed robbery, and burglary. The final entry was the most serious—the warrant for murder that Vogel had mentioned in connection with the bank robbery. Hayden knew, however, that if anybody had been killed during a robbery, all those participating would be charged with murder, regardless of who pulled the trigger. Hayden turned to the next page. There before him was a set of still photos transferred from a video camera mounted above the entrance of the Chase Manhattan Bank in Panama City. The six black-and-white images showed two men. One was running away from the bank and carrying a gunnysack in his right hand, his shoulders bent over as if he were trying to avoid shots fired from inside—a black hood covering his head. The man next to him was aiming a shotgun toward the entrance of the bank. This man's hood had been removed, perhaps to better view his adversaries. In the fourth shot of the series, a barely visible puff of smoke could be seen rising from the shotgun, its muzzle tilted up at a forty-five-degree angle from the recoil. Though the photos were blurry and taken from a distance of at least forty feet, he could see that the man carrying the shotgun was the same person known in Chicago as Salvador Rico. The three-page report of the bank robbery stated that the getaway vehicle was cornered by a police roadblock just minutes after leaving the bank. The driver and another of the bandits had been shot down in a hail of bullets and the money recovered. But Solis had rolled out of the backseat of the vehicle and disappeared into the dense tangle of buildings in the heart of Panama City. The manhunt yielded nothing in the days after the robbery, though it was rumored that the fugitive had fled south into Venezuela. Police intelligence officers were convinced he was still holed up somewhere in his Panama City neighborhood, though frantic searches of suspected hangouts produced nothing. Two days after the robbery, fingerprints on the shotgun identified Liriano Solis as the shooter. Hayden looked over at Kane, who was contentedly munching a donut and reading the morning newspaper. "You need to take a look at this stuff," said Hayden, tossing the Interpol report onto Kane's desk. "I'm going downstairs for coffee." The cafeteria on the second floor of the Federal Building was almost deserted when Hayden took a seat at one of the long tables, far from the cash registers and occasional customers. Since the coffee was always bitter and the collection of day-old pastries unappetizing, there was little activity between meals. Bright fluorescent lights and cheap plastic chairs did nothing to enhance the atmosphere. Still, it was quiet and there were floor-to-ceiling windows for an expansive view of the plaza, which was dominated by an enormous orange metal sculpture by Alexander Calder. Rain fell against the windows as Nick sipped his coffee and tried to absorb the news confirming that Rico was a killer and would be desperate if cornered. Though Panama had no official death penalty, Rico would be keenly aware that prison guards could be counted on to avenge the dead security guard, probably through torture and grisly death. It had suddenly become eerily dark outside. Deep volleys of thunder began to rumble overhead, seeming to shake the building, and rain thudded loudly against the cafeteria windows. The lights flickered off for a moment but almost instantly came back on. Out of nowhere, Tom Kane pulled up a chair across from Hayden. "That report from Panama is priceless," chirped Kane. "The bureau is using a killer as an informant." Kane cackled with delight and rubbed his hands together as though he'd won a pot of money in a poker game. "We've got Byrd by the short and curlies!" "Byrd isn't the issue at the moment," said Nick seriously. "Come on—this stuff on Rico is great." "Great?" "Absolutely. The press will love it, and so will Stark. The magnitude of the case just skyrocketed." Hayden looked at Kane impassively and for a moment felt envious of his partner's blissful approach. "We could arrest Rico right now on a murder warrant," said Nick. "We know where to find him. He could split any time before Thursday." "You mean before the operation?" said Kane, clearly startled by the suggestion. Nick continued. "What if he gets suspicious, decides the whole deal with Miguel doesn't feel right? What if word leaks out about the operation? Byrd finds out, tips off Rico—then what do we have? We lose a killer and end up with nothing but a document case." Kane was incredulous. "You wanna take him down on the warrant and that's it? It isn't just Rico we're after; it's the whole organization! Two more days isn't going to make any difference." "We could still arrest some vendors," Hayden suggested, with little conviction. "Try to flip them on Rico's lieutenants. If they're holding large numbers of documents, we could get the US Attorney to file for possession. That's all they really wanted when this thing started." "So we're supposed to throw away all the work we've done just to arrest Rico two days before we were going to arrest him anyway? Look, we need a criminal prosecution to make our detail a success," Kane said with finality. "I'm not going back to area control without something to show for it. Hell, I might never get out of there again. Stark wants something good, especially since we've briefed him. He's told the front office about it. It's out of our hands now." Hayden stared out the window at the black sky and cascading rain. Kane was right. Stark was salivating at the prospect of a big case going down on his watch. There was no way he would approve of arresting Rico prior to the scheduled operation on Thursday. Kane waved a hand across an invisible plane in front of Hayden's face. "Base to Hayden. You in there, little fella?" he said in a high, mocking tone. "Knock it off, Tom. I need time to figure this thing out." "No, you don't need more time. You're overanalyzing. I know what you're thinking—that Miguel is going in wired and he'll be in danger, and yeah, he will. But I've got a news bulletin for you. That's what informants do." Kane waited for a response, but Hayden looked away and said nothing. "By the way," continued Kane in a lowered voice, "I passed through area control earlier and heard Denton and some other guys talking. I guess you guys ran into each the other night, huh?" "What about it?" Kane leaned forward over the table and whispered. "I'm no shrink, but there's something happening with you, and it ain't good." He paused, hoping Hayden would confide in him, but Hayden, clearly annoyed, stared across the table. It was nothing he could speak candidly about with Kane. "I know it's pretty bizarre, giving them water," said Hayden sarcastically. "It's downright neurotic." "It's not just the thing with Denton," said Kane evenly. "It's ever since we collared Miguel. If you start caring too much about these people, you can't do the job. It's that simple. You're paralyzed." Nick recalled a McCloud lecture about agents caught in the paralysis syndrome—frozen by an exaggerated sense of what might go wrong. That phase wasn't supposed to happen for years, if ever. And though Kane had a valid point, it _wasn't_ that simple. "McCloud used to tell us to never forget these are people we're dealing with," Nick said. "It doesn't mean you can't do what's necessary to get the job done." "OK," said Kane, raising his palms defensively, "but we're getting down to crunch time, and I'm not gonna let a good case go down because of some irrational concern about an informant, so you better get your shit together." Hayden said nothing, knowing his partner had the upper hand. "It's too late to pull back," declared Kane, as he rose from his chair. "Anyway, we have a lot to do to get ready for Thursday." As Kane stalked away, Hayden saw that the rain had stopped and it was suddenly much brighter outside. A column of sunlight slipped through a gap in the skyscrapers, illuminating the wet granite plaza. A few people emerged from buildings, glancing warily at the sky. * * * When informed that Salvador Rico was wanted for murder and armed robbery in Panama, Richard Stark, as expected, insisted that the operation go forward as planned. "We're not even sure it's the same guy," he said. "You can't rely on blurry photos. We'll need prints for a firm ID, and we'll have those on Thursday." Hayden, seeing it was inevitable, kept his silence, and the two agents resumed their preparations. On Wednesday morning they were summoned to Connelly's office to brief him and Stark on the upcoming operation. They split up the briefing—Hayden going over the undercover deal with Rico, Kane outlining the anticipated arrests and searches of document-manufacturing pads in other parts of the city. Everything appeared to be a go for Thursday. Jack Connelly, ninety days from retirement and wary of anything that might disrupt the serenity of his departure, was visibly nervous. "You fellas let Richard know if you need anything," he said, waving a hand toward Stark. "I've told him and the other chiefs that this case gets priority for manpower and equipment." The smell of vodka wafted across the desk. It was more excitement than Connelly could handle in the last weeks of his career, and he'd needed a jolt, even though Stark was for all practical purposes in charge. As the meeting continued, Connelly sat like a spectator watching a tennis match, his head bobbing back and forth between Stark and the agents. Hayden and Kane were relieved when Stark announced that he would remain in the office during the operation. Supervisors in the field were problematic, often feeling the need to show they were in charge, which led to ill-informed decisions. "Call me as soon as it goes down," said Stark with a thrust of his chest. "I'll handle the PR stuff." "And I'll keep Director Farber informed," offered Connelly, glancing at Stark for approval. "He's very interested in this case, as you know." "Yes, that's good, Jack," said Stark with a patronizing grin. Hayden was silently amused. All that was missing was a pat on the head and a cookie. For the rest of the afternoon, Hayden and Kane flung themselves into final preparations. They briefed agents as a group and then each of the three teams separately so that everybody knew exactly what was expected of them. Gradually things died down and the office became deserted and quiet. It was the first chance to consider nightmare scenarios that could scuttle everything and place Miguel in even more danger. By now a lot of people knew about the operation, and the circle of knowledge was likely expanding with each passing minute. "I can just hear them at McGinty's after a few drinks," said Hayden. "We told them to shut up about it," said Kane. "What else can we do? Anyway, a beer sounds good right now." "You go ahead. I want to go over a few things again." "OK. I'll talk to you on the radio in the morning." Kane rapped his knuckles on Hayden's desk and smiled as he swaggered out with a backpack slung over his shoulder. Alone in the office, Hayden continued looking over photos and thinking through the operation. Ten minutes had passed when he heard a slight movement behind him and turned around. It was Joe Willis, who had been forced to retire two weeks before. Though it was highly unusual for Willis to enter a room without loudly announcing his presence, there he was, sitting in Kane's chair, staring morosely at the floor. There were circles under his eyes, and his normally fiery cheeks had gone pale. Wearing one of his familiar black sport coats, he looked more like an undertaker than an agent. "Joe, how long have you been there?" Willis coughed weakly and looked up. "Not long. I was having a beer with Moretti. He mentioned your case." Hayden paused, looking him over. "How are you, Joe? How's retirement?" Willis ignored the question but came suddenly alive. "Hey, listen, I know it's not by the book, but how about I go along with you tomorrow? I'll stay out of the way. It'll be like old times, like the Padilla bust." "It'd be OK with me, but with Stark in charge, there's no way. If he found out, he'd have my badge." That was true enough, but he could also see that Willis was different now—fragile and unsure. Who knew what he might do in the excitement of an ongoing operation? To Hayden's surprise, Willis didn't fight it. "Hmm. I see your point. I guess I shouldn't have asked," he said softly. It was painful to watch him caving in so easily. Willis lifted his eyes pleadingly for a moment, giving Hayden a chance to change his mind. "Sorry, Joe. I'll give you a call to let you know how it went." "No, that's OK. You'll be busy." Willis was standing to leave. "Anyhow, I hope it goes all right," he muttered sadly, and then slipped out the door like a ghost. By the time Hayden left the office, a light rain was falling. On the way to the garage he noticed McGinty's was unusually packed for a weekday, but he resisted the temptation to stop. Back at his apartment, he ordered a pizza and watched a baseball game on television in an effort to slow the pace of his thoughts before going to bed. But he didn't sleep well—waking at four o'clock in a cold sweat. It was the recurring dream of marching figures in the desert. Once again, he'd been unable to make contact with them. # Part III # 16 A bank of cool Canadian air had driven away the heat of the extended summer. This was good, Nick told himself. Miguel could wear a jacket without raising suspicion. It would go fine—unless Rico decided to again shake him down for a wire. Nick and Miguel met in the parking lot of a boarded-up auto repair shop on the North Side. A tall, wooden fence surrounded the lot, so they couldn't be seen by the traffic on Belmont Avenue. Miguel parked next to Hayden's vehicle and remained in his car. Nick grabbed the mic from under the dash. "Five-fourteen to five-eleven, I'm getting ready to wire him. How things look over there?" Kane's voice came over the radio: "The Bolivian was looking around, so we all had to move a block away, but Meadows can still see the bar from his position, and we've got units that can see both ends of the alley behind it." Hayden didn't like it. From that far away it could take the agents two or three minutes to get inside the bar. "Ten-four," said Hayden. "It's nine thirty. I'll let you know when our guy is headed for the bar." Miguel slid into the passenger seat of the Firebird and shut the door. "How you feeling, Miguel?" "Good, Nicolas." Hayden had decided not to tell Miguel about the outstanding murder warrant in Panama, Kane having argued that they still didn't have a firm identification on Rico and that such a disclosure could make Miguel more nervous. Hayden finally backed off after convincing himself that Miguel would not have let the revelation deter him. As for being jittery, there wasn't the slightest hint of nerves on Miguel's part. He appeared to be as cool as the autumn air. It took five minutes to make sure the Nagra recorder and a transmitter were properly fastened to Miguel's body. The Nagra was placed in a spandex holder at the small of his back and its two wires were snaked up his stomach to his chest. The transmitter was fitted inside padding just below Miguel's waist, its wire and tiny microphone taped just below his collarbone. This unit sent a signal to the receiver on the backseat of Hayden's car so that he could monitor the conversation. Draped in wires, Miguel looked like a suicide bomber, thought Hayden, and even a cursory pat-down would be disastrous. Baker had told him smaller devices were available, but their quality and range were very limited. Besides, a thorough pat-down would locate a wire, however small. To make sure the equipment was working properly, Nick had Miguel briefly walk around the parking lot and speak. As Miguel got back into the car, Hayden checked his watch. It was nine forty-five. It would take about ten minutes to drive to El Palacio. He reached inside his leather briefcase and removed an envelope filled with cash. "Here's nine thousand dollars in hundred-dollar bills," said Nick. "They're marked." Miguel slipped the envelope into the inside pocket of his nylon jacket. Though they'd been over it before, Hayden again gave instructions on how the deal should go down. "Remember, ask to see the documents before showing him the money. If he asks to see the money first, just pat the inside of your jacket. As soon as they give you the documents and we hear you counting out the money, we'll be on our way in. I'll be listening to everything. If they start to search you, try to stall them. We'll come in right away. And don't forget, we'll make it look like we're arresting you when we come in." Miguel nodded. "I guess we're all set, Miguel." "I have question, Nicolas. I think about this . . ." He paused and looked out the front window, reluctant to bring it up. "Yes? What is it?" "Is OK if I carry gun when I go there?" Though it was reasonable, it surprised Hayden. He had come to think of Miguel as being almost fearless and above such practical considerations. "No, I can't let you have a gun. Why? Do you have one in the car?" "If you go in there like me, would you have gun?" Miguel asked the question with no bitterness, just curiosity. "Yeah, I would, but I've got a badge. We never let informants carry weapons. It's policy, but I don't blame you for asking." "Is OK," said Miguel, turning to face Hayden. "I no think you let me." "We'll cover for you." "I not worried. The Lord protect me . . . gun or no gun." They sat in silence for a few moments. "I go now?" inquired Miguel. "Let me turn the recorder on. Lean forward a little." Hayden felt for the lever beneath Miguel's jacket and locked it into the ON position. "We know Rico and the others are in there, so there shouldn't be any delays." "OK," said Miguel, opening the passenger door. He had one foot on the gravel and one inside the car when he turned to Hayden. "Thank you, Nicolas. No worry. Whatever happen now is God's will." "Right," Hayden said. There was a moment of awkward silence. "Remember, you're being recorded." Miguel shut the door and returned to his car. Hayden could hear his breathing and the rubbing of the microphone against his shirt through the receiver. It sounded like a scuba diver under water. Hayden picked up the mic. "We're on our way. I'll let you know when he's out of his car." A series of ten-fours came back. Hayden followed Miguel east on Belmont Avenue. Mexican music came from Miguel's car radio through the receiver on the backseat, a lively tune featuring a singer wailing about the woman who had left him, though Miguel's microphone was cutting in and out—fuzzy snaps followed by brief silences. Hayden found it unnerving. He'd tested the equipment with Floyd Baker and everything seemed to be working fine, though Baker had warned it could be temperamental. The pace of Hayden's thoughts accelerated. He thought again of the surveillance units, their distance from the bar. He grabbed the mic. "Tom, if Nieto isn't still out there watching, maybe you can get closer." He knew Kane wouldn't appreciate the suggestion. The silence went on for at least ten seconds. "You read, five-eleven?" said Hayden finally. "We can't start moving around now," said Kane coldly. "It'll draw attention." Nick let the statement linger without a response. Kane was right—again. Hayden sat rigidly at the wheel. Everything that had happened that morning sharpened a sense of looming disaster: the receiver connection to Miguel breaking up, the other agents being too far away, Nieto's nervousness, even Miguel's request for a gun. An image came racing through his mind: _Rico tearing Miguel's shirt off, exposing the network of wires, and throwing Miguel against the wall . . ._ The transmitter cut out again, and Hayden looked up to see the Fairlane turning north on Western Avenue. Nick swung into the passing lane, pressed his foot to the floor, and made a squealing left turn just after the light turned red. The scratchy sound of the microphone and music from Miguel's radio again came through the receiver and then, moments later, another dreamlike image arose: _Rico pulling out a semiautomatic and rapid-firing several rounds into Miguel's chest . . ._ They turned east on Irving Park Road. Though it was cool, Hayden had begun sweating. He concentrated on gripping the wheel firmly to prevent his mind from drifting. In a few minutes, Miguel would enter El Palacio. It was out of his hands. Just let it happen, he told himself, but yet another vision flashed through his mind: _Carmen and the children gathered around a crude memorial—photos of Miguel, a cross, and soft-glowing candles . . ._ Kane's voice seemed to shout through the speaker. "Nick, we have an ETA?" Hayden felt like he was sliding in and out of a dream. He could see the Fairlane passing a cemetery in the distance. "He should be there in less than five minutes," he said, surprised at how calm his voice sounded. They went past the cemetery into a mixed commercial and residential area. Miguel turned south onto Sheridan Road, passed under the elevated tracks, and slowed to find a parking spot across from El Palacio, which was on the other side of the street. Moments later Hayden turned onto Sheridan and pulled over where he couldn't be seen from the bar. He watched as Miguel began squeezing the Fairlane into a vacated spot. Suddenly the receiver made a fuzzy snap and the sound of Miguel's breathing stopped. There was a low hum from the receiver that hadn't been there before, as though the connection had been severed. Nick stretched over the seat to check the dials and settings. The needle was in the red zone, meaning no signal. Perhaps the microphone had worked its way loose, though he had been careful to fasten it securely. But it was too late to intercept Miguel to check the equipment without being seen by somebody at the bar. Hayden grabbed the radio mic. "Our guy is parking on Sheridan, but there's a problem with the transmitter." "It's normal for it to cut out here and there," said Kane dismissively. "It'll come back." Hayden watched as Miguel stood next to his car, waiting for the traffic to clear so he could cross the street. He knew there were only a few seconds to decide what to do. He desperately hoped that Miguel's microphone would come alive, but it remained silent. Then, in a moment of absolute clarity, he knew that it was irresponsible to leave Miguel's fate in the hands of Salvador Rico, especially with no way to monitor the deal. He couldn't let that happen. "The transmitter isn't working," said Hayden into his microphone. "We're gonna have to take 'em down right now. I'm going in." A moment later, Rick Meadows called out over the radio: "Hayden's out of his vehicle—running toward the bar! What should we do, Tom?" Miguel had crossed the street and was twenty feet from the bar when Hayden grabbed his shoulder and spun him around. "Get the hell out of here, Miguel. Go back to the meet site!" he shouted. He looked at the window of El Palacio. The curtains had been pulled back, and he could see faces and somebody, possibly Nieto, waving his arm frantically in a warning. He had to get inside before they destroyed evidence or tried to escape. Hayden pushed on the solid wood door, but it opened only a few inches and then hit against something at the bottom. He could hear the shuffling of feet and somebody shouting. Stepping back, he lowered his right shoulder and drove it into the door, feeling bodies being pushed away as his momentum carried him inside. Two young men moved aside, grinning as though blocking the door had been a joke. Chacon, standing behind the bar, looked terrified and didn't move. Hayden, pulling his .357 revolver from the shoulder holster, ran toward the beaded curtain in front of Rico's office. The door, a few feet to the right behind the curtain, was slightly ajar, and there was light coming from inside, but as he pushed through the beads, the light went off. He swung the door open and turned to face Rico's desk, but the darkness stopped him. The only meager light came through the open door behind him. He could barely make out a figure—he assumed it was Rico—sitting behind a large desk at the far end of the room. "Federal officer," Hayden shouted and pointed his gun toward the figure at the desk. "Get your hands up against the wall." The room was silent as Hayden struggled to see through the darkness. There was a shadowy figure standing against the wall on his left, next to the sofa, and another figure against the wall to the right. They stood motionless, facing him, trying to assess what they were dealing with and, perhaps, waiting for orders. He knew they could see him much better than he could see them, as he was silhouetted by the light behind him. A calm voice came from behind the desk. " _Federales_ no do things alone. Who are you?" "I've got a shield on my belt. Turn on a light, and you'll see it," shouted Hayden, trying to fill the darkness with his voice. But his command was met with silence. "I said get your hands up against the damn wall!" Hayden bellowed. As his eyes slowly adjusted, he could see the large figure to his left had his arms folded across his chest: Nieto. And then he could see Rico's head nodding toward Nieto. Hayden instinctively pivoted toward the Bolivian and fell into a crouch. Nieto was moving, his arms rising. Hayden began to squeeze his trigger slowly, not yet committed, aiming at the center of the man, and then an orange muzzle flash lit up the room, and Hayden completed the squeeze of the trigger, firing twice in quick succession toward the gun, and he felt the heat of a bullet searing his left shoulder, and there was a hollow moan and the metallic sound of a gun bouncing off the tile floor, and before he could swing toward Rico, another shot rang in his ears, its reverberations so loud that he thought for a moment he'd been shot in the head. Some force had stopped Rico, who was motionless in the chair, his elbows pinned awkwardly inside the chair's arms. The man to Hayden's right had turned around, placed his hands against the wall and was looking back over his shoulder. "No shoot, please no shoot," the man cried. Hayden could feel a presence behind him and glanced over his shoulder. Miguel stood with his arms lowered, his hands gripping a blue-steel revolver. "Miguel, what the hell!" he gasped. "See if you can find a light switch." Miguel found the switch for the overhead light and flipped it on. Hayden looked back at the motionless figure of Salvador Rico and a black semiautomatic pistol that lay on the desk. "Get Rico's gun, Miguel," said Hayden, as he kicked Nieto's pistol under the desk and out of reach. Nieto was lying curled on his side, his hands pressed into his abdomen, making soft moaning sounds. There was a pool of blood on the floor next to him. Nick turned toward the other man. "Get on your knees and put your hands behind your head," he shouted at the shaking man, who he could see was Felix Pinal. The man instantly complied. Hayden felt alternating sensations of pain and numbness in his shoulder. "Watch him, Miguel," said Hayden, nodding toward Pinal. Nick stepped around the desk to get a better look at Rico. Salvador Rico had been pushed so far into the chair that his feet dangled, not quite reaching the floor, his head tilted back. There was a fresh bullet hole through his left eye. The bullet had pushed the pupil inside his head, and blood flowed from the hollowed socket, across the side of his nose and into his mouth. He had died instantly. Kane and the team of agents charged noisily into the room, guns drawn. Four agents surrounded Miguel Chavez, grabbed the two pistols he was holding, and threw him against the wall, gamely sticking to the original plan. "The semiauto is Rico's," Hayden called out. "There's a gun under the desk, and that guy needs to be searched." Three agents stepped around a pool of urine near Felix Pinal, who was still on his knees. They did a thorough frisk, finding a semiautomatic pistol wedged into the small of his back, and placed him in handcuffs. Several agents surrounded the curled figure of Rosario Nieto, and one of them grabbed Nieto's gun from under the desk. Moments later, Nieto let out a high-pitched moan and went limp. Hayden sat down on the sofa next to where Nieto lay. His shoulder had gone numb, and he was sweating profusely. Kane used his walkie-talkie to call for an ambulance and had Stark call the police. "Looks like both of these guys are dead," somebody called out. Kane helped Hayden remove his leather jacket and could see that the bleeding was steady but not gushing. He yelled for Meadows to get a towel from the bar. "It may not be too bad," Kane said hopefully. Meadows returned and handed a small towel to Kane, who wrapped it around Hayden's shoulder. The other agents padded nervously around the room, frustrated that the action had occurred before their arrival. A bluish haze of smoke had drifted toward the ceiling, and the smell of gunpowder filled the air. The room had quieted, the agents trying to absorb what had happened and unsure about what to do next. Hayden, though woozy, summoned the strength to jolt them into action. "We better leave the bodies where they are so the cops can take photos. Somebody needs to talk to Pinal about where the documents are located." His voice sounded uncharacteristically loose and slack. The other agents looked at Kane for direction. Hayden became angry at their hesitation and shouted, "Somebody get those cuffs off Miguel! He just saved my life, for chrissakes!" Finally Kane spoke. "Yeah, let's see what we can find. I'll talk to him," he said, motioning toward Pinal. "Meadows—take a couple of guys and serve the search warrant on the bartender and look around out there. The rest of you can search this room." Kane called over to Miguel, who was standing against the wall. Miguel walked over, and Kane used a key to undo the cuffs. Kane winked at Miguel. "Just sit here a minute, amigo." Kane sidled up next to Hayden. "Who the hell shot who here?" "I shot Nieto," said Hayden. "Miguel got Rico. They were ready for us." He nodded toward Felix Pinal. "If this guy hadn't frozen, we would have been in deep shit. And thank God Miguel disobeyed me." "Where'd he get the gun?" "Must have had it in his car." There was a brief pause before Hayden said, "Tom, I had no choice when the transmitter went down. I couldn't let Miguel go in like that." "I know. You did what you thought you had to," said Kane. "Anyway, we have to get you to the hospital. I'll take care of things from here." Hayden was very weak and felt he was about to lose consciousness. # 17 Hernan Garza had moved swiftly since his return to Chicago—reclaiming his basement utility room, and then discreetly following Salvador Rico in an old Buick Regal he'd borrowed from a Peruvian friend. To prevent easy recognition by Rico or the Colombians, Garza now concealed his layers of tattered garb beneath a blue nylon jacket that fell almost to his knees. A navy baseball cap and oversized sunglasses completed the makeover. Garza had discovered that Rico was living in a modest apartment building on Paulina Street. He'd twice seen Rico park his car in the lot behind the building and then walk to a small garage across the alley, briefcase in hand. Rico would spend a few minutes in the garage before heading back to his apartment building. Garza suspected that Rico was storing contraband there. It could be nothing at all, but he couldn't resist making at least one attempt to have a look inside the garage before providing information to the feds that would blow the lid off Salvador Rico's lucrative document empire. At eleven o'clock in the morning on September 27, Garza drove down the alley and saw that Rico's car was gone, so he parked and jumped out of the car. Seeing nobody around, he tried to lift the garage door, but it wouldn't budge. On the side of the garage he found a window protected by iron bars and, nearby, a narrow wooden door. He tried opening the door, but it, too, was locked. Going back to the window, he peered between the bars and could make out an assortment of shovels and rakes, a stepladder, and stacks of old newspapers in the corner. The center of the garage was empty, the cement floor covered with oil spots. In the far corner he could see a large metal trunk, the kind that might be used to store tools, its lid fastened with a heavy padlock. The trunk was intriguing. He would come back after he figured out how to get into the garage. Garza drove off, hopscotching through side streets, and stopped at a liquor store just off Diversey Parkway. Behind the counter an old man with pale skin that hung in folds beneath his chin was sitting on a stool, sleepily watching a small television. Garza's hands were shaking as he stood at the counter and struggled to remove a ten-dollar bill from his wallet. "Give me pint Old Crow," he demanded. As the man went to retrieve the bottle, the flashing red lights on the television screen caught Garza's attention. They had interrupted the regular program for a live news report, and he recognized buildings along Sheridan Road. There was a shot of ambulances on the street, and a reporter was talking excitedly about the shooting deaths of two men at El Palacio. Garza thrust his head forward and leaned over the counter to catch every word. The men were purported to be involved in the sale and distribution of counterfeit documents. Two suspects, Salvador Rico and Rosario Nieto, were dead, and another man was under arrest. An INS agent had been wounded. There was a brief shot of paramedics carrying a covered corpse on a stretcher. Garza grabbed the bottle of whiskey, twisted the cap off, and guzzled the flaming liquid so eagerly that some dripped down his chin and onto the floor. "Hey, this isn't a tavern," said the old man disgustedly. "Go outside if you can't wait." Garza stumbled out, dazed, and piled into the Regal. He took another pull from the pint, felt the biting heat through his chest, and let the news settle in his mind. His plans were now destroyed. _He_ had wanted to take Rico down. He took another swallow of whiskey, wiped his lips with the back of his hand, and let out a warm belch. Well, it was good that Rico was gone, he reasoned, even if it upset his plans for revenge. He considered that for a moment, and then remembered—the metal trunk! It might be too late. The agents might already be on their way to Rico's apartment and the garage. He would need the bolt cutters he'd seen among the janitor's tools in his basement hideout. * * * It was a quiet working-class neighborhood, most of the homes unpretentious brick two-flats. Maple trees filled with maroon leaves lined the street. Marvin Johnson, clad in overalls and a gray sweatshirt, was kneeling down, spreading mulch into a flowerbed when he heard something behind him. He turned and looked up at Hernan Garza. "Hello, sir," said Garza, bowing respectfully. Garza's appearance—the purplish nose, furtive eyes, and smell of alcohol—set Johnson off balance. He waited for Garza to state his business. "My cousin, Salvador Rico . . . he die today," Garza said, struggling to produce his best English. "I come . . . to get properties." Johnson, a tall, elderly man with a long face, rose from his knees and, towering over Garza, looked down suspiciously. "Died? He was a young man. How did he die?" Garza's heart leapt. The old man knew Rico! "He shot today," said Garza, who quickly crossed himself. "The police shoot him dead. Is on the TV." Johnson had always been wary of Salvador Rico, ever since Rico had approached him six months earlier to ask about renting space in his garage. Rico had offered him fifty dollars a month just to use Johnson's metal trunk to store tools. It was easy money. "How do I know you're his cousin?" asked Johnson, noting the absence of any resemblance between this man and Salvador Rico. "Here—I have letter from Salvador," said Garza, pulling a folded piece of paper from the pocket of his jacket and handing it to Johnson. Marvin Johnson held the paper out as far as his arm would extend, his eyes straining to make it out. He read aloud in a plodding, deliberate manner, "I hereby give my cusin, Hernan Garza, all my properties when I die." An unreadable signature was scratched at the bottom. "Well, you're a pretty lucky guy, aren't you?" said Johnson with a wry smile. As he looked down at Garza, he noticed something hard protruding above the belt at Garza's waist, concealed under the blue jacket. This was the sort of guy you would expect to carry a gun, Johnson thought. He assumed the note Hernan Garza had presented was phony. But somehow the man knew Rico well enough to know about the tools in the garage. Or whatever was in there. When Johnson had parked his truck in the garage ten minutes earlier, he'd noticed cars with red lights flashing in front of Rico's apartment building. Perhaps Rico _had_ been killed. But then another thought came to him. What if the police found drugs in the trunk— _his_ trunk and in _his_ garage? Would _he_ be a suspect, somebody who was cooperating with Salvador Rico to hide drugs or other contraband? He suddenly pictured reporters with TV cameras swarming over his garage, wanting to talk to him. And what would this small but dangerous-looking man do if he refused to let him recover whatever was in the trunk? Johnson's most fervent wish was to rid himself of any connection to Salvador Rico, preferably before anything damning could be found on his property. He had heard of homes being seized if they were used for illegal purposes, and envisioned federal agents brusquely taking over his property. "He put a lock on my trunk. Do you have the key?" asked Johnson. _The trunk!_ "No, no have key," he said. "They take Salvador away. But I have tool to cut." Johnson studied Garza, his eyes shifting between Garza's face and hip. It now seemed clear what Garza was up to. He was probably Rico's partner in crime. And Johnson had a sense that for all his attempts to appear congenial, this little gangster was determined to get whatever Rico had in the trunk, with or without his cooperation. He didn't _need_ to know what was there. If he could get rid of whatever was in the trunk and sever any connection to Salvador Rico, so much the better. "Let's go take a look," said Johnson cautiously. "I bring car in alley," said Garza. By the time Garza pulled in front of the garage, Marvin Johnson had lifted up the garage door. But now something else was bothering the old man. What if Rico wasn't dead, as Garza claimed? Rico would no doubt blame Johnson if the trunk had been emptied, and Rico was probably even more dangerous than this character. If he could only verify that part of Garza's story, he would feel better. "Just wait here a minute," said Johnson to Garza, who stood peering anxiously into the interior of the dark garage. Garza's face fell into an angry scowl. "Why? What is wrong?" "I'll be right back," said Johnson, who trudged off in the direction of the rotating lights. For an instant Garza thought of pulling the .38 and forcing him back, but instead he froze. There might be nothing in the trunk. Things could get ugly, and there were cops nearby. There was no way to stop the old man. Garza looked nervously up and down the alley and back into the garage. Perhaps there was time to get it open before the man returned. Garza opened the passenger door of the Regal and pulled out the bolt cutters. He looked back across the alley, but there was no sign of the man. The filthy bastard was going to turn him in—perhaps tell them about the trunk! Garza walked over to the trunk, heaved the bolt cutters into place, and, leaning his full weight into it, cut through the padlock. Flinging the trunk's cover open, he stared in disbelief at what he saw inside: an innocuous collection of tools strewn over a canvas lining. "Hey, I thought you were going to wait," snapped Johnson, stepping into the garage and around his pickup truck. He saw Garza kneeling alongside the opened trunk, his head hanging over the edge as though he were ill. "Well, go ahead and empty it out," said Johnson huffily, "but you can't stay parked in the alley too long. There's an agent out there who says you'll need to move your car. I said you were picking something up and would be gone in a minute. You were right about Rico. They told me he was killed today. I guess he was involved in counterfeit documents or something like that." Johnson walked out, leaving the crestfallen Garza alone in the garage. He'd been pinning his hopes on finding something useful in that trunk. Now what would he do? He suddenly didn't care if INS came charging into the garage to arrest him. What difference did it make? Rico was dead. He might as well return to Peru. There, at least he didn't have an unreasonable hope for riches, a sort of disease that infected everybody in this country. Garza decided to take the tools that appeared to have some value—a large crescent wrench and a power drill. As he removed them, he spotted something curious. The sharp corner of a piece of paper was barely visible along the edge of the canvas liner. Then he noticed that the liner appeared to be about four inches higher than the bottom of the trunk. He pulled back the corner of the liner for a better look and gasped. It was a crisp hundred-dollar bill. His hands shaking, Garza removed the few remaining tools and pulled the liner away. There in front of him was a thick layer of bills that nearly took his breath away. They were stacked carefully to create an even bed beneath the tools. Garza placed the tips of his fingers on the bills and pressed down to confirm they were real and not some illusion that flowed from booze and self-pity. He pushed them around and could see that they were all hundred-dollar bills, perhaps three or four thousand of them. His heart pulsing with glee, Hernan Garza shoveled the loose bills into a large, black garbage bag he found next to the newspapers, afraid that the old man would return at any moment. He had just put the last of the bills and the bolt cutters in the bag when a voice came from behind. "Hey, you there." The deep baritone voice filled the garage and lifted Garza to his toes as he swung around toward the alley. There, just inside the garage was a huge figure, backlit by the sunshine. It was INS agent Tim Reynolds. "We're federal agents. Is this your car parked out here?" asked Reynolds impatiently. "Yes, sir." "Well, it's blocking that parking lot and we need to get in there," said Reynolds, stepping out from the garage and into the sunlight. Garza didn't hesitate. He threw the heavy bag over his shoulder and walked boldly toward the officer, leaving the tools behind. The agent watched Garza, who brushed against him with the loaded bag as he marched quickly to his car. Reynolds could smell alcohol even before Garza spoke. "I move car, sir," said Garza with a shaky smile. Reynolds peered curiously into the garage and back at Garza, who quickly threw the bag into the backseat and fired up the Regal. Something about the little fellow struck Reynolds as suspicious. He not only had a thick Spanish accent and had been drinking but also was a bit too eager to leave the area. Garza drove slowly forward toward Reynolds, who was standing in front of him in the middle of the alley. Reynolds held up a huge arm for Garza to stop. "Hold up a minute," he called out, and Garza rolled to a stop. Reynolds walked to the car window and leaned over to look inside. His eyes shifted from Garza to the plastic bag on the backseat. "You've been drinking," said Reynolds. Garza gave him a big smile that showed his stained and rotting teeth. "Just a little. I not drunk," he said. Garza dropped his right hand from the wheel to his hip, feeling the gun with the inside of his wrist. A white evidence van had entered the parking lot. Reynolds looked toward the van and then back at Garza. He thought there was a good chance this guy was illegal. Though his English was better than most, he smelled of not only liquor but also fear. Still, Reynolds knew that if he questioned the man about his immigration status, _he_ would be responsible for processing him for deportation. Reynolds guessed he wasn't a Mexican, so the processing would take even longer. He was already busy collecting evidence on the Rico case. Who had time to deal with yet another illegal alien? To hell with it. "Well, drive safely and don't stop for another drink, you hear?" "Yes, sir. Thank you, sir." Tim Reynolds looked on as the Regal drove slowly over dried leaves. Garza, watching Reynolds in the side-view mirror, stuck his hand out the window and offered a cheerful parting wave. * * * Nick's shoulder was throbbing, though he also felt a lingering euphoria from whatever narcotic had been administered, and it infused everything with the hazy texture of a dream. Not yet fully awake, he peered out the window at stars shimmering in an ebony sky. Puffs of gray clouds passed through the sky like sheep moving in the night. He finally turned away and glanced around the room, lit only by a small nightlight next to his bed. The door out to the hallway was partly open, and he could hear the soft padding of feet and murmur of conversations among the nurses down the hall. Though warm, the room had a cool antiseptic feel and odor. A nurse stopped by and told him the surgery had gone well. The bullet had caught the outside of the shoulder and exited cleanly. No major arteries had been severed. He should feel lucky, she told him. His arm and shoulder would be placed in a soft cast and sling. Anxious to regain clarity of thought, he refused more pain medication. Tom Kane arrived at the hospital at about eleven thirty. He let out a grateful sigh as he let his weary body collapse in a chair next to Nick's bed. "I had to badge my way in because it's past visiting hours," said Kane with a weak grin. There was an awkward silence as Kane stared gloomily at Hayden's shoulder, swollen with bandages. "I wish we hadn't been parked so far away," said Kane. "We had to break down the front door of the bar. Somebody locked it after you and Miguel got inside." Hayden was expecting Kane to be miffed. Nick was open to charges that his actions were rash—an emotional response that placed the other agents and Miguel at greater risk. No doubt Kane considered it a misguided and unprofessional concern for the safety of an informant who knew well enough the risks involved. Then there was the matter of Miguel having a gun. Nick recalled that Miguel never answered his question about having a gun. He should have swept the vehicle. Then again, if he had, he'd probably be dead now. "I think I'm awake enough," said Hayden. "What happened after I got carted away?" Kane poured some water from a pitcher on the nightstand into a plastic cup, drank half of it, and paused to organize his thoughts. "Well, Pinal helped us out and that made things a lot easier." Kane reported that Felix Pinal, just happy to be alive, had chosen to cooperate fully. Like many inexperienced criminals, he'd assumed the government knew a great deal more than it did and that he had no leverage. After the counterfeit documents earmarked for Miguel were found in a briefcase under the sofa, Pinal led agents to a removable ceiling panel, and behind it were over ten thousand more documents. He then opened Rico's small safe, located behind a wood panel on the wall, where Rico kept his operating cash, and agents seized $81,000, most of it in hundred-dollar bills, along with two hundred bogus Puerto Rican birth certificates. Pinal said they sold the birth certificates for a thousand dollars apiece and that this part of the business was growing rapidly. Though minutes earlier Kane had appeared exhausted, he was now revived. "You're not gonna believe what else he came up with," he said. Pinal had produced a key to a storage locker Rico was renting under another phony name, and there they found dozens of packages of blank counterfeit green cards and social security cards. There hadn't been time to do a complete count, but the initial estimate was staggering: 140,000 green cards and 100,000 social security cards. Street value: several million dollars. "We ended up arresting about twenty-two vendors around the city and seizing a bunch of manufacturing equipment. The arraignments will be tomorrow." Stark was handling press inquiries at the office and had issued a brief press release. Two suspects were dead and one officer had been wounded. That was all. Once the dust settled and official identification of Rico was received, Stark would hold a press conference and get the word out that Salvador Rico was one and the same as Liriano Solis, wanted in Panama for murder. That revelation would help divert attention from the embarrassing fact that an informant carrying an unauthorized weapon had been the one to kill Rico. "I told Stark that what you did was justified. If Miguel had gone in there, gun or no gun, there was a good chance he wasn't coming out alive, especially with the wire down. Pinal said they had decided to search Miguel again and that Rico would have killed him, destroyed the tape, and tried to make a run for it. It looked like some kind of rip-off when you came in alone—that maybe you were a dirty cop." "And what did Stark say?" "Not much, but I could tell he wasn't happy about what you did. You better watch out. I have a feeling he might come after you. He's going to have to explain about Miguel having the gun. It's not as clean as he'd like it to be." Kane sat silently for a moment, reviewing a day crammed with innumerable details. Then his eyes lit up. "Oh, I almost forgot," said Kane, leaning closer. "Pinal says Rico has a stash of several hundred grand in cash hidden somewhere—maybe more. He would always clear out the safe if there was a substantial amount in there. He says Rico was very careful about not letting anyone know where it was kept. He doesn't think it's in a bank because Rico didn't want to draw attention with large cash deposits. But it's out there somewhere. We searched his apartment and vehicle and came up with nothing except a few guns." Neither of them said anything for a few moments, and then Hayden lifted his eyes toward Kane. "Sorry it all fell on you." "Don't worry about it. It worked out well except for what happened to you. This thing has turned out to be a lot bigger than we expected. We got lucky, first with Miguel and then with Pinal." "Yeah, Miguel was the key. He should get a lot of the credit." Kane finished the water and stood up to leave. "Well, I'm gonna grab a beer and get some sleep. Tomorrow will be busy with all the arraignments." He patted Hayden's outstretched leg. "Thanks for coming over, Tom." "I'm just glad you seem to be doing OK. But I'm going to need your help finding Rico's stash of money, so get out of here as soon as you can," said Kane as he trudged wearily toward the door. "I'll keep you posted." As the narcotic effect wore off, Hayden began to review the day's events. Tomorrow he would check on Miguel—make sure he was holding up OK after a bizarre and bloody day. He realized his own problems were minor compared to Miguel's, whose fate now rested precariously in the hands of Richard Stark—hardly a comforting thought. Nick shifted his position, which shot a bolt of pain through his shoulder, and he rang for the nurse. Then he felt a powerful wave of fatigue and closed his eyes. There were ways to keep Miguel here, even if he could no longer be an informant. Maybe Stark could be reasoned with. By the time the nurse arrived he'd fallen into a deep sleep. # 18 The sun, deceptively pale and white, blazed through a cloudless sky. The road curved west from the Everglades into a vast, desolate landscape of sand, wetland scrub grass, and gnarled cypress trees—no sign of anything man-made aside from the road and a line of telephone poles that looked like weathered crucifixes. After exiting the interstate, Nick had seen only one vehicle, a pickup truck heading in the opposite direction. The driver, an old man wearing a straw cowboy hat, had waved and seemed to be laughing, as though amused by what lay ahead for Hayden. The rental car was letting out an occasional gasp, as if it was running out of gas or the engine was misfiring. Nick checked the fuel gauge and saw that he had well over half a tank. Thinking it might be the strain of the air conditioner, he turned it off, rolled down the windows, and was instantly engulfed in hot, steamy air—the heat magnified by the soft cast and sling wrapped around his shoulder. Within minutes, his T-shirt was soaked with sweat. Nick felt fortunate to find somebody at the only business in Hollins, a general store and gas station. The owner, a middle-aged man with a handlebar mustache and a Panama hat, confirmed that Tatum was still living in the area. "Nobody knows him. Keeps to himself," he said. He gave Hayden directions to Tatum's property and then added: "You wanna be careful if he's not expecting you. Some folks around here don't take kindly to strangers." About four miles from the store, Hayden spotted what appeared to be the sandy road the man had described. There was a carved wooden sign off to the side that read, NO TRESPASSING! THIS MEANS YOU! He turned cautiously onto the road. On each side were pools of water covered with swirls of bright green algae. The terrain was flat, dotted with low-lying brush and an occasional willow or cypress tree. Off to the right an egret stood poised at the edge of a lagoon—its white plumage, long neck, and yellow bill etched sharply against a sea of green. After a few minutes of slow driving, Nick saw a cluster of trees on a rise, several feet above the surrounding grasses. An old white trailer home came into view beneath the trees—a faded red pickup parked off to the side. He'd reached the end of the road, and there were no other buildings in sight. About fifty feet beyond the trailer was a small lake of perhaps twelve acres, rimmed by an endless savanna of tall wetland grasses. There was a pungent though not unpleasant smell of moist vegetation. Everything was still, the silence accentuating the landscape's desolate beauty. The trailer was short and squat, resting on cement blocks that lifted it about two feet off the ground. Two small windows were covered with old, yellowed newspaper. Moss-covered branches of a cypress tree hung over the roof, offering a bit of shade and holding moisture that had gradually dripped brown streaks down the metal siding. Hayden shut off the engine, got out of the car, and scanned the area. The door to the trailer had to be on the other side, facing the lake. He waited a few moments for Tatum to acknowledge his presence, but it remained quiet. "Mr. Tatum," he called out. "I'm Michael Landau's son." He waited for a response but heard only the sound of a small animal scurrying beneath the pickup. A well-worn path led to the front of the trailer. He followed it, noticing that the area beyond the trailer sloped down to the lake and a weathered dock. A few steps more and he came alongside a screened porch that had been built onto the trailer. Looking up, Nick froze. A large man was sitting heavily in a captain's chair on the porch, a shotgun resting on his lap. After a brief hesitation, Nick spoke. "Mr. Tatum? I'm Nick Landau . . . Michael Landau's son." The man didn't move, just glared suspiciously at his unexpected visitor. "Now I go by Nick Hayden." "Step closer, if ya don't mind," said the man with a raspy twang. Hayden turned the corner of the rough-hewn porch and paused at the steps up to the screen door. The man furrowed his eyebrows as he scrutinized his visitor, and gradually the taut facial muscles relaxed. He lifted the barrel of the shotgun away. "Come on in," he said, standing and setting the shotgun down against the side of the trailer. Nick went up the steps and inside. Tatum thrust a hand forward. "I'm Buck Tatum. I guess you knew that." After shaking hands, there was a moment of stiff silence as they sized each other up. Buck Tatum could have made a convincing department-store Santa Claus were it not for the palpable air of sadness that enveloped him. White hair fell to his shoulders, and there was a sunburned bald spot on the top of his head. A snowy beard flowed abundantly beneath his chin. His ruddy cheeks gave his face a cherubic glow, which seemed to evaporate beneath the brooding countenance of deep-set, owlish eyes. He was wearing faded blue-jean overalls with straps over his bare shoulders and a pair of knee-high waders. Though large-boned, Tatum was no longer robust. Only his large, thick-fingered hands and muscular forearms projected strength. He appeared deeply exhausted—every movement an effort. "You can use that chair," said Tatum, gesturing toward a metal folding chair leaning against the trailer. "I'll get some water." Everything in Tatum's body language suggested that he was prepared for a serious discussion, as though he was not at all surprised that Nick had tracked him down. He stepped heavily through an open door into the trailer and returned with a pitcher of ice water and two coffee mugs, which he set between them on a small table. They sat facing the lake, their chairs angled toward each other. Hayden filled his mug and looked out at the lake while Tatum stared distractedly at the floor. "Gators give you any trouble, Mr. Tatum?" asked Hayden. "I've had to shoot a couple, but they generally stay clear of the trailer." Hayden noticed that the right corner of Tatum's mouth was slightly palsied, not moving in sync with the left side, but it didn't seem to affect his speech. Tatum reached behind his chair and picked up a canteen off the porch. He unscrewed the top and poured the amber liquid into his ice water. "Want some Jack Daniel's?" "No, thanks." "If you change yer mind, just help yerself. What happened to yer arm?" "A little mishap. It's better now." There was a pause before Tatum spoke. "I know why you're here, son. Nobody told me you were comin', but I'm not surprised . . . you wantin' to know." "I'm sorry to ask you about something like this after so many years," said Nick. He paused for a moment. "I've actually been working for INS in Chicago for the last four years." He then explained how he'd dug into the shooting as best he could, but still didn't have the full picture. Tatum listened, but seemed distracted and uneasy, which made Hayden feel vulnerable with the shotgun leaning against the trailer. "I just wanted to hear from you what really happened . . . the night of the shooting. Do you mind if I call you Buck?" Nick asked gently. Tatum pulled a wrinkled white handkerchief from a side pocket of his overalls and wiped it over his face. His hands were shaking. "Sure, you can call me Buck. I reckon you got a right to call me anything you want, seein' as how I was responsible for yer pa's death." Tatum let the statement hang in the air. He picked up his cup and took a swallow before continuing. "It was bad enough I caused Kelso's death." Though taken aback, Hayden was uncertain about Tatum's mental state and the reliability of his statements. He waited a moment, hoping Tatum would continue on his own, but he'd gone silent again, so Hayden pushed ahead. "Maybe we can go back to the shooting itself." Tatum blinked his eyes and shifted in his chair. "I talked to people and read the shooting report," said Nick. "It didn't say much about what happened when my father tried to help Kelso with the arrest—no specifics." "No, a'course not." Tatum's eyes narrowed, and a bitter smile lifted the left side of his mouth. He reached into a front pocket of his overalls, pulled out a hand-rolled cigarette, and gestured with it to Hayden, who shook his head. Tatum fished a wooden matchstick from the same pocket and scraped it on the porch. He lit the cigarette and released a cloud of bluish smoke. "Yer pa was in a tough situation, havin' to work with a bunch of guys from the Patrol. They didn't take kindly to the idea of hirin' people off the street, an' he was one of the first. They sized him up real quick—guys like Willard Smith. He did the investigation." "Yes, I know." "They knew he'd been a social worker, had a college degree—wasn't one of the good ol' boys. I rode with yer father for a few days. Then he was Kelso's partner. He wasn't tryin' to be somebody else or change to fit in. I liked that about him. He didn't go drinkin' with the others or try to impress 'em . . . wouldn't play the game. They thought he was aloof an' arrogant. "But yer pa wasn't givin' 'em anything to justify firin' him at the end of his probationary year. He was smart, an' he knew how to handle himself. Then it happened, an' Smith had what he was lookin' for. But he needed me to make it stick." Tatum took a deep breath, as though girding himself for what lay ahead. "It looked like any other arrest at the start," he continued. "We were on North Clark Street. I was followin' yer father an' Kelso. When I pulled up, Kelso was already havin' trouble with the guy—yer dad was runnin' over to help. Kelso was wearin' his holster backwards on his left hip. He shoulda known better, a'course—made it real easy for Cano to grab the gun. That's probably what gave Cano the idea; it was just too easy. So Cano got hold of the gun, an' it went from a routine arrest into somethin' a lot worse. The gun was already out when your pa got there. They were strugglin' for control of the gun, an' it was pointed at Kelso. Your pa jumped right in and tried to push the gun away." Tatum paused to flick ashes from the cigarette. "But Cano was strong an' got a round off, even with yer pa an' Kelso tryin' to push it away. By that time, I was close enough to get a clear shot. Once Cano had the gun, if yer father had pulled his hand away to reach for his own gun, Cano probably woulda been able to fire off more than one round into Kelso. Tryin' to push the gun away was the only thing yer father could do at that moment to save Kelso. He needed both hands to try an' throw off Cano's aim. If yer pa hadn't done that, Cano might have gotten all three of us." Tatum took a final drag on the cigarette and crushed the butt on the porch with his boot. "Yer father did nothin' wrong. In fact, he did everything right. He got screwed because Smith was lookin' for an excuse to get rid of him. They were lookin' for a scapegoat because one of their Patrol buddies was dead. In their eyes it was proof that they shouldn'a been hirin' guys off the street. The fact he never fired his weapon looked suspicious to anybody who wasn't there an' had doubts about him in the first place. I could have stopped all that, but then Smith showed up." Tatum's eyes shifted toward the lake. "How soon after the shooting did Smith show up?" Hayden asked. "The next day. Smelled blood in the water." Nick waited, but Tatum seemed reluctant to continue. He'd come to the really difficult part, thought Hayden. "So Smith talked to you about it?" "Wasn't much of an investigator, Smith—wasn't into details. But when he found the file, he figured he had me . . . had the pressure he needed." "What file?" "Cano's file," said Tatum. "Where did he find Cano's file?" "My file cabinet. Been there for almost two years," Tatum said, his voice wavering. "It was assigned to me. Then I knew why the guy's face looked familiar, from the photo in his file. There was a warrant for deportation on Cano. He just had to be picked up. He was walkin' around Chicago the whole time I had the file. His rap sheet was in the file so we knew he was a bad guy, had a criminal record, including an armed robbery. It was easy to forget about those cases with all that was goin' on in area control. But that's no excuse. Because of my negligence, Kelso lost his life. An' yer pa—" Hayden cut in: "Those cases probably weren't considered that important. They still aren't. If they were, your supervisor would have intervened." In reality Hayden suspected that even with low-priority cases, two years was not tolerated—not with call-ups every three months to review case status. But even if Tatum _had_ been negligent, it didn't make him responsible for Kelso's death. "Connelly was my supervisor," Tatum continued. "He hadn't done the case reviews like he was supposed to. Would have messed up his career if they found out. But he an' Smith were buddies—had been at the same station in the Patrol." "So what did Smith say about it?" "That he would bury the information about our negligence if I cooperated. I told him straight what happened with the shooting, but he didn't like how that sounded. He was convinced that the fact that I had to shoot Cano meant yer father wasn't able to pull the trigger, even after I explained it. He didn't wanna hear the truth. He said there was no reason why it had to come out about the Cano case—that he wouldn't put it in his report, an' there'd be no record I ever had the file." "Sounds like he had all the bases covered," said Nick. "An' I let him write his report like he wanted. He said yer pa wasn't right for the job. He would have to go, an' the shootin' incident would convince the probationary review panel. He knew that if any question came up about an agent's willingness to use deadly force, the agent wouldn't be retained. I knew what he wanted. He was obsessed with keepin' the 'old Patrol' in charge. Yer father had no chance without me to clear things up. I stayed quiet because I woulda been tainted in everybody's eyes—the guy whose negligence caused Kelso's death." "Did Smith tape your conversation?" asked Hayden. "Yeah, but he cut it short when he didn't like what I was sayin' about how it went down. I'm pretty sure he destroyed that tape an' the one with yer father. It woulda contradicted what he wanted in his report." "There's an envelope for the tapes in the shooting file," said Nick. "But they aren't there, and it looks like they never were." "No, Smith couldn't risk somebody hearin' them tapes. An' he was determined to get rid of yer pa. So I asked myself: Why should I go down with him? There woulda been disciplinary action against me an' Connelly for how we handled the case." "Did my father ever come to you to talk about it?" Tatum took a sip of Jack Daniel's before answering. "Yeah, he came to me. I said that I'd told Smith the truth, but I never told yer pa he'd done nothin' wrong. Never gave him that peace of mind. He probably took that to mean I thought he screwed up. Smith's version became gospel, maybe even to yer father. The truth is yer father wasn't quite sure he _hadn't_ done somethin' wrong. There was part of him that felt guilty, like maybe he coulda done somethin' different to save Kelso." There were a few moments of silence before Tatum continued. "It was a terrible thing I did—lettin' Smith railroad your pa. It was cowardly. I screwed up an' ended up wreckin' other people's lives just to save myself . . . my goddamn reputation. I know it isn't much consolation, but I'm sorry, son. Real sorry." It was now clear: the resistance to change personified by Smith and the pressure to reject anybody who didn't fit the mold. For Tatum, it was the fear of being judged by his peers that made him believe he had to choose between his own reputation and that of Michael Landau. And it was obvious that Tatum had already paid an enormous emotional price. Tatum wiped his eyes with the handkerchief. "I told myself that he was a smart guy an' was better off leavin'—gettin' away from INS an' guys like Smith. That's how I lived with it. Later I heard about what happened when your pa went to Portland. That's when I retired. I couldn't be there anymore . . . had no right to carry the badge . . . an' couldn't deny it." "Deny what?" "That I managed to kill three guys: Cano, Kelso, _an'_ yer pa." He paused and searched Hayden's eyes. "Nobody knew, except Smith an' Connelly. An' now _you_ know." Tatum stared at Hayden warily—fear in his eyes. It would take very little to send Buck Tatum even deeper into the web of guilt he'd been trapped in for almost two decades. Tatum's pain was so acute, so debilitating, that Hayden could muster no anger, only pity. "By shooting Cano, you probably saved my father's life," said Hayden. "What happened later was the system—the pressures built into it. It wasn't you, Buck." He leaned over and patted Tatum on the knee. Tatum began weeping, tears rolling down his cheeks. Nick, too, felt a rush of emotion—and a profound sadness. But he also felt a deep sense of relief in finally knowing the truth—a long overdue vindication of his father. Tatum took a couple of deep breaths, wiped the moisture off his face, and stuffed his handkerchief into a front pocket. They sat quietly for a minute. "Want to walk down to the dock, Buck?" asked Nick. "OK," said Tatum softly. Standing and moving seemed to relax both of them. As they descended the sandy slope, Tatum noticed Hayden scouring the shoreline. "Don't worry. The gators won't bother us." "Do any fishing from the dock?" "Yeah, there's a lot of bass an' sunfish." They were standing at the foot of the narrow dock—the wood planks sun-dried and cracked. "Will this support both of us?" asked Hayden. "Yeah," said Tatum, brightening. "It's stronger than it looks." # 19 The dismantling of Rico's document empire sparked extensive news coverage, plaudits from headquarters, and even a congratulatory nod from the Justice Department. Stark, Farber, and the entire Chicago office were widely hailed. The fact that an informant had killed Rico with an unauthorized weapon was considered rather minor in light of what had been accomplished. The prosecutor hadn't yet decided what to do about Chacon but was considering seizing the bar in addition to filing criminal charges. Felix Pinal was facing a long prison sentence. The whole affair was a boon for McGinty's, which instantly became a command post for gossip and rumor. Cops from other agencies, envious of any high-profile criminal case that wasn't theirs, now packed the saloon and vented their theories and opinions about how the deal had gone down, most of it based on pure speculation. It was an irony Charlie McCloud had noted on many occasions: those who earned their living collecting hard evidence were often the ones most inclined, when not on the job, to arrive at hasty conclusions tainted by cynicism and ego. During his three weeks of doctor-ordered convalescence, Nick kept in close touch with Kane. He also contacted Joe Willis, as promised, to fill him in on details that hadn't appeared in news stories, and it seemed to lift Joe's spirits a bit. When Hayden returned to the office, now without the need of a sling, several agents expressed concern about his shoulder, but there were few congratulations. Considering the success of the case, the reception was rather cool—apparently the result of lingering suspicion about his conduct during the operation. Meanwhile, Richard Stark was avoiding Hayden as if he were radioactive; all communication suddenly went through Kane. That was how Nick found out that they'd been given another month in fraud, into the middle of November, to clean up loose ends. They'd be informed within the next few weeks about their permanent assignments—whether they would continue in fraud or be moved back to area control. Hayden thought there was the possibility of disciplinary action, if only for negligence in the matter of Miguel's having a gun, but he hoped that the overall success of the case would give him a chance at remaining in fraud. Though Nick had a clear conscience about shooting down Nieto, he still felt a sense of loss—a heaviness that was only gradually diminishing. He quietly resumed his duties but noticed the same questioning eyes his father must have seen—evoking a sort of surreal camaraderie with his father. Over beers at McGinty's, Nick told McCloud what he'd learned from Buck Tatum. "It must be a relief to finally know the truth," said McCloud. "Yeah, like a weight has been lifted off me." "The whole thing shows how important reputation is in this business. Even good, experienced guys like Tatum will do anything to avoid being tagged by their colleagues." They sipped their beers quietly for a minute. "So, have you told your mother what you found out?" asked McCloud. "No. I thought about it. Part of me wants to tell her, but it would only churn up the past and make her feel guilty. She's moved on and dealt with it in her own way." "Too bad that lizard Smith isn't alive," said McCloud. "That was a crime, what he did, literally a fucking crime. An investigation should be done to clear the record." But Hayden knew it was time to let it go. He'd learned the truth about the shooting and the circumstances that led his father to such an acute state of guilt and despair. And Tatum had been through enough. McCloud reported that he'd spotted Alderman Francisco Campos outside Farber's office a few days earlier. "You guys took care of Campos's problem with the merchants on Cermak and Twenty-Sixth Street," said McCloud. "My guess is he's persuaded Farber to back off again. If you guys keep going after vendors, prices will stay high, and Campos's people won't be happy—the wets _or_ their employers. He wants to go back to the good old days—plenty of supply but no visible presence to annoy the business owners. Sweep it under the rug. In return he'll hold off on bashing INS in press conferences for a time. That should be enough for Farber." "The vendors will come back," said Hayden. "All this publicity has changed things. The cops can't just ignore these guys anymore. Campos might be able to have the cops keep them off the street with vagrancy laws or something, but the cops still won't be able to work directly with INS. The document trade will keep going, of course, but in the shadows." "So the vendors go underground," said Hayden disgustedly. "And nothing changes except appearances." "You think they care about anything _but_ appearances? They're politicians, for chrissakes! Appearance is _everything_. By the way, a couple of regional headhunters are in town," said McCloud with an impish grin. "They're going beyond the shooting, looking into the money angle—Rico's money. Like maybe you and Miguel have it stashed somewhere. Stark's directing them." "So Tom and I are just _pretending_ to look for it?" "They're trying to understand what you did, and greed makes more sense to them than a concern for Miguel's safety. They don't trust what they don't understand. Anyway, Stark doesn't figure he can trust you, even though it was your case that's going to make him the next director of investigations. Just make sure you don't give him anything else he can use against you." * * * The internal investigators from the regional office, derisively referred to as "headhunters," made everybody in the office a little nervous. They spent two weeks in Chicago reconstructing the shooting scene and taking statements, and leaned heavily on Miguel, implying that if he "came clean" about Hayden, they could get him permanent legal status. To their chagrin he offered nothing but praise for the agent's conduct. Responding to questions about his ability to shoot down Rico in the dimly lit office at El Palacio, Miguel explained that he had grown up on a ranch where guns were everywhere, and he had learned as a boy to fire accurately. It wasn't as difficult a shot as they seemed to think. He assured them that Hayden knew nothing about the gun he'd retrieved from his car after Nick entered El Palacio. The tape recorder fastened to Miguel's body was downloaded and, to their disappointment, confirmed Hayden's version of events. Baker checked the equipment and found that a damaged wire inside the receiver had cut off audible reception from Miguel. The regional investigators did perfunctory interviews with Kane and Hayden, who had already furnished detailed memos. The investigators informed Stark that Hayden had been negligent in not searching Miguel's vehicle for weapons, but they found no other impropriety. They left Chicago on a cold, dreary day in November. The next morning word swiftly circulated through the office about Joe Willis. The night before, Willis, alone in his apartment, had shoved his beloved .357 Smith & Wesson revolver into his mouth and blown off the back of his head. He was found outfitted in his old, dark green Border Patrol uniform. There was a collection of newspaper articles about the Rico case on a table next to Willis's body. It was only two months since he had been forced to retire at age fifty-seven. Some were shocked, but others had seen it coming. The decibel level in the office dropped to a low hum for the rest of the week. * * * Richard Stark cleared out his inbox and half-listened to the morning radio traffic through the walkie-talkie behind his desk. He lit a cigarette, peered through the floor-to-ceiling window overlooking the plaza, and tried to prepare himself for what promised to be an uncomfortable meeting. For a ruthlessly ambitious man, Stark had a surprisingly difficult time executing decisions on personnel matters. It was one of the reasons he longed for higher office; let his subordinates handle the dirty work. He'd hoped the regional investigators would unearth something damning enough on Hayden to make it simple, but they had found nothing to warrant more than a slap on the wrist. Useless bastards! Connelly, still ostensibly in charge of the investigations branch, was now taking sick leave for weeks at a time without even the pretense of illness. He had made it clear that he wanted nothing to do with it and had named Stark the acting director of investigations in his absence. This was useful to Stark, as District Director Farber would get used to him occupying the post. Stark had his secretary call Hayden and Kane into his office. As the two agents took seats in front of his desk, Stark had the somber look of a man preparing to deliver a funeral oration. "Well, you guys have done a hell of a job," said Stark, forcing a weak smile. He glanced momentarily at Hayden and then fastened his gaze on Kane. "Even with a few unexpected problems, we did a good job of upsetting the flow of documents." He paused, waiting for some agreement or expression of gratitude, but they remained silent, and this made him even more nervous. Stark cleared his throat. "I want to tell you both what is going to happen as far as your permanent assignments, now that your detail is at an end. I've given this some serious thought," he said gravely. He paused and ran a hand over his teal-colored silk tie. "Kane, you're going to stay down here in fraud. Hayden, you're going back to area control. I think it's best for everyone concerned." Nick had prepared himself. He knew what it meant for his career. It wasn't likely he would get another opportunity, certainly as long as Stark was in charge. "Sir, why should Nick have to go back?" asked Kane. "He was more responsible than anybody for this case." "It's a management decision, Kane," he said acidly. "It's not your concern." "With all due respect, it _is_ my concern. He almost lost his life over this case, and now he's sent back to area control? That's not fair." "The last time I checked, Kane, nobody had appointed you director of investigations," said Stark, his eyes smoldering with anger. There was dead silence for a few moments before he continued. "Anyway, it's not like being in area control is some kind of punishment." Hayden began to feel like an object being argued over in a divorce proceeding. If Kane continued his noble defense, they might both be sent back to area control. Besides, he knew there was no way Stark would change his mind during this meeting. "It's OK, Tom," said Hayden evenly. "I don't mind going back." "It doesn't mean he won't be back at some point in the future," said Stark, glaring at Kane. He let that concession hang in the air, where it soon fizzled. "What about the task force, sir?" asked Hayden. "Will Tom and others still be working counterfeit documents?" "Task forces are generally set up to resolve a specific issue," Stark said, leaning back in his chair. He was starting to relax, thinking the worst was over. "You guys accomplished what we wanted. So, no, for now there won't be anybody working documents. Kane will be working other things in fraud." With two sets of disbelieving eyes staring back at him, Stark looked out the window and nervously fiddled with his tie. So, it was true about Campos, thought Hayden. McCloud had guessed right. The alderman, who regularly trashed Farber and the INS, had gotten his way. They had made a conscious decision to again ignore the problem, so long as business was conducted behind the scenes. And there would be no second-guessing from the regional office or headquarters. They were all quite comfortable with the way things were, taking their lead from a Congress that secretly applauded the ineffectiveness of the very laws it had passed. Hayden's detachment began to dissolve. The absurdity of the policy—and its being openly defended—made him slightly nauseous. "Let me get this straight," said Hayden. "We just proved that the sale and manufacture of counterfeit documents is a multimillion-dollar industry, that the counterfeits are necessary so tens of thousands of illegal aliens in Chicago alone can circumvent the law, and you're telling us nobody is going to do anything about it?" "We have a lot of priorities around here, Hayden, and we don't have unlimited manpower. You know that as well as anybody." "But, sir," Kane protested, "if we don't keep the pressure on in some way, it's going to be completely out of control. There'll be fights over turf. The media will want to know what we've done about it, or why we've done nothing." Stark didn't like being on the defensive, especially with two novices who didn't understand the obscure wisdom and logic of the INS bureaucracy. " _We'll_ worry about the media impact," he said, his voice rising. "I'm not going to debate this any further." "It's all right," Hayden quickly offered. "We know you aren't calling the shots on this." As soon as the words left his mouth, he realized that Stark's ego could not handle that sort of candor. "No, you're wrong, Hayden," Stark declared. "I _am_ calling the shots on this. It's _my_ decision!" "I didn't mean to suggest you aren't in charge," said Hayden. Stark searched Hayden's face vainly for any hint of sarcasm. After taking a deep breath, Stark tried to regain his footing by again praising what they had done on the task force, assuring Hayden that it was all but official that his shooting of Nieto would be declared justified. There might be some minor reprimand for not thoroughly checking Miguel for weapons, but it was "nothing to worry about." Calm was momentarily restored. But there was one final matter. "Oh, by the way, Hayden," said Stark casually, "about Miguel Chavez . . . we obviously can't use him as an informant anymore. You'd better take care of the paperwork." Stark had blundered headlong into a very sensitive area. "I thought we might use him for intelligence purposes," said Hayden calmly. "Not on undercover operations, but it would allow us to keep him on as an informant." "No. He's damaged goods. If he does something unpredictable again, whether it's undercover or not, we'll look bad. We can't take that chance." "Even if he's no longer an informant, I assume we can keep him on a schedule of voluntary departure periods," said Hayden, "so he and his family can stay here—for all he's done for us." "No, we'll have to move him," Stark said, waving his hand dismissively. "Yes, out of the Chicago area," said Hayden hopefully. "That might not be a bad idea." "No, Hayden," Stark replied, exasperated. "I mean out of the _country_! He's an illegal alien, remember?" Hayden felt a dangerous stirring. Stark, aware he had struck a nerve, tried to soften it. "Of course, he won't have to leave this week or anything. We need to keep him here until we have pleas from all our defendants. That should happen within a few weeks. Then we can give him a month or so to get his affairs cleaned up." Stark's eyes shifted nervously between Hayden and Kane. Hayden spoke very softly, trying to check his anger. "Sir, this guy just put his life on the line and saved mine. This is how we take care of those who do heroic things—throw them on a bus to Juárez?" "He's an outlaw, Hayden, sort of like you," bellowed Stark, now raging mad. "We can't tolerate that kind of behavior, and we sure as hell aren't going to reward it! He's just another wet, as far as I'm concerned." By now Stark was leaning over the desk, his head thrust forward. With his eyebrows angled sharply to a point above the bridge of his nose, he looked like an enraged gargoyle. His silk tie was hanging down on the desk invitingly, within easy reach of Hayden, who grabbed the tie and jerked it firmly, pulling Stark from his chair, his forehead striking the glass desktop. Seized by a euphoric release of adrenaline, Nick leaned over the desk, pulled Stark upright by the loose folds of his shirt and was winding up with clenched fist to deliver a blow to the center of Stark's face when Kane pulled Hayden by the shoulders and sent him spinning into the window blinds. Wheezing and standing shakily on bended knees, Stark slowly righted himself, loosened the tie around his neck, and fell heavily back into his chair, gasping for air. A trickle of blood curved around his right eyebrow where he had come down on the glass. Hayden disentangled himself from the blinds and was sitting on the radiator against the window, his hair askew, breathing heavily. Tom Kane stood between them with his arms spread out like a boxing referee, looking back and forth to be sure neither would initiate further contact. Nick stared at the floor. Lashing out at Stark, the personification of everything wrong with INS and immigration policy in general, had felt good for a moment, but he already regretted it. He knew he had now blown any chance of getting Stark to alter his decision about Miguel, however unlikely that might have been. He also realized he was facing an eventual thirty- or sixty-day suspension. Stark pulled a handkerchief from his desk drawer and was dabbing the cut over his eyebrow. For several moments there was only the sound of Hayden and Stark breathing heavily. Finally, Stark spoke. "You're a fucking lunatic, Hayden," he croaked. "And we can't afford to have lunatics around here." Hayden thought of Willard Smith . . . of Joe Willis. Their brand of lunacy had always been tolerated. Then his mind shifted to Miguel, who'd been pulled into this mess, performed heroically, and was now being betrayed. Nick knew he had to do something creative—and be damn quick about it. * * * Connie Salinas took the bus into the Loop, walked to the INS office, and asked to speak to Special Agent Tom Kane, who had been mentioned in newspaper stories about the investigation that led to the shootings at El Palacio. She now felt a compelling need to tell the truth about her deceased former husband, Marcos Ortega. The receptionist immediately phoned Kane, who was at his desk in the fraud unit. "There's a woman here who says she has information about a guy named Marcos Ortega," she said. Kane pulled Ortega's file, went to the reception area, and introduced himself. Connie was wearing a black leather coat over a beige pantsuit. She was now thin and pale, her hair cut short and combed back in a masculine style. Kane led her down the hallway to one of the windowless interview rooms. The small room, with only a table and two chairs, was lit by an overhead fluorescent light. Once they were seated, it was Connie who asked the first question. "Are you Catholic, Mr. Kane?" "Yeah, I'm Catholic. Why?" "I was told a few weeks ago that I have cancer . . . pancreatic cancer," she said softly. "I have maybe six months to live. That's what they say, anyways. I don't want the radiation treatments or chemotherapy." "I'm sorry," said Kane. Connie pulled a tissue from the purse on her lap and dabbed her nose with it. She suddenly seemed very far away. "I _am_ sorry about your illness, Ms. Salinas, but what did you want to tell us about Marcos Ortega? Did you know he was involved in selling counterfeit documents?" "No, I didn't know anything about that until I read the stories in the newspaper," she said. "So what's the connection between you two?" "We were married, me and Marcos. That's how he got his immigration papers." As Kane started leafing through the file in search of a marriage certificate, Connie reached into her purse, casually pulled out a revolver, and placed it on the table. Startled, Kane grabbed the gun and her purse. The gun was an old, blue-steel Smith & Wesson .38-caliber snub nose. With a flick of his wrist, Kane rolled out the cylinder to find it was not loaded. "What the hell else do you have in here?" he growled, as he rifled through the purse. He found nothing but tissues and a wallet. "I'm sorry," she said. "I didn't mean to frighten you." He had her stand up with her hands against the wall, opened the door, and called out to a secretary to get a female agent who could do a pat-down. Connie patiently cooperated with the search before resuming her seat. "So, why'd you bring the pistol?" asked Kane, still a bit rattled. "That's the gun that shot Marcos Ortega," she said. "Yeah? And who pulled the trigger?" "Me. I killed Marcos." Though she didn't seem like a violent person, she exuded a grim, take-it-or-leave-it attitude that he found credible. She didn't care whether he believed her or not. He left the interview room to search out an evidence envelope and tape recorder. For a moment he considered cuffing her to the chair but decided it was unnecessary. She _wanted_ to be there. He came back, slipped the gun into the envelope, and placed the recorder in the middle of the table. Kane read the Miranda rights to her, and she signed the waiver. Her story tumbled out with a minimum of questions. "I was stupid and thought I loved him, but he left me before we even lived together. I figured I'd have him deported, but the officer said they can't. That shocked me. My father woulda killed Marcos if I told him. But I was ashamed to even admit how stupid I was, and I didn't want my father to go to jail for something that was my fault. I just wanted to keep it all a secret, so I didn't fight it and I let Marcos pay for a divorce." "Where did you get the gun?" "Some guy outside a gun show on Randolph. He had some guns in his trunk." "Had you ever fired a gun before?" "My father owns lots of guns. He used to take us out to his cousin Eloy's place in Calumet where we would have family picnics, and we all shot at targets on hay bales. I remember my dad saying if you ever really wanted to kill a person you should shoot 'em in the face." "I understand you being hurt, but what made you actually go through with it?" asked Kane. "He broke my heart and made a fool outta me. So I was already mad and hated him, but when I saw him with his Mexican wife and kids on the street it really got to me, and I felt like I had to do something. You guys weren't going to do anything. So I planned it all out. I knew he liked that bowling alley on the North Side. I even went over there one Sunday night when it was closed just to see if it would work. Then I called him and said something about needing money and suggested meeting there. I knew he wouldn't tell his wife he was meeting me. He was secretive that way." Though her voice was steady, she'd begun crying and took a moment to wipe the tears away. "It was a perfect night because the wind was making a lot of noise, and there was nobody around. I got there early and parked in back of the building. I waited a few minutes after he got there and then walked out toward him, and he was standing there, and the light behind him made him stand out real clear, like a big target. The shot wasn't loud because of the wind." Connie dabbed her nose with the tissue. "At first, I didn't feel badly, just sort of numb. I figured he had it coming. But later I started thinking about his wife and kids. I saw them a couple times on the street, and I knew that what I did was a terrible sin, so I started going to church again. Then I got sick." "Have you told anybody else about this?" asked Kane. "Only the priest. I told him last week at confession. He said it wasn't enough—that to make it right with God, I needed to tell somebody official." "Why come to us instead of the police?" "It was all an immigration thing. That's what started it. I don't mean any disrespect, but you shouldn't let guys take advantage—like Marcos did. It doesn't make it right, what I did, but you shouldn't let it happen." "You're right about that, but the law is so weak that it invites scams like the one Marcos pulled on you." Kane left her alone for a minute and called the homicide cops to see what they wanted to do with Connie. The detective seemed annoyed that Kane had taken the confession and said he would be right over to take her into custody. When Kane returned to the interview room, Connie was looking absently at the wall. Her legs were stretched out alongside the table, and Kane noticed she was wearing black cowboy boots with silver tips. "Thanks for listening, Mr. Kane," said Connie softly. "I feel better now." * * * Kane, alone in the office, answered the phone at six o'clock in the evening. "Investigations, Kane speaking." " _¿Habla español, Señor Kane_?" " _Sí_." The man continued in Spanish: "You are the one who was in the paper . . . the story about the fake documents?" "Yes." "I wanted to tell you—there is a man who took over for Salvador Rico." Kane bolted upright in his chair and grabbed a notepad. "What's his name?" "His real name I don't know. They call him 'the Little Umpire' because he wears a blue jacket and baseball cap. He is from Peru. He comes back from California with thousands of the green cards and social security cards." The caller spoke Spanish slowly and distinctly so that Kane had no trouble understanding him. "Where does he live?" "This I don't know. But he drives a new Chevrolet Impala. Most nights you can find him at the Little Lima Bar on Ashland. He always carries a gun—a revolver." "How old is he?" The man laughed. "He could be thirty-five or fifty-five. You can't tell." "What does he look like?" "He is short . . . his teeth are bad." "How do you know about his new business?" There was silence at the other end. "It would be held in confidence," said Kane. "You can talk freely." There was only the sound of breathing. Afraid the man would hang up, Kane continued. "What else do you know about him?" "The Colombians thought he was a government informant. But then they heard that Salvador Rico was the informant, so they are no longer after him. One other thing—'the Little Umpire' suddenly had all this money when Rico died. Before, he had nothing. It is odd, don't you think?" "Yes, it is very odd," said Kane. "We should meet to discuss this further." "I must go now," the man said, and the line went dead. Kane smiled as he set down the receiver. * * * All was quiet on Francis Street. Though the rain had stopped, gray clouds were still thick overhead. Inside the car, condensation clouded the windshield. Nick cleared it with his hand and scanned the street. _If you come through, we'll take care of you. You can trust us to do that_. Those were the words he'd spoken to Miguel. He'd said it because he believed it was true—and Miguel had counted on him, trusted him. As Nick climbed the steps to the porch, Miguel swung the door open. "Paco sees you from window," he said, smiling warmly. "Please, come in." "Let's talk out here on the steps, if that's OK with you," said Nick. " _Claro_. Yes, of course." The porch was damp, so Miguel picked up a rug from inside and spread it over the top step. Hayden noticed that Miguel was wearing a jacket, the same one he had worn the day of the shooting. "Were you headed out somewhere?" "No. Is cold inside." Miguel pulled the collar of his jacket around his neck. "How is arm?" "It's better. I can move it pretty well now," Nick said, rotating his shoulder. Neither of them spoke for a few moments. "Something is wrong?" Miguel asked. Nick had to force the words out. "They want you to go back to Mexico. I tried to stop it . . . you have to believe that." "Yes, I believe, Nicolas." "But I have a plan for you and your family." He reached inside his leather jacket, pulled out a thick envelope, and handed it to Miguel. "With these you'll be able to stay in this country as long as you want—all four of you. You'll have different names, but you'll be as good as US citizens. I can get you a job in California, and you wouldn't have to do anything for INS anymore." Miguel opened the envelope and pulled out the folded documents. There were four official-looking birth certificates that appeared to have been issued by the State of California. The stamps and seals looked genuine. Miguel's name would be Miguel Fernandez. He examined them carefully. "You get to keep your first name," said Hayden. "Those are genuine California forms and seals. They're on file. The social security numbers are good. That was a family that died in a car crash a couple of years ago. Your birth dates will be different, but not by more than a year each." "Where you get these?" "It's better if you don't know about that." Miguel looked down at the papers. Carmen would have to change her name to Luz Fernandez. Paco would be Luis Fernandez. He considered them for several moments and then carefully folded them together, slid them into the envelope, and handed it back to Hayden. "No, thank you, Nicolas." "What do you mean? Why not?" "I no can do this." "Sure you can. Don't let them push you around like a piece of garbage. With these you control your destiny." Miguel spoke evenly. "I no think we control destiny. You risk much and I am grateful, but we no can do this . . . changing our names. I no can ask them to live false life." Hayden hadn't considered that he might refuse the documents. Miguel had already saved his life; now he was saving him from crossing a line into criminal activity. "Is great country here," said Miguel, "but we go back now. Is no good to be where you not wanted. I thought they want us here. That is why I think is all right to come." "You _are_ wanted, Miguel." Miguel smiled. "Is OK, Nicolas. We have many family there. Carmen miss them very much. My parents . . . they old and soon they need us. They be happy we come back." Nick stuffed the envelope back into his leather jacket. They sat quietly for a few moments before Nick spoke. "They want you to leave when the criminal case is over . . . probably about six weeks. Maybe I can get you more time." "Thank you, but we no need more time." Miguel turned to Hayden. "What about you, Nicolas? After all that happen, you are OK?" Hayden was taken aback. How could Miguel possibly think about _him_ at a time like this? It took a moment to shift focus. "Yeah, I'm fine," he said, smiling appreciatively. "Good. Still, I pray for you." The clouds were beginning to break up on the horizon and the retreating sun crowned the rooftops with a stream of pale gold light. "I going to miss this street," said Miguel wistfully. "I remember when I come here and see the street name." "Francis Street?" "St. Francis Xavier—he is patron saint for immigrants. He watch over us." Though he didn't share Miguel's Catholic faith, Nick knew there had been a subtle yet dramatic shift in his own consciousness. He wasn't sure where it was leading him, but he was gradually becoming aware of a higher dimension—a dimension that in some mysterious way binds us all together. "You're a good man, Miguel. You've helped me more than you know." "We help each other same, Nicolas," said Miguel. "What you do at the bar—I not forget this. We always be friends." As they rose from the steps, they shook hands and Hayden said they would talk again soon. * * * Nick turned off Francis Street into brisk traffic on Eighteenth Street. He called in to the radio operator and asked her to check for messages, but she had nothing for him. Heading north on Western Avenue, he came to a stop at a red light. On the corner was a metal drum factory where many area control operations had been conducted over the years. It could always be counted on if a few extra bodies were needed for the day's quota. Nick watched the Mexican workers as they stacked fifty-five-gallon drums on pallets, and realized that he now felt differently about them. Though he didn't condone their illegal status, their mere presence was no longer a source of personal frustration. That burden had been lifted. The last vestiges of the ego-driven gladiator syndrome seemed to have faded away. His thoughts were interrupted by the squawk of the radio and the voice of Richard Stark. "Base to Hayden, do you read?" said the voice, still raspy from their encounter in Stark's office. It was unusual for Stark to be in the office this late and had to be something important. Nick picked up the mic but did not speak. After several moments of silence, Stark repeated: "Base to Hayden." Another pause and then a demand: "Answer the damn radio, Hayden. I just heard you check in a few minutes ago." Nick placed the microphone in its holder, turned the switch off, and watched the red light of the receiver flicker and fade. Stark was saying something, but his voice was too small to make out and disintegrated into nothing. The traffic light turned green, and Nick pulled through the intersection. He would drive north to the Chinese restaurant with the happy cooks and waitresses. # ACKNOWLEDGMENTS * * * I owe an enormous debt of gratitude to many individuals who have assisted in the research and editing of this book. Among them are Nancy Sprinkel, Tim Ohr, Larry Jakus, Vern Loeb, Michael Reiners, Peter Jensen-Moulton, and my wife, Lucy Kading, who devoted countless hours to reviewing the manuscript as it evolved. Her keen observations and support sustained me throughout this process. I am also grateful to my fellow employees with the former United States Immigration and Naturalization Service. Their professionalism and dedication in the face of enormous challenges provided the inspiration for this book. # Sommaire 1. Cover Page 2. Title Page 3. Copyright Page 4. Contents 5. Prologue 6. Part I 1. Chapter 1 2. Chapter 2 3. Chapter 3 4. Chapter 4 5. Chapter 5 7. Part II 1. Chapter 6 2. Chapter 7 3. Chapter 8 4. Chapter 9 5. Chapter 10 6. Chapter 11 7. Chapter 12 8. Chapter 13 9. Chapter 14 10. Chapter 15 8. Part III 1. Chapter 16 2. Chapter 17 3. Chapter 18 4. Chapter 19 9. Acknowledgments ## Pagination de l'édition papier 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 100. 101. 102. 103. 104. 105. 106. 107. 108. 109. 110. 111. 112. 113. 114. 115. 116. 117. 118. 119. 120. 121. 122. 123. 124. 125. 126. 127. 128. 129. 130. 131. 132. 133. 134. 135. 136. 137. 138. 139. 140. 141. 142. 143. 144. 145. 146. 147. 148. 149. 150. 151. 152. 153. 154. 155. 156. 157. 158. 159. 160. 161. 162. 163. 164. 165. 166. 167. 168. 169. 170. 171. 172. 173. 174. 175. 176. 177. 178. 179. 180. 181. 182. 183. 184. 185. 186. 187. 188. 189. 190. 191. 192. 193. 194. 195. 196. 197. 198. 199. 200. 201. 202. 203. 204. 205. 206. 207. 208. 209. 210. 211. 212. 213. 214. 215. 216. 217. 218. 219. 220. 221. 222. 223. 224. 225. 226. 227. 228. 229. 230. 231. 232. 233. 234. 235. 236. 237. 238. 239. 240. 241. 242. 243. 244. 245. 246. 247. 248. 249. 250. 251. 252. 253. 254. 255. 256. 257. 258. 259. 260. 261. 262. 263. 264. 265. 266. 267. 268. 269. 270. 271. 272. 273. 274. 275. 276. 277. ## Guide 1. Cover 2. Début du contenu 3. Contents	{ "redpajama_set_name": "RedPajamaBook" }	8,035
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{"url":"http:\/\/gmatclub.com\/forum\/if-p-q-and-r-are-integers-is-pq-r-even-150503.html?sort_by_oldest=true","text":"Find all School-related info fast with the new School-Specific MBA Forum\n\n It is currently 04 Aug 2015, 12:13\n\nGMAT Club Expert Essay Review: Submit Yours Here\n\n### GMAT Club Daily Prep\n\n#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.\n\nCustomized\nfor You\n\nwe will pick new questions that match your level based on your Timer History\n\nTrack\n\nevery week, we\u2019ll send you an estimated GMAT score based on your performance\n\nPractice\nPays\n\nwe will pick new questions that match your level based on your Timer History\n\n# Events & Promotions\n\n###### Events & Promotions in June\nOpen Detailed Calendar\n\n# If p, q, and r are integers, is pq + r even?\n\nAuthor Message\nTAGS:\nIntern\nJoined: 21 Feb 2013\nPosts: 13\nFollowers: 0\n\nKudos [?]: 1 [1] , given: 0\n\nIf p, q, and r are integers, is pq + r even?\u00a0[#permalink] \u00a007 Apr 2013, 02:26\n1\nKUDOS\n00:00\n\nDifficulty:\n\n75% (hard)\n\nQuestion Stats:\n\n53% (02:47) correct 47% (01:35) wrong based on 89 sessions\nIf p, q, and r are integers, is pq + r even?\n\n(1) p + r is even.\n(2) q + r is odd.\n\n[Reveal] Spoiler:\nManhattan tells me I should make the table which works fine. I tried doing it without the table and that worked too. However, without the table I was less convinced and more confused because in your head it gets jumbled up. So is there another foolproof way of doing these? Or do I have to stick with the Manhattan table?\n[Reveal] Spoiler: OA\n\nLast edited by Bunuel on 12 Apr 2013, 04:53, edited 1 time in total.\nRENAMED THE TOPIC.\nVP\nStatus: Far, far away!\nJoined: 02 Sep 2012\nPosts: 1125\nLocation: Italy\nConcentration: Finance, Entrepreneurship\nGPA: 3.8\nFollowers: 148\n\nKudos [?]: 1461 [1] , given: 219\n\nRe: A proper organised way to solve this type of questions?\u00a0[#permalink] \u00a007 Apr 2013, 02:46\n1\nKUDOS\nkarmapatell wrote:\nIf p, q, and r are integers, is pq + r even?\n\n(1) p + r is even.\n(2) q + r is odd.\n\nManhattan tells me I should make the table which works fine. I tried doing it without the table and that worked too. However, without the table I was less convinced and more confused because in your head it gets jumbled up. So is there another foolproof way of doing these? Or do I have to stick with the Manhattan table?\n\nThe Manhattan table works fine, another method is using real numbers .\n\n(1) p + r is even. $$3+1 = even$$, so is $$3q+1$$ even? depends on q : not Sufficient\n(2) q + r is odd. $$2+1=odd$$, so is $$p2+1$$ even? depends on p : not Sufficient\n\n(1)+(2) p + r is even AND q + r is odd\nExample 1: $$3+1=even$$--$$2+1 = odd$$\n$$23+1=odd$$\nExample 2:$$2+2=even$$--$$3+2=odd$$\n$$23+2=even$$\nNot Sufficient\n_________________\n\nIt is beyond a doubt that all our knowledge that begins with experience.\n\nKant , Critique of Pure Reason\n\nTips and tricks: Inequalities , Mixture \| Review: MGMAT workshop\nStrategy: SmartGMAT v1.0 \| Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant\n\nRules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[\/size][\/color][\/b]\n\nVerbal Forum Moderator\nJoined: 10 Oct 2012\nPosts: 629\nFollowers: 63\n\nKudos [?]: 751 [0], given: 135\n\nRe: A proper organised way to solve this type of questions?\u00a0[#permalink] \u00a008 Apr 2013, 04:13\nExpert's post\nkarmapatell wrote:\nIf p, q, and r are integers, is pq + r even?\n\n(1) p + r is even.\n(2) q + r is odd.\n\nManhattan tells me I should make the table which works fine. I tried doing it without the table and that worked too. However, without the table I was less convinced and more confused because in your head it gets jumbled up. So is there another foolproof way of doing these? Or do I have to stick with the Manhattan table?\n\nFrom F.S 1, assume p=r=0, thus, we get a YES for the question stem. Now assume p=1, r=1,q = 2 we get a NO. Insufficient.\n\nFrom F.S 2, assume q=0,r=1, we get a NO for the question stem.Now assume r=2,q=1 ,p=2, we get a YES. Insufficient.\n\nTaking both together, we have p=0,r=0,q=1, and a YES. Again taking, r=1,p=1,q=0, a NO. Insufficient.\n\nWhat might help you in selecting good numbers is the fact that from the F.S 1,either both p,r are even or both are odd. Similarly, from F.S 2, q and r are odd\/even or even\/odd.\n\nE.\n_________________\nSVP\nJoined: 06 Sep 2013\nPosts: 2046\nConcentration: Finance\nGMAT 1: 770 Q0 V\nFollowers: 30\n\nKudos [?]: 328 [0], given: 355\n\nRe: If p, q, and r are integers, is pq + r even?\u00a0[#permalink] \u00a006 Jan 2014, 08:44\nkarmapatell wrote:\nIf p, q, and r are integers, is pq + r even?\n\n(1) p + r is even.\n(2) q + r is odd.\n\n[Reveal] Spoiler:\nManhattan tells me I should make the table which works fine. I tried doing it without the table and that worked too. However, without the table I was less convinced and more confused because in your head it gets jumbled up. So is there another foolproof way of doing these? Or do I have to stick with the Manhattan table?\n\nOdds and Evens, ok\n\nStatement 1\n\nClearly Insufficient\n\nStatement 2\n\nSame here\n\nStatements 1 and 2 combined\n\np+r = even\nq+r = odd\n\np-q = odd\n\nThen p must be even and q odd or the other way around\n\nIf p is even then pq will be even and 'r' will be even = All even= Answer is YES\nif q is even then pq will again be even and 'r' will be odd= All odd = Answer is NO\n\nHence E is your best choice\n\nCheers!\nJ\nRe: If p, q, and r are integers, is pq + r even? \u00a0 [#permalink] 06 Jan 2014, 08:44\nSimilar topics Replies Last post\nSimilar\nTopics:\nWhich is the greatest among p,q and r? 4 20 Feb 2015, 00:28\n4 Is P the youngest of P,Q ,R and S? 4 13 Nov 2012, 19:54\nIf p,q and r are integers, is pq+r even? 1) p+r is even 3 10 Mar 2011, 12:18\n3 If P, Q, R, and S are positive integers, and P\/Q = R\/S, is R 9 01 Feb 2011, 10:01\n2 If P, Q, R, and S are positive integers, and P\/Q = R\/S, is R divisible 12 02 Jul 2008, 21:20\nDisplay posts from previous: Sort by","date":"2015-08-04 20:13:23","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7179434299468994, \"perplexity\": 3294.0250257035655}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2015-32\/segments\/1438042991951.97\/warc\/CC-MAIN-20150728002311-00280-ip-10-236-191-2.ec2.internal.warc.gz\"}"}	null	null
Het Gymnasium Juvenaat, of voluit het Rooms Katholiek Gymnasium Juvenaat Heilig Hart, is een rooms-katholiek gymnasium met circa 400 leerlingen in Bergen op Zoom. Geschiedenis Juvenaat Het kleinseminarie Juvenaat werd opgericht op 6 december 1900 door priesters van het Heilig Hart van Jezus, een congregatie gesticht door de Franse priester Leo Dehon. De school was tijdelijk gevestigd aan de Wouwsestraat in Bergen op Zoom, waarna de congregatie onderdak vond in het gildehuis Driekoningen aan de (in de jaren 1950 gedempte) Kaai. In 1903 trokken de priesters in een nieuw klooster aan de Antwerpsestraatweg 125. Het Juvenaat en 33 leerlingen verhuisden mee. Met een voorbereidende klas waren er in totaal zeven klassen. Leerlingen tot en met klas 3 werden de "Kleinen" genoemd. Vanaf klas vier hoorde je bij de "Groten". Beide afdelingen werden geleid door een pater Prefect. In 1953 werd Het Juvenaat officieel erkend als gymnasium. Daarmee was de school een van de eerste seminaries met een officieel erkend gymnasium. Eind jaren vijftig studeerden er zo'n 240 leerlingen, begeleid en verzorgd door 40 paters en broeders allen intern. Vanaf 1968 werd de school ook opengesteld voor meisjes, zowaar een revolutie. De brugklas telde toen 48 leerlingen. In 1969 werd het internaat gesloten. Vanaf begin jaren zeventig groeide de school gestaag naar ongeveer 450 leerlingen en 50 personeelsleden nu. De school is na de verhuizing uit het oude Juvenaat (afgebroken in 1993) gehuisvest in een modern gebouw aan de Pater Dehonlaan 63 dat sinds de bouw in 1988 nog tweemaal uitgebreid is. In 2021 fuseerde het Juvenaat met het Mollerlyceum. Vanaf het schooljaar 2022-2023 zullen de leerlingen van het Juvenaat tijdelijk verhuizen naar de Noordzijde Zoom. De nieuwe school gaat verder onder de naam MollerJuvenaat. Oud-leerlingen Dit is een lijst van oud-leerlingen van het Juvenaat met een artikel op Wikipedia. Cornald Maas (1962, televisiepresentator en schrijver) Ties Mellema (1976, saxofonist) Maartje Stokkers (1978, musicologe en radiopresentatrice) Externe link Officiële website Bergen op Zoom Katholieke school in Nederland Gymnasium in Nederland School in Noord-Brabant	{ "redpajama_set_name": "RedPajamaWikipedia" }	5,873
8 Reasons Why Plant-Based Investment is Thriving in Canada ©YamChops Over recent months, there has been a spike in plant-based fundraising taking place in the Canadian market. Around 70 percent of young Canadians believe that plantbased meat is here to stay, 77% of Canadian consumers understand the harmful environmental impact of eating red meat, and 74% of Canadians see meat reduction as essential to reduce their carbon footprint. Here follows eight recent plant-based investment news stories showing that Canada is a market of interest in 2021. Yesterday, Nabati Foods Inc announced a private placement, of up to $4,000,000. With sales growth of more than 85% in 2020 compared to 2019, the company is poised for rapid expansion and plans to enter the European market in 2022. Eat Beyond Global Holdings Inc, an investment issuer focused on the global plant-based and alternative food sector, floated its common shares on the Canadian Securities Exchange at the end of 2020. ©The Very Good Butcher The Very Good Butcher last week celebrated a year of milestones including a record two billion beans "butchered" for its vegan meats. Its record sales in 2020 included 313,286 units of its flagship Very Good Burger. VERY leased two additional facilities in Vancouver and California to increase Canadian retail distribution and launch U.S. retail in 2021. TVGB also recently announced plans to aquire Canadian vegan cheese producer The Cultured Nut as part of its rapid expansion plans. PlantX Life Inc. secured an oversubscribed CA$11.5 million financing at the tail-end of 2020—giving the company a better financial position moving into 2021. ©PlantX The Government of Canada recently awarded CA$1 million to NEXE Innovations. Shortly after that positive gesture, NEXE announced the significant expansion of its research, development and manufacturing facility in Surrey, BC—a move said to double the company's footprint from ~10,000 sq ft to ~20,000 sq ft. Mother Raw, a vegan dressings brand based in Toronto, raised $6.1M for expansion. Mother Raw was launched last year and produces 20 varieties of dressings, including ranch, Caesar, vegan queso, and Greek. Since last year, its sales have surged by 247 percent as the brand expanded to major chains such as Whole Foods, Target, and Sprouts. Specializing in a variety of plant-based meats; Plant & Co Brands recently finalized the acquisition of various Canadian corporations doing business as YamChops. Using the slogan "Grown not raised", YamChopsTM specializes in the preparation, distribution, and retail sales of over 17 proprietary plant-based meats, chicken, pork, fish, and various other vegan style food products in both a B2B and B2C revenue models, and claims to have been Canada's "first plant-based butcher". Sponsored Post What's Trending in the Plant Based World? August 29, 2022 Plant Based World Offered a Glimpse of How Plant-Based… October 26, 2021 The Future of Plant-Based Food and Drinkby Dasha Shor,… November 17, 2022 US Plant-Based Sales Smash $7.4Bn as Conventional Dairy… March 24, 2022 Allen Zelden: My 4 Trend Predictions for 2023 December 20, 2022 What's Behind the Recent Vegan Spam Explosion? Five Reasons… August 17, 2022	{ "redpajama_set_name": "RedPajamaCommonCrawl" }	3,860
\section{Introduction} The advent of Quantum Mechanics (QM) and the problems linked to its ontological nature changed our conception of physical reality in a radical way, problems that before had concerned just philosophers of science became central to the physics debate. Notions like observable, observer and measurement, which had not been problematic to the conception of physical theories, became fundamental and subject of numerous controversies. Furthermore, the classical realist conception of physical objects as independent bearers of properties, on which the ontology of classical theories was based, was also challenged; becoming evident the interpretational difficulties of the theory, a problem which physics had never affronted before.\\ \indent Today, more than one hundred years after Max Planck formulated the quantum hypothesis, we still do not have a settled agreement about what quantum reality is or if there is something as a quantum reality at all. Nevertheless, the theory has been incredibly successful in its predictive role. For this reason, many physicists think that probably there is no necessity of an interpretation of the theory that go further than the interpretation linked to its predictive nature. But, despite this predictive success, it has not been possible to conciliate the theory in its instrumentalist form with General Relativity (GR), and it is becoming evident that a new formalism, which give us a completely new perspective of the theory, will be needed to solve this problem.\\ \indent Numerous proposals have been advanced to solve the interpretational issues of QM, however, none of these have been able to transcend their heuristic argumentations with a solid mathematical machinery that captures and go further than the classical tools, settling the respective interpretation. Our inability to do so is probably a sign that behind the understanding of QM hides the necessity to transcend also the classical mathematical formalism that lies at the foundations of the tools used so far to conceive physical theories.\\ In recent years Topos Theory has captured the attention of people working on the foundations of QM as a possible route to reformulate the theory in a way flexible enough to include relativistic concepts, and where a definite interpretation could be finally settled. The origins of this approach can be traced back to the work developed by Takeuti in 1975 on Boolean Valued Models of Set Theory. Takeuti proved that in a Boolean Valued model of set theory constructed over a complete boolean algebra of projector operators of a Hilbert space, there is a correspondence between the self adjoint operators which spectral family is contained in the boolean algebra of projections and the real numbers of the boolean valued model \cite{takeuti}\cite{ozawa}. In those days the importance of this result respect to its possible relation with interpretational issues of QM was discussed (see \cite{davis}) but no conclusive results were obtained, and maybe due to the fact that the result used advanced tools of set theory and logic, it did not capture the attention of the physics community.\\ \indent Recently the work of C. Isham, A. Doering \cite{isham} \cite{doering} and others have brought the attention back to these methods and particularly to the idea that these tools can be used to obtain a new conception of the continuum useful to formulate Quantum Gravity theories and to obtain a new perspective of QM. Even if not explicitly stated both, Takeuti's and Isham-Doering's approaches, are a reformulation of the old idea proposed several times after the publication of the seminal paper in Quantum Logic (QL) by Von Neumann and Birkhoff, regarding the necessity of a formalism founded over a Quantum Logic as a route to reformulate the theory in a way able to capture the essence of quantum reality. However, it is still not clear that this new approach will give us a better understanding of the theory. Unfortunately, the intrinsic difficulties of Cohen's forcing in the boolean formulation and the abstract categorical machinery of topos theory have obscured the potentiality of these methods to obtain a better picture of QM.\\ In 1995 X. Caicedo introduced what can be considered so far the most user-friendly approach to Kripke-Joyal Semantics \cite{caicedo} (the semantics intrinsic to a topos), giving a new perspective that avoids the technicalities linked to the categorical tools of topoi. Caicedo introduced a model theory of variable structures where it is possible to introduce a definition of genericity and a generic model theorem which unifies set theoretic forcing constructions and the classical theorems of model theory as completeness, compactness, omitting types etc.. In this context the approach to set theoretic forcing generalizes the Scott-Solovay Boolean \cite{scott} and the Fitting intuitionistic \cite{fitting} formulations, simplifying the constructions and clarifying the essence of the proofs of classical independence results as the independence of the continuum hypothesis \cite{benavides} \cite{benavides3}. Another remarkable fact is how interesting connections between classical logic and intuitionistic logic are revealed, showing that the logic of sheaves is not just intuitionistic but that constitutes a continuum of logics between classical and intuitionistic logic, where the independence results of set theory and the classical theorems of model theory can be conceived as a consequence of some limit process over this continuum.\\ \indent In this work I apply these tools to QM, the idea in a few words is to show that the logic intrinsic to QM lies in this continuum of logics and then to show that the emergence of classicality can be conceived as a limit process over these logics. The logic used here will differ from the classical QL of Von Neumann and Birkhoff; its construction arises from the local character of truth of Sheaf Logic, which allows to introduce some contextual features of QM as those derived from the Kochen-Specker theorem and from the Deutsch-Everett multiversal interpretation of interference phenomena. Over this logic a hierarchy of \textit{Quantum Variable Sets} is constructed that generalizes and simplifies the Boolean approach of Takeuti. In this model, two alternative proofs of Takeuti's correspondence, between self adjoint operators and the real numbers of the model, are given. This approach results to be more constructive, showing a direct relation with the Gelfand representation theorem, and revealing also the importance of these results with respect to the interpretation of QM in close connection with the Deutsch-Everett multiversal interpretation of quantum theory. Finally it is shown how the collapse via generic models of this structure of quantum variable sets can help to explain the emergence of classicality also in close relation with the Deutsch-Everett perspective\footnote{I have been recently referred to the work of W. Boos \cite{boos} and R. A. Van Wesep \cite{vanw} which suggest the use of the generic property in an analogous way as proposed here to explain the emergence of classicality in QM. Even if Boos work is motivated in analogous ideas it is in essence different because it is based on the use of measure algebras and not in boolean algebras of projections. On the other hand Van Wesep approach is more closely related to the ideas here presented, it is particularly interesting the study of the emergence of probability that he proposes, however he does not mention Takeuti's result which is fundamental to understand in which sense these tools can explain the collapse to a classical world. Both papers are also based on the classical Boolean approach to Cohen's forcing. As I am suggesting here, Caicedo's work simplifies remarkably the boolean approach in a way closely related with topos theoretic tools and that results fundamental to understand how these methods can help to settle an interpretation of QM. Due to I concluded this work before knowing of the existence of Boos and Van Wesep papers I will postpone the discussion of their results in the context of the tools here presented to a future work.}.\\ I have divided this work in two main sections, the first one is an introduction to sheaf logic as developed in Caicedo's work, giving here an approach oriented to physicists. Even if it is not possible to get a complete picture of these tools without some knowledge of model theory and set theory the guiding ideas are very natural and can be followed without being an expert in these fields. The second part deals with the construction of the hierarchy of Quantum Variable Sets and the results cited above. Hopefully, the ideas contained here will be also useful to people working with applications of topos theory in physics, particularly bringing attention to the fundamental role of logic that sometimes is forgotten giving prevalence to the geometric character of the theory. As I argue in this work, the role of logic in these tools can be fundamental to obtain a new satisfactory picture of QM and probably the connections between geometry and logic, the most remarkable feature of topoi, will be fundamental in the construction of a future Quantum Gravity theory. \section{Sheaves of Structures} The notion of a Sheaf of structures has its origins on the study of the continuation of analytic functions in the XIX century, but the modern definition was introduced just few years after the end of the second world war, by Leray, Cartan and Lazard, in the context of Algebraic topology and Algebraic Geometry. However, the idea of a sheaf of structures is naturally contained in the conception of spacetime which derives from the Galilean relativity principle. The Galilean relativity principle asserts that the dynamical laws are the same when are referred to any frame in uniform motion. This principle forces us to abandon the Aristotelian Picture of a fixed and absolute background space which constitutes a preferential frame where physical objects move. Thus, the idea of considering a point in space as the same point an instant later looses its meaning. Instead, Galilean dynamics implies that there is not one fixed Euclidean 3-dimensional space where the physical world is contained, but that to each instant corresponds a different 3-dimensional world \cite{penrose}, which is attached with the other worlds in a continuous way respect to the temporal order(see fig. \ref{Gspace}). \begin{figure} \centering \includegraphics[scale=0.50]{Gspacetime.pdf} \caption{Galilean Spacetime} \label{Gspace} \end{figure} Each of these worlds is formed by objects which represent a snapshot of an extended object in time. There also exist functions and relations defined over each world, which represent and describe the instantaneous physical attributes of these extended objects. The continuous attachment refers to the possibility of seeing these extended objects as functions that at each time assign an object in the respective world in such a way that they form a continuous object as seeing from the perspective of the hole attachment. In the same way the functions and relations that give instantaneous descriptions attach also in a continuous way when seen as functions and relations of the attachment of the different instantaneous worlds.\\ We can summarize this description of Galilean spacetime as follows. We have a topological space $X=$\textit{temporal line}, for each element $x\in X$ there is an structure $\mathfrak{A}_x$ which is formed by a world $E_x$ which objects constitute a snapshot of extended objects in time, functions $f^{x}_1,f^{x}_2,...$ and relations $R^{x}_1,R^{x}_2,...$ which give the instantaneous properties of the extended objects at the instant $x$. Even if at each instant $x$ we have different worlds $E_x$, this worlds are of a same kind in the sense that the functions, relations and objects can be given analogous interpretations at each instant. The different worlds $E_x$ attach in an extended universe $E$ in such a way that the attachment of the objects, functions and relations are continuous as seeing as extended objects, functions or relations defined in this extended world. In a few words at each instant $x$ we have an structure $\mathfrak{A}_x=(E_x,R^{x}_1, R^{x}_2...,f^{x}_1,f^{x}_2...)$ formed by a world of instantaneous snapshots of extended objects, functions and relations that attach in a continuous way. All this features can be easily formalized and generalized using the notion of a Sheaf of Structures. The ideas presented in this section follow \cite{caicedo}, the proofs of the results presented here can be found there, however I will try to motivate the results and the main ideas can be understood without knowing all the technical details. \subsection{Sheaves and Presheaves} \begin{defin} Let $X$ be a topological space. A sheaf over $X$ is a couple $(E,p)$, where $E$ is a topological space and $p:E\rightarrow X$ is a local homeomorphism, or in other words a continuous function such that for each $e\in E$ there exists a neighbourhood $V$ of $e$ such that: \begin{enumerate} \item $p(V)$ is open in $X$ \item $p\upharpoonright_{V}:V\rightarrow p(V)$ is an homeomorphism. \end{enumerate} Given an open set $U$ in $X$, a function $\sigma:U\rightarrow E$ such that $p\circ \sigma=id_{U}$ is called a local section, if $U=X$, $\sigma$ is called a global section. The set $p^{-1}(x)\subset E$ for $x\in X$ is called the fibre over $x$. \end{defin} Using the sheaf notion it becomes easy to define a generalization which captures the essence contained in the picture of Galilean spacetime as described above. The formalism of the definition given below contains some technicalities of model theory, but the essence of the definition can be understood even if you are not used to the language of this field. \begin{defin} Given a fix type of structures $\tau=(R_1,...,f_1,...,c_1,...)$ a sheaf of $\tau$-structures $\frak{A}$ over a topological space $X$ is given by:\\ a-) A sheaf $( E,p)$ over $X$.\\ b-) For each $x\in X$, a $\tau$-structure $\mathfrak{A}_x=(E_x,R^{x}_1, R^{x}_2...,f^{x}_1,...,c^{x}_1,...)$, where $E_x=p^{-1}(x)$ (the fiber that could be empty) is the universe of the $\tau$-structure $\mathfrak{A}_x$, and the following conditions are satisfied: \\ i. $R^{\mathfrak{A}}=\bigcup_x R_x$ is open in $\bigcup_x E^{n}_{x}$ seeing as subspace of $E^n$, where $R$ is an n-ary relation symbol.\\ ii. $f^{\mathfrak{A}}=\bigcup_{x}f_x:\bigcup_x E_{x}^{m}\rightarrow \bigcup_x E_x$ is a continuous function, where $f$ is an $m$-parameter function symbol.\\ iii. $h:X\rightarrow E$ such that $h(x)=c_x$, where $c$ is a constant symbol, is continuous. \end{defin} The type of a structure mentioned in the definition above is a concept used in logic and model theory. In a few words a type $\tau$ is a language with symbols of relations, functions and constants. A $\tau$-structure $\mathfrak{A}$ is formed by a set of objects $A$ where the different symbols of relations, functions and constants find an interpretation as functions or relations over this set and the constants as elements of this set. For example if $\tau=(\widehat{\times},\widehat{1})$, the structure which has as universe the rational numbers $\mathbb{Q}$, where $\widehat{ \times}$ is interpreted as the multiplication of rational numbers and $\widehat{1}$ is interpreted as the number $1$ is a $\tau$-structure. This can be rather confusing but in some sense is just telling us that we are attaching structures of the same kind. On the other hand the properties (i), (ii),(iii) determine that the structures attach in a smooth or continuous way.\\ \indent A sheaf of structures is a space extended over the base space $X$ of the sheaf as Galilean spacetime extends over time. The elements of this space will not be the points of $E$ but the sections of the sheaf conceived as extended objects. The single values of these sections represent just punctual descriptions of the extended object.\\ Let $U\subset X$ be an open subset of the base space, the set of sections defined over $U$, \[\mathfrak{A}(U)=\{\sigma:U\rightarrow E : \sigma\text{ continuous and } \sigma(x)\in E_x\},\] can be seen also as the universe of an structure of the same type $\tau$ of the sheaf of structures. This follows from the fact that the continuous attachment guarantees that if, for instance, we have sections $\sigma_1,...,\sigma_n$ defined over an open set $V$ and some relation $R(\sigma_1(x),...,\sigma_n(x))$ holds at the node $x\in V$, taking $U'=p^{-1}(Im((\sigma_1,...,\sigma_n))\cap R^{\mathfrak{A}})$ which is an open set by the definition above, we have that for $y\in U=U'\cap V$, $R(\sigma_1(y),...,\sigma_n(y))$ holds. Then we can say that $R(\sigma_1,...,\sigma_n)$ holds in $U$ if $R(\sigma_1(y),...,\sigma_n(y))$ for all $y\in U$. In an analogous way if $f^{\mathfrak{A}}(\sigma_1(x),...,\sigma_n(x))=\mu(x)$ for some section $\mu$ defined over $V$ and a $n$-parameter function symbol $f$, by the definition above we have that $f^{\mathfrak{A}}\circ (\sigma_1,...,\sigma_n)$ is continuous, then there exists an open neighbourhood $U$ of $x$ such that $f^{\mathfrak{A}}\circ (\sigma_1,...,\sigma_n)(U)\subseteq Im(\mu)$, thus $f^{\mathfrak{A}}(\sigma_1(y),...,\sigma_n(y))=\mu(y)$ for all $y\in U$. Using this we can define a function $f^{\mathfrak{A}(U)}$ such that $f^{\mathfrak{A}(U)}(\sigma_1,...,\sigma_n)=\mu$ if $f^{\mathfrak{A}}(\sigma_1(y),...,\sigma_n(y))=\mu(y)$ for all $y\in U$. Considering these kind of structures we have that for any open set $V\subset U$ the restriction of the sections define a natural homomorphism $\rho$ (i.e a function which conserve the relations and commute with functions) between $\mathfrak{A}(U)$ and $\mathfrak{A}(V)$: \begin{align} \rho_{UV}:\mathfrak{A}(U) &\rightarrow \mathfrak{A}(V)\\ \sigma &\mapsto \sigma\upharpoonright_V. \end{align} Sometimes it will be easier to define the structures $\mathfrak{A}(U)$\footnote{Here we are identifying the structure with the universe of the structure $\mathfrak{A}(U)$ this is something common in model theory to avoid some excess of formalism.} than the complete sheaf of structures, as it will be the case of the hierarchy of Quantum Variable Sets. However given the structures $\mathfrak{A}(U)$ for the open sets of $X$ and the morphisms $\rho_{UV}$, it is possible to reconstruct the sheaf of structures. To show how to do this, we need two important definitions. \begin{defin} A presheaf of structures of type $\tau$ over $X$ is an assignation $\Gamma$, such that to each open set $U \subset X$ is assigned a $\tau$-structure $\Gamma(U)=(\Gamma(U), R^{\Gamma(U)}_1,..., f^{\Gamma(U)}_1,...,c^{\Gamma(U)}_1,..)$, and if $V\subset U$ it is assigned an homomorphism $\Gamma_{UV}$ which satisfies $\Gamma_{UU}=Id_{\Gamma(U)}$ and $\Gamma_{VW}\circ\Gamma_{UV}=\Gamma_{UW}$ if $W\subseteq V\subseteq U$. \end{defin} It is clear that it is possible to define a presheaf of structures $\Gamma_{\mathfrak{A}}$ from a sheaf of structures assigning to each open set $U$ a $\tau$-structure which universes are the sets $\mathfrak{A}(U)$, and the homorphism are the $\rho_{UV}$ defined above. Given a presheaf of structures we can construct a Sheaf of structures in the next way: \begin{defin} Let $\Gamma$ a presheaf of structures over $X$. Let $\mathcal{G}\Gamma$ be the sheaf of structures over $X$ such that each fiber $(\mathcal{G}\Gamma)_x$ is defined by: \[(\mathcal{G}\Gamma)_x=\dot{\bigcup} _{U\in \mathcal{V}(x)} \Gamma(U)_{/\sim_x},\] where $\mathcal{V}(x)$ is the set of neighbourhoods of $x$, and given $\sigma\in \Gamma(U)$ and $\lambda\in \Gamma(V)$, \[\sigma\sim_x\lambda \Leftrightarrow \exists W\in \mathcal{V}(x), W\subseteq U\cap V\text{ such that } \Gamma_{UW}(\sigma)=\Gamma_{VW}(\lambda).\] Let $[\sigma]_x$ the equivalence class of $\sigma$ respect to $\sim_x$. We have that: \[([\sigma_1]_x,...,[\sigma_n]_x)\in R^{x}\Leftrightarrow \exists U\in\mathcal{V}(x)\text{ such that }(\sigma_1,...,\sigma_n)\in R^{\Gamma(U)}\] \[f([\sigma_1]_x,...,[\sigma_n]_x)=[f^{\Gamma(U)}(\sigma_1,...,\sigma_n)]_x.\] The space of the fibers $\bigcup_x(\mathcal{G}\Gamma)_x$ is given the topology generated by the images of the sections \begin{align} a_{\sigma}:U&\rightarrow E\\ x & \mapsto [\sigma]_x. \end{align} The sheaf $\mathcal{G}\Gamma$ is called the sheaf of germs of $\Gamma$. \end{defin} This definition can be understood using the analogy of Galilean spacetime in the next way. If to each time interval we assign objects such that their history or part of it develops in such interval, we can recover the instantaneous perspective identifying two objects at each instant if their histories coincide in an interval of time containing that instant. In the same way a relation will hold from the instantaneous point of view if it holds in a time interval containing the respective instant. This kind of contextuality will play a fundamental role in the logic that governs these models as we will see below.\\ The sheaf of germs $\mathcal{G}\Gamma_{\mathfrak{A}}$ associated to the presheaf of sections $\Gamma_{\mathfrak{A}}$ of a sheaf $\mathfrak{A}$, is naturally isomorphic to the original sheaf. Indeed the function \begin{align} H:\bigcup_{x\in X}(\mathcal{G}\Gamma_{\mathfrak{A}})_x&\rightarrow E\\ [\sigma]_x\mapsto \sigma(x), \end{align} defines a natural isomorphism which sends in an isomorphic way each fiber $(\mathcal{G}\Gamma_{\mathfrak{A}})_x$ to the fiber $E_x$. On the other hand given a presheaf $\Gamma$ the presheaf $\Gamma_{\mathcal{G}\Gamma}$ associated to the sheaf of germs $\mathcal{G}\Gamma$, results also isomorphic to the original presheaf just if the presheaf satisfies a further condition. \begin{defin} A presheaf of structures is said to be exact, if given $U=\bigcup_i U_i$ and $\sigma_i\in\Gamma(U_i)$, such that if \[\Gamma_{U_i,U_i\cap U_j}(\sigma_i)=\Gamma_{U_j,U_i\cap U_j}(\sigma_j) \text{ for all } i,j;\] there exists an unique $\sigma\in\Gamma(U)$ such that $\Gamma_{UU_i}(\sigma)=\sigma_i$ for all i. And the same holds for the relations i.e if we have some relations $R^{\Gamma(U_i)}_i, R^{\Gamma(U_j)}_j$ which are sent by the homomorphisms $\Gamma_{U_i,U_i\cap U_j}$, $\Gamma_{U_j,U_i\cap U_j}$ to a same relation for all $i,j$. There exists an unique relation $R^{\Gamma(U)}$ which is sent by the homomorphism $\Gamma_{UU_i}$ to the relation $R^{\Gamma(U_i)}_i$ for all $i$. \end{defin} We have then the next result. \begin{lema} If $\Gamma$ is an exact presheaf then it results isomorphic to the presheaf $\Gamma_{\mathcal{G}\Gamma}$ associated to the sheaf of germs $\mathcal{G}\Gamma$, in the sense that $\Gamma_{\mathcal{G}\Gamma}(U)\cong \Gamma(U)$ as structures and the homomorphisms $\Gamma_{UV}$ transform in the homomorphism $\Gamma_{\mathcal{G}\Gamma_{UV}}$. \end{lema} We will define the Quantum Hierarchy of variable sets defining an exact presheaf, the above results allow to deal indistinctly with the presheaf of structures and the associated sheaf. \subsection{The Logic of Sheaves of Structures}\label{logic1} The notion of `truth" in classical physics is a contextual one. When we affirm that a property holds for a certain object at some instant, we are referring to a measurement realized in an extended interval of time containing that instant. The mathematical models we use to describe such situations, even if based on an absolute notion of truth, permit to capture this contextual character using the notion of limit, which allows to define instantaneous properties in a coherent way. In some sense the notion of limit is what makes classical logic work in the conception of the continuum. It is surprising then, that mathematical models which are based on an absolute notion of truth can capture and describe physical reality, where the notion of truth is contextual, in such an effective way. Nevertheless, it is probably this lack of contextuality what makes the classical formalism inappropriate to give a complete picture of quantum theory. In QM the notion of contextuality recovers total new meanings related to the incompatibility of observables, and interference phenomena as we will see. Therefore, it can be fundamental to have a formalism that allows to include a notion of truth which can contain these contextual features. This is the case of the sheaves of structures, which have a logic based on the next \textit{contextual-truth} paradigm: \begin{center} \textit{If a property for an extended object holds in some point of its domain then it has to hold in a neighbourhood of that point.} \end{center} As the objects of a sheaf of structures are the sections of the sheaf, the logic which governs them should define when a property for an extended object holds in a point of its domain of definition. The next definition contains a lot of logical language but it is very natural. \begin{defin} \label{logic} Let $L_{\tau}$ be a first order language of type $\tau$. Given a sheaf of structures $\frak{A}$ of type $\tau$ over $X$, and a proposition $\varphi(v_1,...,v_n)\in L_{\tau}$ we can define by induction \[\frak{A}\Vdash_x \varphi(\sigma_1,...,\sigma_n)\] (Which means $\frak{A}$ forces $\varphi(\sigma_1,...,\sigma_n)$ in $x\in X$ for the sections $\sigma_1,...,\sigma_n$ of $\frak{A}$ defined in $x$ or in a more elementary fashion, the property $\varphi$ holds at the node $x$ for the sections $\sigma_1,...\sigma_n$ in the sheaf $\mathfrak{A}$) :\\ 1. If $\varphi$ is an atomic formula and $t_1,...,t_k$ are $\tau$-terms: \[\frak{A}\Vdash_x (t_1=t_2)[\sigma_1,...,\sigma_n]\Leftrightarrow t_1^{\frak{A}_x}[\sigma_1(x),...,\sigma_n(x)]=t_2^{\frak{A}_x}[\sigma_1(x),...,\sigma_n(x)]\] \[\frak{A}\Vdash_x R(t_1,...,t_n)[\sigma_1,...,\sigma_n]\Leftrightarrow (t_1^{\frak{A}_x}[\sigma_1(x),...,\sigma_n(x)],...,t_n^{\frak{A}_x}[\sigma_1(x),...,\sigma_n(x)])\in R^{x}\] 1'. The equality between extended objects, or objects defined in function of extended objects holds at some node if and only if the equality holds for their punctual descriptions. Analogous for the relations.\\ 2. $\frak{A}\Vdash_x (\varphi\wedge\psi)[\sigma_1,...,\sigma_n]\Leftrightarrow \frak{A}\Vdash_x\varphi[\sigma_1,...,\sigma_n]$ and $\frak{A}\Vdash_x \psi[\sigma_1,...,\sigma_n]$\\ 2'. The conjunction of two properties holds for some extended objects at some node if and only if each property holds for those extended objects at the same node. \\ 3. $\frak{A}\Vdash_x (\varphi\vee\psi)[\sigma_1,...,\sigma_n]\Leftrightarrow \frak{A}\Vdash_x\varphi[\sigma_1,...,\sigma_n]$ or $\frak{A}\Vdash_x\psi[\sigma_1,...,\sigma_n]$.\\ 3'. The disjunction of two properties holds for some extended objects at some node if and only if one of the properties hold for the extended objects in that node.\\ 4.$\frak{A}\Vdash_x\neg\varphi[\sigma_1,...,\sigma_n]\Leftrightarrow$ exists $U$ neighbourhood of $x$ such that for all $y\in U$, $\frak{A}\nVdash_y \varphi[\sigma_1,...,\sigma_n]$.\\ 4'.The negation of a property for some extended objects hold at some node, if and only if there exists a neighbourhood of the node such that at each point in that neighbourhood the property does not hold for the extended objects.\\ 5. $\frak{A}\Vdash_x (\varphi\rightarrow\psi)[\sigma_1,...,\sigma_n]\Leftrightarrow$ Exists $U$ neighbourhood of $x$ such that for all $y\in U$ if $\frak{A}\Vdash_y\varphi[\sigma_1,...,\sigma_n]$ then $\frak{A}\Vdash_y\psi[\sigma_1,...,\sigma_n]$.\\ 6. $\frak{A}\Vdash_x \exists v\varphi(v,\sigma_1,...,\sigma_n)\Leftrightarrow$ exists $\sigma$ defined in $x$ such that $\frak{A}\Vdash_x\varphi(\sigma,\sigma_1,...,\sigma_n)$\\ 7. $\frak{A}\Vdash_x\forall v\varphi(v,\sigma_1,...,\sigma_n)\Leftrightarrow$ exists $U$ neighbourhood of $x$ such that for all $y\in U$ and all $\sigma$ define in $y$, $\frak{A}\Vdash_y\varphi[\sigma,\sigma_1,...,\sigma_n]$. (In 4,5,7 \quad $U$ has to satisfy $U\subseteq \bigcap_{i}dom(\sigma_i)$) \end{defin} Numerals 1',2',3', 4' clarify the content of the definition without the technicalities of the logical language; 5,6, 7 are more clearly understood using formal language. It is clear from 4,5, 7 how this is a contextual logic, however this contextuality is better expressed in the next result which tell us that a property is verified at some node if and only if it is verified in a neighbourhood of that node. \begin{corol} \label{localtruth} $\frak{A}\Vdash_x \varphi[\sigma_1,...,\sigma_n]$ if and only if there exists a neighbourhood $U$ of $x$, such that $\frak{A}\Vdash_y \varphi[\sigma_1,...,\sigma_n]$ for all $y\in U$. \end{corol} Using the above definition it is possible to introduce a local semantics in a natural way, which will be more useful when dealing with presheaves of structures. Given an open subset $U\subset X$, and sections defined over $U$, we say that a proposition about these sections holds in $U$ if it holds at each point in $U$ or in other words: \[\mathfrak{A}\Vdash_U\varphi[\sigma_1,...,\sigma_n]\Leftrightarrow \forall x\in U, \mathfrak{A}\Vdash_x \varphi[\sigma_1,...,\sigma_n]\] This definition is determined completely by the next result. \begin{teor}[Kripke-Joyal semantics]\label{kripkejoyal} $\frak{A}\Vdash_U\varphi[\sigma_1,...,\sigma_n]$ is defined by:\\ 1. If $\varphi$ is an atomic formula:\\ $\frak{A}\Vdash_U\sigma_1=\sigma_2\Leftrightarrow \sigma_1\upharpoonright_U=\sigma_2\upharpoonright_U$.\\ $\frak{A}\Vdash_U R[\sigma_1,...,\sigma_n]\Leftrightarrow (\sigma_1,...,\sigma_n)(U)\subseteq R^{\frak{A}}$.\\ 2. $\frak{A}\Vdash_U(\varphi\wedge\psi)[\sigma_1,...,\sigma_n]\Leftrightarrow \frak{A}\Vdash_U\varphi[\sigma_1,...,\sigma_n]$ and $\frak{A}\Vdash_U\psi[\sigma_1,...,\sigma_n]$.\\ 3. $\frak{A}\Vdash_U(\varphi\vee\psi)[\sigma_1,...,\sigma_n]\Leftrightarrow$ there exist open sets $V,W$ such that $U=V\cup W$, $\frak{A}\Vdash_V\varphi[\sigma_1,...,\sigma_n]$ and $\frak{A}\Vdash_W\psi[\sigma_1,...,\sigma_n]$.\\ 4. $\frak{A}\Vdash_U\neg\varphi[\sigma_1,...,\sigma_n]\Leftrightarrow$ For any open set $W\subseteq U$,\quad$W\neq\emptyset$,\quad$\frak{A}\nVdash_W\varphi[\sigma_1,...,\sigma_n]$.\\ 5. $\frak{A}\Vdash_U \varphi\rightarrow\psi[\sigma_1,...,\sigma_n]\Leftrightarrow$ for any open set $W\subset U$,\quad if $\frak{A}\Vdash_W\varphi[\sigma_1,...,\sigma_n]$ then $\frak{A}\Vdash_W\psi[\sigma_1,...,\sigma_n]$.\\ 6. $\frak{A}\Vdash_U\exists v\varphi(v,\sigma_1,...,\sigma_n)\Leftrightarrow$ there exists $\{U_i\}_i$ an open cover of $U$ and $\mu_i$ sections defined on $U_i$ such that $\frak{A}\Vdash_{U_i}\varphi[\mu_i,\sigma_1,...,\sigma_n]$ for all $i$.\\ 7. $\frak{A}\Vdash_U\forall v\varphi(v,\sigma_1,...,\sigma_n)\Leftrightarrow$ for any open set $W\subset U$ and $\mu$ defined on $W$, $\frak{A}\Vdash_W\varphi(\mu,\sigma_1,...,\sigma_n)$. \end{teor} The logic just defined can be seen as a multivalued logic with truth values that variate over the Heyting algebra of the open sets of the base space $X$. Let $\sigma_1,..., \sigma_n$ sections of a sheaf $\mathfrak{A}$ defined over an open set $U$, we define the \textit{``truth value"} of a proposition $\varphi$ in $U$ as: \[ [[\varphi(\sigma_1,...,\sigma_n)]]_{U}:=\{x\in U: \mathfrak{A}\Vdash _x \varphi [\sigma_1,...,\sigma_n]\}\] From corollary \ref{localtruth} we know that $[[\varphi(\sigma_1,...,\sigma_n)]]_{U}$ is an open set, thus we can define a valuation as a topological valuation on formulas: \[T_{U}:\varphi\mapsto [[\varphi(\sigma_1,...,\sigma_n)]]_{U}.\] The definition of the logic allows to define the value of the logic operators in terms of the operations of the algebra of open sets. For instance, the proposition $\neg\varphi$ is valid in a point if there exists a neighbourhood of that point where $\varphi$ does not hold at each point of the neighbourhood, then $\neg\varphi$ holds in the interior of the complement of the set where $\varphi$ holds i.e $[[\neg \varphi]]_{U}= Int (U\setminus [[\varphi]]_{U}),$. Reasoning in analogous way we have: \begin{enumerate} \item $[[\sigma_1=\sigma_2]]_{U}=\{x\in U:\sigma_1(x)=\sigma_2(x)\}$. \item $[[R[\sigma_1,...,\sigma_n]]]_{U}=\{x\in U: (\sigma_1(x),...,\sigma_n(x))\in R^{\mathfrak{A}}\}$ \item $[[\neg \varphi]]_{U}= Int ((U\setminus [[\varphi]]_{U}),$ \item $[[\varphi\wedge \psi]]_{U}=[[\varphi]]_{U}\cap[[\psi]]_{U},$ \item $[[\varphi\vee \psi]]_{U}=[[\varphi]]_{U}\cup [[\psi]]_{U},$ \item $[[\varphi\rightarrow \psi]]_{U}= Int((U\setminus[[\varphi]]_{U})\cup [[\psi]]_{U}),$ \item $[[\exists u \varphi (u)]]_{U}=\bigcup_{\sigma\in \mathfrak{A}(W), W\subset U}[[\varphi(\sigma)]]_{W},$ \item $[[\forall u\varphi(u)]]_{U}=Int(\bigcap_{\sigma\in \mathfrak{A}(W), W\subset U}[[\varphi(\sigma)]]_{W}).$ \end{enumerate} It follows then \[\mathfrak{A}\Vdash_{U} \varphi[\sigma_1,...,\sigma_n]\leftrightarrow [[\varphi[\sigma_1,...,\sigma_n]]]_{U}=U.\] Therefore, since the open sets form a complete Heyting algebra, and we have defined the logic operators in terms of the algebra operations, we have that the formulas that get the value 1 in a complete Heyting algebras are forced in every node of the sheaf of structures. This proves that the laws of the intuitionistic logic, which are those that assume the value 1 in a Heyting algebra, are forced in each node of a Sheaf of Structures.\\ In this way each sheaf of structures is ruled by a logic intermediate between intuitionistic logic and classical logic. Intermediate because the geometry of the spaces which determine the sheaf will determine how close or far of each logic is the intrinsic logic of the sheaf (see next section). This connection between logic and geometry is a very interesting fact that can be important in a future theory of Quantum Gravity. \subsection{Excursus: Logic, Physics and Geometry} In recent years the use of topoi has been suggested to construct a kind of Quantum Geometry to unify GR and QM (see for example \cite{crane}), based on the conjectured inadequacy of the classical concept of manifold to construct a theory of Quantum Gravity. The conjecture tacitly contained there is the necessity of an intuitionistic version of spacetime. If an intuitionistic model can capture the essence of quantum mechanics, as I am proposing in this work, it will be natural to think that to unify GR and QM, we will need an intuitionistic version of spacetime. I want to show how probably within General Relativity, using the notion of Sheaf of Structures, we can also find strong motivations to think that this is the right route to follow.\\ \indent The connections between Logic and Geometry included within the formalism I am presenting here (and also in the topos formalism), were one of the main motivations to think that probably these methods can be useful in a future theory of Quantum Gravity. As we will see below the logic structure of quantum mechanics in this context derives in its interpretation. On the other hand, these tools allow to obtain a new description of the continuum which arise from the logic structure of QM. The continuum is what we use in geometry to measure, the notion of Lorentzian manifold is an expression of the continuum to capture the essence of spacetime. If we can construct a definition of manifold which arise from the logic of QM, we will probably get automatically a Quantum Gravity theory. In other words, in some sense Quantum Mechanics represents Logic, and General Relativity is in essence Geometry; if we want to connect these two, the sheaf of structures formalism (or the Topoi formalism) seems to be an appropriate route to follow.\\ To understand better what I mean by connections between logic and geometry lets consider a simple example. Consider $E=\mathbb{R}\cup\{q\}$ and $X=\mathbb{R}$, where $X$ has the usual topology and $E$ has the usual topology of $\mathbb{R}$ plus the open neighbourhoods of $q$ which are of the form $(U\setminus \{0\})\cup\{a\}$ where $U$ is a neighbourhood of $0$. \begin{figure} \centering \includegraphics[scale=0.40]{hausdorff.pdf} \caption{The Hausdorff property in E determines the validity of the excluded middle property. A geometric property determines a logic property.} \label{hausdorff} \end{figure} From $E$ and $X$ we can construct a natural sheaf with $p:E\rightarrow X$ such that $p(x)=x$ if $x\neq q$ and $p(q)=0$ (see Fig \ref{hausdorff}). Consider the sections $a:(-1,1)\rightarrow E$, $b:(-1,1)\rightarrow E$ such that $a(x)=x$ if $x\neq 0$ and $a(0)=q$ and $b(x)=x$ for all $x$. Even if $a$ and $b$ are two different sections, from the perspective of $0$ the sections are either different or equal. In other words on the node $0$ we have: \[ \nVdash_0 (a=b\vee \neg(a=b)).\] Indeed it is clear that $\nVdash_0 a=b$ (i.e $\Vdash_0 a=b$ does not hold) because $a(0)\neq b(0)$ (see 1 in the definition \ref{logic}). On the other hand $\nVdash_0 \neg(a=b)$ because each neighbourhood of $0$ contains points $x$ such that $a(x)=b(x)$. However, note that if $x\in (-1,1)\setminus \{0\}$, $\Vdash_x (a=b)$. The non validity of the excluded middle in $0$ depends on the fact that the Hausdorff property is not valid on the fiber over $0$. It can be proved for an arbitrary sheaf the next result: \[\Vdash_x \forall z,y(z=y\vee\neg(z=y))\Leftrightarrow \exists U\in \mathcal{V}(x) \text{ s.t. } p^{-1}(U) \text{ is a Hausdorff space }.\] Thus, this example shows how the logic of the sheaf of structures is related with the geometric properties of the sheaf.\\ In General Relativity, singularities in a spacetime $M$ can be added as boundary points in an extended manifold $M^{+}=M\cup\partial M$ in such a way that the differential structure of the extended manifold captures the structure of the original manifold in some way. In some of these boundary constructions as those developed by Geroch and Schmidt (see \cite{hawking} p.217 . p.276 respectively) some points, where the Hausdorff property does not hold, appear as a result of the construction of the boundary. Furthermore this situation, in the Schmidt construction, occurs in the Schwarzschild and Friedman solutions \cite{johnson}, which are our paradigms of strong curvature singularities. These non-Hausdorff features have been seen as defects of these boundary constructions, but within the context of the example exposed above, probably what these results are telling us is that the singularities are a result of the breakdown of the logic which governed these models. The breakdown of the Hausdorff property is probably the breakdown of the excluded middle in the singularity point in some appropriate sheaf description of spacetime. The difficulty to construct a satisfactory boundary definition such that the extended manifold conserve all the desirable features of a classical spacetime, is probably due to the fact that this formalism is inadequate to capture these situations. The breakdown of the Hausdorff property is a sign of the breakdown of any possibility of classical description, non- Hausdorff spacetimes affect the formulation of the Cauchy problem, in non-Hausdorff spacetime we can find bifurcating geodesics and classical determinism can loose all its sense. A new conception of manifold is needed, but within this new conception, local determinism will probably have a new meaning based on the ontology of QM, this is why a theory of Quantum Gravity cannot be constructed before settling what Quantum Reality is.\\ \section{Quantum Set Theory} Now we want to construct a mathematical universe which is founded over the logic intrinsic to QM. As we saw above the logic of a sheaf of structures with base space $X$ can be seen as a multivalued logic which take its values over the algebra of open subsets of $X$. Therefore, if we construct sheaves over a topological space which algebra of open sets capture the logic of QM, we will find automatically models ruled by this logic.\\ \indent The mathematical models that have been used so far in physics are founded over classical logic and classical set theory. If we want an alternative mathematical universe founded over the logic of QM, it will be important to find one as a natural generalization of the classical universe. Thus it will be important for this model also to be a kind of model of set theory where all the classical constructions find a natural counterpart.\\ The classical mathematical universe is the Von Neumann Hierarchy, which is constructed inductively in the next way. Let \[ V_0=\emptyset\] \[V_{\alpha+1 }=\mathcal{P}(V_\alpha)\] \[V_\lambda=\bigcup_{\alpha<\lambda}V_{\alpha} \text{ If }\lambda\text{ is a limit ordinal,}\] where $\mathcal{P}(V_{\alpha})$ is the power set of $V_{\alpha}$ (i.e the set of all the subsets of $V_{\alpha}$). The set \[ \mathbb{V}=\bigcup_{\alpha\in On} V_{\alpha},\] where $On$ is the class of all ordinals, is the Von Neumann Hierarchy of classical sets. Probably the notion of ordinal can be new for someone working in physics, but it is not fundamental to understand the model, just think ordinals as a generalization of natural numbers which cover all possible infinities. $\mathbb{V}$ with the classical belonging relation, $\in$, between sets, is the universe of classical mathematics, a model (in the sense of classical logic) of the axioms of ZFC (Zermelo-Fraenkel+Choice). We will construct an analogous model which extend the notion of set, as a variable object over a sheaf, where the $\in$ relation recover a new contextual meaning. \subsection{The Cumulative Hierarchy of Variable Sets} To introduce the definition of the cumulative hierarchy we can use the interpretation that categorists use to introduce the objects of $SET^{\mathbb{P}}$, the advantage here is that the motivation translates literally in the definition; we obtain a truly structure of variable of sets, where using the classical belonging relation between sets it is possible to define an analogous belonging relation between variable sets and not as arrows between objects. The definition I present below was originally introduced in \cite{caicedo} and I used it in \cite{benavides},\cite{benavides3} to get a new proof of the independence of the Continuum Hypothesis. In those articles you can find a more detailed description, here I present a brief introduction enough to follow the main ideas contained below.\\ Using the comprehension axiom of set theory, given a proposition $\varphi(x)$, for any set $A$ we can construct a set $B$ such that $x\in B$ if and only if $x\in A$ and $\varphi(x)$ is ``truth" for $x$ or in other words, \[B=\{x\in A: \varphi(x)\}.\] As we have seen in the sheaves of structures the notion of truth is not absolute but it is based on a contextual truth paradigm. To see how this notion of truth translates when we talk about sets lets consider a particular example. Let $\varphi(x)$ be the next proposition \textit{`` x is an even number greater or equal than 4 and x can be written as the sum of two prime numbers"} . In this moment at my ubication on spacetime $p:=$\textit{``between the 21:00 and the 22:00, of the 5 March 2011, in some place in London"} I cannot assure that $\{z\in\mathbb{N}:\varphi(x)\}=\{x\in \mathbb{N}: x\geq 4 \wedge (x$ is even $)\}$, i.e. that the Goldbach Conjecture is true. However $\varphi$ can be used to define a set at the node $p$, \[\varphi(p)=\{x:\varphi(x) \text{ holds at the node } p.\}\] The Goldbach conjecture has been verified for a huge number of even numbers, and this set of numbers will keep growing each time we will find a new prime number. Probably (maybe not) some day the Goldbach Conjecture will be proved or disproved, but the important feature that follow from this example is that instead of conceiving sets as absolute entities, we can conceive them as variable structures which variate over our \textit{Library of the states of knowledge}. It is natural then to conceive the set of nodes where our states of Knowledge variates as nodes in a partial order or points in a topological space, that can represent, for instance, the causal structure of spacetime. Our "states of Knowledge" will be then structures that represent the sets as we see them in our nodes. Therefore, from each node we will see arise a cumulative Hierarchy of variable sets, which structure will be conditioned by the perception of the variable structures in the other nodes that relate to it. Or more precisely. \begin{defin}\label{hierarchy} Let $X$ be an arbitrary topological space, the cumulative hierarchy of variable sets over $X$ is defined in the next way. Given $U\in Op(X)$\footnote{ $Op(X)$ denote the non empty open sets of $X$} we define inductively: \begin{align} V_0(U)=& \emptyset\\ V_{\alpha+1}(U)=&\{ f:Op(U)\rightarrow \bigcup_{W\subseteq U}\mathcal{P}(V_{\alpha}(W)): 1. \text{ If }W\subseteq U \text{ then } f(W)\subseteq V_{\alpha}(W),\\ & 2. \text{ If }V\subseteq W\subseteq U,\text{ then for all }g\in f(W),\quad g\upharpoonright_{Op(V)}\in f(V),\\ & 3. \text{ Given }\{U_i\}_i \text{ an open cover of } U \text{ and } g_i\in f(U_i)\\ & \text{such that } g_i\upharpoonright_{op(U_i\cap U_j)}=g_j\upharpoonright_{op(U_i\cap U_j)} \text{ for any }i,j,\\ & \text{there exists }g\in f(U) \text{ such that }g\upharpoonright_{op(U_i)}=g_i\text{ for all } i\}\\ V_{\lambda}(U)=&\bigcup_{\alpha<\lambda}V_{\alpha}(U) \text{ if } \lambda\text{ is a limit ordinal,}\\ V(U)=&\bigcup_{\alpha\in On}V_{\alpha}(U). \end{align} The valuation $V$ over the open sets constitute an exact presheaf of structures, which Sheaf of Germs $\mathbb{V}^{X}$ constitute the cumulative hierarchy of variable sets. \end{defin} For each $U\in Op(X)$ the set $V(U)$ is a set of functions defined over $Op(U)$ which values for $W\in Op(U)$ are functions over $Op(W)$ which values for $V\in Op(W)$ are functions over $Op(V)$ and so on.\\ \indent The next step is to define the $\in$ relation. In a natural way we define: \[\Vdash_U f\in g \Leftrightarrow f\in g(U),\] which means that respect to the context $U$, $f$ belongs to $g$ if and only if $f\in g(U)$ as classical sets\footnote{Compare this definition with the definition of the $\in$ relation on Boolean valued models}. At first sight this construction seems to be odd but in the results presented below we will see that the constructions are extremely natural and extremely powerful. The first result is that, as we expect, this model is a natural generalization of the universe of classical sets, a model where the axioms of Set Theory are satisfied respect to the logic of sheaves of structures \cite{villa}\cite{benavides}\cite{benavides3}. \begin{teor} For any topological space $X$, \[\mathbb{V}^{X}\Vdash ZF.\] In other words for any $x\in X$ (or $U\in Op(X)$) , at the node $x$ (at the context $U$) the axioms of set theory are satisfied i.e $\Vdash_x ZF$ ( $\Vdash_U ZF$). \end{teor} To see what this means lets see how the axiom of comprehension cited above is valid in this more general context.\\ \textbf{Axiom of Comprehension:}\textit{ Let $\varphi(x,z,w_1,...,w_n)$ be a formula. For every set $z$ there exists a set $y$ such that, $x\in y$ if and only if $x\in z$ and $\varphi(x)$ holds for $x$ } \begin{lema} Let $X$ be a topological space, in $\mathbb{V}^{X}$ for any $U\in Op(X)$, \[\Vdash_U \forall z\forall w_1,...,w_n \exists y \forall x(x\in y \leftrightarrow x\in z \wedge \varphi)\] \end{lema} \begin{proof} Following the logic of sheaf of structures, contained in theorem \ref{kripkejoyal}, to prove the above result means to prove that for all $W\subseteq U$ and $z,w_1,...,w_n\in V(W)$ there exists an open cover $\{W_i\}_i$ of $W$ and $y_i\in V(W_i)$ such that for any $T_i\subseteq W_i$ and $x\in V(T_i)$ for $Y_i\subseteq T_i$, $x\in y_i(Y_i)$ if and only if\footnote{To be rigorous in this last expression we have to write $x\upharpoonright_{Y_i}\in y_i\upharpoonright_{Y_i}(Y_i)$ however we will omit these technicalities otherwise the notation will become very confusing.} $x\in z(Y_i)$ and $\Vdash_{Y_i}\varphi(x)$. It may seem that proving a result in this new logic is very complicated but as we will see, this and the next results have elementary proofs. Let $z, w_1,...,w_n \in V(U)$ and \[y:Op(U)\rightarrow \bigcup_{W\subseteq U} V(W)\] \[y(W)=\{x\in z(W): \Vdash_W \varphi(x)\}.\] Note that we construct $y(W)$ using the axiom comprehension in the classical universe. It is clear that the variable set $y$ just defined satisfies the result described above taking the appropriate restrictions on the respective sets there cited. Note for example that as an open cover of $W\subseteq U$ we can take the cover formed by the set $W$, in other results below we will need the definition of the existential using a non trivial open cover but here it is not the case. However we need to prove that the $y$ just defined is an element of the structure of variable sets i.e we need to verify properties 1-3 in definition \ref{hierarchy}. Let $\alpha$ the minimum ordinal such that $z\in V_{\alpha+1}(U)$. Since $y(W)\subset z(W)$ then $y(W)\subset V_{\alpha}(W)$, therefore \[y:Op(U)\rightarrow \bigcup_{W\subseteq U} P(V_{\alpha}(W)).\] Given $T\subseteq W\subseteq U$ and $g\in y(W)$ we have $g\in z(W)$ and $\Vdash_W \varphi(g)$. Thus $g\upharpoonright_{Op(T)}\in z(T)$ and $\Vdash_T \varphi(g\upharpoonright_{Op(T)})$, then $g\upharpoonright_{Op(T)}\in y(T)$. Property 3 in the definition follows in analogous way. Therefore $y\in V(U)$. \end{proof} Even if generally $V(U)$ and the classical Von Neumann hierarchy $\mathbb{V}$ are not isomorphic for any open set $U$ there is an standard way to embed $\mathbb{V}$ in $V(U)$. Given an arbitrary set $a\in \mathbb{V}$ let \[\widehat{a}(U):Op(U)\rightarrow\bigcup_{W\subseteq U}V(W)\] \[\widehat{a}(U)(W)=\{\widehat{b}(U)\upharpoonright_{Op(W)}:b\in a\}.\] we have that $\widehat{a}(U)\upharpoonright_{Op(W)}=\widehat{a}(W)$ and it can be proved the next result \cite{benavides3}. \begin{teor} Let $U\subseteq X$ an open subset, then \begin{align} \Psi:\mathbb{V}&\rightarrow V(U)\\ a &\mapsto \widehat{a}(U) \end{align} is a monomorphism. \end{teor} Using this embedding it can be easily proved that the set forced as the empty set on each open set $U$ is precisely $\widehat{\emptyset}(U)$ or in other words it holds \[\Vdash_U \forall y (y\notin \widehat{\emptyset}(U)).\] In the same way it can be proved that the set forced as the set of natural numbers (i.e. the minimum inductive set that contains the empty set) is precisely $\widehat{\mathbb{N}}(U)$ \cite{benavides3}. The sets forced as the integers and the rational numbers are also $\widehat{\mathbb{Z}}(U)$ and $\widehat{\mathbb{Q}}(U)$ respectively. However the set forced as the real numbers generally not coincide with $\widehat{\mathbb{R}}(U)$, for example as we will see below, this is the case of the set that is forced as the real numbers in the case related to a base space which captures the essence of quantum logic.\\ Now we have a way to construct new mathematical universes over arbitrary topological spaces. We need then a topological space able to capture the essence of Quantum Logic to obtain a mathematical Quantum Universe able to capture Quantum Reality. \subsection{The Cumulative Hierarchy of Quantum Variable Sets}\label{QVS} As we saw above one important property of the Logic of sheaves of structures is the possibility to define a contextual notion of truth. This contextual truth paradigm is not just intrinsic to the notion of truth in classical physical reality but within the quantum realm it can recover new fundamental meanings.\\ \indent One first aspect of contextuality arises from the Kochen-Specker theorem \footnote{See \cite{isham4} chapter 9 for a nice discussion about the Kochen-Specker theorem.}. In a few words what the Kochen-Specker theorem says is that in QM does not exist a valuation function from the set of physical observables, intended as self adjoint operators on a Hilbert space $H$, if the dimension of $H$ is greater than two. A valuation is a function $\lambda$ from the set of self-adjoint operators $B_{sa}(H)$ on $H$ to the real numbers, $\lambda:B_{sa}(H)\rightarrow \mathbb{R}$, which satisfies: \[1.\lambda(A) \text{ belongs to the spectrum of }A\in B_{sa}(H)\] \[2.\lambda(B)=f(\lambda(A))\text{ whenever } B=f(A)\] with $f:\mathbb{R}\rightarrow \mathbb{R}$ a Borel function.\\ \indent On the other hand, locally or in a contextual sense, there exist valuations. If we consider an abelian Von Neumann subalgebra $\mathcal{U}$ of the algebra of operators, the elements of the Gelfand spectrum of $\mathcal{U}$ (i.e the positive linear functions $\sigma:\mathcal{U}\rightarrow\mathbb{C}$ of norm 1 such that $\sigma(AB)=\sigma(A)\sigma(B)$ for all $A,B \in \mathcal{U}$) when restricted to the self-adjoint operators in $\mathcal{U}$ constitute a set of valuations which satisfy 1 and 2 above (see \cite{kadison}) . What the Kochen-Specker theorem is telling us is that none of this local valuations can be extended globally.\\ \indent A history is characterized by the values that physical variables take on it; therefore, we can see these valuations as histories, the Kochen-Specker theorem is telling us that the space of histories has a non trivial contextual structure. Thus, a first notion of context is given by the histories associated to an abelian Von Neumann subalgebra of the algebra of operators of a Hilbert space. As the elements of the Gelfand spectrum of an algebra can be extended in different ways in two non compatible extensions of the original algebra, this contextual character is telling us that what is perceived as true by a history is conditioned by the context of similar histories, where similar is intended in this case as histories that can be expressed in function of the same observables.\\ A second notion of contextuality arises from the phenomenon of interference in Quantum Mechanics. Interference as intended in the Deutsch-Everett multiversal interpretation\footnote{See \cite{deutsch} chapter 2, \cite{deutsch4} chapter 11 or \cite{deutsch2} for a non technical explanation of the Quantum Multiverse and \cite{deutsch3} for a more technical approach. } of Quantum Mechanics is the way as two histories can affect each other. Interference phenomenons are strong enough to be detected only between universes or histories that are very similar, thus what is perceived by a history depends on the context of histories close to it, where close is intended in the sense of being similar. To describe this second contextual feature we use projections operators on a Hilbert space $H$. Let $\mathcal{U}$ be an abelian Von Neumann algebra of operators, $S_\mathcal{U}$ the Gelfand spectrum of $\mathcal{U}$ and $P(\mathcal{U})$ the set of projections of $\mathcal{U}$. Given $P'\in P(\mathcal{U})$ and $\sigma\in S_\mathcal{U}$ we have \[\sigma(P')=\sigma(P'^{2})=\sigma(P')\sigma(P')\] then $\sigma(P')\in \{0,1\}$. Consider a self-adjoint operator $A\in \mathcal{U}$ such that \[A=\sum_{n=1}^{N}a_n P'_n\] is the spectral representation of $A$ in $\mathcal{U}$. Let $\lambda\in S_\mathcal{U}$ such that $\lambda(A)=a_m$, then $\lambda(P'_m)=1$. Thus if $A$ represents a physical observable, we have that in all the histories $\lambda$ such that $\lambda(P'_m)=1$ the physical observable $A$ assumes the value $a_m$. Therefore, given a proposition $P'\in P(\mathcal{U})$ the set \[P=\{ \lambda \in S_\mathcal{U}: \lambda(P')=1\}\] is a context of histories which are similar in the sense that some physical observables assume the same values or the values satisfy the same inequalities in each history.\\ The first notion of contextuality has played an important role in the development of the Consistent Histories program (see \cite{griffiths}) and also it is the base of the approach based on topos theory developed by Isham and others (see \cite{isham} and \cite{doering}). The importance of the second notion has not been considered deeply but, as we will see below, this notion is fundamental and probably will explain how to relate Classical and Quantum realities. I conjecture that these two notions of contextuality capture the essence of the logic of classical Quantum Mechanics. Therefore, to develop a formalism able to capture the essence of Quantum Reality using the tools developed above, we need a base space $X$ which structure captures these two notions of contextuality. Unfortunately to capture both notions we will probably need something more general than a topological space and the respective generalization of the tools developed above, and it is here that tools of topos theory will be probably needed, this will be developed in a future work. However, we can limit ourselves to a context $X=S_\mathcal{U}$ where $\mathcal{U}$ is an abelian Von Neumann algebra, and on $X$ we can consider the topology which open sets are the sets $P$ associated to a projector operator $P'\in P(\mathcal{U})$ as defined above. This will be enough to capture the importance of the second notion of contextuality. The topology $\{P\}_{P'\in P(\mathcal{U})}$ is a topology where all the open sets are clopen and where the algebra of open sets is a boolean algebra isomorphic to the boolean algebra of projector operators $P(\mathcal{U})$. The Cumulative hierarchy of variable sets constructed over the topological space $\langle X=S_\mathcal{U}, \{P\}_{P'\in P(\mathcal{U})}\rangle$ where $\mathcal{U}$ is an abelian Von Neumann Algebra is what we will call \textit{The Cumulative Hierarchy of Quantum Variable Sets.} The objects of this model will be the sections of the sheaf $\mathbb{V}^{X}$, which result to be extended objects that variate over the space of histories or universes $X=S_{\mathcal{U}}$, in a few words multiversal objects. This characteristic will probably be ideal to describe quantum particles, to put it in D. Deutsch words: \begin{center} \textit{Thanks to the strong internal interference that it is continuously undergoing, a typical electron is an irreducibly multiversal object, and not a collection of parallel-universe or parallel-histories objects. \footnote{ See \cite{deutsch4} page 291.}} \end{center} We will see that in this new mathematical universe the tools we use to understand Quantum Mechanics recover new fundamental meanings that can be fundamental to settle a definite interpretation of QM. Indeed, once we construct the continuum in this mathematical universe we find a fundamental result which shows the interpretative power of this model respect to Quantum theory. \subsection{The Quantum Continuum} As in the previous section consider $\mathcal{U}$ an abelian Von Neumann subalgebra of the algebra of operators of a Hilbert space $H$, and $X=S_\mathcal{U}$ the Gelfand spectrum of $\mathcal{U}$ with the topology given by the sets $\{P\}_{P'\in P(\mathcal{U})}$ as defined above. We want to construct the continuum, or in other words, the set which is forced as the real numbers on the hierarchy of variable sets over $X$. To construct this set we will use the definition of the real numbers given by Dedekind cuts, therefore at each open (clopen) set $P$ the object $\mathbb{R}(P)$ will be the set that is forced as the set of Dedekind cuts i.e \[\Vdash_{P} \mathbb{R}(P)=\{(L,U)\in \mathcal{P}(\widehat{\mathbb{Q}}(P))\times \mathcal{P}(\widehat{\mathbb{Q}}(P)): (L,U) \text{ is a Dedekind cut }\};\] where being a Dedekind cut means: \begin{enumerate} \item $\Vdash_{P} \exists q\in \widehat{\mathbb{Q}}(P)(q\in L)\wedge \exists r\in \widehat{\mathbb{Q}}(p)(r\in U).$ \item $\Vdash_{P} \forall q,r\in\widehat{\mathbb{Q}}(P)(q<r\wedge r\in L \rightarrow q\in L).$\\ $\Vdash_{P} \forall q,r\in \widehat{\mathbb{Q}}(P)(r<q\wedge r\in U\rightarrow q\in U).$ \item $\Vdash_P q\in\widehat{\mathbb{Q}}(P) (q\in L\rightarrow \exists r\in\widehat{\mathbb{Q}}(P)((r\in L\wedge q<r)).$\\ $\Vdash_P q\in\widehat{\mathbb{Q}}(P) (q\in U\rightarrow \exists r\in\widehat{\mathbb{Q}}(P)((r\in U\wedge q>r)).$ \item $\Vdash_P \forall q,r\in\mathbb{Q}(q<r\rightarrow (q\in L \vee r\in U)).$ \item $\Vdash_P L\cap U=\emptyset $. \end{enumerate} Since the set $\widehat{\mathbb{Q}}(P)$ is the embedding of $\mathbb{Q}$ in $V(P)$, and the construction of the order relation does not introduce anything new, the order relation on $\widehat{\mathbb{Q}}(P)$ is equivalent to the order relation in $\mathbb{Q}$, i.e. \[\Vdash_P \widehat{q}(P),\widehat{r}(P)\in\widehat{\mathbb{Q}}(P)\wedge \widehat{q}(P)<\widehat{r}(P)\quad \text{if and only if}\quad q<r \text{ in the classical sense. }\] Using \ref{kripkejoyal} the above conditions mean: \begin{enumerate} \item i) There exist $q\in \widehat{\mathbb{Q}}(P)(P)$ such that $q\in L(P)$ (Analogously for $U$) or\\ ii) There exist an open cover $\{P_i\}_{i\in I}$ of $P$ such that there exists $q\in \widehat{\mathbb{Q}}(P_i)(P_i)$ and $q\in L(P_i)$. (Analogously for $U$) \item For all the open sets $Q\subseteq P$ if $T\subseteq Q$ is open, $\widehat{q}(T),\widehat{r}(T)\in \widehat{\mathbb{Q}}(T)(T)$, $q<r$ and $\widehat{r}(T)\in L(T)$ then $\widehat{q}(T)\in L(T)$. (Analogously for $U$). \item For all the open sets $Q\subseteq P$ if $\widehat{q}(Q)\in \widehat{\mathbb{Q}}(Q)(Q)$ then there exists an open cover $\{Q_i\}$ of $Q$ and $\widehat{r}(Q_i)\in \widehat{\mathbb{Q}}(Q_i)(Q_i)$ such that $r> q$ and $\widehat{r}(Q_i)\in L(Q_i)$. (Analogously for $U$). \item For all the open sets $Q\subseteq P$, given $\widehat{q}(Q), \widehat{r}(Q)\in \widehat{\mathbb{Q}}(Q)(Q)$ if $T\subseteq Q$, $q<r$ then there exists open sets $T_1$, $T_2$ such that $T=T_1\cup T_2$, $\Vdash_{T_1}\widehat{q}(T_1)\in L$ and $\Vdash_{T_2}\widehat{r}(T_2)\in U$. \item For all the open sets $Q\subseteq P$ and $\widehat{q}(Q)\in\widehat{\mathbb{Q}}(Q)(Q)$ not both $\widehat{q}(Q)\in L(Q)$ and $\widehat{q}(Q)\in U(Q)$ \end{enumerate} Given a self adjoint operator $A\in \mathcal{U}$, let $\{P'_r\}_{r\in\mathbb{R}}$ be the spectral family of operators associated to $A$ (see \cite{kadison}). The family $\{P'_r\}_{r\in\mathbb{R}}$ is a family of operators contained in $P(\mathcal{U})$ which satisfy: \begin{enumerate} \item $P'_q\wedge P'_r=P'_{min\{r,s\}}$, \item $\bigwedge_{r\in\mathbb{R}} P'_r=0$, \item $\bigvee_{r\in\mathbb{R}} P'_r=1$, \item $\bigwedge_{q\leq r}P'_r=P'_q$ for every $q\in\mathbb{R}$ \end{enumerate} Thus the above spectral family defines a family of clopen subsets, $\{P_r\}_{r\in\mathbb{R}}$ which satisfy the analogous properties: \begin{enumerate} \item $P_q \cap P_r=P_{min\{r,s\}}$, \item $\bigcap_{r\in\mathbb{R}} P_r=\emptyset$, \item $\bigcup_{r\in\mathbb{R}} P_r=X$, \item $\bigcap_{q\leq r}P_r=P_q$ for every $q\in\mathbb{R}$ \end{enumerate} Using this family of clopen subsets for $P\in Op(X)$ we define: \begin{align} U_A(P):Op(P)& \rightarrow \bigcup_{Q\subseteq P}V(Q)\\ Q & \mapsto \{\widehat{q}(Q)\in \widehat{\mathbb{Q}}(Q)(Q): \exists r\in\mathbb{Q}, r<q, Q\nsubseteq P_r^{c} \} \end{align} \begin{align} L_A(P):Op(P)& \rightarrow \bigcup_{Q\subseteq P}V(Q)\\ Q & \mapsto \{\widehat{q}(Q)\in \widehat{\mathbb{Q}}(Q)(Q): Q\subseteq P_q^{c}\} \end{align} where $P^{c}_q$ denotes the complement of $P_q$ in $X$. We want to show that $U_A$ and $L_A$ define a real number\footnote{We will use the notation $U_A, L_A$ instead of $U_A(P), L_A(P)$, here again we have $U_A(P)\upharpoonright_{Op(Q)}=U_A(Q)$ if $Q\subseteq P$, then we can use this notation without generating confusion}, proving that the conditions 1-5 above hold: \begin{enumerate} \item a-) $\{P\cap P_q^{c}\}_{q\in\mathbb{Q}}$ is an open cover of $P$, indeed, \begin{align} \bigcup_{q\in \mathbb{Q}} (P\cap P^{c}_q)&=P\cap (\bigcup_{q\in\mathbb{Q}} P^{c}_q)\\ &=P\cap (\bigcap_{q\in\mathbb{Q}} P_q)^{c}\\ &=P. \end{align} We have $P\cap P^{c}_q\subseteq P^{c}_q$ thus $\widehat{q}(P\cap P^{c}_q)\in L_A(W\cap P^{c}_q)$.\\ b-) Since $P\neq \emptyset$, there exists $r\in\mathbb{Q}$ such that $P\nsubseteq P^{c}_ r$, otherwise $P\subseteq \bigcap_{q\in\mathbb{Q}} P^{c}_q=\emptyset$. Therefore, taking $q>r$ by definition we have $\widehat{q}(P)\in U_A(P)$. \item a-) Let $Q\subseteq P$ be an open set and $\widehat{q}(Q),\widehat{r}(Q)\in \widehat{\mathbb{Q}}(Q)(Q)$. Suppose $r<q$ and $\widehat{q}(Q)\in L_A(Q)$, then $Q\subseteq P^{c}_q$. Since $P_r\cap P_q=P_r$ we have $P_r\subset P_q$ and $P^{c}_q\subset P^{c}_r$. Thus $Q\subset P^{c}_r$ which implies $\widehat{r}(Q)\in L_A(Q)$.\\ b-) On the other hand if we suppose $r<q$ and $\widehat{r}(Q)\in U_A(Q)$, there exists $s\in\mathbb{Q}$, $s<r$ such that $Q\nsubseteq P^{c}_s$. Since $s<q$ we can conclude that $\widehat{q}(Q)\in U_A(Q)$. \item a-) Let $Q\subseteq P$ be an open set and $\widehat{q}(Q)\in\mathbb{Q}(Q)(Q)$ be such that $\widehat{q}(Q)\in L_A(Q)$. Since $Q\subseteq P^{c}_q$, $\{Q\cap P^{c}_r\}_{r\in\mathbb{Q},r>q}$ is an open cover of $Q$; indeed \[ \bigcup_{r\in\mathbb{Q},r>q}(Q\cap P^{c}_r)=Q\cap(\bigcup_{r\in\mathbb{Q},r>q}P^{c}_r)=Q\cap (\bigcap_{r\in\mathbb{Q},r>q}P_r)^{c}=Q\cap P^{c}_q=Q. \] We have then $Q\cap P^{c}_r\subset P^{c}_r$, which implies $\widehat{r}(Q\cap P^{c}_r)\in L_A(Q\cap P^{c}_r)$.\\ b-) If $\widehat{q}(Q)\in U_A(Q)$ by definition there exists $r<q$ such that $Q\nsubseteq P^{c}_r$. Therefore given $s\in\mathbb{Q}$, such that $r<s<q$ we have $\widehat{s}(Q)\in U_A(Q)$. \item $Q\subseteq P$ be an open set and $\widehat{q}(Q),\widehat{r}(Q)\in\mathbb{Q}(Q)(Q)$ such that $q<r$. Suppose $\nVdash_{Q} \widehat{q}(Q)\in L_A$ then $Q\nsubseteq P^{c}_q$. Thus for $r$ exists $q$ such that $q<r$ and $Q\nsubseteq P^{c}_q$, then $\widehat{r}(Q)\in U_A(Q)$. On the other hand if we suppose $\nVdash_Q\widehat{r}(Q)\in U_A$, then for all $s<r$, $Q\subseteq P^{c}_s$. Particularly $Q\subseteq P^{c}_q$ then $\widehat{q}(Q)\in L_A(Q)$. \item Let $Q\subset P$ be an open set and $\widehat{q}(Q)\in\widehat{\mathbb{Q}}(Q)(Q)$. Suppose $\widehat{q}(Q)\in L_A(Q)$, then $Q\subseteq P^{c}_q$ and for all $r<q$, $Q\subset P^{c}_r$ thus $\widehat{q}(Q)\notin U_A(Q)$. In the same way if we suppose $\widehat{q}(Q)\in U_A(Q)$, there exists $r<q$ such that $Q\nsubseteq P^{c}_r$, since $P^{c}_q\subseteq P^{c}_r$ we have $Q\nsubseteq P^{c}_q$. Thus $\widehat{q}(Q)\notin L_A(Q)$. \end{enumerate} Thus each spectral resolution of the identity defines a real number in $V(P)$. \\ On the other hand if \[U(P):Op(P)\rightarrow \bigcup_{Q\subseteq P} V(Q)\] \[L(P):Op(P)\rightarrow \bigcup_{Q\subseteq P} V(Q)\] define a real number in $V(P)$ we can find an spectral resolution of the identity in the next way. Given $r\in\mathbb{Q}$ consider the set \[P_r=\bigcup\{P\in Op(X): \forall q>r, \Vdash_P \widehat{q}(P)\in U\}.\] \begin{lema} \[\bigcap_{r\in\mathbb{Q}} P_r=\emptyset\] \end{lema} \begin{proof} From (1) in the definition of a Dedekind cut, for any $P\in Op(X)$, $P\neq \emptyset$, there exists an open cover $\{Q_i\}_{i\in I}$ of $P$ and $\widehat{q_i}(Q_i)\in \widehat{\mathbb{Q}}(Q_i)(Q_i)$ such that $\widehat{q_i}(Q_i)\in L(Q_i)$. On the other hand from (5) in the definition of a Dedekind cut we have that for any $T\subseteq Q_i$, $\nVdash_T \widehat{q_i}(T)\in U$. Summarising we have an open cover $\{Q_i\}_i$ of $P$ and $\widehat{q_i}(Q_i)\in\widehat{Q}(Q_i)(Q_i)$ such that for every open set $T\subseteq Q_i$, $\nVdash \widehat{q_i}(T)\in U$. Therefore we have proved: \begin{equation}\label{sf1} \Vdash_P \exists \widehat{q}(P)\in\widehat{\mathbb{Q}}(P)(\widehat{q}(P)\notin U), \end{equation} for all $P\in Op(X)$. If \[R=\bigcap_{r\in\mathbb{Q}} P_r\neq \emptyset\] we have \[\Vdash_R\widehat{q}(R)\in U\] for all $\widehat{q}(R)\in\widehat{\mathbb{Q}}(R)(R)$ but this contradicts \ref{sf1}. \end{proof} \begin{lema} \[\bigcup_{r\in\mathbb{Q}} P_r=X\] \end{lema} \begin{proof} Let $\sigma\in X$ and $P$ an open neighbourhood of $\sigma$. From (1) in the definition of a Dedekind cut there exists an open set $Q_i$, and $\widehat{q_i}(Q_i)\in\widehat{\mathbb{Q}}(Q_i)(Q_i)$ such that $\sigma\in Q_i\subseteq P$ and $\Vdash_{Q_i}\widehat{q_i}(Q)\in U$. Then by property (2) of the definition of a Dedekind cut for all $q>q_i$ we have $\Vdash_{Q_i} \widehat{q}(Q_i)\in U$. Therefore $\sigma\in P_{q_i}$, since $\sigma$ was arbitrary we have $\bigcup_{r\in\mathbb{Q}} P_r=X$. \end{proof} \begin{lema} \[\bigcap_{q<r}P_r=P_q\] \end{lema} \begin{proof} If $\sigma\in P_q$, there exists a neighbourhood $P$ of $\sigma$ such that $\Vdash_P \widehat{s}(P)\in U$ for all $s>q$. Let $r>q$ arbitrary, then $\Vdash_P \widehat{s}(P)\in U$ for all $s>r$, then $\sigma\in P_r$ for all $r>q$ thus $\sigma\in\bigcap_{q<r}P_r$. On the other hand if $\sigma\in \bigcap_{q<r}P_r$, for all $r>q$ there exists a neighbourhood $Q_r$ of $\sigma$ such that $\Vdash_{Q_r}\widehat{s}(Q_r)\in U$ for all $s>r$. Let $Q=\bigcap_{r>q}Q_r$, then $\Vdash_Q\widehat{s}(Q)\in U$ for all $s>q$ and $\sigma\in Q$. Then $\sigma\in P_q$. \end{proof} Given a real number $r\in\mathbb{R}$, define \[P_r=\bigcap_{q\in\mathbb{Q}, r<q} P_q.\] From the above results it is clear that the projections $\{P'_r\}_{r\in\mathbb{R}}$ associated to the family of clopen subsets $\{P_r\}_{r\in\mathbb{R}}$ form a spectral resolution of the identity. Since there is a correspondence between self-adjoint operators in $\mathcal{U}$ and spectral families in $\mathcal{U}$, we have a correspondence between the real numbers of the cumulative hierarchy of variable sets over $X=S_{\mathcal{U}}$ and the self-adjoint operators in $\mathcal{U}$. This is the correspondence proved by Takeuti in the context of Boolean valued models of set theory, the advantage here is that we get an explicit construction of the real numbers in function of the spectral representation of the respective self-adjoint operator. This construction will be probably fundamental to understand the relation of quantum expressions and its classical counterparts.\\ There is an alternative proof of Takeuti's correspondence in this context that even if it is less constructive than the proof presented above, it has a theoretical interest and it will probably be useful in more general contexts; for the sake of completeness we include this proof here. We start with a result which is proved in a more general context in \cite{maclane} ( theorem 2, chapter VI), we give here the proof for the hierarchies of variable sets. \begin{teor} Let $X$ be a topological space, and $\mathbb{V}^{X}$ the hierarchy of variable sets constructed over $X$. Let $P\in Op(X)$, then there is a correspondence between the objects forced as real numbers in $V(P)$ and the real valued continuous functions over $P$. \end{teor} \begin{proof} Let $P\in Op(X)$, $\lambda \in P$ and \[U(P):Op(P)\rightarrow \bigcup_{Q\subseteq P} V(Q)\] \[L(P):Op(P)\rightarrow \bigcup_{Q\subseteq P} V(Q)\] such that define a real number in $V(P)$. Consider \[L_{\lambda}=\{q\in \mathbb{Q}: \exists Q\subseteq P \text{ open set s.t. }\lambda\in Q,\quad \widehat{q}(Q) \in L(P)(Q)\}\] \[U_{\lambda}=\{r\in\mathbb{Q}: \exists Q\subseteq P\text{ open set s.t. }\lambda \in Q,\quad \widehat{r}(Q)\in U(P)(Q)\}\] From the properties 1-5 above we have that the above sets defined a Dedekind cut in the classical sense then a real number $a_{\lambda}=(L_{\lambda},U_{\lambda})$. Define the function \[f_{L,U}: P\rightarrow \mathbb{R}\] such that $f_{L,U}(\lambda)=a_{\lambda}$. To show that the function $f_{L,U}$ is continuous consider an interval $(q,r)$ with $q,r\in\mathbb{Q}$ and $\lambda\in f^{-1}_{L,U}((q,r))$. We have in particular that $q\in L_{\lambda}$ and $r\in U_{\lambda}$ since $q<f_{L,U}(\lambda)=a_{\lambda}<r$, then there exists $Q$ and $T$ neighbourhoods of $\lambda$ such that $\widehat{q}(Q)\in L(P)(Q)$ and $\widehat{r}(T)\in U(P)(T)$. Thus, for every $\sigma\in Q\cap T$, we have $q\in L_{\sigma}$ and $r\in U_{\sigma}$ thus $\sigma\in f^{-1}((q,r))$ therefore $Q\cap T\subseteq f^{-1}_{L,U}((q,r))$. Since $\lambda$ was arbitrary and the rational intervals form a base we have proved the continuity of $f_{L,U}$.\\ Consider now $f:P\rightarrow \mathbb{R}$ a continuous function and \begin{align} U_f(P):Op(P)& \rightarrow \bigcup_{Q\subseteq P}V(Q)\\ Q & \mapsto \{\widehat{q}(Q)\in \widehat{\mathbb{Q}}(Q)(Q): \forall \lambda\in Q, q>f(\lambda) \} \end{align} \begin{align} L_f(P):Op(P)& \rightarrow \bigcup_{Q\subseteq P}V(Q)\\ Q & \mapsto \{\widehat{q}(Q)\in \widehat{\mathbb{Q}}(Q)(Q): \forall \lambda \in Q,q< f(\lambda) \} \end{align} We want to prove that $L_f(P), U_f(P)$ define a real number in $V(P)$ i.e. that the conditions 1-5 above are satisfied. Let $Q\subseteq P$ an open set:\\ 1. Let $Q_n=\{\lambda \in Q: -n<f(\lambda)<n\}$, then $\{Q_n\}_{n\in\mathbb{N}}$ form an open cover of $Q$, and we have $\widehat{-n}(Q_n)\in L_f(P)(Q_n)$ and $\widehat{n}(Q_n)\in U_f(P)(Q_n)$.\\ 2. Follows directly from the definitions of $L_f$ and $U_f$.\\ 3. Let $T\subseteq Q$ and $\widehat{q}(T)\in L_f(P)(T)$, then for any $\lambda\in T$ we have $q<f(\lambda)$. Since $f$ is continuous there exists a neighbourhood of $\lambda$, $T_{\lambda}$ and $r_{\lambda}\in\mathbb{Q}$ such that for any $\sigma\in T_{\lambda}$ we have $q< r_{\lambda}<f(\sigma)$, then $\widehat{r}_{\lambda}\in L_f(P)(T_{\lambda})$. (Analogously for $U_f(P)$).\\ 4. Let $T\subseteq Q$ and $q, r\in\mathbb{Q}$ such that $q<r$. Consider $T_1=\{\lambda\in T: q<f(\lambda)\} $ and $T_2=\{\lambda\in T: f(\lambda)<r\}$. We have $T=T_1\cup T_2$ and $\widehat{q}(T_1)\in L_f(P)(T_1)$, $\widehat{r}(T_2)\in U_f(P)(T_2)$.\\ 5. Clear from the definition. \end{proof} \begin{corol} Let $\mathcal{U}$ an abelian Von Neumann subalgebra of operators of a Hilbert space $H$, and $X=S_{\mathcal{U}}$ the Gelfand spectrum of $\mathcal{U}$ with the topology given by the sets $\{P\}_{P'\in P(\mathcal{U})}$ as defined above. There is a correspondence between the real numbers of the hierarchy $\mathbb{V}^{X}$ and the self adjoint operators of $\mathcal{U}$. \end{corol} \begin{proof} Let $A\in \mathcal{U}$ be a self adjoint operator and as before $\{P'_{r}\}_{r\in \mathbb{R}}$ the associated spectral family. Define the function $f_A: X\rightarrow \mathbb{R}$ such that $f_A(\lambda)=\lambda(A)$. We want to show that $f_A$ is continuous. Consider $q,r\in\mathbb{R}$ such that $q<r$, from the construction of the spectral family (see \cite{kadison} theorem 5.2.2) we know $f_A^{-1}((q,r))=P_r\setminus P_q$ which is an open set, then $f_A$ is a continuous function and by the above theorem it is associated with a real number in $V(P)$ for each $P\in Op(X)$.\\ Consider now $U, L$ such that \[U(P):Op(P)\rightarrow \bigcup_{Q\subseteq P} V(Q)\] \[L(P):Op(P)\rightarrow \bigcup_{Q\subseteq P} V(Q)\] define a real number for each $P\in Op(X)$, then from the above theorem we know there exists a continuous function $f:X\rightarrow \mathbb{R}$ associated to $L,U$. We know that the sets $\{P\}_{P'\in P(\mathcal{U})}$ are clopen sets also in the weak* topology over $X$ (see again \cite{kadison} theorem 5.2.2), then the function $f$ is also continuous in the weak* topology. Therefore by the Gelfand representation theorem (\cite{kadison} Theorem 4.4.3) to $f$ corresponds an operator $B_f$ such that $f(\lambda)=\lambda(B_f)$ for all $\lambda\in X$. Since $f(\lambda)=\lambda(B_f)\in \mathbb{R}$ for all $\lambda\in X$, we have that $B_f$ is a self adjoint operator (see \cite{kadison} theorem 4.3.8). \end{proof} The above results show how in this model deep results of operator theory recover a new interesting meaning. The value of this new perspective is that it probably contains the way to obtain a new picture of QM with a definite interpretation. Lets see why.\\ \indent Given $a\in\mathbb{R}$, $\widehat{a}(P)$ is a constant Dedekind cut over $P$, given by : \[U_{\widehat{a}}(Q)=\{\widehat{q}(Q)\in \widehat{\mathbb{Q}}(Q)(Q): a<q\}\] \[L_{\widehat{a}}(Q)=\{\widehat{q}(Q)\in \widehat{\mathbb{Q}}(Q)(Q): q<a\},\] with $Q\subseteq P$ open. On the other hand, consider the spectral family $\{Q'_r\}_{r\in\mathbb{R}}$ such that $Q'_r=0$ if $r<a$ and $Q'_r=I$ if $r\geq a$, then the real number $(L,U)$ associated to this spectral family over an open set $P$ satisfies: \begin{align} U(Q)&=\{\widehat{q}(Q)\in \widehat{\mathbb{Q}}(Q)(Q): \exists r\in\mathbb{Q}, r<q, Q\nsubseteq P_r^{c} \}\\ &=\{\widehat{q}(Q)\in \widehat{\mathbb{Q}}(Q)(Q): a<q\} \end{align} for any open set $Q\subseteq P$ since $Q\nsubseteq P^{c}_a=\emptyset$ for any $Q$ non empty. In the same way we have $L(Q)=\{\widehat{q}(Q)\in \widehat{\mathbb{Q}}(Q)(Q): q<a\}$ for any $Q\subseteq P$. Therefore $\widehat{a}(P)$ is the real number associated to the operator defined by $\{Q'_r\}_{r\in\mathbb{R}}$ (which is the operator $aI$).\\ As above consider again a self-adjoint operator $A\in\mathcal{U}$, $\{P'_r\}_{r\in\mathbb{R}}$ the spectral family associated to $A$ and $(L_A,U_A)$ the real number defined by $A$. In $P_a$, with $a\in\mathbb{R}$, consider $Q\subseteq P_a$. Since $Q\nsubseteq P^{c}_a$ we have \[ \{\widehat{q}(Q)\in \widehat{\mathbb{Q}}(Q)(Q): a<q\}\subseteq U_A(Q)=\{\widehat{q}(Q)\in \widehat{\mathbb{Q}}(Q)(Q): \exists r\in\mathbb{Q}, r<q, Q\nsubseteq P_r^{c} \}. \] In the same way considering $P^{c}_a$ and $Q\subseteq P^{c}_a$, since $P^{c}_a\subseteq P^{c}_q$ for any $q<a$ we have $Q\subseteq P^{c}_q$ for any $q<a$; then \[\{\widehat{q}(Q)\in \widehat{\mathbb{Q}}(Q)(Q): q<a\}\subseteq L_A(Q)=\{\widehat{q}(Q)\in \widehat{\mathbb{Q}}(Q)(Q): Q\subseteq P_q^{c} \}. \] Now remember that in the classical sense if we have two real numbers $a,b\in\mathbb{R}$ with $a=(L_a,U_a)$ and $b=(L_b, U_b)$ we define $a\leq b$ if and only if $U_b\subseteq U_a$ and $a\geq b$ if and only if $L_b\subseteq L_a$. Applying this definition to our model the results above translate as \[\Vdash_{P_a} A\leq \widehat{a}(P_a)\] and \[\Vdash_{P^{c}_a} \widehat{a}(P^{c}_a)\leq A\] respectively, where we have denoted the real number defined by the self-adjoint operator $A$ using the same symbol. Remember from section \ref{logic} that $[[A\leq \widehat{a}]]_X$, $[[\widehat{a}\leq A]]_X$ represent the set of elements of $X$ where the respective propositions hold, since $P_a\cup P^{c}_a= X$ we have shown that \[P_a=[[A\leq \widehat{a}]]_X\] \[P^{c}_a=[[\widehat{a}\leq A]]_X.\] Let $c,d\in\mathbb{R}$ such that $c<d$, we have \begin{align} [[\widehat{c}\leq A \leq \widehat{d}]]_X&=[[(\widehat{c}\leq A)\wedge(A\leq \widehat{d})]]_X\\ &=[[\widehat{c}\leq A]]_X\cap [[A\leq \widehat{d}]]_X\\ &=P^{c}_c\cap P_d\\ &=P_d\setminus P_c. \end{align} The proof of this result was given in the context of boolean valued models in \cite{ozawa} (theorem 6.2), comparing it with the proof here presented, it becomes clear that the sheaf based approach gives an important simplification.\\ As before we denote by $[[\widehat{c}\leq A \leq \widehat{d}]]_X'$ the projector associated to the open set $[[\widehat{c}\leq A\leq \widehat{d}]]_X$. If $h\in H$ is a state vector, we know from the classical formalism of QM that the probability of the observable $A$ to assume some value in the interval $[c, d]$ in the state $h$ is given by \[ \|\| [[\widehat{c}\leq A\leq \widehat{d} ]]_X' h \|\|^{2}=\|\|(P'_d-P'_c)h\|\|^{2}, \] but within our model we see that $h$ is just measuring the set $[[\widehat{c}\leq A\leq \widehat{d}]]_X$ of histories or universes where the proposition $\widehat{c}\leq A\leq \widehat{d}$ holds. Indeed, each quantum state $h\in H$ defines a measure $\mu_{h}$ over $X$ given by: \begin{align} \mu_{h}:Op(X)&\rightarrow \mathbb{R}\\ P & \mapsto \|\|P'h\|\|^{2}. \end{align} As we just saw these open sets are of the form $P=[[\varphi]]_X$, where $\varphi$ is a proposition about the quantum system, thus $P$ is the set of histories where the proposition $\varphi$ is verified and $\mu_h$ is measuring the proportion of histories where any proposition is verified. This is literally the interpretation given to quantum states in the Deutsch-Everett multiverse interpretation of Quantum Mechanics. It is important to note that the type of propositions about the Quantum System are not limited just to propositions referring to the values of physical variables as in the example above; in this case the results are valid for any kind of propositions about the quantum system that can be expressed with the language of set theory, probably even propositions about emergent properties related to the conception of classical spacetime.\\ \subsection{Generic Models and the Emergence of Classical Reality} Any new mathematical model that will improve our understanding of QM has to explain or give us a hint of how the classical reality of our everyday experience emerges from the deep Quantum reality of the elementary particles that constitute everything. Surprisingly, in the models developed above there is a way to collapse the multiversal model of Quantum Variable sets to a classical model in such a way that what is perceived by the classical universe is conditioned by the structure of the multiversal model. This can be done over any Sheaf of structures, however, for the sake of clarity, we will explain how this process work on the hierarchy of Variable Sets. The main idea in this section will be the notion of generic model and genericity. This notion was originally introduced by Paul Cohen in his works on the independence of the Continuum Hypothesis and the Axiom of Choice; becoming then fundamental in modern set theory and model theory. In the context of sheaves of structures it is possible to introduce the notion of generic model and genericity in a more general framework which unifies previous approaches, and where hypothesis about enumerability are not required (see \cite{caicedo}). We will see then how to connect these ideas related to the foundations of mathematics to Quantum Mechanics via the hierarchy of Quantum Variable Sets.\\ We start with an easy definition. \begin{defin} Let $X$ be a topological space and $Op(X)$ the set of open sets of $X$. Let $\mathcal{F}\subset Op(X)$, $\mathcal{F}$ is called a filter of open sets of $X$ if:\\ i. $X\in\mathcal{F}$.\\ ii. If $U,V\in\mathcal{F}$ then $U\cap V\in\mathcal{F}$.\\ iii.Given $V\in\mathcal{F}$ If $V\subset U$ then $U\in\mathcal{F}$. \end{defin} Filters over the base space $X$ of a Sheaf of Structures will be the tools we will use to collapse the intuitionistic sheaf to a classical model. To do this we need an special kind of filters where the essence of being classical is captured in such a way that for each proposition the excluded middle holds in an open set of the filter, and for each existential proposition there exists an open set where the existential is verified in the classical sense. In other words: \begin{defin} Let $\mathcal{F}$ be a filter of open sets of $X$, we say that $\mathcal{F}$ is a Generic Filter of $\mathbb{V}^{X}$ if:\\ i. Given $\varphi(v_1,...,v_n)$ a first order formula (a proposition) and $\sigma_1,...,\sigma_n$ arbitrary sections of $\mathbb{V}^{X}$ defined on $P\in\mathcal{F}$, there exists $Q\in\mathcal{F}$ such that \[\Vdash_Q\varphi[\sigma_1,...,\sigma_n] \text{ or } \Vdash_Q\neg\varphi[\sigma_1,...,\sigma_n].\] ii. Given $\sigma_1,...,\sigma_n$ arbitrary sections of\quad $\mathbb{V}^{X}$ defined on $P\in\mathcal{F}$, and $\varphi(v,v_1,...,v_n)$ a first order formula. If $\Vdash_P\exists v\varphi(v,\sigma_1,...,\sigma_n)$ then there exist $Q\in\mathcal{F}$ and $\sigma$ defined on $Q$ such that $\Vdash_Q\varphi(\sigma,\sigma_1,...,\sigma_n)$. \end{defin} The next important result shows that generic filters exist, the proof of this result is contained in \cite{caicedo}. \begin{teor}\label{generic} A filter is a generic filter of $\mathbb{V}^{X}$ if and only if it is a maximal filter of $X$. \end{teor} Using a generic filter we can construct a classical model from a sheaf of structures. \begin{defin} We can associate a classical model to $\mathbb{V}^{X}$ in the next way:\\ let \[\mathbb{V}^{X}[\mathcal{F}]=\lim_{\rightarrow P\in\mathcal{F}}V(U)\] i.e \[\mathbb{V}^{X}[\mathcal{F}]=\dot{\bigcup}_{P\in\mathcal{F}}V(P)/_{\sim_{\mathcal{F}}}\] where for $\sigma\in V(P)$ and $\mu\in V(Q)$ \[\sigma\sim_{\mathcal{F}}\mu\Leftrightarrow\text{ there exists }R\in\mathcal{F}\text{ such that }\sigma\upharpoonright_R=\mu\upharpoonright_R.\] Let $[\sigma]$ be the class of $\sigma$. We define relations and functions in the next way: \[([\sigma_1],...,[\sigma_n])\in \mathcal{R}^{\mathbb{V}^{X}[\mathcal{F}]} \Leftrightarrow\text{ there exists }U\in\mathcal{F}:(\sigma_1,...,\sigma_n)\in R^{V(U)}\] \[f^{\mathbb{V}^{X}[\mathcal{F}]}([\sigma_1],...,[\sigma_n])= [f^{V(U)}(\sigma_1,...,\sigma_n)]\] $\mathcal{F}.$ If $\mathcal{F}$ is a generic filter over $X$ for $\mathbb{V}^{X}$ we say that $\mathbb{V}^{X}[\mathcal{F}]$ is a generic model. \end{defin} What is perceived by these classical universal models depends on the structure of the multiversal sheaf of variable sets. This is clearly expressed in the following result (see \cite{caicedo}). \begin{teor} Let $\mathcal{F}$ be a generic filter over $X$ for $\mathbb{V}^{X}$, then: \begin{eqnarray} \mathbb{V}^{X}[\mathcal{F}]\models\varphi([\sigma_1],...,[\sigma_n])&\Leftrightarrow&\text{ there exists }P\in\mathcal{F}\text{ such that } \Vdash_P\varphi^G(\sigma_1,...,\sigma_n)\\ &\Leftrightarrow&\{\lambda\in X:\Vdash_{\lambda}\varphi^G(\sigma_1,...,\sigma_n)\}\in\mathcal{F}, \end{eqnarray} where $\varphi^G$ is the G\"odel translation\footnote{See \cite{benavides} section 0.2.} of the formula $\varphi$. \end{teor} It is not important here to know what is precisely the G\"{o}del translation, it is enough to know that $\varphi^{G}$ is a form to reformulate $\varphi$ in a classical equivalent way, for example, the G\"{o}del translation of the proposition $(a=b)$ is $(a=b)^{G}=\neg\neg (a=b)$ which in the sense of classical logic is equivalent. The important fact to know is that a proposition can be deduced classically if and only if its G\"{o}del translation can be deduced intuitionistically. \begin{corol} Let $X$ be a topological space and $\mathcal{F}$ a generic filter of $\mathbb{V}^{X}$, then \[\mathbb{V}^{X}[\mathcal{F}]\models ZF.\] \end{corol} As an example we can choose the base space $X$ in such a way that in the collapsed model of $\mathbb{V}^{X}$ the Axiom of Choice is valid but the Continuum hypothesis does not hold, this is the intrinsic essence of Paul Cohen's proof (see \cite{benavides}, \cite{benavides3} \cite{cohen}).\\ To see how these results can be applied to Quantum Mechanics, lets consider again the cumulative hierarchy of quantum variable sets over the spectrum $X=S_\mathcal{U}$ of an abelian Von Neumann sub algebra of the algebra $B(H)$ of bounded operators of a Hilbert space $H$. The important result here is that each history $\lambda \in X$ determines a Generic Filter. \begin{teor} Considering $\lambda \in X=S_{\mathcal{U}}$, the set \[\mathcal{F}_{\lambda}=\{P\in Op(X): \lambda(P')=1\},\] where $P'$ is the projection operator associated to the open set $P$, is a generic filter of $\mathbb{V}^{X}$. \end{teor} \begin{proof} Remember that $P=\{\sigma\in X: \sigma(P')=1\}$. If $P, Q\in \mathcal{F}_{\lambda}$, we have $\lambda(P')=1=\lambda(Q')$, then \[\lambda((P\cap Q)')=\lambda(P'\wedge Q')=\lambda(P'Q')=\lambda(P')\lambda(Q')=1.\] Then $P\cap Q\in \mathcal{F}_{\lambda}$. On the other hand if $R\in \mathcal{F}_{\lambda}$ and $S\in Op(X)$ is such that $R\subset S$, this implies that $\lambda \in S$, therefore $\lambda(S')=1$ then $S\in \mathcal{F}_\lambda$. Finally as $X'=I$ where $I$ is the identity operator, we have for any operator $P'$ and any $\lambda$ in $X$ \[\lambda(P')=\lambda(IP')=\lambda(I)\lambda(P'),\] then $\lambda(I)=1$, thus $X\in F_{\lambda}$. We have shown that $\mathcal{F}_{\lambda}$ is a filter, to see that it is maximal suppose that $\mathcal{G}$ is a filter such that $\mathcal{F}_{\lambda}\subset \mathcal{G}$. Let $P\in \mathcal{G}\setminus \mathcal{F}_{\lambda}$, then $\lambda (P')=0$. Therefore \[\lambda((P^{c})')=\lambda((X\setminus P)')=\lambda(I)-\lambda(P')=1,\] then $P^{c}\in \mathcal{F}_{\lambda}$. So we conclude that $P^{c}\in\mathcal{G}$ and $\emptyset=P\cap P^{c}\in \mathcal{G}$, then $\mathcal{G}=Op(X)$. Thus $F_{\lambda}$ is a maximal filter and by theorem \ref{generic} a generic filter. \end{proof} This last result tells us that to each history corresponds a classical universe, the collapsed universe $\mathbb{V}^{X}[\mathcal{F}_{\lambda}]$ obtained from the sheaf $\mathbb{V}^{X}$ via the generic filters $\mathcal{F}_{\lambda}$. In collapsed universes the propositions about the Quantum System assume definite truth values as in classical reality. And these truth values depend on the structure of similar histories, which is represented by the filters $\mathcal{F}_{\lambda}$ which structures depend themselves on the structure of the Hilbert Space from which they arise. To understand how this process works we will need to complete the reformulation of Quantum Mechanics within these models, but if this approach to understand emergence of classical reality is correct, it will reflect a new way to understand emergence in physics. In this case we will not have the emergence as a weak classical limit where some parameters as velocity, scale or gravity tend to certain values but we will have a kind of emergence more close to the sense of emergence as intended in computation or biology, where a lower level structure, represented in this case by a sheaf of structures, determines what is perceived by a higher level structure represented in this case by the collapsed Generic Models.\\ Any satisfactory reformulation of QM should have three fundamental characteristics; first it has to settle a definite interpretation of the theory, second it has to explain the emergence of classical reality and finally it has to be flexible enough to be extended to General Relativity. In this work we saw that the model presented here is a good candidate to fulfil the first two conditions. And probably these kind of models are perfect to include GR from a totally new perspective (see \cite{bell} for example). All these results show that probably we really need a formalism founded over a quantum logic to understand quantum reality and to construct quantum gravity theories.	{ "redpajama_set_name": "RedPajamaArXiv" }	4,049
package jason.environment.grid; import java.io.Serializable; public final class Location implements Serializable { public int x, y; public Location(int x, int y) { this.x = x; this.y = y; } /** calculates the Manhattan distance between two points / public int distanceManhattan(Location l) { return Math.abs(x - l.x) + Math.abs(y - l.y); } /* calculates the Manhattan distance between two points / public int distance(Location l) { return Math.abs(x - l.x) + Math.abs(y - l.y); } /* calculates the Euclidean distance between two points / public double distanceEuclidean(Location l) { return Math.sqrt(Math.pow(x - l.x, 2) + Math.pow(y - l.y, 2)); } /* returns the chessboard king (or Chebyshev) distance between two locations : max( \|this.x - l.x\| , \|this.y - l.y\|) / public int distanceChebyshev(Location l) { return Math.max( Math.abs(this.x - l.x) , Math.abs(this.y - l.y)); } /* @deprecated renamed to distanceChessboard / public int maxBorder(Location l) { return Math.max( Math.abs(this.x - l.x) , Math.abs(this.y - l.y)); } public boolean isInArea(Location tl, Location br) { return x >= tl.x && x <= br.x && y >= tl.y && y <= br.y; } public boolean isInArea(Area a) { return a.contains(this); } public boolean isNeigbour(Location l) { return distance(l) == 1 \|\| equals(l) \|\| Math.abs(x - l.x) == 1 && Math.abs(y - l.y) == 1; } @Override public int hashCode() { final int PRIME = 31; int result = 1; result = PRIME result + x; result = PRIME * result + y; return result; } @Override public boolean equals(Object obj) { if (obj == null) return false; if (this == obj) return true; if (getClass() != obj.getClass()) return false; final Location other = (Location) obj; if (x != other.x) return false; if (y != other.y) return false; return true; } public Object clone() { return new Location(x,y); } public String toString() { return (x + "," + y); } }	{ "redpajama_set_name": "RedPajamaGithub" }	4,127
\section{Introduction}\label{intro} The aim of the present paper is to study the local regularity of weak solutions to the following parabolic problem \begin{align}\label{DP} \begin{cases} u_t+\fl{s}{u}=f &\mbox{ in }\;\Omega\times(0,T)=:\Omega_T, \\ u\equiv 0 &\mbox{ on }\;({\mathbb{R}}^N\setminus\Omega)\times(0,T), \\ u(\cdot,0)\equiv 0 &\mbox{ in }\;\Omega, \end{cases} \end{align} where $\Omega\subset{\mathbb{R}}^N$ is an arbitrary bounded open set, $f$ is a given distribution and, for all $s\in(0,1)$, $(-\Delta)^s$ denotes the fractional Laplace operator, which is defined as the following singular integral \begin{align}\label{fl} (-\Delta)^su(x):=C_{N,s}\,\mbox{P.V.}\int_{{\mathbb{R}}^N}\frac{u(x)-u(y)}{\|x-y\|^{N+2s}}\;dy,\;\;x\in{\mathbb{R}}^N. \end{align} In \eqref{fl}, $C_{N,s}$ is a normalization constant given by \begin{align} C_{N,s}:=\frac{s2^{2s}\Gamma\left(\frac{2s+N}{2}\right)}{\pi^{\frac N2}\Gamma(1-s)}, \end{align} $\Gamma $ being the usual Gamma function. We are interested in analyzing the local regularity for solutions to the parabolic problem \eqref{DP}. We first introduce the functional setting. Given $\Omega\subset{\mathbb{R}}^N$, an arbitrary open set, for $p\in (1,\infty )$ and $s\in (0,1)$, we denote by \begin{equation} W^{s,p}(\Omega ):=\left\{ u\in L^{p}(\Omega):\;\int_{\Omega}\int_{\Omega } \frac{\|u(x)-u(y)\|^{p}}{\|x-y\|^{N+ps}}dxdy<\infty \right\}, \end{equation} the fractional order Sobolev space endowed with the norm \begin{equation} \Vert u\Vert _{W^{s,p}(\Omega )}:=\left( \int_{\Omega }\|u\|^{p}\;dx+\int_{\Omega }\int_{\Omega }\frac{\|u(x)-u(y)\|^{p}}{\|x-y\|^{N+ps}} dxdy\right) ^{\frac{1}{p}}. \end{equation} \noindent We let \begin{align} W_0^{s,p}(\overline{\Om}):=\Big\{u\in W^{s,p}({\mathbb{R}}^N):\; u=0\;\mbox{ on }\;{\mathbb{R}}^N\setminus\Omega\Big\}, \end{align} and we shall denote by $W^{-s,2}(\overline{\Om})$ the dual of the Hilbert space $W_0^{s,2}(\overline{\Om})$, that is, $W^{-s,2}(\overline{\Om}):=(W_0^{s,2}(\overline{\Om}))^\star$. The following continuous embeddings hold \begin{align} W_0^{s,2}(\overline{\Om})\hookrightarrow L^2(\Omega)\hookrightarrow W^{-s,2}(\overline{\Om}). \end{align} \noindent Next, if $s>1$ is not an integer, we write $s=m+\sigma$ where $m$ is an integer and $0<\sigma<1$. In this case \begin{align} W^{s,p}(\Omega):=\Big\{u\in W^{m,p}(\Omega):\; D^\alpha u\in W^{\sigma,p}(\Omega)\;\mbox{ for any }\;\alpha\;\mbox{ such that }\;\|\alpha\|=m\Big\}. \end{align} Then $W^{s,p}(\Omega)$ is a Banach space with respect to the norm \begin{align} \\|u\\|_{W^{s,p}(\Omega)}:=\left(\\|u\\|_{W^{m,p}(\Omega)}^p+\sum_{\|\alpha\|=m}\\|D^\alpha u\\|_{W^{\sigma,p}(\Omega)}^p\right)^{\frac 1p}. \end{align} \noindent If $s=m$ is an integer, then $W^{s,p}(\Omega)$ coincides with the classical integral order Sobolev space $W^{m,p}(\Omega)$. We also recall the following definition of the Besov space $B^{s}_{p,q}$, according to \cite[Chapter V, Section 5.1, Formula (60)]{STEIN}: \begin{align}\label{besov-def} B^{s}_{p,q}({\mathbb{R}}^N) :=\left\{u\in L^p({\mathbb{R}}^N):\; \left(\int_{{\mathbb{R}}^N}\frac{\norm{u(x+y)-u(y)}{L^p({\mathbb{R}}^N)}^q}{\|y\|^{N+qs}}\,dy\right)^{\frac{1}{q}}<\infty \right\}, \;\;\;1\le p,q\le\infty,\;\; 0<s<1. \end{align} Notice that, when $p=q$, we have $B^{s}_{p,p}({\mathbb{R}}^N) = W^{s,p}({\mathbb{R}}^N)$. Finally, we recall the definition of the following potential space \begin{align}\label{sp-stein} \mathscr{L}^p_{2s}({\mathbb{R}}^N):=\Big\{u\in L^p({\mathbb{R}}^N):\; \fl{s}{u}\in L^p({\mathbb{R}}^N)\Big\},\;\;\;1\le p\le\infty, \;\;s\ge 0, \end{align} introduced, for example, in \cite[Chapter V, Section 3.3, Formula (38)]{STEIN}. Note that this same space is sometimes denoted as $H^s_p({\mathbb{R}}^N)$ (see, e.g., \cite[Section 1.3.2]{TRIEB}). Here we adopt the notation $\mathscr{L}^p_{2s}({\mathbb{R}}^N)$. Let us now introduce the notion of solution that we shall consider. Following \cite{LPPS}, we first consider weak solutions of \eqref{DP} defined as follows. \begin{definition}\label{weak_sol_def_fe} Let $f\in L^2((0,T);W^{-s,2}(\overline{\Om}))$. We say that $u\in L^2((0,T);W_0^{s,2}(\overline{\Om}))\cap C([0,T];L^2(\Omega))$ with $u_t\in L^2((0,T);W^{-s,2}(\overline{\Om}))$ is a finite energy solution to the parabolic problem \eqref{DP}, if the identity \begin{align}\label{weak-sol-fe} &\int_0^T\int_{\Omega} u_tw\,dxdt + \frac{C_{N,s}}{2}\int_0^T\int_{{\mathbb{R}}^N}\int_{{\mathbb{R}}^N}\frac{(u(x)-u(y))(w(x)-w(y))}{\|x-y\|^{N+2s}}\,dxdydt \notag\\ =& \int_0^T \langle f,v\rangle_{W^{-s,2}(\overline{\Om}),W_0^{s,2}(\overline{\Om})}\,dt, \end{align} holds, for any $w\in L^2((0,T);W_0^{s,2}(\overline{\Om}))$, where $\langle \cdot,\cdot\rangle_{W^{-s,2}(\overline{\Om}),W_0^{s,2}(\overline{\Om})}$ denotes the duality pairing between $W^{-s,2}(\overline{\Om})$ and $W_0^{s,2}(\overline{\Om})$. \end{definition} \begin{remark} {\em We observe the following facts. \begin{enumerate} \item According to \cite[Theorem 10]{LPPS}, if $u\in L^2((0,T);W_0^{s,2}(\overline{\Om}))$ and $u_t\in L^2((0,T);W^{-s,2}(\overline{\Om}))$, then $u\in C([0,T];L^2(\Omega))$. Thus the identity $u(\cdot,0)=0$ makes sense in $L^2(\Omega)$. \item When considering right hand side terms $f\in L^p((0, T);L^p(\Omega))=L^p(\Omega\times(0,T))$ with $p\ge 2$, since we have the continuous embedding $L^p(\Omega\times(0,T))\hookrightarrow L^2((0,T);W^{-s,2}(\overline{\Om}))$, this notion of weak finite energy solution suffices. \item When $f\in L^p(\Omega\times(0,T))$ with $1\le p< 2$, the regularity of the right hand side term does not suffice to define weak finite energy solutions as above. We shall rather consider those defined by duality or transposition. \end{enumerate} } \end{remark} Duality or transposition solutions of \eqref{DP} are given by duality with respect to the following class of test functions \begin{align} \mathcal{P}(\Omega_T) = \Big\{\phi(\cdot,t)\in C^1((0,T),C_0^{\beta}(\Omega)) : \phi\textrm{ is a solution to Problem (P)}\Big\}, \end{align} where \begin{align} (P) = \begin{cases} -\phi_t+\fl{s}{\phi}=\psi &\mbox{ in }\;\Omega\times(0,T)=:\Omega_T, \\ \phi\equiv 0 &\mbox{ on }\;({\mathbb{R}}^N\setminus\Omega)\times(0,T), \\ \phi(\cdot,T)\equiv 0 &\mbox{ in }\;\Omega \end{cases} \end{align} for $\psi\in C_0^{\infty}(\Omega_T)$. \begin{definition}\label{weak_sol_def} Let $f\in L^1(\Omega\times(0,T))$. We say that $u\in C([0,T];L^1(\Omega))$ is a weak duality or transposition solution to the parabolic problem \eqref{DP}, if the identity \begin{align}\label{weak-sol} &\int_0^T\int_{\Omega} u\psi\,dxdt = \int_0^T\int_{\Omega} f\phi\,dxdt \end{align} holds, for any $\phi\in\mathcal{P}(\Omega_T)$ and $\psi\in C_0^{\infty}(\Omega_T)$. \end{definition} \begin{remark} {\em The existence and uniqueness of finite energy weak solutions or the duality/transposition ones (depending on the regularity imposed on the right hand side term $f$) to problem \eqref{DP} is guaranteed by \cite[Theorem 26]{LPPS} and \cite[Theorem 28]{LPPS}, respectively. If $f\in L^p(\Omega\times(0,T))$, with $p\ge 2$, finite energy solutions of \eqref{DP} will be considered while, if $1<p<2$, solutions will be understood in the sense of duality/transposition. In both cases we shall refer to them as weak solutions. } \end{remark} \noindent Our first regularity result concerns the case $p=2$. It reads as follows: \begin{theorem}\label{reg-thm-2} Assume $f\in L^2(\Omega\times(0,T))$ and let $u\in L^2((0,T);W^{s,2}_0(\overline{\Om}))\cap C([0,T];L^2(\Omega))$ with $u_t\in L^2((0,T);W^{-s,2}(\overline{\Om}))$ be the unique finite energy solution of system \eqref{DP}. Then \begin{align} u\in L^2((0,T);W^{2s,2}_{\rm loc}(\Omega))\cap L^{\infty}((0,T);W^{s,2}_0(\overline{\Om}))\;\;\mbox{ and }\; u_t\in L^2(\Omega \times (0, T)). \end{align} \end{theorem} \noindent Theorem \ref{reg-thm-2} can be extended to the $L^p$-setting as follows. \begin{theorem}\label{reg-thm-p} Let $1<p<\infty$ and $f\in L^p(\Omega \times (0,T))$. Then, problem \eqref{DP} has a unique weak solution $u\in C([0,T];L^p(\Omega))$ such that $u\in L^p\Big((0,T);\mathscr{L}^p_{2s, {\rm loc}}(\Omega)\Big)$ and $u_t\in L^p(\Omega \times (0,T))$. As a consequence we have the following result. \begin{enumerate} \item If $1<p<2$ and $s\ne 1/2$, then $u\in L^p\Big((0,T);B^{2s}_{p,2, {\rm loc}}(\Omega)\Big)$. \item If $1<p<2$ and $s= 1/2$, then $u\in L^p\Big((0,T);W^{2s,p}_{\rm loc}(\Omega)\Big)=L^p\Big((0,T);W^{1,p}_{\rm loc}(\Omega)\Big)$. \item If $2\leq p<\infty$, then $u\in L^p\Big((0,T);W^{2s,p}_{\rm loc}(\Omega)\Big)$. \end{enumerate} \end{theorem} In Theorem \ref{reg-thm-p}, with $\mathscr{L}^p_{2s, \textrm{loc}}(\Omega)$ we indicate the potential space \begin{align}\label{sp-stein-loc} \mathscr{L}^p_{2s, \textrm{loc}}(\Omega):=\Big\{ u\in L^p(\Omega): u\eta \in \mathscr{L}_{2s}^p({\mathbb{R}}^N) \;\textrm{ for any test function $\eta\in\mathcal{D}(\Omega)$} \Big\}. \end{align} Analogously, with $B^{2s}_{p,2, {\rm loc}}(\Omega)$ we indicate the Besov space \begin{align}\label{besov-loc} B^{2s}_{p,2, {\rm loc}}(\Omega):=\Big\{ u\in L^p(\Omega): u\eta \in B^{2s}_{p,2}({\mathbb{R}}^N) \;\textrm{ for any test function $\eta\in\mathcal{D}(\Omega)$} \Big\}. \end{align} Moreover, our results guarantee that when the right hand side belongs to $L^p(\Omega \times (0, T))$ for $2\le p<\infty$ and for $1<p<2$, $s=1/2$, then the corresponding solution gains locally the maximum possible regularity, that is, it gains one time derivative and up to $2s$ space derivatives, locally, in $L^p(\Omega)$. For $1<p<2$ and $s\neq 1/2$, instead, the local regularity is obtained in the Besov space $B^{2s}_{p,2, {\rm loc}}(\Omega)$, which is strictly larger than $W^{2s,p}_{\textrm{loc}}(\Omega)$. For the classical Laplace operator (which corresponds to the case $s=1$), this kind of results are standard, see e.g., \cite[Theorem X.12]{brezis}, \cite[Section 9]{Gris-abs}, \cite[Section 4.1]{LSU}. Also, we recall \cite[Theorem 1]{lamberton} for a more general result in an abstract setting. Theorems \ref{reg-thm-2} and \ref{reg-thm-p} are natural extensions of analogous results of local regularity for the elliptic problem associated to the fractional Laplacian on a bounded domain, which have been obtained recently in \cite{fl_reg,fl_reg_add}. In the recent years, research on regularity of heat equations involving non-local terms has been very active. For instance, H\"older regularity was proved in \cite{FR,KS}. Boundary regularity has also been analyzed showing that, if $f=0$ and taking initial data $u(\cdot,0)=u_0\in L^2(\Omega)$, the corresponding solution to \eqref{DP} is such that $u(\cdot,t)$ belongs to $C^s({\mathbb{R}}^N)$ for all $t>0$ and satisfies $u(\cdot,t)/\rho^s\in C^{s-\varepsilon}(\Omega)$ for any $\varepsilon>0$, $\rho(x)=\textrm{dist}(x,\partial\Omega)$ being the distance to the boundary function. Concerning regularity in the Sobolev setting, we refer instead to \cite[Theorem 26]{LPPS}, where it has been proved the existence of a finite energy solution to \eqref{DP}, according to Definition \ref{weak_sol_def} above. However, to the best of our knowledge, our Theorems \ref{reg-thm-2} and \ref{reg-thm-p} providing maximal space-time local regularity are new. The controllability of parabolic equations involving non-local terms has also been investigated. We refer for instance to \cite{FLZ} where null controllability issues were addressed for heat equations involving non-local lower order terms. On the other hand, \cite{MZ,miller} dealt with the control of heat equations involving the \textit{spectral} fractional Laplacian (see \cite[Section 1]{MZ} for the definition of this operator), proving that null controllability holds for $s>1/2$, while for $s\leq 1/2$ the equation fails to be controllable. Notice that this operator does not coincide with \eqref{fl}. The present paper is organized as follows. In Section \ref{elliptic_sec}, we will recall the sharp local regularity results obtained in \cite{fl_reg,fl_reg_add} for the elliptic problems associated to the fractional Laplacian. These results will be necessary in the proof of Theorems \ref{reg-thm-2} and \ref{reg-thm-p}. In Section \ref{L2-reg}, we give the proof of Theorem \ref{reg-thm-2}, using the corresponding result for the classical Laplace operator in \cite[Section 7.1.3, Theorem 5]{evans}, employing a cut-off argument and using \cite[Theorem 1.2]{fl_reg}. In Section \ref{Lp-reg} we give the proof of Theorem \ref{reg-thm-p} by applying the results contained in \cite{lamberton}. Finally, in Section \ref{open_pb}, we present some open problems and perspectives that are closely related to our work. \section{Regularity results for the elliptic problem}\label{elliptic_sec} In this section, we recall some regularity results for weak solutions to the elliptic problem associated to the fractional Laplacian on a bounded open set. These results have been recently obtained in \cite{fl_reg,fl_reg_add}, and they will be fundamental in the proof of Theorems \ref{reg-thm-2} and \ref{reg-thm-p}. Therefore, throughout this section we are going to consider the following elliptic problem \begin{align}\label{DP-ell} \begin{cases} \fl{s}{u}=f &\mbox{ in }\;\Omega, \\ u\equiv 0 &\mbox{ on }\;{\mathbb{R}}^N\setminus\Omega. \end{cases} \end{align} \noindent Let us start by recalling the definition of a weak solution, according to \cite{fl_reg,LPPS}. \begin{definition}\label{weak_sol_def-en} Let $f\in W^{-s,2}(\overline{\Om})$. A function $u\in W_0^{s,2}(\overline{\Om})$ is said to be a finite energy solution to the Dirichlet problem \eqref{DP-ell} if for every $v\in W_0^{s,2}(\overline{\Om})$, the equality \begin{align}\label{wek-sol-en} \frac{C_{N,s}}{2}\int_{{\mathbb{R}}^N}\int_{{\mathbb{R}}^N}\frac{(u(x)-u(y))(v(x)-v(y))}{\|x-y\|^{N+2s}}\;dxdy=\langle f,v\rangle_{W^{-s,2}(\overline{\Om}),W_0^{s,2}(\overline{\Om})} \end{align} holds. \end{definition} We notice that, when $f\in L^p(\Omega)$ with $1<p<2$ and it does not belong to $W^{-s,2}(\overline{\Om})$, it is not natural to consider finite energy solutions for the problem \eqref{DP-ell}. As for the parabolic problem above, we shall introduce an alternative notion of solution. This will be given by duality with respect to the following class of test functions: \begin{align} \mathcal{T}(\Omega) = \Big\{\phi : \fl{s}{\phi} = \psi\;\;\textrm{ in }\;\Omega,\;\phi=0\;\;\textrm{ in }\;{\mathbb{R}}^N\setminus\Omega,\;\psi\in C_0^{\infty}(\Omega)\Big\}. \end{align} \begin{definition}\label{weak-sol-def} Let $f\in L^1(\Omega)$. We say that $u\in L^1(\Omega)$ is a weak duality or transposition solution to \eqref{DP-ell} if the equality \begin{align} \int_{\Omega} u\psi\,dx = \int_{\Omega}f\phi\,dx, \end{align} holds for any $\phi\in\mathcal{T}(\Omega)$ and $\psi\in C_0^{\infty}(\Omega)$. \end{definition} The existence and uniqueness of finite energy weak solutions or the duality/transposition ones (depending on the regularity imposed on the right hand side term $f$) to problem \eqref{DP-ell} are guaranteed by \cite[Theorem 12]{LPPS} and \cite[Theorem 23]{LPPS}, respectively. If $f\in L^p(\Omega)$, with $p\ge 2$, finite energy solutions of \eqref{DP-ell} will be considered while, if $1<p<2$, solutions will be understood in the sense of duality/transposition. In both cases, we shall refer to them as weak solutions. Moreover, we notice that, according to Definition \ref{weak-sol-def}, duality solutions do not require that $f$ belongs to the dual space $W^{-s,2}(\overline{\Om})$. Finally, we also notice that, if $f\in L^p(\Omega)$ with $p\geq 2$, we have the continuous embedding $L^p(\Omega)\hookrightarrow L^2(\Omega)\hookrightarrow W^{-s,2}(\overline{\Om})$, meaning that the property $f\in W^{-s,2}(\overline{\Om})$ is automatically guaranteed. Concerning the regularity of the solutions to \eqref{DP-ell}, the following result has been proved in \cite{fl_reg,fl_reg_add}. \begin{theorem}[\bf $L^p$-Local elliptic regularity]\label{reg-p-ell} Let $1<p<\infty$. Given $f\in L^p(\Omega)$, let $u$ be the unique weak solution to the Dirichlet problem \eqref{DP-ell}. Then $u\in \mathscr{L}^p_{2s, {\rm loc}}(\Omega)$. As a consequence we have the following result. \begin{enumerate} \item If $1<p<2$ and $s\ne 1/2$, then $u\in B^{2s}_{p,2, {\rm loc}}(\Omega)$. \item If $1<p<2$ and $s= 1/2$, then $u\in W_{\rm loc}^{2s,p}(\Omega)=W_{\rm loc}^{1,p}(\Omega)$. \item If $2\leq p<\infty$, then $u\in W^{2s,p}_{\rm loc}(\Omega)$. \end{enumerate} \end{theorem} The proof of Theorem \ref{reg-p-ell} requires a cut-off argument that allows us to reduce the problem to the whole space case, for which the result is already known. In particular, we have the following. \begin{theorem}\label{re-r-N} Let $1<p<\infty$. Given $F\in L^p({\mathbb{R}}^N)$, let $u$ be the unique weak solution to the fractional Poisson type equation \begin{equation}\label{PE} \fl{s}{u}=F\;\;\mbox{ in }\;{\mathbb{R}}^N. \end{equation} Then $u\in \mathscr{L}^p_{2s}({\mathbb{R}}^N)$. As a consequence we have the following. \begin{enumerate} \item If $1<p<2$ and $s\ne 1/2$, then $u\in B^{2s}_{p,2}({\mathbb{R}}^N)$. \item If $1<p<2$ and $s= 1/2$, then $u\in W^{2s,p}({\mathbb{R}}^N)=W^{1,p}({\mathbb{R}}^N)$. \item If $2\leq p<\infty$, then $u\in W^{2s,p}({\mathbb{R}}^N)$. \end{enumerate} \end{theorem} Theorem \ref{re-r-N} is a classical result whose proof can be done by combining several results on singular integrals and Fourier transform contained in \cite[Chapter V]{STEIN}. See also \cite{fl_reg,fl_reg_add}. In particular: \begin{itemize} \item If $1<p<2$ and $s\ne 1/2$, then the result follows from \cite[Chapter V, Section 5.3, Theorem 5(B)]{STEIN}, which provides the inclusion $\mathscr{L}^p_{2s}({\mathbb{R}}^N)\subset B^{2s}_{p,2}({\mathbb{R}}^N)$. Moreover, an explicit counterexample showing that sharper inclusions are not possible has been given in \cite[Chapter V, Section 6.8]{STEIN}. \item If $1<p<2$ and $s= 1/2$, then applying \cite[Chapter V, Section 3.3, Theorem 3]{STEIN} we have $\mathscr{L}^p_{2s}({\mathbb{R}}^N)=\mathscr{L}^p_{1}({\mathbb{R}}^N)=W^{1,p}({\mathbb{R}}^N)$. \item If $2\leq p<\infty$, then \cite[Chapter V, Section 5.3, Theorem 5(A)]{STEIN} yields $u\in B^{2s}_{p,p}({\mathbb{R}}^N)$ and this latter space, by definition, coincides with $W^{2s,p}({\mathbb{R}}^N)$ (see, e.g., \cite[Chapter V, Section 5.1, Formula (60)]{STEIN}). \end{itemize} While developing the cut-off argument that we mentioned above, as an intermediate step we need to show that $u\in W^{s,p}(\Omega)$. Notice that, for $p\geq 2$, this is true for all weak solutions to \eqref{DP} by classical embedding results. When $1<p<2$, instead, according to \cite[Theorem 23]{LPPS}, weak duality solutions to \eqref{DP-ell} are such that \begin{align}\label{reg} \fl{\frac{s}{2}}{u}\in L^p(\Omega), \;\;\;\forall \;p\in(1, N/(N-s)) \end{align} an this implies that $u\in W^{s,p}(\Omega)$ too. \begin{proof}[Proof of Theorem \ref{reg-p-ell}] For the sake of completeness we include the proof. We start by noticing that, assuming $f\in L^p(\Omega)$, $1<p<\infty$, we have that \eqref{DP-ell} has a unique weak solution $u$ (either the finite-energy or the duality one) and that, from the discussion above, we have $u\in W^{s,p}(\Omega)$. In particular, $u\in L^p(\Omega)$. As we have mentioned above, our strategy is based on a cut-off argument that will allow us to show that the solutions of the fractional Dirichlet problem in $\Omega$, after cut-off, are solutions of the elliptic problem on the whole space ${\mathbb{R}}^N$, for which Theorem \ref{re-r-N} holds. For this purpose, given $\omega$ and $\widetilde\omega$ two open subsets of the domain $\Omega$ such that $\widetilde\omega\Subset\omega\Subset\Omega$, we introduce a cut-off function $\eta\in \mathcal D(\omega)$ such that \begin{equation}\label{eta} \begin{cases} \eta(x)\equiv 1\;\;\;&\mbox{ if }\; x\in\widetilde\omega\\ 0\le \eta(x)\le 1&\mbox{ if }\; x\in\omega\setminus\widetilde\omega\\ \eta(x)=0&\mbox{ if }\; x\in{\mathbb{R}}^N\setminus\omega. \end{cases} \end{equation} Let $\omega$ and $\eta\in\mathcal D(\omega)$ be respectively the set and the cut-off function constructed in \eqref{eta}. We consider the function $u\eta\in W^{s,p}({\mathbb{R}}^N)$ and we have that $(-\Delta)^s(u\eta)$ is given by (see, e.g., \cite[Proposition 1.5]{fl_reg} or \cite{ROS}) \begin{align}\label{for-del-prod} \fl{s}{(u\eta)} = \eta f + u\fl{s}{\eta} - I_s(u,\eta), \end{align} where $I_s(u,\eta)$ is a remainder term which is given by \begin{align}\label{Is-formula} I_s(u,\eta)(x):=C_{N,s}\int_{{\mathbb{R}}^N}\frac{(u(x)-u(y))(\eta(x)-\eta(y))}{\|x-y\|^{N+2s}}\;dy,\;\;x\in{\mathbb{R}}^N. \end{align} Let $\omega_1, \omega_2$ be open sets such that \begin{align}\label{omega12} \overline{\omega}\subset\omega_1\subset\overline{\omega}_1\subset\omega_2 \subset\overline{\omega}_2\subset\Omega. \end{align} Since the function $\eta$ and the set $\omega$ in \eqref{eta} are arbitrary, it follows that $u\in W^{s,p}(\omega_2)$. Thus we have $u\in W^{s,p}(\omega_2)\cap L^p(\Omega)$. Let \begin{align} g:=u(-\Delta)^s\eta -I_s(u,\eta). \end{align} We now claim that $g\in L^p({\mathbb{R}}^N)$ and there exists a constant $C>0$ such that \begin{align}\label{norm-f-p} \\|g\\|_{L^p({\mathbb{R}}^N)}\le C\left(\\|u\\|_{W^{s,p}(\omega_2)}+\\|u\\|_{L^p(\Omega)}\right). \end{align} Indeed, it is clear that $g$ is defined on all ${\mathbb{R}}^N$. Moreover \begin{align}\label{est1-p} \\|u(-\Delta)^s\eta\\|_{L^p({\mathbb{R}}^N)}^p=\int_{\Omega}\|u(-\Delta)^s\eta\|^p\;dx\le \\|(-\Delta)^s\eta\\|_{L^\infty(\Omega)}^p\\|u\\|_{L^p(\Omega)}^p. \end{align} For estimating the term $I_s$, we use the decomposition \begin{align} I_s(u,\eta)(x):=&C_{N,s}\int_{{\mathbb{R}}^N}\frac{(u(x)-u(y))(\eta(x)-\eta(y))}{\|x-y\|^{N+2s}}\;dy\\ =&C_{N,s}\int_{\omega_1}\frac{(u(x)-u(y))(\eta(x)-\eta(y))}{\|x-y\|^{N+2s}}\;dy\\ &+C_{N,s}\eta(x)\int_{{\mathbb{R}}^N\setminus\omega_1}\frac{u(x)-u(y)}{\|x-y\|^{N+2s}}\;dy =\mathbb I_1(x)+\mathbb I_2(x),\;\;x\in{\mathbb{R}}^N, \end{align} where we have set \begin{align* \mathbb I_1(x):=C_{N,s}\int_{\omega_1}\frac{(u(x)-u(y))(\eta(x)-\eta(y))}{\|x-y\|^{N+2s}}\;dy,\;\;x\in{\mathbb{R}}^N, \end{align} and \begin{align \mathbb I_2(x):=C_{N,s}\eta(x)\int_{{\mathbb{R}}^N\setminus\omega_1}\frac{u(x)-u(y)}{\|x-y\|^{N+2s}}\;dy,\;\;x\in{\mathbb{R}}^N. \end{align} Let $p':=p/(p-1)$. Using the H\"older inequality, we get that for a.e. $x\in{\mathbb{R}}^N$, \begin{align}\label{CS1-p} \|\mathbb I_1(x)\|\le C_{N,s}\left(\int_{\omega_1}\frac{\|u(x)-u(y)\|^p}{\|x-y\|^{N+sp}}\;dy\right)^{\frac 1p}\left(\int_{\omega_1}\frac{\|\eta(x)-\eta(y)\|^{p'}}{\|x-y\|^{N+sp'}}\;dy\right)^{\frac 1{p'}}. \end{align} Let $x\in\omega_1$ be fixed and $R>0$ such that $\omega_1\subset B(x,R)$. Using the Lipschitz continuity of the function $\eta$, we obtain that there exists constant $C>0$ such that \begin{align}\label{CS2-p} \int_{\omega_1}\frac{\|\eta(x)-\eta(y)\|^{p'}}{\|x-y\|^{N+sp'}}\;dy\le C\int_{\omega_1}\frac{dy}{\|x-y\|^{N+sp'-p'}}\le C\int_{B(x,R)}\frac{dy}{\|x-y\|^{N+sp'-p'}}\le C. \end{align} In what follows, we will employ the following estimate. Let $A\subset{\mathbb{R}}^N$ be a bounded set and $B\subset{\mathbb{R}}^N$ an arbitrary set. Then there exists a constant $C>0$ (depending on $A$ and $B$) such that \begin{align}\label{ine-dist} \|x-y\|\ge C(1+\|y\|),\;\;\forall\;x\in A,\;\forall\;y\in {\mathbb{R}}^N\setminus B,\;\mbox{dist}(A,{\mathbb{R}}^N\setminus B)=\delta>0. \end{align} Now, using \eqref{CS1-p}, \eqref{CS2-p} and \eqref{ine-dist}, we get \begin{align}\label{I1-p} \int_{{\mathbb{R}}^N}\|\mathbb I_1(x)\|^p\;dx\le& C\left(\int_{\omega_2} \int_{\omega_1}\frac{\|u(x)-u(y)\|^p}{\|x-y\|^{N+sp}}\;dydx+\int_{{\mathbb{R}}^N\setminus\omega_2} \int_{\omega_1}\frac{\|u(x)-u(y)\|^p}{\|x-y\|^{N+sp}}\;dydx\right)\notag\\ \le &C\left(\\|u\\|_{W^{s,p}(\omega_2)}^p+\int_{{\mathbb{R}}^N\setminus\omega_2} \int_{\omega_1}\frac{\|u(x)\|^p+\|u(y)\|^p}{(1+\|x\|)^{N+sp}}\;dydx\right)\notag\\ \le &C\left(\\|u\\|_{W^{s,p}(\omega_2)}^p+\\|u\\|_{L^p(\Omega)}^p\right) , \end{align} where we have also used that $u=0$ on ${\mathbb{R}}^N\setminus\Omega$. Recall that $\mathbb I_2=0$ on ${\mathbb{R}}^N\setminus\omega$. Then using the H\"older inequality, we get that \begin{align}\label{E1-1} \|\mathbb I_2(x)\|^p\le C\left(\int_{{\mathbb{R}}^N\setminus\omega_1}\frac{\eta^{p'}(x)dy}{\|x-y\|^{N+sp'}}\right)^{p-1}\int_{{\mathbb{R}}^N\setminus\omega_1}\frac{\|u(x)-u(y)\|^p}{\|x-y\|^{N+sp}}\;dy. \end{align} For any $y\in {\mathbb{R}}^N\setminus\omega_1$, we have that \begin{align} \frac{\eta^{p'}(x)}{\|x-y\|^{N+sp'}}=\frac{\chi_{\overline{\omega}}(x)\eta^{p'}(x)}{\|x-y\|^{N+sp'}}\le \chi_{\overline{\omega}}(x)\eta^{p'}(x)\sup_{x\in\overline{\omega}}\frac{1}{\|x-y\|^{N+sp'}}. \end{align} So there exists a constant $C>0$ such that \begin{align}\label{E2-2} \int_{{\mathbb{R}}^N\setminus\omega_1}\frac{\eta^{p'}(x)dy}{\|x-y\|^{N+sp'}}\le \chi_{\overline{\omega}}(x)\eta^{p'}(x)\int_{{\mathbb{R}}^N\setminus\omega_1}\frac{dy}{\mbox{dist}(y,\partial\overline{\omega})^{N+sp'}}\le C\chi_{\overline{\omega}}(x)\eta^{p'}(x). \end{align} In \eqref{E2-2} we have also used that the integral is finite which follows from the fact that $\mbox{dist}(\partial\omega_1,\partial\overline{\omega})\ge\delta>0$ together with the fact that $\mbox{dist}(y,\partial\overline{\omega})$ grows linearly as $y$ tends to infinity and $N+sp'>N$. Since $\chi_{\overline{\omega}}\eta^{p'}\in L^\infty(\omega)$, and using \eqref{E1-1}, \eqref{E2-2} and \eqref{ine-dist}, we also get that there exists a constant $C>0$ such that \begin{align}\label{I2-p} \int_{{\mathbb{R}}^N}\|\mathbb I_2(x)\|^p\;dx=&\int_{\omega}\|\mathbb I_2(x)\|^p\;dx\le C\int_{\omega}\int_{{\mathbb{R}}^N\setminus\omega_1}\frac{\|u(x)-u(y)\|^p}{\|x-y\|^{N+sp}}\;dydx\notag \\ \le &C\int_{\omega}\int_{{\mathbb{R}}^N\setminus\omega_1}\frac{\|u(x)\|^p+\|u(y)\|^p}{(1+\|y\|)^{N+sp}}\;dydx\le C\\|u\\|_{L^p(\Omega)}^p, \end{align} where we have used again that $u=0$ on ${\mathbb{R}}^N\setminus\Omega$. Estimate \eqref{norm-f-p} follows from \eqref{est1-p}, \eqref{I1-p}, \eqref{I2-p} and we have shown the claim. We therefore proved that $\eta u$ is a weak solution to the Poisson equation \eqref{PE} with $F$ given by $F=\eta f+g$. Since $F\in L^p({\mathbb{R}}^N)$, it follows from Theorem \ref{re-r-N} that $\eta u\in \mathscr{L}^p_{2s}({\mathbb{R}}^N)$. We have shown that $u\in \mathscr{L}^p_{2s, \textrm{loc}}(\Omega)$. As a consequence we have the following results. \begin{enumerate} \item If $1<p<2$ and $s\ne 1/2$, then $\eta u\in B^{2s}_{p,2}({\mathbb{R}}^N)$, hence $u\in B^{2s}_{p,2, \textrm{loc}}(\Omega)$. \item If $1<p<2$ and $s= 1/2$, then $\eta u\in W^{2s,p}({\mathbb{R}}^N)=W^{1,p}({\mathbb{R}}^N)$, hence $u\in W^{2s,p}_{\textrm{loc}}(\Omega)=W^{1,p}_{\textrm{loc}}(\Omega)$. \item If $2\leq p<\infty$, then $\eta u\in W^{2s,p}({\mathbb{R}}^N)$, hence $u\in W^{2s,p}_{\textrm{loc}}(\Omega)$. \end{enumerate} \noindent The proof is finished. \end{proof} We conclude this section mentioning that Theorem \ref{reg-p-ell} can be proved also using techniques from pseudo-differential calculus (see, e.g., \cite[Section 7]{grubb} or \cite[Chapter XI, Theorem 2.5]{taylor}). Our approach is different and provides a proof based on basic estimates of solutions of general elliptic operators. In particular, our proofs do not require any knowledge of pseudo-differential operators theory. \section{Proof of Theorem \ref{reg-thm-2}}\label{L2-reg} \noindent The proof of Theorem \ref{reg-thm-2} employs a cut-off argument, as in Theorem \ref{reg-p-ell}. In particular: \begin{itemize} \item Firstly, we treat the case $\Omega={\mathbb{R}}^N$, adapting the proof in \cite[Section 7.1.3, Theorem 5]{evans} for the classical Laplace operator. \item The case of a general $\Omega$ is reduced to the previous one applying a cut-off argument. \end{itemize} \subsection{The $W^{2s,2}$-regularity on ${\mathbb{R}}^N$} In this Section, we prove the $W^{2s,2}$-regularity result in the case where $\Omega$ is the whole space ${\mathbb{R}}^N$. We will adapt the proof presented in \cite[Section 7.1.3, Theorem 5]{evans} for the local case. \begin{theorem}\label{reg-thm-r} Assume $f\in L^2({\mathbb{R}}^N\times (0, T))$ and let $u\in L^2((0,T);W^{s,2}({\mathbb{R}}^N))\cap C([0,T];L^2({\mathbb{R}}^N))$ with $u_t\in L^2((0,T);W^{-s,2}({\mathbb{R}}^N))$ be the unique finite energy solution of the system \begin{align}\label{DPR} \begin{cases} u_t+\fl{s}{u}=f\;\;&\mbox{ in }{\mathbb{R}}^N\times (0,T), \\ u(\cdot,0)\equiv 0\;&\mbox{ on } {\mathbb{R}}^N. \end{cases} \end{align} Then \begin{align} u\in L^2((0,T);W^{2s,2}({\mathbb{R}}^N))\cap L^{\infty}((0,T);W^{s,2}({\mathbb{R}}^N)),\;\; u_t\in L^2({\mathbb{R}}^N\times (0, T)) \end{align} \end{theorem} \begin{proof} First of all, we notice that the function $v:=ue^{-t}$ solves the system \begin{align}\label{DPRV} \begin{cases} v_t+\fl{s}{v}+v=g & \mbox{ in } {\mathbb{R}}^N\times [0,T], \\ v(\cdot,0)\equiv 0 & \mbox{ on } {\mathbb{R}}^N, \end{cases} \end{align} with $g:=fe^{-t}\in L^2({\mathbb{R}}^N\times (0, T))$. Now, multiplying \eqref{DPRV} by $v_t$ and integrating by parts over ${\mathbb{R}}^N$ we obtain that \begin{align} (v_t,v_t) + B[v,v_t] + (v,v_t) = (g,v_t), \end{align} where $(\cdot,\cdot)$ is the classical scalar product on $L^2({\mathbb{R}}^N)$, while with $B[\cdot,\cdot]$ we indicated the bilinear form \begin{align} B[\phi,\psi]:=\frac{C_{N,s}}{2}\int_{{\mathbb{R}}^N}\int_{{\mathbb{R}}^N}\frac{(\phi(x)-\phi(y))(\psi(x)-\psi(y))}{\|x-y\|^{N+2s}}\,dxdy. \end{align} Moreover, we observe that \begin{align} B[v,v_t] = \frac{1}{2}\frac{d}{dt}B[v,v]\;\mbox{ and }\; (v,v_t)=\frac{1}{2}\frac{d}{dt}(v,v). \end{align} Hence, using Young's inequality we have that, for every $\varepsilon>0$, \begin{align} \norm{v_t}{L^2({\mathbb{R}}^N)}^2 + \frac{1}{2}\frac{d}{dt}\Big(B[v,v] + (v,v)\Big) = (g,v_t)\leq \frac{C}{\varepsilon}\norm{g}{L^2({\mathbb{R}}^N)}^2 + \varepsilon\norm{v_t}{L^2({\mathbb{R}}^N)}^2. \end{align} Choosing $\varepsilon\le 1$ and integrating in time we find that \begin{align} \int_0^T\norm{v_t}{L^2({\mathbb{R}}^N)}^2\,dt + \sup_{t\in[0,T]}\Big(B[v(t),v(t)] + (v(t),v(t))\Big) \leq C\int_0^T\norm{g}{L^2({\mathbb{R}}^N)}^2\,dt, \end{align} which implies that \begin{align} \norm{v_t}{L^2({\mathbb{R}}^N \times (0, T))}^2 + \norm{v}{L^{\infty}((0,T),W^{s,2}({\mathbb{R}}^N))} \leq C\norm{g}{L^2({\mathbb{R}}^N \times (0, T))}^2. \end{align} Therefore, \begin{align} v\in L^{\infty}((0,T);W^{s,2}({\mathbb{R}}^N)),\;\;\; v_t\in L^2({\mathbb{R}}^N\times (0, T)) \end{align} and, by definition, $u$ has the same regularity too. Finally, the $W^{2s,2}$ regularity for $u$ in the space variable is obtained in the following way. From \eqref{DPR} we have that $\fl{s}{u} = f-u_t\in L^2({\mathbb{R}}^N\times (0, T))$. Hence, a. e. $t\in(0,T)$, we have that $\fl{s}{u}(\cdot,t) = h(\cdot,t)\in L^2({\mathbb{R}}^N)$ and, applying the regularity results for the elliptic case (see Theorem \ref{re-r-N}) we get that $u(\cdot,t)\in W^{2s,2}({\mathbb{R}}^N)$ a. e. $t\in (0,T)$. Furthermore $u\in L^2((0,T);W^{2s,2}({\mathbb{R}}^N))$ and the proof is finished. \end{proof} \subsection{The $W^{2s,2}_{\textrm{loc}}$-regularity in $\Omega$} \begin{proof}[\bf Proof of Theorem \ref{reg-thm-2}] As we have mentioned above, our strategy is based on a cut-off argument that will allow us to show that solutions of the fractional parabolic problem in $\Omega$, after cut-off, are solutions of a problem on the whole space ${\mathbb{R}}^N$, for which Theorem \ref{reg-thm-r} holds. Let $f\in L^2(\Omega\times (0,T))$ and $u\in L^2((0,T);W_0^{s,2}(\overline{\Om}))\cap C([0,T];L^2(\Omega))$ with $u_t\in L^2((0,T);W^{-s,2}(\overline{\Om}))$ be the unique finite energy solution to the system \eqref{DP}. Let $\omega$ and $\eta\in\mathcal D(\omega)$ be respectively the set and the cut-off function constructed in \eqref{eta}. We consider the function $v:=u\eta$ and we write the equation satisfied by $v$. Recall from \eqref{for-del-prod} that the fractional Laplacian of $v$ is given by \begin{align} \fl{s}{v}=\fl{s}{(u\eta)}=u\fl{s}{\eta}+\eta\fl{s}{u}-I_s(u,\eta), \end{align} where the remainder term $I_s$ has been defined in \eqref{Is-formula}. Then, $v$ is a solution to the following problem on ${\mathbb{R}}^N$: \begin{align \begin{cases} v_t+\fl{s}{v}=F\ & \mbox{ in }{\mathbb{R}}^N\times (0,T), \\ v(\cdot,0)\equiv 0 & \mbox{ on } {\mathbb{R}}^N, \end{cases} \end{align} with $F=\eta f + u(-\Delta)^s\eta - I_s(u,\eta)$. Following the proof of \cite[Theorem 1.2]{fl_reg}, we can show that $F\in L^2({\mathbb{R}}^N\times (0,T))$. Hence, from Theorem \ref{reg-thm-r} we obtain that \begin{align} v\in L^2((0,T);W^{2s,2}({\mathbb{R}}^N))\cap L^{\infty}((0,T);W^{s,2}({\mathbb{R}}^N)),\;\;\ v_t\in L^2({\mathbb{R}}^N\times (0,T)). \end{align} This implies that $u\in L^2((0,T);W^{2s,2}_{\textrm{loc}}(\Omega))\cap L^{\infty}((0,T);W_0^{s,2}(\overline{\Om}))$ and $u_t\in L^2(\Omega\times (0,T))$. The proof is finished. \end{proof} \section{Proof of Theorem \ref{reg-thm-p}}\label{Lp-reg} In this section, we prove the local regularity for the solutions to the parabolic problem \eqref{DP}, corresponding to a right hand side $f\in L^p(\Omega\times (0,T))$, with $1<p<\infty$. First of all, notice that the following developments also apply to the case $p=2$. This special case has already been treated in the previous section, and there the proof of our local regularity Theorem \ref{reg-thm-2} has been developed taking advantage of the Hilbert structure of the spaces $L^2(\Omega)$ and $L^2(\Omega\times (0,T))$. Clearly that strategy cannot be extended to the general $L^p$ setting, and we have to adopt a different approach. This approach relies on an abstract result due to Lamberton \cite{lamberton}. In particular, the proof of Theorem \ref{reg-thm-p} will be a direct consequence of \cite[Theorem 1]{lamberton}. For the sake of completeness, we recall its statement here. \begin{theorem}\label{thm-lamberton} Let $(\Omega,\Sigma,m)$ be a measure space and let $A$ be the generator of a strongly continuous semigroup of linear operators $(\mathbb{T}_t)_{t\geq 0}$ on $L^2(\Omega,\Sigma,m)$ satisfying the following hypothesis: \begin{enumerate} \item The semigroup $(\mathbb{T}_t)_{t\geq 0}$ is analytic and bounded on $L^2(\Omega,\Sigma,m)$. \item For every $p\in [1,\infty]$ and $\phi\in L^p(\Omega)\cap L^2(\Omega)$ we have the estimate \begin{align} \norm{\mathbb{T}_t\phi}{L^p(\Omega)}\leq \norm{\phi}{L^p(\Omega)}, \mbox{ for all }\; t\geq 0. \end{align} \end{enumerate} Let $p\in(1,\infty)$. If $f\in L^p(\Omega\times (0,T))$, then the system \begin{align \begin{cases} u_t-Au=f,& t\in (0,T) \\ u(0)=0 \end{cases} \end{align} admits a solution $u\in C([0,T];L^p(\Omega))$, such that $u_t$, $Au\in L^p(\Omega\times (0,T))$. \end{theorem} \begin{proof}[\bf Proof of Theorem \ref{reg-thm-p}] First of all notice that the operator $A=-\fl{s}$ with domain \begin{align}\label{dom-op} \mathcal{D}(A) = \Big\{u\in W_0^{s,2}(\overline{\Om}),\,\;\;\fl{s}{u}\in L^2(\Omega)\Big\} \end{align} is the generator of a submarkovian strongly continuous semigroup $(\mathbb{T}_t)_{t\geq 0}$ which is also ultracontractive (see, e.g., \cite[Lemma 2.4]{fl_reg}). Let $f\in L^p(\Omega\times (0,T))$ and let $u$ be the corresponding weak solution to the system \eqref{DP}. Then, it follows from Theorem \ref{thm-lamberton} that $u_t,\fl{s}{u}\in L^p(\Omega\times (0,T))$. In particular we have that $\fl{s}{u}(\cdot,t)=(f-u_t)(\cdot,t)\in L^p(\Omega)$ a. e. $t\in (0,T)$ and, according to Theorem \ref{reg-p-ell}, this implies that $u(\cdot,t)\in \mathscr{L}^p_{2s, {\textrm{loc}}}(\Omega)$ a. e. $t\in(0,T)$. Therefore, for all $t\in(0,T)$ we have the following results. \begin{enumerate} \item[(i)] If $1<p<2$ and $s\ne 1/2$, then $u(\cdot,t)\in B^{2s}_{p,2, \textrm{loc}}(\Omega)$, a. e. $t\in (0,T)$. \item[(ii)] If $1<p<2$ and $s= 1/2$, then $u(\cdot,t)\in W^{2s,p}_{\textrm{loc}}(\Omega)=W^{1,p}_{\textrm{loc}}(\Omega)$, a. e. $t\in (0,T)$. \item[(iii)] If $2\leq p<\infty$, then $u(\cdot,t)\in W^{2s,p}_{\textrm{loc}}(\Omega)$, a. e. $t\in (0,T)$. \end{enumerate} Furthermore: \begin{enumerate} \item If $1<p<2$ and $s\ne 1/2$, then $u\in L^p((0,T);B^{2s}_{p,2, \textrm{loc}}(\Omega))$. \item If $1<p<2$ and $s= 1/2$, then $u\in L^p((0,T);W^{2s,p}_{\textrm{loc}}(\Omega))=L^p((0,T);W^{1,p}_{\textrm{loc}}(\Omega))$. \item If $2\leq p<\infty$, then $u\in L^p((0,T);W^{2s,p}_{\textrm{loc}}(\Omega))$. \end{enumerate} The proof of the theorem is finished. \end{proof} \noindent We conclude this section with the following remark. \begin{remark} {\em Recall that we have said in the proof of Theorem \ref{reg-thm-p} that the operator $A=-\fl{s}$ with domain given by \eqref{dom-op} generates a strongly continuous submarkovian semigroup $(\mathbb{T}_t)_{t\geq 0}$ on $L^2(\Omega)$ and the semigroup is analytic and ultracontractive. This implies that the semigroup can be extended to contraction semigroups on $L^p(\Omega)$ for all $p\in [1,\infty]$ and each semigroup is strongly continuous if $p\in [1,\infty)$ and bounded analytic if $p\in (1,\infty)$. Let $A_p$ denote the generator of the semigroup on $L^p(\Omega)$ for $p\in [1,\infty]$ so that $A_2$ coincides with $A$. By Theorem \ref{thm-lamberton} if $1<p<\infty$ and $f\in L^p(\Omega\times (0,T))$, then the unique solution $u\in C([0,T];L^p(\Omega))$ of the system \eqref{DP} has the following regularity: \begin{align} u\in L^p((0,T); D(A_p)). \end{align*} This trivially implies that $A_pu\in L^p(\Omega\times (0,T))$ and $u_t\in L^p(\Omega\times (0,T))$. Our contribution in the present paper was to show that $D(A_p)\subset \mathscr{L}^{p}_{2s, {\rm loc}}(\Omega)$ for every $1<p<\infty$. } \end{remark} \section{Open problems and perspectives}\label{open_pb} In the present paper we proved that weak solutions to the parabolic problem for the fractional Laplacian, with a non-homogeneous right-hand side $f\in L^p(\Omega\times (0,T))$ ($1<p<\infty$) and zero initial datum, belong to $L^p((0,T);\mathscr{L}^p_{2s, {\textrm{loc}}}(\Omega))$. The following comments are worth considering. \begin{enumerate} \item A natural interesting extension of our result would be the analysis of the global maximal regularity in space for weak solutions to \eqref{DP}. The problem is delicate however. Indeed, already at the elliptic level, we know that even if $\Omega$ has a smooth boundary, then the global maximal regularity up to the boundary does not hold. To be more precise, assume that $\Omega$ has a smooth boundary, $f\in L^p(\Omega)$ ($1<p<\infty$) and let $u$ be the associated weak solution to the Dirichlet problem \eqref{DP-ell}. It is known that, if $p\ge 2$, then $u$ does not always belongs to $W^{2s,p}(\Omega)$ and, if $1<p<2$, then $u$ does not always belong to $B_{p,2}^{2s}(\Omega)$. This shows that in general, the corresponding weak solution $u$ to the parabolic system \eqref{DP} does not always belong to $L^p((0,T);W^{2s,p}(\Omega))$ if $p\ge 2$ and does not always belong to $L^p((0,T);B_{p,2}^{2s}(\Omega))$ if $1<p< 2$. On the one hand, Theorem \ref{thm-lamberton} shows that $u\in L^p((0,T);D(A_p))$, that is, in particular $u(\cdot,t)\in D(A_p)$ for a.e. $t\in (0,T)$. On the other hand, according to the discussions given in \cite[Section 5]{fl_reg}, at least if $\Omega$ has a sufficiently smooth boundary, one has that $u(\cdot,t)=\rho^sv(\cdot,t)$ where $v(\cdot,t)$ is a regular function up to the boundary. Here, $\rho(x):=\textrm{dist}(x,\partial\Omega)$ for $x\in\Omega$. In addition one could expect that $\rho^{-s}u, \rho^{1-s}u\in L^p((0,T);L^p((0,T);W^{2s,p}(\Omega))$ if $2\le p<\infty$, and $\rho^{-s}u, \rho^{1-s}u\in L^p((0,T);L^p((0,T);B_{p,2}^{2s}(\Omega))$ if $1< p<2$. This constitutes an interesting open problem. We refer to \cite[Section 5]{fl_reg} for a more complete discussion on related topics and the difficulties that it raises. \item It would be interesting to consider the case of a non-zero initial datum in equation \eqref{DP}. In the Hilbert space framework, i.e. when working in the $L^2(\Omega)$ setting, the strategy of Section \ref{L2-reg} can be extended to deal with initial data in $W_0^{s,2}(\overline{\Om})$. To the best of our knowledge, the corresponding analogous result in the case $p\in (1,\infty)$, $p\ne 2$, is still unknown. \end{enumerate}	{ "redpajama_set_name": "RedPajamaArXiv" }	39
\section{Introduction} Heterotic compactifications with flux have attracted recently lot of interest, as a promising way of getting phenomenologically viable string vacua. Supersymmetric solutions have to solve the so-called 'Strominger system', known for a long time~\cite{Strominger:1986uh} (see also~\cite{Hull:1986kz,Becker:2002sx,Curio:2001ae,Louis:2001uy,LopesCardoso:2003af,Becker:2003yv, Becker:2003sh,Becker:2005nb,Benmachiche:2008ma} later developments). However, having a non-trivial $\mathcal{H}$-flux results in the metric loosing K\"ahlerity and being conformally balanced instead of Calabi-Yau~\cite{Mich,Ivanov:2000ai,LopesCardoso:2002hd}. An additional complication comes from anomaly cancellation, which requires satisfying the generalized Bianchi identity, that uses the spin connection with torsion: \begin{equation}\label{bianchi} \mathrm{d} \mathcal{H} = \alpha' (\text{tr}\, \mathcal{R} (\Omega_{-}) \wedge\, \mathcal{R}(\Omega_{-})-\text{Tr}\, \mathcal{F}\wedge \mathcal{F})\, . \end{equation} A proof of the existence of a family of smooth solutions to the Bianchi identity has only appeared recently, for the $T^2 \hookrightarrow \mathcal{M} \to K3$ supersymmetric vacua found in~\cite{Dasgupta:1999ss} using dualities. A proof was given in~\cite{Fu:2006vj} using the Hermitian connection, but can be made simpler using another choice of connection as explained in~\cite{Becker:2009df}. The fibration induces a warping of the base and the appearance of torsion. Those backgrounds can be equipped with a gauge bundle that is the tensor product of an Hermitian-Yang-Mills bundle over the $K3$ base with an holomorphic line bundle on $\mathcal{M}$. With a non-compact Eguchi-Hanson base, this construction was made fully explicit~\cite{Fu:2008ga}. The warp factor was computed order by order in a $\alpha'/(g_s a)^2$ expansion, where $a$ stands for the resolution parameter. As is shown in~\cite{Carlevaro:2008qf,Carlevaro:2009jx,Carlevaro:xxx}, another regime of interest is when the blow-up parameter $a$ is significantly smaller (in string units) than the total fivebrane charge. Then, one can define a sort of 'near-bolt' geometry, that describes the latter in the neighborhood of the resolved singularity. This region can be decoupled from the asymptotic Ricci-flat region by defining a {\it double scaling limit} which sends the asymptotic string coupling $g_s$ to zero, while keeping the ratio $g_s/ a$ fixed in string units. In this limit the solutions are still weakly coupled and weakly curved, hence amenable to a supergravity description. We have also found in~\cite{Carlevaro:2009jx} a new family of supersymmetric smooth torsional solutions, where the singularity of an orbifoldized conifold is smoothed out by a four-cycle, again supported by an Abelian gauge flux. The supersymmetry equations can be solved numerically in the asymptotically Ricci-flat case. Furthermore, in a double-scaling limit analogous to the previous example, one obtains an analytic solution, solving the Bianchi identity at leading order. Heterotic torsional geometries, having only NSNS three-form and gauge fluxes, are expected to allow for a solvable worldsheet description. By taking the double-scaling limit, as defined above, of torsional Eguchi-Hanson or resolved conifold geometries, we have shown in~\cite{Carlevaro:2008qf,Carlevaro:2009jx} that the corresponding worldsheet non-linear sigma models admit solvable worldsheet \textsc{cft} descriptions, belonging to a particular class of gauged \textsc{wzw} models. The existence of a worldsheet \textsc{cft} first implies that these backgrounds are exact heterotic string vacua to all orders in $\alpha'$, once included the worldsheet quantum corrections to the defining gauged \textsc{wzw} models; in particular, the corrected background will be a solution of the modified Bianchi identity. This proof of existence is particularly welcomed since the supergravity backgrounds as they are are not generically an exact solution of the Bianchi identity, rather give an approximate solution of the latter in the limit where the fivebrane charge is large. Having a full control over the \textsc{cft} provides also information about worldsheet instanton corrections. These worldsheet non-perturbative effects are captured by Liouville-like interactions correcting the sigma-model action. We analyze under which conditions these worldsheet operators are compatible with the whole construction (in particular with the orbifold and~\textsc{gso} projections). This allows to understand several constraints satisfied by consistent heterotic vacua from a worldsheet perspective, such as the tadpole condition, the evenness of the first Chern class, charge quantization and the corresponding moduli stabilisation. \section{The supergravity solutions} \label{secsugra} Let us consider first the heterotic supergravity vacua corresponding to the local torsional supersymmetric compactifications. While the Eguchi-Hanson solutions were known, the conifold ones are new. \subsection{Fibrations over Eguchi-Hanson} The $T^2 \hookrightarrow \mathcal{M} \to CY_2$ supersymmetric vacua have a metric of the form \begin{equation}\label{metric2} \mathrm{d} s^2_6 = \eta_{\mu\nu}\,\mathrm{d} x^\mu \mathrm{d} x^\nu + \frac{\alpha' U_2}{T_2}\left\|\mathrm{d} x^1 + T \mathrm{d} x^2+ (w^1 + w^2 T) \mathcal{A} \right\|^2 + e^{2(\Phi-\Phi_\infty)} \,\mathrm{d} s^2_\textsc{eh}\,. \end{equation} where $U$ and $T$ are the K\"ahler and complex structure moduli of the torus and $w^{1,2}$ are the Kaluza-Klein charges of the fibration. The warped non-compact base is chosen to be Eguchi-Hanson space~\cite{Eguchi:1978xp}: \begin{equation}\label{EHmetric} \mathrm{d} s^2_\textsc{eh} = \frac{ \mathrm{d} r^2}{1-\tfrac{a^4}{r^4}} + \frac{r^2}{4} \left( (\sigma^\textsc{l}_1)^2 + (\sigma^\textsc{l}_2)^2 + \Big(1-\frac{a^4}{r^4}\Big) (\sigma^\textsc{l}_3 )^2 \right)\,, \end{equation} here written in terms of the left-invariant $SU(2)$ one-forms. The existence of a unique anti-selfdual $(1,1)$-form on EH dictates the choice of the connexion one-form on the base \begin{equation} \mathcal{A} = \frac{a^2}{2r^2} \sigma^\textsc{l}_3 \, , \end{equation} preserving $\mathcal{N}_{\textsc{st}}=2$ supersymmetry. One can add a supersymmetric Abelian gauge bundle of the form $\mathcal{F} = \vec{\ell} \cdot \vec{\mathfrak{T}}\, \mathrm{d} \mathcal{A}$, where $\mathfrak{T}^{i}$ are the Cartan generators of $\mathfrak{so}(32)$ and the vector $\vec{\ell}$ encodes the magnetic charges. The heterotic Bianchi identity cannot be solved easily. One can consider an approximate solution of~(\ref{bianchi}) by taking a {\it large charge limit}~\cite{Carlevaro:2008qf}. This is possible $e.g$ for $\vec{\ell}^2\gg 1 $. We have then \begin{equation}\label{bianchilow} \mathrm{d} \mathcal{H} -\alpha ' \,\text{Tr} \mathcal{F} \wedge \mathcal{F} + \mathcal{O}\big(1) = 0\, , \end{equation} and the charges should satisfy the tadpole condition \begin{equation}\label{tad} \mathcal{Q}_5 - \frac{U_2}{2T_2} \|w^1 + w^2 T\|^2 - \vec{\ell}^{\,2}= 0 \,. \end{equation} \subsection{Resolved conifold} As a second example we consider a warped conifold geometry~\cite{Candelas:1989js}. The singularity is resolved by a K\"ahler deformation corresponding to blowing up a $\mathbb{C} P^1\times \mathbb{C} P^1$ four-cycle. This is topologically possible only for a $\mathbb{Z}_2$ orbifold of the conifold. The geometry is conformal to a six-dimensional smoothed cone over a non-Einstein $T^{1,1}$ space~: \begin{subequations} \label{sol-ansatz} \begin{align} \mathrm{d} s^2 & = \eta_{\mu\nu}\mathrm{d} x^{\mu}\mathrm{d} x^{\nu} +\tfrac{3}{2}\,e^{\Phi-\Phi_\infty} \,\biggl[ \frac{\mathrm{d} r^2}{f^2(r)} + \frac{r^2}{6}\big(\mathrm{d}\theta_1^2+\sin^2\theta_1\,\mathrm{d}\phi_1^2 + \mathrm{d}\theta_2^2+\sin^2\theta_2\,\mathrm{d}\phi_2^2\big) \notag\\ & \hspace{2cm} +\,\frac{r^2}{9} f(r)^2 \big(\mathrm{d} \psi + \cos \theta_1 \,\mathrm{d} \phi_1 + \cos \theta_2 \,\mathrm{d} \phi_2 \big)^2 \biggr]\,,\\ \mathcal{H} & = \frac{\alpha'k}{6}\,g_1(r)^2\,\big( \Omega_1+\Omega_2\big)\wedge \tilde{\omega}\,, \end{align} \end{subequations} with the volume forms of the two $S^2$s and the connection one-form $\tilde{\omega}$ defined by \begin{subequations} \begin{align} \Omega_i&=\sin \theta_i \,\mathrm{d} \theta_i\wedge \mathrm{d} \phi_i\,,\quad \text{for }i=1,2\,,\qquad \tilde{\omega} = \mathrm{d} \psi + \cos \theta_1 \,\mathrm{d} \phi_1 + \cos \theta_2 \,\mathrm{d} \phi_2\,. \end{align} \end{subequations} One can consider again an Abelian gauge bundle, supported both on the four-cycle $\mathbb{C} P^1\times \mathbb{C} P^1$ at the bolt and on a non-compact cycle: \begin{equation}\label{gauge-ansatz} \mathcal{A}=\tfrac{1}{4}\Big(\left(\cos\theta_1\,\mathrm{d}\phi_1 - \cos \theta_2\,\mathrm{d} \phi_2 \right)\vec{p} + g_2(r)\,\tilde\omega\,\vec{q}\Big) \cdot \vec{\mathfrak{T}}\,. \end{equation} characterized this time by two charge vectors $\vec{p}$ and $\vec{q}$, that should be orthogonal. To determine the radial profile of the three-form $\mathcal{H}$, $i.e.$ the function $g_2(r)$ in the ansatz~(\ref{sol-ansatz}), we solve the Bianchi identity in the large charges limit $\vec{p}^{\, 2} \gg 1$. We obtain: \begin{equation}\label{g3} g_1^2(r)=\tfrac34\big[1-g_2^2(r)\big]= \tfrac34\Big[1-\left(\frac{a}{r}\right)^8\Big] \end{equation} with the relation $\vec{p}^{\, 2} = \,\vec{q}^{\, 2} = k$. Having analytical expressions for the functions $g_1$ and $g_2$, we can consider solving the first order supersymmetry equations for the remaining functions $f$ and $\Phi$. If we ask the conformal factor $e^{\Phi}$ to be asymptotically constant, they can only be solved numerically. \subsection{Double-scaling limit} An important quantity is the value of the conformal factor evaluated at the bolt $r=a$; when it is large, the resolved cycle sits deep in the region of strong warping. One can then consider the flux background corresponding to the 'near-bolt' geometry. Let us start with the Eguchi-Hanson case. In order to isolate the region near the two-cycle of the resolved $A_1$ singularity, where the interesting physics takes place, one can define a certain {\it double-scaling limit} of the the type \textsc{ii} and heterotic solutions as follows: \begin{equation}\label{DSL} g_s \to 0 \quad , \qquad \lambda= \frac{g_s \sqrt{\alpha'}}{a} \quad \text{fixed}\,, \end{equation} with $g_s = e^{\Phi_\infty}$. The effective string coupling constant, set by the double-scaling parameter $\lambda$, stays finite and can chosen within the perturbative regime. In terms of a new radial coordinate defined by $\cosh \rho = (r/a)^2$, which is held fix in this limit, on obtains the metric, independently of $a$, as \begin{equation}\label{metric3} \mathrm{d} s^2 = \mathrm{d} x^\mu \mathrm{d} x_\mu + \frac{\alpha' U_2}{T_2} \left\| \mathrm{d} y^1 + T \mathrm{d} y^2 + \frac{\mathfrak{q}\,\sigma_3^{\textsc{l}}}{2\cosh\rho} \right\|^2 + \frac{\alpha' Q_5}{2}\Big[ {\rm d}\rho^2 + (\sigma^\textsc{l}_1)^2 + (\sigma^\textsc{l}_2)^2 + \tanh^2 \rho \, (\sigma^\textsc{l}_3 )^2\Big]\,. \end{equation} In the conifold case, the double-scaling limit is slightly different, as now $\mu=\frac{g_s \alpha'}{a^2}$ is held fixed. It again isolates the dynamics near the four-cycle of the resolved singularity, keeping the transverse space to be conformal to the non-singular resolved orbifoldized conifold. The supersymmetry equations can in this case be solved analytically: \begin{equation}\label{Hfg} e^{\Phi} =\mu k \left(\frac{a}{r}\right)^2\,,\qquad f^2(r)=g_1^2(r)=\tfrac{3}{4}\Big[1-\left(\frac{a}{r}\right)^8\Big]\, . \end{equation} \section{The worldsheet description} A remarkable feature of the $T^2 \hookrightarrow \mathcal{M} \to EH$ and resolved orbifoldized conifold solutions is that they admit a solvable worldsheet CFT description in the double-scaling limit. We start by discussing the former. \subsection{Blow-down limit} It is easier to start with the blow-down limit of the background, such that the Abelian instanton becomes point-like. In this limit the solution boils down to the near-horizon five-brane solution (the so-called \textsc{chs} background~\cite{Callan:1991dj}), transverse to a $\mathbb{C}^2/\mathbb{Z}_2$ orbifold and compactified on a two-torus: \begin{equation} \mathrm{d} s^2 = \mathrm{d} x_\mu \mathrm{d} x^\mu +\tfrac{U_2}{T_2}\left\|\mathrm{d} x_1 + T \mathrm{d} x_2 \right\|^2 + \alpha' k \left[ \mathrm{d} \rho^2 + \mathrm{d} s^2 (S^3/\mathbb{Z}_2) \right]\, , \end{equation} that features a linear dilaton and a non-zero NSNS three-form flux. We consider the case of $Spin(32)/\mathbb{Z}_2$ heterotic strings. The worldsheet CFT is \begin{equation} \mathbb{R}^{2} \times T^2 \times \mathbb{R}_Q \times SU(2)_{k}/\mathbb{Z}_2 \times \left. SO(32)_1 \right\|_\textsc{r} \label{blowdowncft} \end{equation} The background charge of the linear dilaton, $Q=\sqrt{2/k}$, is related to the level $k$ of the supersymmetric $SU(2)$ WZW model. $k$ has to be even in order to allow for a $\mathbb{Z}_2$ orbifold of this WZW model. \subsection{Blown-up theory and Liouville potentials} In order to get the resolved background it is easier to use a dual formulation (generalizing~\cite{fzz}) of the deformation. We add to the conformal field theory~(\ref{blowdowncft}) the following generalized Liouville interaction~\cite{Carlevaro:xxx} \begin{equation} \label{Liouvillepotgenericgeneric} \delta S = \mu \int \mathrm{d}^2 z \, \left\{ G_{-1/2}, \, e^{-\sqrt{k}\left(\varrho (z,\bar z) + i Y_L (z) \right)}\right\} e^{i \tilde{p}_a \tilde{X}^a (\bar z) + i \vec{\ell} \cdot \vec{Z}_R (\bar z)} + c.c. \end{equation} As discussed below, the target-space of the corresponding non-linear sigma model correspond indeeds to~~(\ref{metric3}). One can consider either an operator belonging to the right NS sector, with $\vec{\ell} \in \mathbb{Z}^{16}$, or to the right Ramond sector, with $\vec{\ell} \in (\mathbb{Z}+\tfrac{1}{2})^{16}$. The former case corresponds to bundles with vector structure, and the latter to bundles without vector structure. In order to get this marginal deformation from the physical spectrum of the blow-down theory, the lattice of the two-torus should contain an element with \begin{subequations} \label{chiralpot} \begin{align} p_{a} &= 0 \quad , \qquad a = 1,2 \label{condrat1}\\ G_{ab}\tilde{p}^a \, \tilde{p}^b +2\vec{\ell}^2 &=k+2 \label{condrat2} \end{align} \end{subequations} The first condition~(\ref{condrat1}) implies that the underlying $T^2$ conformal field theory is rational (as it is characterized then by a having chiral algebra). For this the torus moduli $T$ and $U$ need to be valued in the same {\it maginary quadratic number field}~\cite{Gukov:2002nw}. The second condition~(\ref{condrat2}) is the worldsheet version of the integrated space-time Bianchi identity, and is exact to all orders in $\alpha'$. In order to satisfy the right GSO projection, the right fermion number of the operator in~(\ref{Liouvillepotgenericgeneric}) should be even ($i.e.$ that $\sum_i \ell_i \equiv 0 \mod 2$). This constraint corresponds exactly to the condition that the first Chern class of the gauge bundle belongs to the even integral second cohomology group, found in~\cite{Witten:1985mj,Freed:1986zx}. Furthermore, the operator~(\ref{Liouvillepotgenericgeneric}) belongs necessarily to the twisted sector of the $SU(2)/\mathbb{Z}_2$ orbifold. Hence, as in supergravity, one should have the identification $\psi \sim \psi +2 \pi$. \subsection{The conifold case} Let us consider briefly the conifold case. In the blow-down limit, one gets a linear dilaton, together with a non-Einstein $T^{1,1}$ space. The latter is described by an asymmetric gauged WZW model $U(1)\backslash (SU(2)_k\times SU(2)_k)$. This gauging, acting only by left multiplication, is anomalous. The anomaly is cancelled by coupling minimally the 32 right worldsheet fermions of $SO(32)_1$. This corresponds in spacetime to the gauge bundle specified by the vector of magnetic charges $\vec{p}$ in eq.~(\ref{gauge-ansatz}). One considers a $\mathbb{Z}_2$ supersymmetric orbifold of the conifold, corresponding to the half-period shift $\psi \sim \psi +2 \pi$, as for Eguchi-Hanson. The CFT for the resolved conifold solution~(\ref{sol-ansatz}), with a generic Abelian gauge bundle over the resolved conifold, is obtained from the blow-down theory $\mathbb{R}_Q \times T^{1,1} \times SO(32)_1 \|_\textsc{r}$ by the marginal deformation \begin{equation} \label{Liouvintgen} \delta S = \mu_\textsc{l} \int \mathrm{d}^2 z (\psi^\rho +i\psi^\textsc{x})e^{-\frac{\sqrt{\vec{q}^{\,2}-4}}{2} (\rho + i X_\textsc{l})} \, e^{\frac{i}{2}\vec{q} \cdot \vec{Y}_\textsc{r}} + c.c. \,. \end{equation} Again we require this operator to be part of the physical spectrum of the blow-down theory, taking into account the \textsc{gso} and orbifold projections. We consider bundles with $\vec{p}^{\, 2}\equiv 2 \mod 4$, for which no action in the $Spin(32)/\mathbb{Z}_2$ lattice is requested by orbifold invariance. We find that the operator in~(\ref{Liouvintgen}) is GSO-invariant provided that \begin{equation} \frac{1}{2}\sum_{i=1}^{16} (q_i \pm p_i) \equiv 0 \mod 2 \,. \label{fwcondcft} \end{equation} This condition is again the same as $c_1 (\mathcal{F}) \in H^2(\mathcal{M}_6,2\mathbb{Z})$. This remarkable relation between topological properties of the gauge bundle and the \textsc{gso} parity of worldsheet instanton corrections may originate from modular invariance, that relates the existence of spinorial representations of the gauge group to the projection with the right-moving worldsheet fermion number. \subsection{The gauged WZW model approach} The algebraic construction of the worldsheet \textsc{cft} outlined above gives, in both cases, non-linear sigma-models whose background fields are identical, at leading order in $\alpha'$, to the solutions given in section~\ref{secsugra}. It is shown by using a complementary description of these worldsheet theories in terms of gauged WZW models. For instance, theCFT with warped deformed orbifoldized conifold as target space is given by the asymmetric $\mathcal{N}_{\textsc{ws}}=(1,0)$ super-coset: \begin{equation} \frac{SL(2,\mathbb{R})_{k/2} \times\, \left(\text{\small \raisebox{-1mm}{$U(1)_\textsc{l}$}\! $\backslash$ \!\!\raisebox{1mm}{$SU(2)_k \times SU(2)_k$}}\right)\times SO(32)_1 \|_\textsc{r}}{U(1)_\textsc{l} \times U(1)_\textsc{r}} \,, \label{cosetdef} \end{equation} which combines a left gauging of $SU(2) \times SU(2)$ with a pair of chiral gaugings which also involve an $SL(2,\mathbb{R})$ \textsc{wzw} model. The whole coset is made anomaly-free by coupling the $SO(32)_1$ right-moving gauge sector. The total action for the gauged \textsc{wzw} model defined above is given schematically as follows: \begin{equation}\label{Stot} S_{\textsc{wzw}}(A,{\bf B}) = S_{SL(2,\mathbb{R})_{k/2+2}} + S_{SU(2)_{k-2},\, 1} + S_{SU(2)_{k-2},\, 2} + S_\text{gauge}(A,{\bf B}) + S_\text{Fer} (A,{\bf B})\, , \end{equation} where the first three factors correspond to bosonic \textsc{wzw} actions, the fourth one to the bosonic terms involving the gauge fields and the last one to the action of the minimally coupled fermions realizing the $\mathfrak{so}(32)_1$ algebra. Finding the background fields, at leading order in $\alpha'$, amount then to integrate out classically the worldsheet gauge fields $A$ and ${\bf B}$. For heterotic cosets this is in general more tricky because of the worldsheet anomalies generated by the various pieces of the model~\cite{Johnson:1994jw,Johnson:2004zq}. When the dust settles we eventually find a heterotic sigma-model corresponding, as promised, to the torsional heterotic solutions of interest. \section{Conclusions} We have analyzed local models of smooth torsional heterotic compactifications preserving 4d space-time supersymmetry. From the supergravity viewpoint we have found a class of conifold solutions, that are the first explicit examples of genuinely $SU(3)$ structure heterotic solutions. We have argued that one can define a double-scaling limit that focuses on the resolved singularities of these manifolds In this limit, we have shown that the associated worldsheet theory becomes a fully solvable conformal field theory. We have found an interesting interplay between worldsheet non-perturbative effects, corresponding to Liouville-like interactions, and constraints on heterotic vacua usually considered in supergravity: charge quantization and associated moduli stabilization, evenness of the first Chern class, or avoidance of conical singularity at a bolt. Among the possible followups of these work, it would be extremely interesting to compute the perturbative corrections to these solutions, using the methods of~\cite{Tseytlin:1992ri,Bars:1993zf}, which would give a corrected background {\it to all orders} in $\alpha'$. In particular, it would give exact solutions to the modified Bianchi identity. It is highly desirable to consider not only local models, but genuine compactifications with torsion. In~\cite{Adams:2006kb} linear sigma-models of $T^2 \hookrightarrow \mathcal{M} \to K3$ where constructed. Using the methods described here, one should be able to obtain explicit conformal field theories corresponding to their infrared fixed points. This would give solid grounds for extracting low-energy four-dimensional physics out of heterotic flux compactifications.	{ "redpajama_set_name": "RedPajamaArXiv" }	346
Finding a new home – Slovakia Foreigners moving to Slovakia must start planning their journey much earlier than packing their suitcases. (Source: Sme) Read also: Frequently asked questions If they want to avoid potential difficulties, they should prepare all necessary documents and arrange several things in advance and then report to the respective authorities as soon as they arrive in the country, the experts in relocation recommend. They stress that not only nationals from countries outside the European Union, but also EU residents should find information before moving here. "Foreigners from non-visa countries are often wrong when they think that if they do not need a visa and request a stay in Slovakia, they can be here without limitations," Ivona Demáčková from Pro Relocation company told The Slovak Spectator. After having obtained a job or a course of study in Slovakia, it is advisable to search for due accommodation. The quality of the rental market and the availability of temporary housing have been improving, but it still may not reach the level of housing offered by some other developed countries; the perception of what standard means can vary, as well. Many of the villas and houses in Slovakia are not furnished, while most apartments are rented with furnishings included. For those outside the EU who wish to bring their own furniture, it is advisable to stay in Slovakia for two years at least and have a residency permit, so that they can avoid having to pay duties. It usually takes four to five weeks to obtain it from the foreign police, Jeremie Cohen from AGS Bratislava International Movers told The Slovak Spectator. Prepare for paperwork Slovakia has had a rich history in red tape – since the Austro-Hungarian Empire, in fact – and moving here from a foreign country means a lot of paperwork. However, the conditions for a citizen of the EU, the European Economic Area (EEA) or the Swiss Confederation versus those for citizens of other countries differ quite markedly. Another decisive aspect is the intended length of stay in Slovakia, of which there are three categories: temporary residency (more than 90 days), or permanent residency (for a duration of five years, for an unlimited period of time, or the stay of third-country national with acknowledged status of a person with long-term stay in the EU, i.e. long-term residence). The third type of stay is the so-called tolerated residence which applies to third-country nationals under special conditions and is temporary by definition. For inhabitants of the EU/EEA member states and the Swiss Confederation, the rules are the simplest. For temporary stay, they have to announce their place of residence, and if they intend to be employed here, also to register this with the labour office (their employer can do this for them). If they intend to stay in Slovakia for longer than 90 days, they should report this with the Alien Police, confirming their address and the purpose of their stay. To stay in Slovakia for longer than 90 days, there should be a specific purpose stated, such as employment, study, research, family reunion, or to stay as a person with granted status of a Slovak living abroad. The documents necessary to register residence with the Alien Police (within 10 days after arrival in Slovakia) for an EU citizen include a passport or other ID document; a written statement or work contract from the employer if they intend to be employed; a document confirming self-employment, if applicable; documents or other evidence proving the applicants have enough resources for themselves and their family; and a document proving health insurance. If necessary, the applicants must submit further documents proving they are going to study in Slovakia and have enough resources to do so, or documents proving family ties of accompanying family members, all of which must be officially translated and notarised. If the EU/EEA citizen comes to Slovakia for the purpose of employment, the employer is obliged to notify the local office of labour, social affairs and family within seven days of the start of the employment by sending a so-called information card, according to the slovak-republic.org website. Students wishing to stay in Slovakia must prove they have enough finances to pay for their health insurance, which is obligatory in Slovakia, and support their stay. Conditions for stays differ For permanent residence, foreigners have to fulfil certain conditions: to be a spouse or a child of a citizen of Slovakia with permanent residence in Slovakia; a child of a foreigner who is married to a Slovak citizen with permanent residence; to be married for at least three years to a foreigner with residence for at least three years, or to be his/her child; or to be here for an uninterrupted period of at least 10 years doing business or being employed, or to be married to such a person or be their child. The last instance is when it is in the interest of Slovak foreign policy. The first permission for permanent stay is granted for five years, and the Alien Police must decide within 90 days after the application submission, and within 180 days in complicated cases. The next permission can be granted for an unlimited period of time. The application for the next permission must be submitted by the foreigner personally, on an official form at a police department, 60 days before the first permission elapses at the latest. The permission can be, however, cancelled by police under certain conditions, or expire, as stipulated by law. Citizens of countries outside the EU fall under a different category. When coming to Slovakia for a brief period of time, they should notify the Alien Police. If they are accommodated in a hotel or boarding house, this will be done for them; if they are accommodated privately, they should do it themselves. When staying for longer than 90 days, they should ask for a temporary stay, contacting the Slovak representation in their home country. A third country national must enter the territory of Slovakia within 180 days after having been granted temporary residence, the International Organisation for Migration (IOM) writes on its website. Within three working days from their arrival in Slovakia, the third country national must report the beginning of their residence at the Alien Police, and within three working days from obtaining the residence document he or she has to secure a health insurance policy. Within 30 days from obtaining the residence document, it is also necessary to submit at the competent Alien Police department a document on health insurance in Slovakia and a medical report not older than 30 days confirming that the third country national does not suffer from any disease endangering public health. In case of temporary residence for the purpose of business, the foreign national must also submit a Commercial Registry Extract within 60 days from collecting the residence document, according to IOM. It is important to note that the Alien Police have a 30-day deadline to handle the application for work permit and 90 days to handle the application for residence permit. If the application form was filed by an embassy, add two more weeks for the diplomatic post. Reporting to authorities necessary Even if already having started the due procedures from the country of origin, all foreigners must report to the Alien Police within three days after they arrive, Demáčková said. When striving to get a permit for permanent residence, the place of stay must be confirmed by a rental contract, an official invitation, or in any other written form. All people with permanent residence in Slovakia have to pay a health insurance policy, unless, for example, they are employed abroad and have health insurance there. Generally, health insurance is obligatory for everyone with permanent residence in Slovakia, including those who are self-employed, students, asylum holders, children without legal guardians, or those detained in Slovakia. However, sometimes the employer or the (Slovak) state can pay the insurance, so it is advisable to check with the IOM or with the health insurance companies (state-owned vszp.sk; union.sk – both also in English; and dovera.sk, in Slovak only). To apply for a residence permit for a stay longer than 90 days – i.e. temporary or permanent residence – foreigners have to go to the next department of Alien Police and bring: a filled-in form of reporting a residence, completed in Slovak, available in seven languages at minv.sk/?pobyt-cudzinca; a criminal background check; an ID/passport; and a work permit or a work statement. Most foreigners have also to report with the Alien Police if they leave Slovakia for abroad for longer than 180 days or leave their stated place of residence for more than 30 days within five days. Some information on arriving to Slovakia and on the conditions necessary for a longer stay can be also found at the Foreign Ministry's website (mzv.sk), also in English. Nationals of third countries generally need a visa to stay in Slovakia, but it is recommended to check at the due Slovak consulate in their home country. Visa applications can be filed three months prior to the planned trip at the earliest, and granting the visa may take between 15 and 60 days. Citizens of countries in the Schengen area do not need a Slovak visa. The rules surrounding visas to enter the Schengen area can be found at ec.europa.eu/immigration. Foreigners can get help Foreigners who are busy or who need to concentrate rather on business issues than on the arrangements concerning their stay in Slovakia can turn to relocation companies specialising in procuring all documents, accommodation and other pre-requisites, as well as facilitating the first steps and getting accustomed in a new country. Among the most frequent questions foreigners ask are the living costs, the location of schools or places to meet other foreigners, information about medical assistance, or the attitude to foreigners, relocation companies say. They can also help with moving in family members, including pets, finding out about Do's and Don'ts, insurances, available health care, schools, driving licences, expats' clubs, religious services in foreign languages, and more. Those already coming to Slovakia still complain about the heavy administration process which requires many documents to be certified by a notary, Cohen and Demáčková agree. Another problem is the Border and Alien Police, especially in Bratislava, Demáčková said. Though it may sound contradictory, the situation at the Border and Alien Police in Bratislava has improved in past 10 years, though minimally, she added, stressing it would be good if the Interior Ministry allocated some money for this facility. (Sources: euroinfo.gov.sk, 4expat.com, slovak-republic.org, mic.iom.sk, minv.sk, mzv.sk, ) Useful contact details Banks in Slovakia with web pages in English Citibank: www.citibank.com/slovakia ING Bank: www.ingcommercialbanking.sk Komerční banka (Member of Société Générale): www.koba.sk OTP Bank: www.otpbanka.sk Privatbanka: www.privatbanka.sk SBERBANK: www.sberbank.sk Slovenská sporiteľňa (Member of Erste Group Bank): www.slsp.sk Tatra banka (Member of Raiffeisen Bank International): www.tatrabanka.sk UniCredit Bank: www.unicreditbank.sk Všeobecná úverová banka (Member of Intesa Sanpaolo): www.vub.sk Private international schools & kindergartens Bilingual English Slovak School (Trnava): www.besst.sk The British International School (Bratislava): www.bis.sk Cambridge International School (Bratislava): www.cambridgeschool.eu English International School (Bratislava): www.eisb.sk GALILEO SCHOOL (Bratislava): www.galileoschool.sk QSI International School (Bratislava): www.bratislava.qsischool.org QSI International School (Košice): www.qsi.org/slovakia/ksc International kindergartens (only) BlueBerry Hill (Košice): www.bbhill.sk Brilliant Stars Intl. Kindergarten (Bratislava, Stupava): www.brilliantstars.sk The Children´s House - International Montessori Kindergarten (Bratislava): www.montessori-bratislava.sk English Kindergarten KIDS (Košice): www.anglickaskolkakids.sk English / German Kindergarten Wonderland (Bratislava): www.wonderland.sk Unity House International Montessori Kindergarten (Bratislava): www.unity-house.sk Universities in Slovakia Academy of Arts in Banská Bystrica (AU): www.aku.sk Academy of Performing Arts (VŠMU): www.vsmu.sk Alexander Dubček University of Trenčín: www.tnuni.sk Catholic University in Ružomberok: www.ku.sk College of Management / City University of Seattle: www.vsm.sk Comenius University in Bratislava (UK): www.uniba.sk Constantine the Philosopher University in Nitra (UKF): www.ukf.sk Matej Bel University in Banská Bystrica (UMB): www.umb.sk Pan-European University: www.paneurouni.com Pavol Jozef Šafárik University in Košice (UPJŠ): www.upjs.sk Police Academy in Bratislava (Akadémia PZ): www.akademiapz.sk Slovak University of Agriculture in Nitra (SPU): www.uniag.sk Slovak University of Technology in Bratislava (STU): www.stuba.sk Technical University in Zvolen (TU ZVO): www.tuzvo.sk Technical University of Košice (TUKE): www.tuke.sk University of Cyril & Methodius in Trnava (UCM): www.ucm.sk University of Economics in Bratislava (EU BA): www.euba.sk University of Prešov: www.unipo.sk University of Trnava (TU TT): www.truni.sk University of Veterinary Medicine and Pharmacy (UVLF): www.uvlf.sk University of Žilina (ŽU): www.uniza.sk 22. Dec 2014 at 12:35 \| Radka Minarechová , Zuzana Vilikovská Theme: Foreigners in Slovakia Blog: Five magic words Coronavirus crisis decreases number of foreigners working in Slovakia Equality only on paper. Migrants from third countries face many obstacles in Slovakia The residence status of UK citizens in Slovakia will change Pass a Slovak language dictation so you can work with foreigners	{ "redpajama_set_name": "RedPajamaCommonCrawl" }	9,142
Q: Icinga2 - ExternalCommands filling my DB Today I noticed all external commands received goes to the IDO, myicinga_externalcommands table on Postgres is over 350Gb (probably around 98% of DB). As you may have guess, my setup is a bit particular and receives A LOT of external commands, and I need to find some solution for this. This external commands are all performance data, it then goes to a RRD db and pnp4nagios, so I don't need icinga to keep anything but the very latest command for each host. So, I have 2 questions I would like help with: 1) Can I safely delete all those external commands from the DB? 2) Can I stop icinga logging this? If relevant, I'm now on Icinga 2.6.3-1 I hope somebody can help with this, thanks! A: You can safely delete them. You can also configure which categories should be written. The default value attempts to set anything required for Icinga Web 2. https://docs.icinga.com/icinga2/latest/doc/module/icinga2/toc#!/icinga2/latest/doc/module/icinga2/chapter/object-types#objecttype-idomysqlconnection The external commands table was never used, and isn't populated when calling API actions either. So we removed it from the default in the upcoming v2.7 release. https://github.com/Icinga/icinga2/commit/21ce07046c4438bc5e56f016d5a4c40b87e2f233 Tip for better and secure tranports: Switch to the Icinga 2 API as command transport in Icinga Web 2. The docs for v2.7 will highlight that too :) https://github.com/Icinga/icinga2/issues/5077	{ "redpajama_set_name": "RedPajamaStackExchange" }	3,080
Stages of a Long Journey is het eerste live-album van de Duitse contrabassist Eberhard Weber. In 2005 bestond het Theaterhaus in Stuttgart twintig jaar en in datzelfde jaar vierde Stuttgarter Eberhard Weber zijn 65ste verjaardag. Deze gebeurtenissen werden gecombineerd door Weber een tweetal concerten te laten geven in het kader van het Jazztage festival. Weber nodigde een aantal gastmusici uit en kreeg begeleiding van het Radio Symfonie Orkest Stuttgart SWR. De composities waarbij het orkest meespeelde kregen een bigbandachtige klank, voor het overige zijn de melancholieke zweverige basklanken, zo eigen aan Weber, alom vertegenwoordigd. Musici Gary Burton - vibrafoon Jan Garbarek - saxofoons (sopraan en tenor) Rainer Brüninghaus - piano en toetsen Marilyn Mazur - percussie Wolfgang Dauner - piano Reto Weber - Hang Nino G - beatbox Radio Symfonie Orkest Stuttgart SWR onder leiding van Roland Kluttig Composities Silent Feet (E. Weber) met Burton, Garbarek, Brüninghaus, Mazur en orkest Syndrome (Carla Bley) met Burton, Garbarel, Brüninghaus en Mazur Yesterdays (Jerome Kerr) met Dauner Seven Movements (Weber) met Garbarek; daarna de Birthday Suite The Colours of Chloë (E. Weber) Piano transition (Brüninghaus) Mauritius (E. Weber) Percussion transition (Mazur) Yellow Fields (E. Weber), door Burton, Garbarek, Brüninghaus, Mazur en orkest Hang Around (Reto Weber); met Nino G, Reto Weber The Last Stages Of A Long Journey (E. Weber) met de uitgebreide bezetting Air (E. Weber), solo voor de jubilaris Muziekalbum uit 2007 Jazzalbum Muziekalbum van Eberhard Weber Muziekalbum van Marilyn Mazur Muziekalbum uitgegeven door ECM Records	{ "redpajama_set_name": "RedPajamaWikipedia" }	388
Q: What happens if I delete dump.txt file in Android studio? After finishing my project, I found that there is a huge (55 MB) dump.txt file inside app\build\outputs\mapping\release in android studio project. I googled and found that this is from ProGuard. Now, my question is if I delete that file, will there be any problem? It's making my whole project size greater than 100 MB A: dump.txt is a file created by ProGuard. As stated on developer.android.com: describes the internal structure of all the class files in the .apk file You can safely delete the file, the important thing to remember is to save in a safe place mapping.txt as it is necessary to debug the obfuscated APK. See Decoding Obfuscated Stack Traces for more information.	{ "redpajama_set_name": "RedPajamaStackExchange" }	958
\section{Introduction} \input{sec_intro} \section{Harmonic Radar} \label{sec:2} \input{sec_HR} \subsection{Distributed HR System with Auxiliary (Helper) Nodes} \label{sec:DS} \input{sec_DS} \section{Benefits of Using Helper Nodes} \label{sec:TS} \input{sec_TS} \section{Phase Adaptation for Coherent Helper Node Signal Combining at the Tag} \label{sec:PA} \input{sec_PA} \section{ Phase Adjustment Accuracy} \input{sec_AN} \section{Numerical Example} \label{sec:Num} \input{sec_Num} \section{Conclusions} The weak return signal in harmonic radar severely limits its range. The conventional remedy is ever-higher power at the uplink transmitter, but the inverse sixth power dependence on range in HR makes this an expensive method. In contrast, our approach is based on new physical and signal configurations. Unconventionally, we use ``helper nodes'' to transmit tones that arrive as a single composite tone at the nonlinear tag while the ranging node transmits its own signal. Adding $M$ helper nodes increases the achievable range by a factor of $\sqrt[3]{2M}$, giving a $100\%$ increase for 4 helper nodes and a $152\%$ range increase for 8 helpers. For this benefit, the ranging node (RN) receiver must correlate against transmitted signal $x(t)$, instead of $x^2(t)$, but would not have to increase its transmit power. In contrast, a conventional HR system would have to increase the transmit power of its RN in order to increase its range. For a proper comparison, the conventional RN would be allotted the aggregate power of the helper-based system ($M$ helper nodes plus the RN). It would then experience a range extension factor of $\sqrt[3]{M+1}$. Numerically, this is a range increase of only $71\%$ for $M=4$, and $108\%$ for $M=8$, significantly lower than that of the helper-based system. This benefit however, requires the helper tones to arrive coherently, at the tag. Ensuring that condition is the focus of this paper. Our phase-adaptation algorithm causes each helper, one at a time, to adjust its phase at the tag, aligning it with the composite tone from previously-aligned helpers. Receiver noise causes adjustment error and consequent statistical variation in the composite helper sum at the tag. Our analysis, which provides the closed form of the helper sum distribution for $M=2$ and a recursion for $M>2$, demonstrates a long-tailed distribution in which the 50th percentile is close to the maximum value, but the 10th percentile can be much lower, depending on the SNR and $M$. % Assessment of the method based on a measurement set from a prototype HR ranging node \cite{sto2020low} showed that a single helper ($M=1$) provides $26\%$ more range, although a conventional system with doubled power can do the same. Adding a second helper causes the 50th percentile range to increase more quickly than can the range of a conventional system with equal total power. However, the noise-affected 10th percentile range can actually shrink, because there is some probability that the two helper phases might oppose each other. Additional helpers increase the 10th percentile range and, with 5 and more helpers, even the $10$th percentile range grows beyond the range of the conventional system. An alternative to increasing the range is to reduce the uplink and downlink antenna gains. For example, with $M = 4$ helper nodes and phase coherence (17), the SNR improvement at the Rx is $18$ dB. Then the transmit and received antenna gains can each be reduced by 6 dB. Since gains of the RN antennae in HR are typically at least 15 dBi, a reduction to 9 dBi can provide savings in size and cost. In the pursuit of range increase, it is an implementation issue whether our helper-based system or the conventional system is preferable. We note that conventional ranging nodes become bigger, heavier and costlier as their transmit power increases, and they may require additional linearization. In contrast, the helper-based system can add power incrementally by adding nodes as needed, without requiring upgrades to the RNs. Moreover, for systems with multiple RNs, a single set of helpers boosts the effective power of every RN. The success of the helper-node structure prompts questions that should be addressed in further research. One issue is that powerful tones, as emitted from the helpers, are generally unwelcome near other electronics. Are there alternative helper signals that have a lower power spectral density, do not interfere with the ranging application and still allow easy separation of intermodulation components for estimate of phase errors, or other property? Another question is additional application areas. Could our adaptive phase coherence at a point in space be used for, say, backscatter communications? \ifCLASSOPTIONcaptionsoff \newpage \fi \bibliographystyle{IEEEtran} \subsection{Phase Estimation} Consider \eqref{eq:phase_estim} and rewrite ${G}_{0, i}$, ${G}_{1, i}$ in terms of $\gamma_{0, i}, \gamma_{1, i}$ \begin{align} {G}_{0, i}{G}_{1, i}^* = \sigma_n^2 \sqrt{\gamma_{0, i} \gamma_{1, i}}e^{\jmath \varphi_{{\rm o}, i+1}} + n_{{\rm t}, i}, \label{eq:g0g1} \end{align} where \begin{equation} n_{{\rm t}, i} = \sigma_n\sqrt{\gamma_{1, i}} e^{-\jmath\arg(\dot{G}_{1, i})} n_{0, i}+\sigma_n\sqrt{\gamma_{0, i}} e^{-\jmath\arg(\dot{G}_{0, i})}n_{1, i} + n_{0, i}n_{1, i}^. \label{eq:noise} \end{equation} % From \eqref{eq:g0g1}, the phase offset $\varphi_{{\rm o}, i+1}$ can be written as \begin{equation} \hat{\varphi}_{{\rm o},i+1} = \arg({G}_{0, i}{G}_{1, i}^) = \varphi_{{\rm o}, i+1} + \varphi_{{\rm er}, i}, \label{eq:phase_off_est} \end{equation} where $\varphi_{{\rm er}, i}$ is the noise-induced phase estimation error in the $i$-th phase adjustment slot. The three terms that constitute $n_{{\rm t}, i}$ in \eqref{eq:noise} are uncorrelated, so its variance is \begin{equation} \sigma_{i}^2 = \left( \gamma_{0, i}+ \gamma_{1, i}+1 \right) \sigma_n^4. \end{equation} Because of the quadratic term $n_{0, i} n_{1, i}^$ the noise $n_{{\rm t}, i}$ is not strictly Gaussian. Nevertheless, when its two linear components dominate the quadratic term ($\gamma_{0, i} + \gamma_{1,i} \geq 1$), $n_{{\rm t}, i}$ can be well approximated as zero-mean complex Gaussian. In this case, ${G}_{0,i}{G}_{1, i}^$ has a non-central complex Gaussian distribution with a K-factor (ratio of the squared mean to the variance, another SNR measure) equal to \begin{equation} \label{eq:K_ifactor} K_i \overset{\Delta}{=} \frac{\left(\sigma_n^2 \sqrt{\gamma_{0, i} \gamma_{1, i}}\right)^2}{\left( \gamma_{0, i}+ \gamma_{1, i}+1 \right) \sigma_n^4} = \frac{\gamma_{0,i} \gamma_{1,i}}{ \gamma_{0, i}+ \gamma_{1, i}+1}. \end{equation} As for the phase error $\varphi_{{\rm er}, i}$, its distribution is that of the phase of \eqref{eq:g0g1} when $\varphi_{{\rm o},i+1} = 0$. From \cite[eq.~(5.33)]{molisch2012wireless}, its PDF is \begin{align} \label{eq:phase_pdf} f_{\varphi_{{\rm er}, i}}(\varphi_{{\rm er}, i}, K_i) = \frac{e^{-K_i}}{2\pi} \Big( 1+ \sqrt{4\pi K_i} x e^{{K_i}x^2} Q(-\sqrt{2K_i}x )\Big), \end{align} where $x = \cos \varphi_{{\rm er}, i}$ and $Q(\cdot)$ denotes the complementary cumulative distribution function (CCDF) of a standard Gaussian distribution. \subsection{Phase Adjustment} \label{sec:phase_adjtsm_acc} Consider now the phase adjustment process exemplified by Frame 1 in Fig.~\ref{fig:Schdl}. Suppose, for simplicity, that all signals arrive at the tag with amplitudes equal to that of the ranging node $A_{\rm r}$, so that $A_{{\rm h}, m} = A_{\rm r}$ and $\eta_m = \eta, m = 1, \ldots M$. Our primary interest then is how the partial helper set amplitude $A_{{\rm p}, i}$ changes from slot to slot with respect to $A_{\rm r}$. To evaluate this, we introduce the amplitude ratio $\alpha_i$, defined as \begin{equation} \alpha_i = \frac{A_{{\rm p}, i}}{A_{\rm r}}. \label{eq:alpha_n} \end{equation} In the first phase adjustment slot when $i=1$, we have that $A_{{\rm p}, 1} = A_{{\rm h}, 1} = A_{\rm r}$ so that $\alpha_1 = 1$. In the second slot ($i=2$), we obtain from elementary geometry that \begin{equation} A_{{\rm p}, 2} = \sqrt{ A^2_{\rm r}+2A_{{\rm p}, 1}A_{\rm r} \cos \varphi_{{\rm er}, 1} + A_{{\rm p}, 1}^2} = \alpha_2 A_{\rm r} \label{eq:first_slot} \end{equation} where $\alpha_2 = \sqrt{ 1+2\alpha_1 \cos \varphi_{{\rm er}, 1} + \alpha_1^2} \in [0, 2]$. Generally, $A_{{\rm p}, i} = \alpha_{i} A_{\rm r}$ where \begin{equation} \alpha_i = \sqrt{1+2\alpha_{i-1}\cos(\varphi_{{\rm er},i-1})+\alpha_{i-1}^2}, \label{eq:alpha} \end{equation} so that $\alpha_i \in [0, i]$ for any $2 \leq i \leq M$. Combining \eqref{eq:K_ifactor} with \eqref{eq:gamma_0i}-\eqref{eq:gamma_1i}, the K-factor in the adjustment slot $i$ becomes % \begin{equation} K_i = \frac{4 \alpha_{i}^6 \gamma_2^2}{\alpha_{i}^4\gamma_2+4\alpha_{i}^2\gamma_2+1}, \label{eq:Kn} \end{equation} where $\gamma_2 =\eta^2 T_{\rm s} A_{\rm r}^4/N_0$. From \eqref{eq:alpha}, the amplitude ratio $\alpha_i$ for $i>1$ is a random variable that depends both on the phase estimation error and the amplitude ratio in the previous slot. In order to derive its distribution, we first compute a conditional PDF $f(\alpha_i\| \alpha_{i-1})$. Assuming that $\varphi_{{\rm er}, i}$ ($1 \leq i \leq M-1$) are independent random variables distributed according to \eqref{eq:phase_pdf}, we can use \eqref{eq:alpha} and a change of variables \cite{davenport1958introduction} to compute \begin{align} \label{eq:PDF_x} f_{\alpha_i}(\alpha_i\| \alpha_{i-1}) = &\frac{e^{-K_{i-1}}}{\pi} \frac{\alpha_i}{\alpha_{i-1}} \frac{1}{\sqrt{1-z^2}} \\ &\qquad \times \Big( 1+ \sqrt{4\pi K_{i-1}} z e^{K_{i-1}z^2} Q(-\sqrt{2K_{i-1}}z )\Big) , \notag \end{align} where $z = \left(\alpha_i^2-\alpha_{i-1}^2-1\right)/{2\alpha_{i-1}}$. Note that although it is not shown explicitly in \eqref{eq:PDF_x}, $K_{i-1}$ depends on $\alpha_{i-1}$ via \eqref{eq:Kn}. Expression \eqref{eq:PDF_x} highlights the Markov nature of the change of the amplitude ratio from slot to slot. Marginalizing it over the distribution of $\alpha_{i-1}$, we obtain the following recursive formula for the PDF of $\alpha_i$ % \begin{align} f_{\alpha_i}(\alpha_i) &= \int_0^{i-1} f(\alpha_i\| \alpha_{i-1}) f(\alpha_{i-1})\text{d}\alpha_{i-1}. \label{eq:alpha_pdf} \end{align} The closed-form solution to \eqref{eq:alpha_pdf} can be obtained for $\alpha_2$ as % \begin{equation} f_{\alpha_2}(\alpha_2) = \frac{e^{-K_{1}}}{\pi} \sqrt{\frac{4}{4-\alpha_2^2}} \Big( 1+ \sqrt{\pi K_{1}} z e^{K_{1}z^2/4} Q(-\sqrt{0.5K_{1}}z )\Big), \label{eq:final_a2} \end{equation} % where $z = {\alpha_2^2-2}$. For any $i>2$, $f_{\alpha_i}(\alpha_i)$ can subsequently be found from \eqref{eq:alpha_pdf} by applying numerical methods\footnote{Note that with minor modifications the presented analysis also holds for a more general case of unequal helper node amplitudes.}. Fig.~\ref{fig:PDFs} illustrates \eqref{eq:alpha_pdf} by showing $f_{\alpha_i}(\alpha_i)$ for different values of $i$ and input SNR $\gamma_2$. In Fig.~\ref{fig:Kappa_PDF_2}, we observe that the theoretical PDFs computed via \eqref{eq:final_a2} coincide well with the empirical ones for both considered SNRs. Fig.~\ref{fig:Kappa_PDF} on the other hand, illustrates that, as the phase adjustment proceeds from slot to slot and the number of helpers $i$ grows, so does the likelihood that the partial set amplitude $A_{{\rm p}, i}$ increases, as higher values of the amplitude ratio in previous slots lead to improved phase estimation performance (via increased K-factor) and thus better chances for obtaining higher amplitude ratio and higher SNR in the current slot. Further, the long-tailed asymmetry of the PDFs shows that, while $A_{{\rm p},i}$ is almost always close to $i A_{\rm r}$, it can fall to very low values on rare occasions. Therefore, our design analysis should be based on performance percentiles, rather than on the average values. \begin{figure}[t!] \centering \begin{subfigure}[b]{0.9\linewidth} \input{figures/Kappa_PDF2.tex} \caption{\small{}} \label{fig:Kappa_PDF_2} \end{subfigure} \begin{subfigure}[b]{0.9\linewidth} \centering \input{figures/PDF_alphan.tex} \caption{\small{}} \label{fig:Kappa_PDF} \end{subfigure} \caption{\small{Exemplary PDFs of $\alpha_i$ for (a) $i=2$ and (b) $i \in [2, 5]$.}} \vspace{-0.3cm} \label{fig:PDFs} \end{figure} \begin{figure}[t!] \centering \input{figures/REF_prcnt.tex} \vspace{-0.1cm} \caption{\small{REF percentiles as a function of the number of helpers $M$ for input SNR $\gamma_2 = - 5$~dB. The solid black line indicates REF of the conventional brute-force HR system without helper nodes $\zeta_{\rm conv} = \sqrt[3]{M+1}$ \eqref{eq:ref_conv} while the dashed line shows REF of a fully coherent helper-based system $\zeta_{\rm coh} = \sqrt[3]{2M}$ \eqref{eq:z_coh}.}} \label{fig:ref_prcnt} \vspace{-0.3cm} \end{figure} \subsection{Effect on Ranging SNR and REF} Now we demonstrate the range extension provided by our helper-based system and compare it to the range extension achievable by a conventional system that is given the same total transmit power. The helper-based HR system uses the intermodulation term (the second term of \eqref{eq:r_final}) for ranging. Previously, we saw that its instantaneous power is \begin{equation} P_{\rm i} = 4 A_{\rm h}^2 A_{\rm r}^2 \leq 4A_{\rm r}^2 \left(\sum_{m=1}^M A_{{\rm h}, m}\right)^2, \label{eq:power_inst} \end{equation} with the upper limit being achieved when all $M$ helper tones perfectly phase-align at the tag. Suppose again that $A_{{\rm h}, m} = A_{\rm r}$ for all $m\leq M$ and consider \eqref{eq:power_inst}. We can express it as \begin{equation} P_{\rm i} = 4 \alpha_{M}^2 A_{\rm r}^4, \label{eq:ranging_pwr} \end{equation} where $\alpha_{M} = A_{\rm h}/A_{\rm r} \in [0, M]$ is the amplitude ratio after the last, $(M-1)$-th, phase adjustment slot. Comparing \eqref{eq:ranging_pwr} with the power of the ranging term (term 1 in \eqref{eq:r_final}), we see that the SNR boost is proportional to $4\alpha_M^2$ while the corresponding REF for phase adjustment is then $\zeta_{\rm pa} = \sqrt[3]{2 \alpha_{M}}$. With another change of variable, we obtain the PDF of $\zeta_{\rm pa}$ as \begin{align} f_{\zeta_{\rm pa}} (\zeta_{\rm pa}) &= 1.5\zeta^2_{\rm pa} f_{\alpha_M} (\zeta_{\rm pa}). \label{eq:pdf_ref} \end{align} Its CDF is $F_{\zeta_{\rm pa}}(\zeta_{\rm pa})=\int_0^{\zeta_{\rm pa}} f_{\zeta_{\rm pa}} (\zeta_{\rm pa}) \mathrm{d}\zeta_{\rm pa}$. We also define the inverse function of the CDF as \begin{equation} G_{\zeta_{\rm pa}}(p) \overset{\Delta}{=} \zeta_{\rm pa}: F_{\zeta_{\rm pa}} (\zeta_{\rm pa}) = 0.01p. \end{equation} That is, $G_{\zeta_{\rm pa}}(p)$ is the value of the REF $\zeta_{\rm pa}$ at the $p$-th percentile. Note that since $\zeta_{\rm pa} = \sqrt[3]{2 \alpha_{M}}$, $G_{\zeta_{\rm pa}}(p)$ depends both on the input SNR $\gamma_2$ and the number of helpers $M$. Fig.~\ref{fig:ref_prcnt} depicts $G_{\zeta_{\rm pa}}(p)$ as a function of $M$ for input SNR $\gamma_2 = - 5$~dB. It shows a conservative 10th percentile as a worst acceptable case, as well as the more optimistic 50th percentile along with the corresponding REFs of a brute-force conventional HR system $\zeta_{\rm conv} = \sqrt[3]{M+1}$ \eqref{eq:ref_conv} and a fully coherent helper-based system $\zeta_{\rm coh} = \sqrt[3]{2M}$ \eqref{eq:z_coh}. All three systems have the same total transmitted power. We observe from Fig.~\ref{fig:ref_prcnt} that, at this SNR ($\gamma_2 = -5$ dB), one could expect a range extension factor greater than one ($\zeta_{\rm pa}>1$) even in the worst-case scenario\footnote{At lower SNRs the long tails of $f_{\alpha_M}(\alpha_M)$ can cause the $10$th percentile REF for $M>1$ to fall below that of the constant REF provided by a single helper, which we observe in Fig.~\ref{fig:ref_prcnt} for $M=2$. Nevertheless, adding more helpers consistently improves the $10$th percentile performance }, while in $50\%$ of cases the REF of the helper-based system well exceeds that of the conventional brute-force approach when both systems are given the same total transmission power. \vspace{-0.2cm} \subsection{Slot duration limitations} \label{sec:SLD} In our helper-based system, the phase adjustment interval consists of $M-1$ slots followed by a ranging interval. Each phase adjustment slot lasts $T_{\rm s}$ seconds during which the A-mode helper sweeps its phase according to the sweep function $\varphi(t) = 2 \pi t/T_{\rm s}$ and collects the tag response in order to compute its phase correction according to \eqref{eq:phase_estim}. While it appears that the slot duration $T_{\rm s}$ is a free parameter of choice, there are several considerations that limit its practical range. The $i$-th phase adjustment slot ($i>1$) is launched with the helper node phases of nodes $1$ to $i$ obtained by the end of the preceding slot. The primary concern then is the phase drift due to frequency errors in LOs of the helpers and, if they or the tag are moving, differences in their Doppler shifts. Phase drift causes increasing de-coherence among helpers across the slot time, with a corresponding slow reduction of the amplitude ratio $\alpha_i$ through the shrinking of the $A_{{\rm p}, i}$ factor. Suppose that due to LO and movement-induced frequency shifts the $k$-th helper signal arriving at the tag has a frequency error $\omega_{{\rm er}, k}$ at the end of the phase adjustment slot $T_{\rm s}$, which causes a growing phase difference between the different helper tones. The longer the slot duration, the greater the phase difference. Since the phase difference must be contained over all $M-1$ phase adjustment slots, we require that \begin{equation} T_{\rm s} \leq \frac{\Delta \theta_{\rm max}}{(M-1)\omega_{{\rm er}, \rm max}}, \label{eq: freq_drift_limit} \end{equation} where $\Delta \theta_{\rm max}$ is the maximum allowable phase difference and $\omega_{{\rm er}, \rm max}$ is the maximum frequency error of each helper. According to \eqref{eq: freq_drift_limit}, the phase drift limits the slot duration from above. However, the slot duration cannot be too brief either. Since the SNR $\gamma_{2, i}$ is proportional to $T_{\rm s}$, it sets a minimum value for slot duration $T_{\rm s}$ required for reliable phase estimation so that \begin{equation} T_{\rm s} \geq \frac{\gamma_{2, {\rm min}}N_0}{P_{\rm h, min}}, \label{eq:noise_limit} \end{equation} where $\gamma_{2, {\rm min}}$ is the minimum allowable input SNR for a desired performance level, while $P_{\rm h, min}$ indicates the minimum individual incident helper-tone power received by any A-mode node. In addition, because of the time it takes the signal from the A-mode helper to reach the tag, the phase offset that maximizes the helper node sum at the tag differs from the estimated one by $\theta_{\rm d} = 2 \pi \tau_k/T_{\rm s}$. Clearly, when $\tau_k \ll T_{\rm s}$ the phase delay $\theta_{\rm d}$ is negligible, which is why it was omitted earlier. Nevertheless, it contributes to the total phase difference and has to be accounted for when setting the SNR limit in \eqref{eq:noise_limit}. Finally, combining \eqref{eq: freq_drift_limit} and \eqref{eq:noise_limit} we arrive at \begin{equation} \frac{\gamma_{2, {\rm min}}N_0}{P_{\rm h, max}} \leq T_{\rm s} \leq \frac{\Delta \theta_{\rm max}}{(M-1)\omega_{{\rm er}, \rm max}}, \label{eq:bounds_on_slot} \end{equation} which shows how the combination of noise, mobility and the number of helpers bounds the slot duration $T_{\rm s}$. In the following, we explore \eqref{eq:bounds_on_slot} in more detail. \subsection{Conventional Harmonic Radar} \label{sec:sec2A} In classical radar, the radar transmitter emits an RF pulse at frequency $\omega_{\rm 0} = 2\pi f_{\rm 0}$ and the radar receiver listens for reflections from a passive target at the same frequency. In contrast, a HR target is nonlinear, as well as passive, so its response is rich in harmonics. Typically, such a harmonic response is induced by attaching a battery-less harmonic transponder tag to the target of interest. HR tags typically combine a resonant antenna, a low-voltage diode and possibly a simple impedance matching network \cite{colpitts2004harmonic, rasilainen2015transponder, lav2019design}. The antenna voltage drives the diode, creating a rectified current that contains harmonics of the received signal, as sketched in Fig.~\ref{fig:Diode}. The second harmonic is usually the strongest, so the tag's transmit antenna is tuned to $2\omega_0$. The second harmonic signal is thus emitted from the tag and subsequently detected at the HR receiver. The main advantage of harmonic operation is that the background clutter is greatly reduced, since radio frequency reflection from most objects is linear, producing a backscattered response only at $\omega_0$. Below, we provide a model of conventional HR that combines the effects of the uplink (HR transmitter to tag antenna input), the tag (tag antenna input, nonlinearity and tag antenna output), and the downlink (tag antenna output to the HR receiver). We assume for simplicity that the HR transmitter is collocated with the HR receiver, forming a single HR node (the ranging node, or RN). Note that ranging systems can have more than one RN, e.g., in order to locate the tag by multilateration. For simplicity of presentation, our analysis considers just one. Throughout, we also distinguish real bandpass signals from their complex envelopes by a tilde; for example, we denote the real bandpass signal transmitted at $\omega_0$ by $\tilde{s}(t) = \mathrm{Re}\{s(t) e^{\jmath \omega_0t}\}$ and its baseband complex envelope by ${s}(t)$. In the uplink, the RN sends a pulse with complex envelope % \begin{equation} s_{\rm r}(t) = \sqrt{2P_{\rm r}R_{\rm tx}}x(t), \label{eq:s_r} \end{equation} % where $P_{\rm r}$ is the transmit RF power and $R_{\rm tx}$ is the transmit antenna resistance. Furthermore, we assume that the ranging signal $x(t)$ is a biphase $(+1,-1)$ sequence with good autocorrelation properties. With line of sight transmission, the RN signal is received at the tag antenna with the complex envelope % \begin{equation} v_{\rm in}(t) = \sqrt{k_{\rm in} \frac{R_{\rm F}}{R_{\rm tx}}} h_{\rm u}(d_{\rm r}) s_{\rm r} (t-\tau_{\rm r})e^{\jmath \theta_{\rm r}}, \label{eq:v_in} \end{equation} % in which $R_{\rm F}$ and $k_{\rm in}$ are the effective tag antenna resistance and the input tag power transfer efficiency at $\omega_0$, respectively, $h_{\rm u}(d_{\rm r})= \sqrt{G_{\rm tx} G_{\rm tag}(\omega_0) \left( {c}/{2\omega_0 d_{\rm r}}\right)^2}$ is the uplink gain with $G_{\rm tx}$, $ G_{\rm tag}(\omega)$ denoting the transmitter and tag antenna gains, respectively, $c$ is the speed of light, and $d_{\rm r}$ the distance from the RN to the tag. The propagation delay is $\tau_{\rm r} = {d_{\rm r}}/{c}$ and the corresponding phase shift is $\theta_{\rm r} = -\omega_0 \tau_{\rm r}$. \begin{figure}[t!] \centering \includegraphics[width=0.95\linewidth]{figures/Tag_OP_v3.jpg} \caption{\small{ Relationship between the input voltage and the output current of a harmonic transponder tag, in time and frequency.}} \label{fig:Diode} \vspace{-0.2cm} \end{figure} The tag can be modeled as a series circuit with the real bandpass voltage $\tilde{v}_{\rm in}(t) = \mathrm{Re}\{v_{\rm in}(t) e^{\jmath \omega_0t}\}$ as input and real multiband current $\tilde{i}_{\rm T}(t)$ as response, linked by the nonlinear equation \begin{equation} \frac{\tilde{v}_{\rm in}(t)}{n_{\rm i}V_{\rm T}} = \rho \frac{\tilde{i}_{\rm T}(t)}{I_{\rm s}}+\ln \left( \frac{\tilde{i}_{\rm T}(t)}{I_{\rm s}}+1\right). \label{eq:diode_eq} \end{equation} Here, $n_{\rm i}$ and $V_{\rm T}$ are diode thermal voltage and the ideality factor, respectively, $I_{\rm s}$ is its saturation current and $\rho = I_{\rm s}R_{\rm F}/n_{\rm i}V_{\rm T}$. An explicit solution to \eqref{eq:diode_eq} has been obtained in \cite{lav2020two-region} in terms of the Lambert W-function. From that, \cite{lav2020two-region} also provides the closed-form expressions for the relation between the complex envelope $v_{\rm in}(t)$ at the fundamental frequency $\omega_0$ and the complex envelope $i_2(t)$ of the current at the second harmonic $2\omega_0$, in two conditions: \begin{itemize} \setlength\itemsep{0.5em} \item small-signal conditions ($v_{\rm in}(t)/n_iV_{\rm T} < -1- \ln \rho - \rho$), where \begin{equation} i_{2}(t) \approx \frac{\beta}{R_{\rm F}} v_{\rm in}^2(t), \label{eq:second_complx} \end{equation} in which $\beta = \frac{1}{4(n_iV_{\rm T})} \sum_{n=1}^{\infty} {n^{n +1}} \frac{(-1)^{n-1}}{n!} \rho^n e^{n\rho}$. For $\rho < 0.04$ it simplifies further to $\beta \approx \rho/4n_{\rm i}V_{\rm T}$; \vspace{0.1cm} \item large-signal conditions ($v_{\rm in}(t)/n_iV_{\rm T} \gg 1$), where \begin{equation} i_{2}(t) \approx \frac{2}{3\pi} \frac{1}{R_{\rm F}} \|v_{\rm in}(t)\| e^{\jmath 2\varphi_{\rm in}(t)}, \label{eq:current_second_large} \end{equation} in which $\varphi_{\rm in}(t) = \arg(v_{\rm in}(t))$. \end{itemize} From \eqref{eq:second_complx} and \eqref{eq:current_second_large}, the phase of the tag output current at the second harmonic is double that of the input signal, while its magnitude grows quadratically in the small-signal region and linearly in large signal conditions. Our principal interest is to extend the limits of the operating range where signals at the tag are weak. Consequently, in the following we consider the small-signal quadratic\footnote{However, our numerical results in Section~\ref{sec:num3} show that the phase-adaptation approach that we develop based on the small-signal model continues to work well in the tag regions above quadratic.} model \eqref{eq:second_complx}. With $R_{\rm H}$ as the effective output impedance of the tag at $2\omega_0$, the complex envelope of the tag output voltage in the small-signal conditions becomes \begin{equation} v_{\rm out} = R_{\rm H} i_2(t) \approx \frac{R_{\rm H}}{R_{\rm F}} \beta v_{\rm in}^2(t), \label{eq:tag_output} \end{equation} with the corresponding bandpass equivalent provided by $\tilde{v}_{\rm out}(t) = (\beta R_{\rm H}/R_{\rm F}) \mathrm{Re}\{ v_{\rm in}^2(t) e^{\jmath 2\omega_0t}\}$. Note that for the rest of the paper, we drop the approximation sign in \eqref{eq:tag_output}, bearing in mind that it is a small-signal approximation. Finally, the downlink mirrors the uplink, such that at the HR receiver we obtain \begin{equation} r(t) = h_{\rm d}\sqrt{k_{\rm out}\frac{ R_{\rm rx}}{R_{\rm H}}} v_{\rm out}(t-\tau_{\rm r}) e^{\jmath 2\theta_{\rm r}} + n(t), \label{eq:received_sig} \end{equation} where $h_{\rm d} = \sqrt{G_{\rm rx} G_{\rm tag}(2\omega_0) \left( {c}/{4\omega_0 d_{\rm r}}\right)^2}$ is the downlink gain, in which $G_{\rm rx}$ is the receiver antenna gain, $R_{\rm rx}$ is the resistance of the Rx antenna, and $k_{\rm out}$ is the output tag power transfer efficiency at $2\omega_0$. The complex noise $n(t)$ in \eqref{eq:received_sig} is considered to be white Gaussian with power spectral density (PSD) $N_0 = R_{\rm rx}k_{\rm B}T_{\rm n}$ where $k_{\rm B}$ is the Boltzman constant and $T_{\rm n}$ is the noise temperature. For notational convenience, we combine \eqref{eq:s_r} and \eqref{eq:v_in} to represent the input voltage at the tag as \begin{equation} v_{\rm in}(t) = A_{\rm r}x(t-\tau_{\rm r})e^{\jmath \theta_{\rm r}}, \label{eq:v_in2} \end{equation} where $A_{\rm r}=\sqrt{2R_{\rm F}k_{\rm in} P_{\rm r}} h_{\rm u}(d_{\rm r})$. Lastly, we also combine \eqref{eq:tag_output}, \eqref{eq:received_sig} and \eqref{eq:v_in2} so that \begin{equation} r(t) = \eta A_{\rm r}^2 x^2(t-2\tau_{\rm r})e^{\jmath 4\theta_{\rm r}} + n(t), \label{eq:recieved_sig2} \end{equation} where $\eta = h_{\rm d}(d_{\rm r})\beta \sqrt{R_{\rm H}R_{\rm rx}k_{\rm out}}/R_{\rm F}$. The product $\eta A_{\rm r}^2$ represents the total gain of the Tx--tag--Rx link. In the absence of noise, \eqref{eq:v_in}, \eqref{eq:tag_output} and \eqref{eq:received_sig} combined make the received amplitude $\|r(t)\|$ proportional to $h_{\rm u}^2(d_{\rm r})h_{\rm d}(d_{\rm r})$, and hence inversely proportional to $d_{\rm r}^3$. The received power in harmonic radar is then inversely proportional to $d_{\rm r}^6$, i.e., an inverse sixth-power law. \subsection{System Parameters} In this section, we numerically evaluate proposed HR system with adaptive self-coherent auxiliary helper nodes and compare it against conventional HR without helpers. As a benchmark, we consider an X-band HR system reported in \cite{sto2020low} with operational parameters summarised in Table~\ref{tabl:params}. With an output transmit power of $P_{\rm r} = 10$Watt and Tx/Rx antenna gains of $15$dBi, its reported maximum detection range is 15m. For modelling the behaviour of the harmonic tag, we consider a wire-based tag design from \cite{colpitts2004harmonic, lav2019design} where the tag consists of a single dipole antenna that acts both as the receive antenna at $\omega_0$ and the transmit antenna at $ 2 \omega_0$, a Schottky diode and a parallel inductive loop. In our evaluation we use a Skyworks Schottky diode SMS7630-040 \cite{SkyWorksDiode} with parameters specified in Table~\ref{tabl:params_diode}. For simplicity, we also assume perfect matching conditions at both $\omega_0$ and $2 \omega_{0}$ such that $k_{\rm in} = k_{\rm out} = 1$. To facilitate this, we assume that the tag antenna is a half-wavelength dipole at $\omega_0$ with an arm ratio of $(2:1)$, which, as outlined in \cite{aumann2012asymmetrical, law2020evaluation}, ensures a double resonant structure necessary to maximise the power transfer efficiency of the tag. Using an antenna-analysis tool MMANA-GAL \cite{MMANA-GAL}, we find that for a copper wire with a diameter of 0.31mm this yields $R_{\rm F} \approx 132\Omega$, $R_{\rm H} \approx 146\Omega$, $G_{\rm tag}(\omega_0) = 2.2$dBi, $G_{\rm tag}(2\omega_0) = 3.15$dBi. The tag antenna gains, together with the parameters from Table~\ref{tabl:params}, determine the uplink gain $h_{\rm u}(d)$ \eqref{eq:v_in} and the downlink gain $h_{\rm d}(d)$ \eqref{eq:received_sig}. \begin{table}[t!] \renewcommand{\arraystretch}{1.3} \caption{\small{Parameters of a HR system reported in \cite{sto2020low}}} \label{table:summary} \centering \begin{tabular}{\|l\|\|c\|c} \hline \bfseries Parameter & \bfseries Value \\ \hline \hline Frequency $f_0/2f_0$& 9.3/18.6 GHz \\ \hline Receiver bandwidth $B_{\rm r}$ & 125 kHz\\ \hline Output power $P_{\rm r}$ & 10 Watt \\ \hline Tx/Rx antenna gain $G_{\rm tx}= G_{\rm rx}$ & 15 dBi\\ \hline Rx noise figure $N_{\rm F}$ & 2.5 dB\\ \hline \end{tabular} \label{tabl:params} \end{table} \begin{table}[t!] \renewcommand{\arraystretch}{1.3} \caption{\small{Parameters of a Schottky diode SMS7630-040 \cite{SkyWorksDiode}}} \label{table:summary} \centering \begin{tabular}{\|l\|\|c\|c} \hline \bfseries Parameter & \bfseries Value \\ \hline \hline Saturation current $I_{\rm s}$& 5 $\mu$A \\ \hline Ideality parameter $n_i$& 1.05 \\ \hline Thermal voltage $V_{\rm T}$ & 26 mV \\ \hline Coefficient $\rho$ & 0.024 \\ \hline \end{tabular} \label{tabl:params_diode} \vspace{-0.2cm} \end{table} Given an arbitrary transmit waveform $x(t)$, a transmit power $P_{\rm r}$ and a downlink gain $h_{\rm d}(d)$, we can determine the input voltage at the tag antenna $v_{\rm in}(t)$ according to \eqref{eq:v_in}. Throughout this paper, we made use of the quadratic small-signal approximation \eqref{eq:second_complx} to model the relation between the input voltage $v_{\rm in}(t)$ at the tag and the tag output current at the second harmonic $i_2(t)$. Here, we employ the more general explicit solution to \eqref{eq:diode_eq} instead \cite{lav2020two-region}: \begin{equation} \tilde{i}_{\rm T}(t) = \left(\frac{ W_0\left(\rho e^{\left(\rho+\tilde{v}_{\rm in}(t)/n_{\rm i}V_{\rm T}\right)}\right)}{\rho} -1 \right)I_{\rm S}, \label{eq:full_current} \end{equation} in which $W_0(\cdot)$ denotes the principal branch of the Lambert function \cite{corless1996lambertw}. Given \eqref{eq:full_current}, we compute $i_{2}(t)$ numerically as \begin{equation} i_2(t) = a_2(t) -\jmath b_2(t), \label{eq:current_2} \end{equation} % where $a_2(t), b_2(t)$ are the second harmonic Fourier coefficients of $\tilde{i}_{\rm T}(t)$ (see \cite{lav2020two-region} for details). As before, the output tag voltage is % \begin{equation} v_{\rm out} = R_{\rm H} i_2(t). \end{equation} % Using \eqref{eq:full_current} allows us to test how well our quadratic model holds and evaluate how the proposed algorithm behaves outside the quadratic region. \subsection{Conventional HR System} We begin our study by determining operational conditions of a conventional X-band HR system without helper nodes with parameters specified in Table~\ref{tabl:params}. Fig.~\ref{fig:PowVSDist} shows input signal power at the tag antenna, $P_{\rm in} = h_{\rm u}^2(d)P_{\rm r}$, and at the harmonic radar receiver, $P_{\rm rec} = h_{\rm d}^2(d) R_{\rm H} I_2^2/2$, for a tone input, where $I_2$ denotes the amplitude of the second harmonic current. We can clearly observe the change in the curve slope of $P_{\rm rec}$ appearing around $d = 4$m. It illustrates the transition from the quasi-linear regime characteristic of the large-signal conditions to the quadratic regime in the small-signal region. We also indicate here the point corresponding to the reported maximum detection range $d_{\rm max}= 15$m \cite{sto2020low}, which is clearly in the quadratic region. It determines the minimum received signal power of $P_{\rm min} = -115.5$dBm with a corresponding tag input power of $P_{\rm in} = -48$dBm. From this, we also compute a minimum required voltage amplitude at the tag, which is $A_{\rm r} = 2.43 n_i V_{\rm T} = 63$mV. Finally, we determine the receiver noise power as $P_{\rm n} = 2 B_{\rm r} N_0 \approx -118$dBm, in which $N_0 = R_{\rm rx} k_{\rm B} T_{\rm n}(N_{\rm f}-1)$ where $T_{\rm n} = 290$K is the standard room temperature and $N_{\rm f}$ is the Rx noise figure in linear scale. \begin{figure}[t!] \vspace{-\baselineskip} \centering \input{figures/PowVSDist.tex} \caption{\small{Signal power as a function of the distance to the tag $d$ in a conventional HR system without auxiliary helper nodes.}} \label{fig:PowVSDist} \vspace{-0.2cm} \end{figure} \begin{figure}[t!] \vspace{-\baselineskip} \begin{subfigure}{0.49\textwidth} \centering \input{figures/CDFalphaM_Ts.tex} \caption{\small{}} \label{fig:AlphaM_Prc_Ts} \end{subfigure} \begin{subfigure}{0.49\textwidth} \centering \input{figures/CDFalphaM_d.tex} \vspace{-0.4cm} \caption{\small{}} \label{fig:AlphaM_Prc_d} \end{subfigure} \caption{\small{Normalized amplitude ratio percentile $G_{\tilde{\alpha}_M} (p)$ as a function of the input SNR $\gamma_2$ (a) at a fixed distance $d=d_{\rm max}$ and (b) at a fixed slot duration $T_{\rm s} = 1$ns.}} \label{fig:AlphaM_Prc} \vspace{-0.3cm} \end{figure} \begin{figure}[t!] \vspace{-\baselineskip} \begin{subfigure}{0.49\textwidth} \centering \centering \input{figures/SlotDurationvsAlphaM.tex} \caption{} \label{fig:Ts_AlphaM_Prc} \end{subfigure} \begin{subfigure}{0.49\textwidth} \centering \centering \input{figures/SlotDurationvsAlphaM_freq.tex} \caption{} \label{fig:Ts_AlphaM_Prc_freq} \end{subfigure} \caption{\small{Slot duration required for 10th percentile of helper-based HR amplitude $G_{2\alpha_M} (10)$ to exceed conventional HR amplitude $M+1$: (a) minimum required $T_{\rm s}$ in the presence of the propagation delay $\theta_{\rm d}=2 \pi d_{\rm max} /cT_{\rm s}$ and (b) maximum allowed $T_{\rm s}$ in the presence of the frequency error $\omega_{\rm err} = 10^{-6} p_{\rm e} \omega_0$.}} \label{eq:slotduration} \vspace{-0.3cm} \end{figure} \subsection{HR System with Auxiliary Helper Nodes} \label{sec:num3} This section examines the benefits of introducing helpers into the operational scenario described above. As before, we assume for simplicity that all helper tones arrive at the tag with the same amplitude $A_{\rm r}$ so that when they are perfectly phase-aligned at the tag the composite helper node amplitude $A_{\rm h}$ is equal to $MA_{\rm r}$ and the amplitude ratio at the end of the phase adjustment interval is $\alpha_M = M$. First, we present the statistical distributions of the normalized amplitude ratio $\tilde{\alpha}_M = \alpha_M/M \in [0, 1]$. Previously, we saw that $f_{\alpha_M}(\alpha_M)$ depends on the input SNR\footnote{In light of using \eqref{eq:full_current} for determining the tag output, we define $\gamma_2$ here as the SNR at the output of the third Fourier integrator \eqref{eq:Fintegral3} during the first phase adjustment slot, i.e., $\gamma_2 = \gamma_{2, 1} = \|\dot{G}_{2, 1}\|^2/T_{\rm s}N_0$.} $\gamma_2$, which in turn depends both on the phase adjustment slot duration $T_{\rm s}$ via the integration time in \eqref{eq:Fintegral3} and the distance to the tag $d_{\rm r}$ via the amplitude of the receiver input. Suppose now that the tag is positioned at the maximum range of the conventional system such that $d_{\rm r} = d_{\rm max}$. Then, the amplitude $A_{\rm r}$ is fixed and $\gamma_2$ is determined by the slot duration $T_{\rm s}$. Fig.~\ref{fig:AlphaM_Prc_Ts} shows $10$th and $50$th percentiles $G_{\tilde{\alpha}_M} (p)$ of the normalized amplitude ratio $\tilde{\alpha}_M$ as a function of the input SNR $\gamma_2$, together with the values of $T_{\rm s}$ corresponding to the SNRs. We observe good correspondence between the empirical results obtained using \eqref{eq:full_current} and the theoretical ones derived from the asymptotic quadratic model \eqref{eq:second_complx}. Fig.~\ref{fig:AlphaM_Prc_Ts} also demonstrates that the phase adjustment performance improves both with $M$ and the input SNR. For instance, when $M=2$ and the slot duration is greater than one microsecond (i.e., $\gamma_2>0$), $90\%$ of the outcomes achieve more than $60\%$ of the maximum possible amplitude amplification (i.e., $\alpha_M$ is greater than $0.6M=1.2$) while for $M=4$ it exceeds $85\%$ (i.e, $\alpha_M$ is greater than $0.85M=3.4$). To test how well our approach performs outside of the quadratic region, we fix the slot duration $T_{\rm s}$ and change the distance to the tag $d$ instead. Note that the slot duration is set to $T_{\rm s} = 1$ns, an extremely low value, solely to avoid excessively large SNR values when the distance is small and the tag operates far above the quadratic region. Fig.~\ref{fig:AlphaM_Prc_d} demonstrates the results. It indicates that the move towards the quasi-linear ($d<<d_{\rm max}$) region does not significantly affect the ability of our phase adaptation algorithm to phase-align helper signals at the tag. Next, we return to Section~\ref{sec:SLD} considerations and determine the upper and lower bounds on slot duration that allow the helper-based HR system to outperform conventional HR, when both systems are given the same total transmit power budget. To this end, we again consider system performance at the maximum range by setting the tag distance to $d_{\rm max}$, as it is our primary region of interest. First, we study the lower bound \eqref{eq:noise_limit} on slot duration $T_{\rm s}$. To account for the propagation delay in the sweep function $\varphi(t)$, we introduce an additional error $\theta_{\rm d} = 2 \pi d_{\rm max} /cT_{\rm s}$ into the phase offset estimate \eqref{eq:phase_off_est}. As our performance metric we choose the amplitude of the helper-based system measured by the pessimistic 10th percentile point, i.e., $G_{2{\alpha}_M}(10)$. Recall that the amplitude of the signal into the tag is proportional to $2\alpha_M$ for helper-assisted HR \eqref{eq:ranging_pwr} and to $M+1$ for conventional HR \eqref{eq:convent_power}. Thus, Fig.~\ref{fig:AlphaM_Prc_Ts} shows the minimum slot duration required for that 10th percentile amplitude to exceed the conventional HR amplitude, i.e., $G_{2\alpha_M}(10) > M+1$. For comparison, we also show theoretical and empirical curves obtained under the initial assumption that ${\theta}_{\rm d} = 0$. Fig.~\ref{fig:AlphaM_Prc_Ts} suggests that a slot duration of about $1\mu$s ensures that the SNR boost of the helper-node system exceeds that of a comparable conventional system in $90\%$ of the cases. The slot duration can be further reduced by accepting a lower percentage of outcomes in which $2\alpha_M > M+1$, e.g., by considering a $50$th percentile instead. We now turn to evaluating the upper bound \eqref{eq: freq_drift_limit} on slot duration $T_{\rm s}$ that still allows the pessimistic 10th amplitude percentile in helper-based HR to exceed the amplitude of the conventional HR. We introduce a frequency error $\omega_{\rm er}$ as a portion of the fundamental carrier frequency $\omega_0$, so that $\omega_{\rm er}/\omega_0 = 10^{-6} p_{\rm e} $ where $p_{\rm e}$ is the frequency instability expressed in parts per million (ppm). Given $\omega_{\rm er}$, the maximum phase error between any two helpers over the slot duration is $2\omega_{\rm er}T_{\rm s}$. Fig.~\ref{fig:Ts_AlphaM_Prc_freq} shows the maximum slot duration $T_{\rm s}$ that permits $G_{2\alpha_M}(10\%) > M+1$ as a function of the number of helpers $M$, for two values of $p_{\rm e}$. As expected, the upper bound begins to approach the lower one from Fig.~\ref{fig:Ts_AlphaM_Prc} when the frequency error is increased. As a result, for large enough frequency errors there might be no suitable slot duration that fulfills \eqref{eq:bounds_on_slot} for the performance metric of choice, so one would have to accept a higher probability of low-power outcomes. On the other hand, Fig.~\ref{eq:slotduration} shows that when the frequency error is within several ppm, the interplay between noise, frequency instability and the number of helpers provides enough room to choose $T_{\rm s}$ that ensures that the probability of low-power outcome does not exceed a desired value ($10\%$ in our case). \begin{figure}[t!] \centering \input{figures/REF_FINAL.tex} \vspace{0.2cm} \caption{\small{CDFs of the REF $\zeta_{\rm pa}$ of the phase-adaptive helper-based system with the slot duration of $1\mu$s and a frequency instability of 1 ppm. Individual circle and rhomboid markers show the corresponding REFs of a fully coherent helper-based system $\zeta_{\rm coh} = \sqrt[3]{2M}$ and a brute-force conventional system without helpers $\zeta_{\rm conv} = \sqrt[3]{M+1}$, respectively.}} \label{fig:REF_final} \vspace{-0.3cm} \end{figure} Our third, and final, assessment is to fix the slot duration and evaluate the REF of our phase-adaptive helper-based system ($\zeta_{\rm pa}= \sqrt[3]{2\alpha_M}$) taking into account both the phase delay $\theta_{\rm d}$ and the frequency error $\omega_{\rm err}$. Fig.~\ref{fig:REF_final} shows the CDF of $\zeta_{\rm pa}$ for $T_{\rm s} = 1\mu$s (i.e., $\gamma_2 = 0.4$dB at $d_{\rm max}$) and $p_{\rm e} = 1$ ppm. For comparison, it also provides corresponding values for the fully coherent system ($\zeta_{\rm coh} = \sqrt[3]{2M}$, marked by circles) and the brute-force conventional system ($\zeta_{\rm conv} = \sqrt[3]{M+1}$, marked by filled rhomboids). We observe that setting the slot duration within the limits determined by the performance bounds from Fig.~\ref{eq:slotduration} results in the phase-adaptive system outperforming the conventional HR with equivalent total transmit power with high probability, i.e., in more than $80\%$ of the cases. Furthermore, the performance gap between the two increases with $M$. These results show that helpers can be added incrementally in order to achieve the desired range or SNR increase, as long as the system design satisfies \eqref{eq:bounds_on_slot}. \subsection{Two-mode Transmission with Phase Adjustment} \label{sec:transm_schm} From Section~\ref{sec:DS}, helper nodes transmit a fixed-phase tone, a mode which we will call T-mode (tone). However, from \eqref{eq:power_interm_coh} and \eqref{eq:z_coh}, we want the individual helper node tones to combine coherently at the tag, in order to maximize the tag's output power. That requires an additional mode (A, for adjustment) in which a helper node adjusts its transmit phase $\theta_m$ in response to the tag output signal $\tilde{v}_{\rm out}(t)$, which implies that helper nodes must also be able to receive signals on the downlink. Fig.~\ref{fig:adaptive} outlines the helper node structure that supports this two-mode operation. When in mode A, the helper node sweeps its phase around the circle as $\theta_m + \varphi(t)$, where $\varphi(t) = 2 \pi {t}/{T_{\rm s}}, 0\leq t \leq T_{\rm s}$ and $T_{\rm s}$ is the phase sweep duration. During this time, it processes the received response from the tag in order to calculate the new value of transmit phase to use when it next returns to T mode. To coordinate the change between the two different modes at each helper and the operation of the ranging node, the transmission time consists of a series of frames. Each frame begins with a phase adjustment interval of $M-1$ time slots, each of duration $T_{\rm s}$, used for helper phase adjustments, followed by a ranging interval of duration $T_{\rm r}$, resulting in a total frame duration of $T_{\rm f} = (M-1)T_{\rm s} +T_{\rm r}$. Furthermore, during phase adjustment slots only a single helper is in mode A at any given time. Fig.~\ref{fig:Schdl} exemplifies a simple frame structure for $M=3$ helpers. In slot 1, helper 1, which is in mode T, sends a tone and helper 2, in mode A, sends a phase sweep that allows it to align its phase with that of helper 1. In slot 2, helpers 1 and 2 send their now-aligned tones in mode T, while helper 3, in mode A, sends the phase sweep in order to align its phase with that of the sum of helpers 1 and 2. The adjustment interval continues to add one helper at a time, slot by slot, until all $M$ helpers are aligned. In the absence of receiver noise, $M-1$ phase adjustment slots are sufficient here to achieve exact phase coherence. During the ranging interval that follows (slot 3 in Fig.~\ref{fig:Schdl}), the RN sends the ranging signal while the helpers, all now in mode T, send tones which arrive coherently at the tag, thereby boosting the amplitude of the intermodulation term at the tag output. \begin{figure}[t!] \vspace{-\baselineskip} \centering \includegraphics[width =0.85\linewidth]{figures/HNA-T2.jpg} \caption{\small{ Block scheme of a helper node that can operate in one of two modes: a phase adjustment mode (A) or a fixed-phase transmission mode (T). QM and QD here stand for the quadrature modulator and demodulator, respectively.}} \vspace{-0.3cm} \label{fig:adaptive} \end{figure} In more detail, the signal arriving at the tag in phase adjustment slot $i$, $i = 1, \ldots, M-1$, is composed of the phase-sweep of helper $i+1$ and the fixed-phase tones of helpers $1$ to $i$, so the complex envelope of the tag input is \begin{align} \label{eq:vin_a} v_{\rm in}(t-(i-1)T_{\rm s}) &= A_{{\rm h}, i+1} e^{\jmath \bar{{\theta}}_{i+1}}e^{\jmath \varphi(t-(i-1)T_{\rm s})} + \sum_{m=1}^i A_{{\rm h}, m} e^{\jmath \bar{\theta}_{m}} \notag \\ & = A_{{\rm h}, i+1} e^{\jmath \bar{\theta}_{i+1}}e^{\jmath \varphi(t-(i-1)T_{\rm s})} + A_{{\rm p}, i} e^{\jmath \theta_{{\rm p},i}}, \end{align} where $A_{{\rm p}, i} e^{\jmath \theta_{{\rm p},i}} = \sum_{m=1}^i A_{{\rm h}, m} e^{\jmath \bar{\theta}_{m}}$ is the slot-$i$ partial sum of helper node signals, since only a subset of helpers is in T mode during any phase adjustment slot. After the final adjustment in slot $M-1$, the sum is no longer partial so that $A_{\rm h}e^{\jmath \theta_{\rm h}} = A_{{\rm p}, M} e^{\jmath \theta_{{\rm p},M}}$. Moving to the downlink, \eqref{eq:vout_final} gives the second-harmonic complex envelope at the tag output as \begin{align} \label{eq:vout_a} v_{\rm out}(t-(i-1)T_{\rm s}) & = \frac{R_{\rm H}}{R_{\rm F}} \beta {v}_{\rm in}^2(t-(i-1)T_{\rm s}) \\ &= \frac{R_{\rm H}}{R_{\rm F}} \beta \left( {A}_{{\rm h}, i+1} e^{\jmath\left(\bar{\theta}_{i+1}+\varphi(t-(i-1)T_{\rm s})\right)}+ A_{{\rm p},i} e^{\jmath \theta_{{\rm p},i}} \right)^2 \notag \end{align} and \eqref{eq:r_final} then gives the second-harmonic receiver input at helper $i+1$, which is in mode A, as \begin{align} \label{eq:baseband_recieved_kth} r_{i+1}(t-(i-1)T_{\rm s}) & = \eta_{i+1} \Big( A_{{\rm h}, i+1}^2e^{\jmath 2\bar{\theta}_{i+1}}e^{\jmath 2\varphi(t-(i-1)T_{\rm s})} \\ & \quad \qquad +2A_{{\rm h}, i+1}A_{{\rm p}, i}e^{\jmath (\bar{\theta}_{i+1}+ \theta_{{\rm p},i})}e^{\jmath \varphi(t-(i-1)T_{\rm s})} \notag \\ & \quad \qquad + A_{{\rm p}, i}^2e^{\jmath 2{\theta}_{{\rm p},i}}\Big)e^{-\jmath 2\omega_0\tau_{i+1}} +n_{i+1}(t), \notag \end{align} where $\eta_{i} = h_{\rm d}(d_i) \beta \sqrt{k_{\rm out}R_{\rm H}R_{\rm rx}}/{R_{\rm F}}$. For simplicity, in \eqref{eq:vin_a}--\eqref{eq:baseband_recieved_kth} we ignore the propagation delay in $\varphi(t)$, on the grounds that $\tau_{i+1} \ll T_{\rm s}$, but we revisit this point later. From \eqref{eq:vout_a}, the partial sum $A_{{\rm p},i}e^{\jmath \theta_{{\rm p}, i}}$ in adjustment slot $i$ reflects prior adjustments, so that helper $i+1$ should change its phase to equal that of the partial sum, $\theta_{{\rm p}, i}$. In the absence of error, this maximizes the amplitude of the next partial sum so that $A_{{\rm p}, i+1} = A_{{\rm h}, i+1} +A_{{\rm p}, i}$. According to \eqref{eq:baseband_recieved_kth}, the phase offset required to achieve this is \begin{equation} \varphi_{{\rm o}, i+1} = \theta_{{\rm p}, i}-\bar{\theta}_{i+1} = \theta_{{\rm p}, i} - \theta_{i+1} +\omega_0\tau_{i+1}. \label{eq:phase_offcet} \end{equation} Below, we describe a method to estimate $\varphi_{{\rm o}, i+1}$ from the received signal $r_{i+1}(t-(i-1)T_{\rm s})$. \begin{figure}[t!] \centering \includegraphics[width=0.8\columnwidth]{figures/Schedule_StartUp_v2.jpg} \caption{\small{Simplified transmission frame structure for $M=3$ helper nodes. The frame $T_{\rm f}$ is organized in $M$ time slots: $M-1$ phase adjustment slots of duration $T_{\rm s}$ each followed by a $T_{\rm r}$-long slot for ranging, i.e., $T_{\rm f} = (M-1)T_{\rm s} + T_{\rm r}$. }} \label{fig:Schdl} \vspace{-0.3cm} \end{figure} \subsection{Phase Offset Estimation} \label{sec:phase_estm} Consider \eqref{eq:baseband_recieved_kth} and note that the individual terms that constitute it are separable with respect to $\varphi(t)$ via the following integrals \begin{align} {G}_{0, i} &= \overset{{iT_{\rm s}}}{\underset{{(i-1)T_{\rm s}}}{\int}} r_{i+1}(t-(i-1)T_{\rm s}) \text{d}t \label{eq:Fintegral1} \\ &= \underbrace{\eta_{i+1} T_{\rm s} A^2_{{\rm p}, i}e^{\jmath2\left(\theta_{{\rm p}, i}-\omega_0\tau_{i+1}\right)}}_{\dot{G}_{0, i}} + \int_0^{T_{\rm s}} n(t) \text{d}t = \dot{G}_{0, i} + n_{0, i}, \notag \end{align} % \begin{align} {G}_{1, i} & = \overset{{iT_{\rm s}}}{\underset{{(i-1)T_{\rm s}}}{\int}} r_{i+1}(t-(i-1)T_{\rm s}) e^{-\jmath 2 \pi \frac{t-(i-1)T_{\rm s}}{T_{\rm s}}} \text{d}t \label{eq:Fintegral2} \\ &= \underbrace{2 \eta_{i+1} T_{\rm s} A_{{\rm h}, i+1}A_{{\rm p},i} e^{\jmath\left(\bar{\theta}_{i+1}+\theta_{{\rm p}, i} -2\omega_0\tau_{i+1} \right)}}_{\dot{G}_{1, i}} \notag \\ & \qquad \qquad \qquad \qquad \qquad + \int_0^{T_{\rm s}}n(t) e^{-\jmath 2 \pi \frac{t}{T_{\rm s}}} \text{d}t \notag \\ &= \dot{G}_{1, i} +n_{1, i}. \notag \\ {G}_{2, i} & = \overset{{iT_{\rm s}}}{\underset{{(i-1)T_{\rm s}}}{\int}} r_{i+1}(t-(i-1)T_{\rm s}) e^{-\jmath 4 \pi \frac{t-(i-1)T_{\rm s}}{T_{\rm s}}} \text{d}t \label{eq:Fintegral3} \\ & = \underbrace{\eta_{i+1} T_{\rm s} A^2_{{\rm h}, i+1}e^{\jmath2\left(\bar{\theta}_{i+1}-\omega_0\tau_{i+1}\right )}}_{\dot{G}_{2, i}} + \int_{0}^{T_{\rm s}} n(t) e^{-\jmath 4 \pi \frac{t}{T_{\rm s}}} \text{d}t \notag \\ &= \dot{G}_{2, i} +n_{2, i},\notag \end{align} where $n_{k, i} = \int_0^{T_{\rm s}}n(t) e^{-\jmath 2 \pi \frac{(k-1)}{T_{\rm s}}t} \text{d}t$ and the overhead dot denotes the noise-free component. Since the basis functions $\exp(-\jmath 2 \pi \frac{k}{T_{\rm s}}t)$ in \eqref{eq:Fintegral1}-\eqref{eq:Fintegral3} are orthogonal and have equal energy, the noise terms $n_{0, i}$, $n_{1, i}$, $n_{2, i}$ are independent and have equal variance $\sigma_n^2 = T_{\rm s} N_0$. For each of the integration outputs, we can define individual SNRs \begin{align} \label{eq:gamma0} \gamma_{0, i} &= \frac{\|\dot{G}_{0, i}\|^2}{\sigma_n^2} = \frac{\eta_{i+1}^2 A^4_{{\rm p}, i}T_{\rm s}}{N_0}, \\ \gamma_{1, i} & = \frac{\|\dot{G}_{1, i}\|^2}{\sigma_n^2} = \frac{ 4 \eta_{i+1}^2 A_{{\rm h}, i+1}^2A^2_{{\rm p},i}T_{\rm s}}{N_0}, \label{eq:gamma1} \\ \gamma_{2, i} &= \frac{\|\dot{G}_{2, i}\|^2}{\sigma_n^2} = \frac{\eta_{i+1}^2 A_{{\rm h}, i+1}^4 T_{\rm s}}{N_0}. \label{eq:gamma2} \end{align} In the above, both $\eta_{i+1}^2$ and $N_0$ are proportional to $R_{\rm rx}$. Consequently, the SNRs do not depend on the Rx antenna resistance. Using \eqref{eq:Fintegral1}-\eqref{eq:Fintegral3} the phase offset $\varphi_{{\rm o}, i+1}$ can then be computed as \begin{equation} \hat{\varphi}_{{\rm o}, i+1} = \arg({G}_{0,i}{G}_{1,i}^), \label{eq:phase_estim} \end{equation} where $(\cdot)^{}$ denotes complex conjugate. Note that while we do not directly use the output $G_{2, i}$ of the third integrator for phase estimation, it provides a useful SNR reference that is independent of the partial set amplitude $A^4_{{\rm p}, i}$, so that, expressing \eqref{eq:gamma0}--\eqref{eq:gamma1} via \eqref{eq:gamma2}, we obtain \begin{align} \label{eq:gamma_0i} \gamma_{0, i} &= \frac{A^4_{{\rm p}, i}}{A^4_{{\rm h}, i+1}} \gamma_{2, i}, \\ \gamma_{1, i} & = 4 \frac{A^2_{{\rm p}, i}}{A^2_{{\rm h}, i+1}} \gamma_{2, i}. \label{eq:gamma_1i} \end{align} Phase estimation in \eqref{eq:phase_estim} is similar to a phase error detection in a phase-locked loop. In contrast to operating directly on the magnitude of received measurements, it first projects the received signal onto a set of orthogonal subspaces and then extracts the phase. This separates the individual signal components and, by averaging over the sweep time, reduces the effect of additive noise. \subsection{Coherent Transmission Scheme} A coherent transmission scheme ensures that HN signals arrive at the tag in phase, in spite of drifts in distances and in oscillator phases. In Section~\ref{sec:PA}, we introduce an adaptive phase coherence method to achieve such a system. Here, we show that the benefits of coherent operation are substantial. Consider the amplitude $A_{\rm h}$ of the helper node contribution introduced in \eqref{eq:signal_tag}: \begin{equation} A_{\rm h} \overset{\Delta}{=} \left\|\sum_{m=1}^M A_{{\rm h}, m} e^{\jmath\bar{\theta}_m}\right\|. \label{eq:magnitude_hn} \end{equation} If all $\bar{\theta}_m = \bar{\theta}$, then \begin{equation} A_{\rm h} = \left\|e^{\jmath\bar{\theta}} \sum_{m=1}^M A_{{\rm h}, m} \right\| = \sum_{m=1}^M A_{{\rm h}, m} = M A_{\rm r}, \end{equation} where the last equality assumes, for simplicity, that all helper tones arrive at the tag with the same amplitude as the ranging signal. Then, the power of the intermodulation term in \eqref{eq:r_final} is proportional\footnote{For notational convenience, here and in the following the signal power is assumed to be normalised to the link gain $\eta(d_{\rm r})$ defined below \eqref{eq:recieved_sig2}.} to \begin{equation} P_{\rm i} = 4M^2A^4_{\rm r}, \label{eq:power_interm_coh} \end{equation} which is $4M^2$ times the power of the ranging signal in a conventional HR system (first term in \eqref{eq:r_final}). As a result, the helper-based system provides an SNR boost of $20 \log (M) + 6$~dB, or about 18~dB for $M=4$ helpers. Since received signal power in HR varies as inverse sixth power of distance, a coherent helper system provides a range extension factor (REF) of \begin{equation} \zeta_{\rm coh} = (4M^2)^{1/6} = \sqrt[3]{2M}. \label{eq:z_coh} \end{equation} This implies that $M=4$ helper nodes can double the range, compared to conventional HR. Even for the simplest case,i.e., a single helper ($M=1$) where coherence is no longer a consideration, \eqref{eq:z_coh} shows that REF is 1.26. A $26\%$ increase in range for almost no effort is appealing. \subsection{Basic scheme -- Incoherent Transmission} \label{sec:basicscheme} Although the focus of this paper is ensuring that helper tones arrive coherently at the tag, there may be a role for a simpler incoherent system, one which omits the adaptive phase coherence algorithm, as in \cite{lav2019on}. According to \eqref{eq:magnitude_hn}, if the phases $\bar{\theta}_m$ are mutually independent and uniformly distributed in $[-\pi, \pi)$, then the mean helper node power at the tag is the power-wise sum % \begin{equation} \bar{P}_{\rm h} = \sum_{m=1}^MA_{{\rm h}, m}^2 =MA_{\rm r}^2, \end{equation} where the last equality, for simplicity, sets all helper amplitudes equal to $A_{\rm r}$. The mean power of the intermodulation term then becomes \begin{equation} \bar{P}_{\rm i} = 4\bar{P}_{\rm h} A_{\rm r}^2 = 4 M A_{\rm r}^4. \label{eq:power_interm_mean} \end{equation} This is $4M$ times the power of the signal term in a conventional HR system. On the other hand, this average is $M$ times smaller than the constant power \eqref{eq:power_interm_coh} of the coherent transmission. At the mean power of the intermodulation term \eqref{eq:power_interm_mean}, the SNR boost is then $10\log(M)+6$ dB, equating to 12dB for $M=4$ with a corresponding REF of $1.58$. What about the instantaneous power $P_{\rm i} = 4A_{\rm h}^2 A_{\rm r}^2$? From \eqref{eq:magnitude_hn}, the magnitude $A_{\rm h}$ varies as the individual phases drift with changing distances to the tag and different individual LO phase offsets. Suppose that there are many helpers. Then, invoking the central limit theorem we can model the real and imaginary components of the helper node contribution as Gaussian variables with weak mutual dependence. It is well known that the resulting complex Gaussian process has a Rayleigh distributed amplitude ($A_{\rm h}$) and an exponentially distributed power ($P_{\rm h} = A_{\rm h}^2$) \cite{cavers2006mobile}. Consequently, the cumulative distribution function (CDF) of $P_{\rm i}$ for many helpers is asymptotically \begin{equation} \text{Pr}[P_{\rm i} \leq z] = 1-e^{- \displaystyle \frac{z}{\bar{P}_{\rm i} }} = 1-e^{- \displaystyle \frac{z}{4 M A_{\rm r}^4} }. \label{eq:prob_nonch} \end{equation} From \eqref{eq:prob_nonch}, the instantaneous power of the helper-based HR system with incoherent transmissions is $4M$ times the power of conventional HR approximately $37\%$ of the time, and when the phases are almost aligned it can occasionally approach the power of coherent transmission, which is $4M^2$ times that of conventional HR. However, infrequent deep fades can take it \textit{below} the power of conventional HR, with probability $1-\exp(-1/4M) \approx 1/4M$ ($6.1\%$ for four helpers). If the range is extended by a factor $\zeta_{\rm inc}$, then the dropout probability becomes $1-\exp(-\zeta_{\rm inc}^6/4M)$ which grows rapidly. For such a system, range extension may not be an appropriate measure. Instead, if this incoherent system operates at the same range as conventional HR, it provides much higher SNR on average, at the cost of dropouts a fraction $1/(4M)$ of the time. Therefore, applications that can tolerate infrequent dropouts may well find incoherent transmission attractive. \subsection{Brute Force Conventional HR} \label{sec:brute_force} A helper-based system invests the power of the ranging node and $M$ helpers into SNR improvement or range increase. Assume, again for simplicity, that all helpers have the same transmit power as the ranging node and that all path losses are equal. A fair comparison might then allow conventional HR to increase its transmit power by a factor of $M+1$. With this brute-force improvement, the received power at the tag in conventional HR is \begin{equation} P_{\rm r} = (M+1)^2A_{\rm r}^4. \label{eq:convent_power} \end{equation} Comparison with \eqref{eq:power_interm_coh} and consideration of the inverse sixth power dependence on range gives the REF as \begin{equation} \zeta_{\rm conv} = \sqrt[\displaystyle 3]{M+1}. \label{eq:ref_conv} \end{equation} For a single helper ($M=1$), therefore, SNR and REF of the conventional HR system are as good as those of the coherent helper-based system \eqref{eq:power_interm_coh}. However, conventional HR rapidly falls behind the coherent helper system as the number of helper nodes increases, leaving the coherent system with an asymptotic $26\%$ greater range. To match the range of a helper-based system, the conventional system must increase the transmit power of its RN, which also increases the weight and cost of the amplifier and power supply. It is worth noting here that HR systems have increased linearity requirements on the RN in order to minimize the parasitic 2nd harmonic leakage, leading to the need for more carefully designed amplifiers and, depending on the modulation, implementation of additional linearization techniques \cite{gallagher2014linearization, lav2019parasitic}. In contrast, the helper-node approach is distributed and incremental, so that helpers can be added only as needed. Also, the set of helper nodes boosts the effective power of every RN, in case there is more than one.	{ "redpajama_set_name": "RedPajamaArXiv" }	8,098
Q: Entity Framework - adding additional properties to model I'm new to the Entity Framework but I managed to create a database and several models. Here's my Rider model: namespace Dash.Data { public partial class Rider { public int ID { get; set; } public int AccountID { get; set; } public string Name { get; set; } } } I also have another partial class to include additional properties: namespace Dash.Data { public partial class Rider { public Room Room { get; set; } } } And this is my context class: public class DashContext : DbContext { public DashContext() : base(Constants.ConnectionString) { this.Configuration.LazyLoadingEnabled = true; this.Configuration.ProxyCreationEnabled = false; } protected override void OnModelCreating(DbModelBuilder modelBuilder) { Database.SetInitializer<DashContext>(null); } public DbSet<Rider> Riders { get; set; } } However, when initializing my context I receive this error: System.InvalidOperationException: 'Unable to determine the principal end of an association between the types 'Dash.Game.Room' and 'Dash.Data.Rider'. The principal end of this association must be explicitly configured using either the relationship fluent API or data annotations.' Now, I do understand it's thinking that Dash.Game.Room is another field, but I don't want it to treat it like a field, but as a property I'm adding so the class can interact with my program. I want to include the columns inside my first class, and the additional properties in the other one. How can I achieve this? A: public partial class Rider { [NotMapped] public Room Room { get; set; } }	{ "redpajama_set_name": "RedPajamaStackExchange" }	1,880
\section{Introduction} Continuous, automated surveillance systems that use machine learning models to identify adverse patient events are being incorporated into healthcare environments with increasing frequency. One of the most notable adverse events is sepsis, a life-threatening medical condition contributing to one in five deaths globally \citep{world2020global} and stands as one of the most important cases for automated in-hospital surveillance. Sepsis is formally defined as life-threatening organ dysfunction caused by a dysregulated host response to infection \citep{singer2016third}. Delays in recognizing sepsis and initiating appropriate treatment can adversely impact patient outcomes. In a recent study of adult sepsis patients, each hour of delayed treatment was associated with higher risk-adjusted in-hospital mortality (odds ratio, 1.04 per hour) \citep{seymourTimeTreatmentMortality2017}. It logically follows that early recognition of the physiologic aberrations preceding sepsis would afford clinicians more time to intervene and may contribute to improving outcomes and reducing costs. Many machine learning methods have been developed to predict the onset of sepsis, utilizing data from the electronic medical record (EMR) \citep{fleuren2020machine,reyna2019early,shashikumarDeepAISEInterpretableRecurrent2021}. While many approaches can be designed to provide an alert preceding an event, most are not designed to discover and report the causal chains that preceded an adverse event. Developing and reporting a causal chain of events not only serves as a foundation for prognosticating adverse event occurrence, but more importantly it reveals the pathways of deterioration which may afford clinicians the additional context to corroborate or modify existing treatment modalities in a way that is superior to a simple alarm. Recently, Hawkes processes \citep{hawkes1971point,hawkes1971spectra,hawkes1974cluster}, which model self- and mutual- exciting patterns among continuous-time events, have drawn a lot of attention in the field of health analytics \citep{meyer2014power,choi2015constructing,bao2017hawkes,schoenberg2019recursive,wei2021inferringb}. In our problem, a linear multivariate Hawkes process (MHP) seems appealing, since (1) the support of the excitation matrix enjoys a natural interpretation as a Granger Causal (GC) graph \citep{xu2016learning}, (2) given its interpretation as a clustering process \citep{hawkes1974cluster}, we can infer the commonly observed chain pattern that precedes sepsis from the learned GC graph, and (3) with proper domain expertise, simple methods, such as (generalized) linear model, are proven effective in outputting highly explainable results \citep{choi2015constructing,wei2021inferringb}. However, there are two major challenges preventing us from applying linear MHP to recover the GC graph. First and foremost, without a non-linear link function, linear MHP itself fails to model inhibiting effects (e.g., proper medication will inhibit occurrence of a certain disease), since ``negative triggering effect'' could lead to negative conditional intensity and thus intractable likelihood. Second, a well-established expectation–maximization (EM) based stochastic declustering algorithm \citep{zhuang2002stochastic,fox2016spatially} sufferers from scalability issue and cannot be applied to EMR data with thousands of patients' trajectories. One common solution to the first challenge is adopting a non-liner link function, e.g., exponential link, which maps all negative values to non-negative ones. Recently, \citet{bonnet2022inference} adopt $g(x) = x^+ := \max\{0,x\}$ link function. To evaluate and maximize likelihood, they calculate the ``re-start'' time, at which the conditional intensity becomes nonzero. However, such a calculation has quadratic complexity, making it unscalable. Scalable methods to infer GC graph with both exciting and inhibiting effects for MHP are still largely missing. \begin{figure}[!htp] \centerline{ \includegraphics[width = .5\textwidth]{tex_files/DAG_Hawkes/realdata/sep_graph_1.pdf} \includegraphics[width = .5\textwidth]{tex_files/DAG_Hawkes/realdata/fullgraph.pdf} } \caption{Granger Causal graphs over Sepsis-Associated Derangement fitted on Sepsis-3 patient cohort (left) and full patient cohort (right) via linear multivariate Hawkes processes.} \label{fig:graph} \end{figure} \vspace{0.05in} \noindent {\it Contribution.} In this paper, we adopt $g(x) = x^+$ link function in MHP, in order to recover a GC graph with both exciting and inhibiting effects. The contribution is three-fold. Firstly, we propose to maximize a surrogate of the true likelihood, which is essentially the likelihood of the linear MHP (i.e., we remove the non-differentiable link in the conditional intensity). The reason is three-fold: (i) within the feasible region, this surrogate serves as a good approximation to the true likelihood; (ii) the gradient filed of this surrogate enjoys a simple closed-form evaluation, which makes the powerful yet simple gradient-based method applicable; (iii) even though this gradient field is not the gradient of true likelihood, it enjoys an interpretation as a strong monotone vector field \citep{juditsky2019signal,juditsky2020convex,wei2021inferring}, which may explain its empirical success. Secondly, we develop a scalable two-phase gradient-based algorithm \footnote{Implementation is available at \url{https://github.com/SongWei-GT/two-phase-MHP}} coupled with a proper learning rate decaying scheme based on the gradient norm to solve the optimization problem. Our proposed algorithm fixes (i) the unscalablity issue of projected gradient descent (GD), which is similar to the ``re-start'' time method \citep{bonnet2021maximum,bonnet2022inference}; (ii) the divergence issue of vanilla GD due to potential inhibiting effect. Moreover, we use extensive numerical simulation to demonstrate our method's empirical success. Lastly, we report graphs (i.e., Figure~\ref{fig:graph}) that afford clinicians a simple mechanism for interpreting both inhibitory and promoting causal relationship amongst the data. Networks are exceptionally important for syndromic (i.e. a constellation of different physiologic derangements can be manifested) conditions like sepsis. These graphs can be used to differentiate cohorts and to identify important, intra-cohort relationships. For clinicians the utility of these graphs is two fold: they can be used to (i) quantify a patient's risk of developing subsequent physiologic derangements in the future and (ii) discover new relationships. The learned Granger causal graphs in this work are highly interpretable and can be used to create or augment surveillance systems for high-risk patients. Here, we demonstrate the effectiveness of our approach in learning a Granger causal graph over Sepsis Associated Derangements (SADs), but it can be generalized to other applications with similar requirements. \subsection{Related work} The study of Granger Causality in time series literature via vector autoregressive (VAR) time series has been a heated topic for years. Recent advancements mainly focus on non-linear dynamics \citep{sindhwani2012scalable,tank2018neural} and tackling high-dimensionality via regularization \citep{bolstad2011causal,basu2015network,basu2019low}. For a comprehensive survey of the recent development of Granger Causality in the context of time series, we refer readers to \citet{shojaie2021granger}. VAR models and mutivariate Hawkes process (MHP) models share many similarities and some have recently recognized that the self- and mutual- excitation matrix in the Hawkes process model can be interpreted as Granger Causal graph in a similar way. The study of GC under the context of MHP can be traced back to \citet{kim2011granger}. Recent development includes leveraging alternating direction method of multipliers to infer the low-rank structure in mutual excitation matrix \citep{zhou2013learning}, applying EM algorithm with various constraints \citep{xu2016learning,chen2022learning,ide2021cardinality} and using powerful neural networks \citep{zhang2020cause} to infer the GC graph. Even outside the context of Granger Causality, estimation of MHP has been a research hotspot for years. The most famous method would be the stochastic declustering algorithm, which is based on the EM algorithm. Such algorithms have been applied to Hawkes process parameter estimation with various kernel functions, e.g., probability weighted kernel estimation with adaptive bandwidth \citep{zhuang2002stochastic}, probability weighted histogram estimation \citep{marsan2008extending} and with inhomogeneous spatial background rate \citep{fox2016spatially}, etc. In addition, there are also a lot of neural network based methods, including neural Hawkes process \citep{mei2017neural}, Transformer Hawkes process \citep{zuo2020transformer} and so on. Moreover, there are also recent attempts to explore powerful yet simple gradient-based method to infer the problem parameters; notable contributions include \citet{wang2020uncertainty,cartea2021gradient}. Here, we want to mention that the $g(x) = x^+$ link function is novel in literature \citep{bonnet2021maximum,bonnet2022inference}. Since there have not been many methods tailored to this particular parameterization, we only numerically compare our method with the re-start time method \citep{bonnet2021maximum,bonnet2022inference} and some naive gradient-based methods. \section{Background} \subsection{Multivariate Hawkes Process} A counting process $$N = (N^1,\dots,N^d),$$ where each process $N^i = \{N^i_t: t\in [0,T]\}$ itself is a counting measure on time horizon $T$ and records the number of type-$i$ events before time $t$, is called a multivariate linear Hawkes process (MHP) if the conditional intensity of $i$-th process $(i=1, \cdots, d)$ is defined as follows $$ \lambda_{i}(t)=\mu_{i}+\sum_{j=1}^d \int_{0}^t \varphi_{i,j}\left(s\right)d N_{t-s}^j, $$ where $\mu_i$ is the exogenous background intensity for type-$i$ event, independent of the history and kernel function $\varphi_{i, j}(\cdot)$ captures the impact from historical type-$j$ event to subsequent type-$i$ event. In this work, we adopt a very common and popular kernel function --- exponential kernel, i.e., $$\varphi_{i, {j}}(t) = \alpha_{i,j}\exp\{-\beta t\}.$$ Here, parameter $\alpha_{i,j}$ represents the magnitude of the impact from type-$j$ event to type-$i$ event and $\beta$ characterizes the rate of decay of that impact. Most importantly, unlike classic model, we consider not only exciting effect, but also inhibiting effect by allowing negative magnitude parameters $\alpha_{i,j}$'s. However, this could lead to negative intensity, which contradicts the understanding of conditional intensity as the instantaneous probability of event occurrence. To fix this issue, we apply operator $(\cdot)^+ = \max\{0,\cdot\}$ to the linear conditional intensity \citep{bonnet2021maximum} and get \begin{equation}\label{eq:condi_intensity_def} \lambda_{i}(t)=\bigg(\mu_{i}+\sum_{j=1}^d \int_{0}^t \alpha_{i,j}e^{-\beta s}d N_{t-s}^j\bigg)^+. \end{equation} We denote the background intensity vector as $\mu = (\mu_1,\dots,\mu_d)^T$ and excitation/inhibition matrix as $A = (\alpha_{i,j}) \in \mathbb{R}^{d \times d}$. We will show the support of matrix $A$ enjoys a natural interpretation as a Granger Causal graph. \subsection{Granger causality} The notion of Granger Causality was introduced to multivariate Hawkes process by \citet{eichler2017graphical,xu2016learning}. In the seminal paper, \citet{eichler2017graphical} showed that the Granger causal structure of the MHP is fully encoded in the excitation/inhibition matrix. Under our multivairate linear Hawkes process (with exponential decay kernel) model, the Granger Causality can be formally defined as follows: \begin{proposition}[\citet{eichler2017graphical}] Let $N = (N^1,\dots,N^d)$ be a $d$-dimensional multivariate Hawkes process with conditional intensity defined in \eqref{eq:condi_intensity_def}, then $N^j$ does NOT Granger-cause $N^i$ if and only if $\alpha_{i,j} = 0$. \end{proposition} We need to remark that inferring Granger Causality needs ``all the information in the universe'' and hence we can only learn Granger non-causality and {\it prima facie causality} given partially observed data \citep{granger1969investigating,granger1980testing,granger1988some}. In the graph induced by the excitation/inhibition matrix $A = (\alpha_{i,j})$, the absence of an edge means Granger non-causality whereas the presence of an edge in $A$ only implies prima facie causality. However, since unobserved confounding is outside the scope of this work, we will call this matrix $A$ Granger causal graph, assuming that the observed information is ``enough'' to infer Granger Causality. Moreover, this excitation/inhibition matrix $A$ can be understood as a directed information graph (DIG) \citep{etesami2016learning}, which is a generalized causal notion of Granger Causality. To be precise, in DIG, we determine the causality by comparing two conditional probabilities in KL-divergence sense: one is the conditional probability of $N^i_{t+dt}$ given full history, and the other one is the conditional probability of $N^i_{t+dt}$ given full history except that of type-$j$ event. Last but not least, both Granger causal graph and DIG are equivalent to minimal generative model graphs \citep{quinn2011equivalence} and therefore can be used for causal inference in the same manner Bayesian networks are used for correlative statistical inference. \section{Estimation} Consider we observe a sequence of events over time horizon $T$: $$(u_1, t_1),\dots,(u_N, t_N),$$ where $u_i \in \{1,\dots,d\}$ represents the type of the event and $$0 \leq t_1 < \dots < t_N \leq T$$ denote the exact occurrence times of those events. The conditional intensity function of type-$i$ event at time $t$ is as follows: $$ \lambda_{i}(t)=\bigg(\mu_{i}+\sum_{j: t_{j}<t} \alpha_{i, u_{j}} e^{-\beta\left(t-t_{j}\right)}\bigg)^+. $$ Typically, we apply Maximum likelihood estimation (MLE) to learn model parameters, where the log-likelihood is defined as: \begin{equation}\label{eq:true_lik} \ell(\mu,A;\beta) = \sum_{i=1}^{d}\left(\int_{0}^{T} \log \lambda_{i}(t) d N_{t}^{i}-\int_{0}^{T} \lambda_{i}(t) d t\right). \end{equation} However, the $(\cdot)^+$ operator makes the above likelihood function non-differentiable. To leverage the powerful gradient method, we simply remove the $(\cdot)^+$ operator in the conditional intensity --- we denote $\tilde \lambda_{i}(t) = \mu_{i}+\sum_{j: t_{j}<t} \alpha_{i, u_{j}} e^{-\beta\left(t-t_{j}\right)}$ and define a surrogate log-likelihood, which is an approximation to the true likelihood, as follows: \begin{equation}\label{eq:surrogate_lik} \tilde \ell(\mu,A;\beta) = \sum_{i=1}^{d}\left(\int_{0}^{T} \log \tilde \lambda_{i}(t) d N_{t}^{i}-\int_{0}^{T} \tilde \lambda_{i}(t) d t\right). \end{equation} We say it is an approximation, since even for parameter $(\mu,A)$ within the feasible region \begin{equation}\label{eq:feasible_region} \Theta = \{(\mu,A): \tilde \lambda_{u_n}(t_n) > 0, n=1,\dots,N\}, \end{equation} the values between true likelihood \eqref{eq:true_lik} and its surrogate \eqref{eq:surrogate_lik} could differ since $\tilde \lambda_{i}(t)$ can be negative on some intervals. Nevertheless, this surrogate $\tilde \ell(\mu,A;\beta)$ enjoys a very simple closed-form expression: \begin{align} \sum_{i=1}^d \sum_{j=1}^{N-1} \frac{\alpha_{i,u_j}}{\beta} \left(e^{-\beta (t_{N}-t_j)} - 1\right) - T\sum_{i=1}^d \mu_i + \sum_{n=1}^N \log \bigg(\mu_{u_n} + \sum_{j < n} \alpha_{u_n,u_j} e^{-\beta (t_n-t_j)} \bigg). \label{eq:log-lik} \end{align} We will maximize this surrogate likelihood to estimate the problem parameters, i.e., \begin{equation}\label{eq:MLE} \hat \mu, \hat A = {\rm argmin}_{\mu,A \in \Theta} - \tilde \ell(\mu,A;\beta). \end{equation} Since the objective function \eqref{eq:MLE} is convex with respect to (w.r.t.) $(\mu, A)$ \citep{bacry2015hawkes}, projected Gradient Descent (GD) is a tempting choice, which enjoys strong convergence guarantee. Despite the simple closed-form expression of $\tilde \lambda_{i}(t)$, its evaluation as well as the projection back to $\Theta$ are computationally intense, making projected GD unscalable. Fortunately, the gradient field of this surrogate remains well-defined even outside the feasible region $\Theta$, making the vanilla GD possible. However, vanilla GD (without projection) will suffer from divergence issue, as the iterate can easily go outside the feasible region $\Theta$. Thus, we need to gradually decay the learning rate during the learning process. Since the (surrogate) log-likelihood is also intractable, it cannot be used to fulfill this purpose. To handle those difficulties, we propose a two-phase GD-based algorithm coupled with a learning rate decaying scheme based on the gradient norm; this algorithm is illustrated in Figure~\ref{fig:illus_2phase} and one can see its good performance in Figure~\ref{fig:illus_adj}. Next, we will briefly introduce this algorithm. \begin{figure}[htp] {% \subfigure[Illustration of the two-phase algorithm. After Phase 1, we select nodes \# 3 and \# 6 (percentage threshold $p=0.85$ in Algorithm~\ref{algo:2_phase_2_index}), on which we further perform phase 2 batch coordinate GD.]{\label{fig:illus_2phase}% \includegraphics[width = .56\textwidth]{tex_files/DAG_Hawkes/2phase_fig/convergence_analysis.pdf}}% $ \quad $ \subfigure[Demonstration of effectiveness of our proposed algorithm. The $\ell_1$ norm of $A$ recovery error is $1.4$, and the Hamming distance and Structural Hamming distance between the true and fitted adjacency matrix $A$ are both zeros. ]{\label{fig:illus_adj}% \includegraphics[width = .42\textwidth]{tex_files/DAG_Hawkes/2phase_fig/fitted_adi_mat.pdf}} } \caption{Illustration of our proposed algorithm via a $d=10$ toy example.}\label{fig:toy_illus} \end{figure} \vspace{0.05in} \paragraph{{\it Phase 1: Projected Gradient Descent.}} In the first phase, we constrain all parameters to be non-negative and perform projected GD with fixed step length. We denote $\hat \mu_t, \hat A_t$ as iterates at $t$-th step and the update rule is\begin{align} \hat \mu_t & \leftarrow \hat \mu_{t-1} + \gamma \nabla_{\mu} \tilde \ell/\\|\nabla_{\mu} \tilde \ell\\|_2, \\ \hat A_t & \leftarrow \hat A_{t-1} + \gamma \nabla_{A} \tilde \ell/\\|\nabla_{A} \tilde \ell \\|_F, \end{align} where $\gamma$ is step size (learning rate), $\\|\cdot\\|_2$, $\\|\cdot\\|_F$ represent vector $\ell_2$ norm and matrix Frobenius norm and the gradient fields are defined as: $\nabla_{\mu} \tilde \ell = \nabla_{\mu} \tilde \ell(\hat \mu_{t-1},\hat A_{t-1};\beta), \quad \nabla_{A} \tilde \ell = \nabla_{A} \tilde \ell(\hat \mu_{t-1},\hat A_{t-1};\beta).$ Here, parameter $\beta$ is assumed to be known and in practice we will perform grid search to select the best $\beta$. In order to make sure we do not get negative intensity, we perform the following projection: \begin{align} \hat \mu_t &\leftarrow {\rm argmin}_{\mu \in \mathbb{R}_+} \norm{\hat \mu_t - \mu}_2, \\ \hat A_t &\leftarrow {\rm argmin}_{A \in \mathbb{R}_+^{d\times d}} \norm{\hat A_t - A}_F, \end{align} which can be easily achieved by setting all negative entries to zeros. Complete details of the project GD algorithm can be found in Algorithm~\ref{algo:2_phase_1} in Appendix~\ref{appendix:add_alg}. The advantage of this phase is three-fold: (1) it guides us to a neighborhood around the global optimizer and meanwhile (2) ensures the stability/convergence of the algorithm and (3) reduces the computation cost by finding a small batch of coordinates to further optimize (see Figure~\ref{fig:illus_2phase} and the description of phase 2 below). \vspace{0.05in} \paragraph{\it Phase 2: Batch Coordinate Gradient Descent.} In the second phase, we consider those nodes whose corresponding rows could have negative values. We identify those nodes by the $\ell_2$ norm of the gradient (w.r.t. $A$) row vector --- large value indicates that convergence of the corresponding row is not achieved after phase 1 (see the right panel in Figure~\ref{fig:illus_2phase}) and thus we should apply gradient descent without the constraint/projection to recover the parameters. See complete details on how to identify those rows in Algorithm~\ref{algo:2_phase_2_index}. Last but not least, we only need to perform gradient descent for those selected rows in $A$ (and corresponding background intensities). Despite intractable log-likelihood in this phase, we develop a learning rate decaying scheme based on the gradient $F$-norm in order to achieve convergence. Details of the algorithm can be found in Algorithm~\ref{algo:2_phase_2_main} in Appendix~\ref{appendix:add_alg}. Recently, \citet{juditsky2019signal,juditsky2020convex} showed that a projected GD along some (strong) monotone vector filed can be interpreted as a solution to a stochastic variation inequality (VI) and enjoys both signal recovery guarantee and convergence guarantee. However, since we do not constraint the iterate within $\Theta$ in phase 2, the vector fields $\nabla_{\mu} \tilde \ell,$ $\nabla_{A} \tilde \ell$ are no longer monotone. Hence, we could only use numerical evidence to demonstrate the effectiveness of our method. Nevertheless, this vector field view under VI framework might give us a chance to theoretically explain our heuristic's empirical success. \section{Numerical simulation}\label{sec:exp} In this section, we will demonstrate the good performance of our proposed two-phase method (coupled with grid search for unknown $\beta$) via numerical simulation. We will use the likelihood at the end of phase 1 as the goodness-of-fit (GoF) criterion to select (hyper-)parameter $\beta$. \begin{table}[!htbp] % {\caption{Performance of proposed algorithm when $\beta$ is unknown. The last row corresponds to selected $\beta$ based on end-of-phase 1 log-likelihood, where we can observe its performance is almost the same with the optimal $\beta$'s performance.}\label{table:exp:beta_grid_saerch_lik}} \resizebox{1\textwidth}{!}{% \begin{tabular}{lcccccccccccccr} \toprule[1pt]\midrule[0.3pt] & \multicolumn{4}{c}{$d=5$} & \multicolumn{4}{c}{$d=10$} & \multicolumn{4}{c}{$d=20$} \\ $\beta$ & \texttt{$\mu $ err.$^\star$} & \texttt{$A$ err.} & \texttt{$A$ HD} & \texttt{$A$ SHD} & \texttt{$\mu $ err.$^\star$} & \texttt{$A$ err.} & \texttt{$A$ HD} & \texttt{$A$ SHD} & \texttt{$\mu $ err.$^\star$} & \texttt{$A$ err.} & \texttt{$A$ HD} & \texttt{$A$ SHD} \\ \cmidrule(l){2-5} \cmidrule(l){6-9} \cmidrule(l){10-13} 0.4 & 5.01 (3.16) & 1.51 (0.85) & 0.06 (0.092) & 1.5 (2.3) & 8.53 (3.81) & 4.39 (0.63) & 0.03 (0.052) & 3.0 (5.27) & 14.97 (5.13) & 13.46 (2.14) & 0.047 (0.044) & 19.0 (17.82) \\ 0.5 & 5.78 (3.3) & 1.26 (0.86) & 0.04 (0.08) & 1.0 (2.01) & 10.57 (4.39) & 3.49 (0.6) & 0.02 (0.033) & 2.0 (3.39) & 20.51 (6.16) & 10.59 (2.27) & 0.043 (0.047) & 17.5 (18.88)\\ 0.6 & 5.39 (3.24) & 1.05 (0.88) & 0.02 (0.071) & 0.5 (1.79) & 10.04 (4.36) & 2.58 (0.64) & 0.02 (0.023) & 2.0 (2.38) & 21.18 (6.41) & 8.55 (2.35) & 0.045 (0.046) & 18.0 (18.67)\\ 0.7 & 5.2 (3.12) & 0.86 (0.88) & 0.0 (0.065) & 0.0 (1.64) & 8.94 (4.05) & 1.86 (0.61) & 0.01 (0.024) & 1.0 (2.47) & 19.35 (6.09) & 6.54 (2.43) & 0.048 (0.048) & 19.5 (19.24)\\ 0.8 & 4.67 (3.02) & 0.74 (0.89) & 0.0 (0.039) & 0.0 (0.99) & 7.54 (3.74) & 1.4 (0.46) & 0.01 (0.018) & 1.0 (1.85) & 17.11 (5.65) & 4.98 (2.5) & 0.06 (0.053) & 24.0 (21.52)\\ 0.9 & 4.51 (2.94) & 0.66 (0.9) & 0.0 (0.036) & 0.0 (0.91) & 6.79 (3.53) & 1.52 (0.41) & 0.01 (0.02) & 1.0 (2.08) & 16.34 (5.21) & 5.11 (2.13) & 0.07 (0.055) & 28.0 (22.32)\\ 1 & 4.46 (2.87) & 0.79 (0.92) & 0.0 (0.034) & 0.0 (0.86) & 7.16 (3.47) & 1.84 (0.39) & 0.01 (0.022) & 1.0 (2.28) & 18.0 (5.29) & 5.93 (1.82) & 0.088 (0.055) & 35.5 (22.29)\\ 1.1 & 4.56 (2.79) & 1.03 (0.91) & 0.0 (0.035) & 0.0 (0.87) & 7.73 (3.47) & 2.3 (0.34) & 0.02 (0.026) & 2.0 (2.65) & 19.95 (5.55) & 6.83 (1.64) & 0.103 (0.056) & 41.5 (22.52)\\ 1.2 & 4.75 (2.74) & 1.2 (1.22) & 0.0 (0.032) & 0.0 (0.85) & 8.4 (3.46) & 2.72 (0.38) & 0.03 (0.033) & 3.0 (3.36) & 22.84 (6.08) & 7.8 (1.53) & 0.121 (0.052) & 48.5 (21.1)\\ $-$ & 4.57 (2.96) & 0.74 (0.89) & 0.0 (0.036) & 0.0 (0.9) & 7.04 (3.55) & 1.62 (0.41) & 0.01 (0.021) & 1.0 (2.17) & 16.7 (5.34) & 5.06 (2.19) & 0.07 (0.055) & 28.0 (22.02)\\ \midrule[0.3pt] \bottomrule[1pt] \multicolumn{12}{l}{$\star$ the value times $10^{-2}$ is the true $\mu$ recovery error; we omit $\times 10^{-2}$ in the value due to space consideration.} \\ \end{tabular} } \end{table} \paragraph{\it Experiment 1.} We perform grid search on $\beta \in \{0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1, 1.1, 1.2\}$ (ground truth is $0.8$). For each grid value, we fit the model to randomly generated synthetic data ($50$ sequences with $T=500$) and repeat this procedure independently for 100 times. At each trial, we select $\beta$ with the largest end-of-phase 1 likelihood. We report (1) $\ell_1$ norm of $\beta$ recovery error (\texttt{$\beta$ err.}), (2) $\ell_1$ norm of $\mu$ recovery error (\texttt{$\mu$ err.}), (3) $\ell_1$ norm of $A$ recovery error (\texttt{$A$ err.}), (4) Hamming Distance (\texttt{$A$ HD}) and (5) Structural Hamming Distance (\texttt{$A$ SHD}) between ground truth and fitted adjacency matrix $A$ over 100 trials in Table~\ref{table:exp:beta_grid_saerch_lik}. We can observe that the grid search approach achieves comparably good performance with the optimal and true parameter cases, which are all satisfying. In addition, we also show that those errors will decrease with increasing sequence length $T$ (or sequence number). To be precise, we study the behavior of those errors with respect to (w.r.t.) the time horizon $T$ and total number of sequences, assuming that we know the ground truth $\beta$. We generate (1) one single sequence on time horizon $T \in \{500,2000,5000,$ $10000,20000\}$ and (2) multiple sequences (total sequence number chosen from $\{1,10,20,50,100\}$) on time horizon $T = 500$ and learn the parameter via our proposed two-phase method. We report similar evaluation metrics over 100 independent trials. The results for $d=5, 10$ cases can be found in Table~\ref{table:exp:T_consistency}. We can see that with longer sequence (or more sequences), all those errors decrease monotonically, which further demonstrates the effectiveness of our proposed method. \begin{table}[H] {\caption{Consistency of our proposed two-phase algorithm when $\beta$ is assumed to be known.}\label{table:exp:T_consistency}}% \rule{0pt}{.1ex} \\ \resizebox{1\textwidth}{!}{% \begin{tabular}{lcccccccccccccr} \multicolumn{11}{c}{\large{Varying Sequence Time Horizon $T$ (Seq. Num. fixed to be 1).}} \\ \toprule[1pt]\midrule[0.3pt] & \multicolumn{5}{c}{\large{$d=5$}} & \multicolumn{5}{c}{\large{$d=10$}}\\ T & 500 & 2000 & 5000 & 10000 & 20000 & 500 & 2000 & 5000 & 10000 & 20000 \\% Column names row \cmidrule(l){2-6} \cmidrule(l){7-11} \texttt{$\mu$ err.$^\star$} & 7.41 (3.42) & 5.34 (2.93) & 4.25 (2.76) & 3.81 (2.8) & 3.69 (2.72) & 17.96 (5.98) & 11.26 (4.47) & 8.65 (4.01) & 8.78 (3.8) & 7.58 (3.75)\\ \texttt{$A$ err.} & 8.94 (5.96) & 2.26 (2.81) & 1.01 (0.82) & 0.75 (0.43) & 0.57 (0.23) & 20.95 (12.55) & 4.93 (2.55) & 2.6 (1.04) & 1.87 (0.61) & 1.52 (0.48) \\ \texttt{$A$ HD} & 0.24 (0.13) & 0.08 (0.091) & 0.04 (0.076) & 0.04 (0.059) & 0.0 (0.056) & 0.245 (0.075) & 0.07 (0.063) & 0.03 (0.035) & 0.015 (0.025) & 0.01 (0.018)\\ \texttt{$A$ SHD} & 6.0 (3.43) & 2.0 (2.28) & 1.0 (1.9) & 1.0 (1.48) & 0.0 (1.41)& 24.5 (7.72) & 7.0 (6.34) & 3.0 (3.57) & 1.5 (2.55) & 1.0 (1.86) \\ \midrule[0.3pt] \bottomrule[1pt] \end{tabular} } \rule{0pt}{.1ex} \\ \resizebox{1\textwidth}{!}{% \begin{tabular}{lcccccccccccccr} \multicolumn{11}{c}{\large{Varying Sequence Number (Time Horizon $T$ fixed to be $500$).}} \\ \toprule[1pt]\midrule[0.3pt] & \multicolumn{5}{c}{\large{$d=5$}} & \multicolumn{5}{c}{\large{$d=10$}}\\ Seq. Num. & 1 & 10 & 20 & 50 & 100 & 1 & 10 & 20 & 50 & 100 \\% Column names row \cmidrule(l){2-6} \cmidrule(l){7-11} \texttt{$\mu$ err.$^\star$} & 6.25 (3.29) & 3.91 (2.81) & 3.86 (2.72) & 3.41 (2.66) & 2.91 (2.50) & 17.96 (5.98) & 8.61 (4.01) & 8.67 (3.78) & 7.54 (3.74) & 6.9 (3.49)\\ \texttt{$A$ err.} & 9.42 (5.50) & 1.19 (1.22) & 0.86 (1.00) & 0.6 (0.91) & 0.54 (0.91) & 20.96 (12.56) & 2.62 (1.04) & 1.84 (0.61) & 1.4 (0.46) & 1.51 (0.47) \\ \texttt{$A$ HD} & 0.26 (0.120) & 0.06 (0.075) & 0.04 (0.061) & 0.04 (0.045) & 0.0 (0.050) & 0.245 (0.075) & 0.03 (0.036) & 0.015 (0.026) & 0.01 (0.018) & 0.01 (0.017)\\ \texttt{$A$ SHD} & 7.0 (3.14) & 1.5 (1.89) & 1.0 (1.53) & 1.0 (1.14) & 0.0 (1.27)& 24.5 (7.72) & 3.0 (3.66) & 1.5 (2.71) & 1.0 (1.85) & 1.0 (1.76) \\ \midrule[0.3pt] \bottomrule[1pt] \multicolumn{5}{l}{$\star$ we omit $\times 10^{-2}$ in the value due to space consideration.} \\ \end{tabular} } \end{table} We also perform experiment for $d=20$ case. We report the same evaluation metrics in Tables~\ref{table:exp:T_consistency_d20} and \ref{table:exp:T_consistency_d20_2}. However, due to the computational limitation, we only report the results for smaller number of sequences and shorter time horizons. Nevertheless, we can still see the decaying error pattern as observed in the above $d=5, 10$ cases. \begin{table}[htp] \caption{Consistency w.r.t. Sequence Time Horizon $T$ (Seq. Num. fixed to be 1)}\label{table:exp:T_consistency_d20} \begin{center} \begin{small} \begin{sc} \resizebox{.6\textwidth}{!}{% \begin{tabular}{lcccc} \toprule[1pt] T & 500 & 2000 & 5000 & 10000 \\% Column names row \cmidrule(l){2-5} \texttt{$\mu$ err.$^\star$} & 58.45 (19.23) & 33.75 (11.3) & 24.88 (8.87) & 21.01 (7.67) \\ \texttt{$A$ err.} & 39.43 (15.93) & 12.07 (4.14) & 6.98 (2.26) & 5.51 (2.19)\\ \texttt{$A$ HD} & 0.24 (0.064) & 0.068 (0.051) & 0.032 (0.037) & 0.025 (0.044) \\ \texttt{$A$ SHD} & 96.0 (25.91) & 27.5 (20.66) & 13.0 (14.97) & 10.0 (17.64) \\ \bottomrule[1pt] \multicolumn{5}{l}{$\star$ we omit $\times 10^{-2}$ in the value due to space consideration.} \\ \end{tabular} } \end{sc} \end{small} \end{center} \caption{Consistency w.r.t. Sequence Number (Time Horizon $T = 500$)}\label{table:exp:T_consistency_d20_2} \begin{center} \begin{small} \begin{sc} \resizebox{.5\textwidth}{!}{% \begin{tabular}{lccc} \toprule[1pt] Seq. Num. & 1 & 10 & 20 \\% Column names row \cmidrule(l){2-4} \texttt{$\mu$ err.$^\star$} & 57.91 (19.71) & 24.16 (8.84) & 20.34 (7.56) \\ \texttt{$A$ err.} & 39.62 (16.33) & 6.88 (2.42) & 5.24 (2.22) \\ \texttt{$A$ HD} & 0.24 (0.068) & 0.03 (0.034) & 0.02 (0.041) \\ \texttt{$A$ SHD} & 96.0 (27.47) & 12.0 (13.8) & 8.0 (16.52) \\ \bottomrule[1pt] \multicolumn{4}{l}{$\star$ we omit $\times 10^{-2}$ in the value due to space consideration.} \\ \end{tabular} } \end{sc} \end{small} \end{center} \end{table} \paragraph{\it Experiment 2.} We compare our proposed method with two benchmark methods. Here, we consider vanilla gradient descent (GD) and ``re-start time'' method \citep{bonnet2021maximum,bonnet2022inference}. Details on these benchmarks can be found in Appendix~\ref{appendix:benchmark}. We report similar metrics over 100 independent trials in Table~\ref{table:exp:baseline_single_seq}. As we can see, for both cases, our proposed method outperforms benchmarks in terms of most evaluation metrics. In case 1, even though GD with proper stopping criterion achieves slightly better $\ell_1$ estimation error (for $\beta$ and $A$), its pattern recovery of $A$ is not as good as our proposed method (its HD and SHD are larger). \begin{table}[htp] \caption{Comparison with benchmarks. The best results are highlighted.}\label{table:exp:baseline_single_seq} \begin{center} \begin{small} \begin{sc} \resizebox{.75\textwidth}{!}{% \begin{tabular}{lcccc} \multicolumn{5}{c}{{Case 1: single sequence with time horizon $T=10000$.}} \\ \toprule[1pt]\midrule[0.3pt] Method & Two-phase method & Vanilla GD & early stopped GD & re-start \\% Column names row \cmidrule(l){2-5} \texttt{$\beta$ err.} & .312 (.112) & .393 (.035) & \textbf{.264} (.137) & .837 (.246) \\ \texttt{$\mu$ err.} & \textbf{.0386} (.0252) & .0413 (.0317) & .0398 (.0281) & .239 (.102) \\ \texttt{$A$ err.} & 1.726 (0.785) & 23.58 (7.93) & \textbf{1.494} (0.731) & 8.828 (1.213) \\ \texttt{$A$ HD} & \textbf{.0304} (.0416) & .1336 (0.118) & .0936 (.0926) & .3576 (.0459)\\ \texttt{$A$ SHD} & \textbf{0.76} (1.04) & 3.37 (2.96) & 2.34 (2.32) & 8.98 (1.19) \\ \midrule[0.3pt]\bottomrule[1pt] \end{tabular} } \end{sc} \end{small} \end{center} \begin{center} \begin{small} \begin{sc} \resizebox{0.75\textwidth}{!}{% \begin{tabular}{lcccc} \multicolumn{5}{c}{{Case 2: multiple (100) sequences with time horizon $T = 500$.}} \\ \toprule[1pt]\midrule[0.3pt] Method & Two-phase method & Vanilla GD & early stopped GD & re-start \\% Column names row \cmidrule(l){2-5} \texttt{$\beta$ err.} & \textbf{.219} (.157) & .377 (.058) & .286 (.120) & $-$ \\ \texttt{$\mu$ err.} & .0367 (.0235) & \textbf{.0335} (.0216) & .0363 (.0251) & $-$ \\ \texttt{$A$ err.} & \textbf{.820} (.369) & 21.350 (7.386) & 1.551 (.577) & $-$ \\ \texttt{$A$ HD} & \textbf{.0124} (.0231) & .105 (.120) & .0660 (.0687) &$-$ \\ \texttt{$A$ SHD} & \textbf{.31} (.58) & 2.64 (3.06) & 1.65 (1.72) & $-$ \\ \midrule[0.3pt]\bottomrule[1pt] \end{tabular} } \end{sc} \end{small} \end{center} \end{table} We defer detailed experiment settings and additional results to Appendices~\ref{appendix:exp_detail} and \ref{appendix:add_exp}. \section{Real data experiment} {We created a retrospective cohort of patients utilizing in hospital data derived from rady hospital system in Atalanta, GA spanning 2018-2019. This data was collected and analyzed in accordance with Emory Institutional Review Board (IRB) approved protocol \#STUDY00000302. Patients were included in the Sepsis-3 cohort if they met Sepsis-3 criteria while in the hospital and were admitted for $\geq$ 24 hours. Patients were included in the Non-Septic cohort if they had a SOFA score $\geq$2. A total of 37 patient features comprised of laboratory results (labs) and observations (vital signs) were examined for this work. Treatments were limited to two classes of medication: antimicrobial therapy (e.g., antibiotics) and vasopressor therapy. We defer further details of the patient cohort construction to Appendix~\ref{appendix:lab_vital_SAD}. Here, we report the resulting descriptive statistics in Table~\ref{table:demo}. } \begin{table}[H] \caption{Median and interquartile range (IQR) of patients demographics.}\label{table:demo} \begin{center} \begin{small} \begin{sc} \resizebox{0.75\textwidth}{!}{% \begin{tabular}{lcccc} \toprule[1pt]\midrule[0.3pt] & \multicolumn{2}{c}{{Sepsis-3 patients}} & \multicolumn{2}{c}{{Non-sepatic patients}} \\ year & 2018 ($n=409$) $^\star$ & 2019 ($n = 454$) & 2018 ($n = 960$) & 2019 ($n = 1169$) \\% Column names row \cmidrule(l){2-5} \texttt{Age (median and IQR)} & 58 (38 - 68) & 59 (46 - 68) & 56 (38 - 67) & 55 (37 - 66) \\ \texttt{Female (percentage)} & 30.1 $\%$ & 36.6 $\%$ & 37.1 $\%$ & 35.8 $\%$ \\ \texttt{Average sofa score} & 3.32& 3.14 & 2.18 & 2.28 \\ \texttt{Traj. len. (median)} & 25 (25 - 25) & 25 (25 - 25) & 17 (13 - 22) & 17 (13 - 22) \\ \midrule[0.3pt]\bottomrule[1pt] \multicolumn{5}{l}{$\star$ $n$ represents the total number of patients in the corresponding cohort.} \end{tabular} } \end{sc} \end{small} \end{center} \end{table} Integrating high-dimensional information (via, e.g., clustering) is essential in causal discovery and explainable machine learning \citep{sanchez2022causal}; examples include \citet{uleman2021mapping,braman2021deep,wei2021inferringb}. While the Sepsis-3 definition provides the explicit features necessary for identifying the presence of sepsis, there is no consensus as to which features are best for prognosticating the disease. To reduce the complexity of our computations expert medical opinion was utilized to identify common and clinically relevant Sepsis-Associated Derangements (SADs) that could be detected using structured EMR data. A total of $18$ SADs and $2$ relevant treatments shown in Table~\ref{table:SADname} were identified using 37 patient features and treatments gathered from the medical record. A SAD was considered present if the patient features were outside of normal limits. Details on how SADs were constructed based on vital signs and labs can be found in Table~\ref{table:SADcutoff} in Appendix~\ref{appendix:lab_vital_SAD}. \begin{table}[htp] \caption{Measurements in sepsis-associated events construction.}\label{table:SADname} \begin{center} \begin{small} \begin{sc} \resizebox{\textwidth}{!}{% \begin{tabular}{lll} \multicolumn{3}{c}{\Large{Sepsis-Associated Derangement (SAD)}}\\ \toprule[1pt]\midrule[0.3pt] Full name & Abbreviation & Measurement name \\ \midrule[0.3pt] \textbf{Renal Dysfunction} & RenDys &creatinine, blood\_urea\_nitrogen\_(bun)\\ \textbf{Electrolyte Imbalance} & LyteImbal &calcium, chloride, magnesium, potassium, phosphorus\\ \textbf{Oxygen Transport Deficiency} & O2TxpDef &hemoglobin\\ \textbf{Coagulopathy} & Coag &partial\_prothrombin\_time\_(ptt), fibrinogen, platelets, \\ & & d\_dimer, thrombin\_time, prothrombin\_time\_(pt), inr\\ \textbf{Malnutrition} & MalNut &transferrin, prealbumin, albumin\\ \textbf{Cholestatsis} & Chole &bilirubin\_direct, bilirubin\_total\\ \textbf{Hepatocellular Injury} & HepatoDys &aspartate\_aminotransferase\_(ast), ammonia,\\ & & alanine\_aminotransferase\_(alt)\\ \textbf{Acidosis} & Acidosis &base\_excess, ph\\ \textbf{Leukocyte Dysfunction} & LeukDys &white\_blood\_cell\_count\\ \textbf{Hypercarbia} & HypCarb & partial\_pressure\_of\_carbon\_dioxide\_(paco2),\\ & & end\_tidal\_co2\\ \textbf{Hyperglycemia} & HypGly &glucose\\ \textbf{Mycardial Ischemia} & MyoIsch &troponin\\ \textbf{Tissue Ischemia} & TissueIsch &base\_excess, lactic\_acid\\ \textbf{Diminished Cardiac Output} & DCO &best\_map\\ \textbf{CNS Dysfunction} & CNSDys &gcs\_total\_score\\ \textbf{Oxygen Diffusion Dysfunction} & O2DiffDys &spo2, fio2\\ \textbf{Thermoregulation Dysfunction} & ThermoDys &temperature\\ \textbf{Tachycardia} & Tachy &pulse\\ \midrule[0.3pt]\bottomrule[1pt] \rule{0pt}{1ex} \\ \multicolumn{3}{c}{\Large{Other Sepsis-Associated Events}}\\ \toprule[1pt]\midrule[0.3pt] Full name & Abbreviation & Measurement name \\ \midrule[0.3pt] \textbf{Vasopressor Support} & VasoSprt &norepinephrine\_dose\_weight, epinephrine\_dose\_weight, \\ & & dobutamine\_dose\_weight, dopamine\_dose\_weight, \\ & & phenylephrine\_dose\_weight, vasopressin\_dose\_weight\\ \textbf{Antibiotic Therapy} & ABX & $-$ \\ \textbf{Sepsis} & SEP3 & $-$\\ \midrule[0.3pt]\bottomrule[1pt] \end{tabular} } \end{sc} \end{small} \end{center} \end{table} \begin{figure}[htp] \centerline{ \includegraphics[width = .8\textwidth]{tex_files/DAG_Hawkes/realdata/SAD_percentage_occur.pdf}} \caption{Percentage of SAD's occurrence. Most SADs' occurrences are more frequent in Sepsis-3 cohort. } \label{fig:SAD_percent} \end{figure} Sepsis often shares symptoms with other disease processes making discrimination challenging. To evaluate the appropriateness of the constructed SADs the percentage of SAD occurrence (within the selected time window) was calculated for both septic and non-septic patients and can be seen for both years in Figure~\ref{fig:SAD_percent}. It is expected that SADs would be present in both cohorts; however, the Sepsis-3 cohort demonstrated patterns showing a closer relationship with the SADs than the Non-Septic cohort. \begin{figure}[!htp] \centerline{ \includegraphics[width = .45\textwidth]{tex_files/DAG_Hawkes/realdata/mat_sep1_plus.pdf} \includegraphics[width = .45\textwidth]{tex_files/DAG_Hawkes/realdata/mat_full_plus.pdf} } \caption{Adjacency matrices of the Granger Causal graphs for Sepsis-3 (left) and full (right) patient cohorts in Figure~\ref{fig:graph}. ``+'', ``++'' and ``+++'' correspond to the (absolute) value in $(0,.0005)$, $[.0005,.001)$ and $[.001,\infty)$, respectively, where the original values in the adjacency matrices are reported in Figures~\ref{fig:mat_num_sep} and \ref{fig:mat_num_full} in the Appendix. Nodes (i.e., SADs or SAEs) named along the X-axis can have either an inhibitory (red) or promoting effect (blue) on the nodes named in the Y-axis.} \label{fig:mat_plus} \end{figure} \noindent {\it Recovering the GC graph.} To study the temporal interactions between SADs (and other SAEs), we fit two GC graphs --- one graph is on Sepsis-3 cohort and the other is on full patient cohort (i.e.,the Sepsis-3 and Non-Septic cohorts combined). We report the results in Figure~\ref{fig:mat_plus} and defer the training details to Appendix~\ref{appendix:realdata_GC}. Both graphs demonstrate examples of clinically reasonable interactions between individual SADs (i.e.,Oxygen Diffusion Dysfunction promotes Renal Dysfunction in the Septic cohort) and between SADs and Sepsis (i.e.,Diminished Cardiac Output promotes Sepsis in both graphs). Interestingly the graph examining only the Sepsis-3 cohort identified more interactions between SADs than the one for the full patient cohort whereas the graph for the full patient cohort presented a higher number of strong relationships between SADs and sepsis suggesting that a time dependent, causal relationship exists between individual SADs and sepsis. A key finding across both graphs was the inhibitory effect of antibiotics on most SADs, which is consistent with the known ability of antibiotics to reduce in hospital mortality in sepsis patients \citep{seymourTimeTreatmentMortality2017} presumably through preventing organ dysfunction like those identified via SADs. While most of the relationships identified in these graphs are expected or feasible, vassopressors appear to unexpectedly inhibit both sepsis and the administration of antibiotics. In year 2018, among 409 (960) selected septic (non-septic) patients, there were 15 (96) who receive vasopressor support and 84 (231) who received antibiotics during the window, and only 3 (38) who received both vassopressors and antibiotics. This low number of vassopressor patients in the Sepsis-3 cohort is not unexpected as the time window for analysis is 24 hours prior to meeting the Sepsis-3 definition when most patients are not severely ill (see Appendix~\ref{appendix:lab_vital_SAD} for more details). Additionally, antibiotics are dosed on scheduled intervals (e.g.,once every six hours) whereas vassopressors are administered in a continuous fashion. These two attributes of the data set create a number of instances where vassopressors are administered without a formal antibiotic administration event in the following hour (though the patient may be on antibiotics). Additionally, each patient in the Sepsis-3 cohort is right censored after sepsis which means there is only one hour where the sepsis label is positive. Taken together these attributes of the data set likely explain why this unexpected relationship is seen. \noindent {\it Identifying the GC chain.} The recovered GC graphs help reduce the problem of enumerating combinatorially many possible chains to finding the chains that only exist in the Sepsis-3 graph. However, even for a 2-by-2 sub-adjacency matrix, there could be multiple potential chain interpretations. We validate whether or not the chain structure reflects a unique pattern in Sepsis-3 cohort by performing Fisher's exact test and report the $p$-value. Here, we only focus on ``++'' and ``+++'' exciting effect when forming all possible chains. This method allows chains to be ranked in order of significance, affording those with domain expertise an efficient mechanism to inspect results. We report the top GC chains which are unique in the Sepsis-3 cohort for years 2018 (in-sample test) and 2019 (out-of-sample test) in Table~\ref{table:chain}. More details on those chains (including how to perform the test) and more identified chains can be found in Appendix~\ref{appendix:realdata_chain}. \begin{table}[!htp] \caption{Granger causal chains which are significantly unique in Sepsis-3 cohort in both years 2018 and 2019.}\label{table:chain} \begin{center} \begin{small} \begin{sc} \resizebox{0.6\textwidth}{!}{% \begin{tabular}{crcccc} \toprule[1pt]\midrule[0.3pt] Chain: & TissueIsch & $\rightarrow$ & O2DiffDys \\ P-val: & \multicolumn{2}{c}{{ 0.004 (2018)}} & \multicolumn{2}{c}{{ 0.092 (2019)}} \\ \cmidrule(l){1-6} Chain: & O2DiffDys & $\rightarrow$ & RenDys & $\rightarrow$ & O2DiffDys \\ P-val: & \multicolumn{2}{c}{{ 0.107 (2018)}} & \multicolumn{2}{c}{{ 0.004 (2019)}} \\ \cmidrule(l){1-6} Chain: & VasoSprt & $\rightarrow$ & TissueIsch & $\rightarrow$ & HepatoDys \\ P-val: & \multicolumn{2}{c}{{ 0.052 (2018)}} & \multicolumn{2}{c}{{ 0.088 (2019)}} \\ \cmidrule(l){1-6} Chain: & LyteImbal & $\rightarrow$ & Acidosis & $\rightarrow$ & O2DiffDys \\ P-val: & \multicolumn{2}{c}{{ 0.009 (2018)}} & \multicolumn{2}{c}{{ 0.088 (2019)}} \\ \cmidrule(l){1-6} Chain: & Acidosis & $\rightarrow$ & O2DiffDys & $\rightarrow$ & HypGly \\ P-val: & \multicolumn{2}{c}{{ 0.039 (2018)}} & \multicolumn{2}{c}{{ 0.063 (2019)}} \\ \midrule[0.3pt]\bottomrule[1pt] \end{tabular} } \end{sc} \end{small} \end{center} \end{table} In Table~\ref{table:chain}, the chains possess a statistically strong relationship with patients in the Sepsis-3 cohort and correlate with clinical patterns that are often seen in sepsis. For example, Oxygen Diffusion Dysfunction (i.e., low oxygen saturation in the blood) is found to promote Renal Dysfunction and subsequent Oxygen Diffusion Dysfunction. Though not reflected in this table, septic patients could experience multiple chains simultaneously in addition to experiencing other discrete SADs simultaneous to events in a chain. This method to select and rank chains affords clinicians the ability to efficiently discover or follow those temporal patterns that differentiate septic patients from those experiencing organ injury caused by other diseases. \section{Discussion}\label{sec:discussion} To conclude this paper, we briefly summarize the contribution and limitations of current work in this section. Our proposed method for Granger causal chain discovery provides a novel and scalable way to leverage clinical expertise to elucidate patterns of interest amongst large amounts of related EMR data. Though we do not build or validate a clinical alarm, this is very useful and logical extension of this work. Additionally, knowledge from the GC chains could be used to estimate risk of a future SAD (e.g., Renal Dysfunction) which might prompt a clinician to alter treatment (e.g., modify IV fluids therapy). A limitation of this work stems from the grouped nature of many lab results and vital sign measurements. It is not uncommon for multiple patient features to be recorded in the EMR with identical timestamps which means that multiple SADs can occur simultaneously. This presents challenges to our point process model which can not capture relationships between simultaneously occurring SADs. This could be remedied by incorporating second or third order interaction effect in ANOVA into the work to evaluate the effect of combined SADS on future patient states. Another limitation of the method arises from the way treatments are administered. Some treatments (i.e., antibiotics) are dosed on an interval whereas others (i.e., vasopressors) are dosed continuously. This results in a higher number of ``vasopressor'' events than antibiotic events for certain patients and can lead to the false conclusion that vasopressors are inhibiting antibiotics which is not an expected finding. Future solutions could include representing antibiotics as a continuous medication similar to vasopressors so that the continuous effects of antibiotics are appreciated by the model. From a modelling perspective an obvious drawback of Granger Causality is pointed out by \citet{eichler2010granger}, namely that $A$ Granger-causes $B$ does not imply that intervening in $A$ would affect (the distribution on) $B$. A famous example is that the purchase of Christmas trees Granger-causes Christmas but this is clearly not the case. Another example is that disease $B$ will lead to symptom $A$, say fever. Typically a person will first observe $A$ and after diagnostic testing be diagnosed with $B$. Therefore, we should expect $A$ Granger-caused $B$; however, we should not expect that taking fever reducing medication (e.g., Tylenol), will help cure disease $B$ (though it will alter the value of $A$). This issue could be fixed in two possible ways: First, we should NOT treat the observed time as the exact event occurrence time. Instead, the exact occurrence time could be earlier than this observed time. By incorporating this time uncertainty, perhaps we can infer the true causal structure. Second, we can try to conduct counterfactual analysis by sampling counterfactual trajectories. This might be a direct application of \citet{noorbakhsh2021counterfactual}, though we may need to extend this work to multivariate setting. Moreover, our simple linear MHP fails to perform the sequential prediction task. This could be explained by the over-simplification of our model: on one hand, the dynamics within human body is too complex to be captured by simple linear relationship; on the other hand, exponential decaying kernel is problematic since an abnormal lab test result or vital sign for a small time period is ``acceptable'' whereas prolonged abnormality/dysfunction could lead to severe problem. Therefore, properly choosing the decaying kernel is very important. Nevertheless, since (1) it is easy to develop a scalable method to fit a simple model and (2) we do demonstrate its usefulness in identifying unique chain pattern in a real data experiment, we believe this is still a meaningful contribution to literature. Future work on how to utilize such chain patterns to perform sequential prediction, or how to use more complex yet explainable models (e.g., \citet{wei2021inferringb}) to fulfill such prediction purpose, needs to be done. Lastly, from the optimization perspective, we only give a heuristic, i.e., our proposed two-phase algorithm, that works well in practice. Reformulating the problem via Lagrangian duality and using projected gradient descent to solve the dual problem could both work well in practice and enjoy strong convergence guarantee in theory. To be precise, the expansive projection for primal variables onto feasible region $\Theta$ \eqref{eq:feasible_region} is reduced to the simple projection for dual variables onto $\mathbb{R}_+^{d \times d}$. Moreover, it is also worthwhile (numerically) explore the effect of other structures/regularizations on adjacency matrix, e.g., DAG structure \citep{zheng2018dags,ng2020role} or low-rank structure \citep{fang2020low}. \newpage \bibliographystyle{plainnat} \section{Introduction} Automated surveillance tools for identifying hospitalized patients' deterioration conditions are becoming more common, enhancing a clinician's situational awareness. We are particularly interested in sepsis prediction, which is a life-threatening medical condition contributing to one in five deaths globally \citep{world2020global} and stands as one of the most important cases for automated in-hospital surveillance. Sepsis is formally defined as life-threatening organ dysfunction caused by a dysregulated host response to infection \citep{singer2016third}. Delays in recognizing sepsis and initiating appropriate treatment can adversely impact patient outcomes. In a recent study of adult sepsis patients, each hour of delayed treatment was associated with higher risk-adjusted in-hospital mortality (odds ratio, 1.04 per hour) \citep{seymourTimeTreatmentMortality2017}. It stands to reason that early recognition of the physiologic aberrations preceding sepsis would afford clinicians more time to intervene and may contribute to improving outcomes and reducing costs. Many machine learning methods have been developed to predict the onset of sepsis, utilizing data from the electronic medical record (EMR) \citep{fleuren2020machine}. A recent sepsis prediction competition \citep{reyna2019early} demonstrated both the popularity and robust performance of XGBoost models \citep{du2019automated,zabihi2019sepsis,yang2020explainable}; meanwhile, Deep Neural Networks \citep{shashikumarDeepAISEInterpretableRecurrent2021} are also commonly used. However, most approaches offer an alert adjudicator very little information pertaining to the reasons for the alert/prediction, leading many to refer to them as ``black box'' techniques. Thus, model predictions related to disease identification, particularly for complex diseases, still need to be adjudicated (i.e., interpreted) by a clinician before further action (i.e., treatment) can be initiated. Among the aforementioned works, \citet{yang2020explainable} provided one of the best attempts at identifying causality for their models' predictions by reporting feature importance at a global level for all patients; still, this does not convey which features were most important in arriving at a given prediction for an individual patient. The common lack of interpretability of many clinical models, particularly those related to sepsis, suggests a strong need for principled methods (with theoretical guarantee) to study the interactions among time series in medical settings. \begin{figure}[!htp] \centerline{ \includegraphics[width = 0.45\textwidth]{fig/network_graph/new_network.pdf} } \vspace{-0.1in} \caption{Granger Causal graph over endogenous Sepsis Associated Derangement (SAD) indicators obtained via Discrete Hawkes Network with forward feature selection.} \label{fig:new_net_structure} \vspace{-0.1in} \end{figure} One approach to obtain interpretable predictive models for sepsis is to consider its syndromic nature --- there is often a constellation of different physiologic derangements that can combine to create the condition. Figure~\ref{fig:new_net_structure} shows a series of different nodes representing these types of physiologic derangements. For example, a clinical adjudicator may be more inclined to arrive at a concordant opinion regarding sepsis if they know that the alert was caused by the combined effects from the Renal Injury and Diminished Cardiac Output nodes. Likewise, this same adjudicator might be less inclined to corroborate an alert on a different patient if the main contributing cause was from Electrolyte Imbalance alone. In modeling relationships between nodes and their effect on sepsis, a natural approach is through {\it Granger causal graphs}, which analyze the interactions among time series. A popular approach to capture Granger causal graph is the Linear Vector Autoregressive (VAR) model \citep{lutkepohl2005new}. However, it has been recognized that traditional time series models such as VAR have many limitations, including linearity and assuming continuous-valued observations \citep{shojaie2021granger}. However, the observations can be continuous and categorical-valued in many real applications, including medical data. Moreover, the traditional time series model such as VAR assumes that the observations are synchronous and indexed by integers. In the medical setting, the observations can be both discrete and continuous-valued, and they can also be asynchronous and sampled with different frequencies. For example, vital signs are recorded regularly, whereas laboratory (lab) tests are only ordered when clinically necessary; thus, this cannot be simply formulated into a missing data problem In this paper, we present a new Granger causal graph based on the generalized linear model (GLM) to handle observations that are (i) asynchronous and (ii) mixed type (real-valued, integer-valued, binary, or categorical valued). The model estimation is achieved by solving a monotone operator variation inequality problem, a general convex optimization problem. This approach also enables us to establish performance guarantees via recent advances in optimization \citep{juditsky2019signal,juditsky2020convex}. In particular, we develop (i) a sharp non-asymptotic upper bound on estimation error verified by numerical examples and (ii) quantifiable uncertainty by establishing confidence interval for the estimated graph structure by solving a linear program. We demonstrate via real data experiments that our proposed GLM with forward-feature selection can achieve comparable performance to a powerful method such as XGBoost. Moreover, our learned Granger causal graph is highly interpretable, thus making the future adoption of these models to conduct continuous surveillance of high-risk patients by clinicians much more likely. Here, we demonstrate the effectiveness of our approach in learning a Granger causal graph over Sepsis Associated Derangements (SADs), but it can be generalized to other applications with similar requirements. {\textbf{Related work. }} Recent advancements on the Granger causal graph mainly focus on non-linear dynamics and tackling high-dimensionality via regularization: the former includes applying a separable matrix-valued kernel \citep{sindhwani2012scalable} and neural networks \citep{tank2018neural} to learn non-linear Granger causality; other approaches address the high-dimensionality caused by viewing all series as endogenous. Techniques include group Lasso \citep{bolstad2011causal,basu2015network} and nuclear norm regularization \citep{basu2019low}. Another notable work \citep{nicholson2017varx} modeled endogenous and exogenous variables separately (instead of treating all series endogenous) and used different penalties on endogenous and exogenous variables to learn the sparse graph structure. Our method closely resembles \citet{nicholson2017varx} in the following sense: part of features comes from direct observations and is treated exogenous (e.g., vital signs and lab test results), whereas the remaining SADs are derived from the first part and viewed as endogenous. We also want to emphasize that, even though our model is stationary and becomes a Markov process when we only consider one-step memory, it is different from Markov Chain because we avoid defining the state space. This is beneficial since (1) the state space is enormous since each state is a binary representation of whether or not each node variable is ``on''; (2) learning a smaller (latent) state-space from data \citep{alaa2017learning} would sacrifice the interpretability of the model. \begin{table}[!htp] \vspace{-0.2in} \caption{SAD construction based on thresholding exogenous observations via medical knowledge.}\label{table:node_construction} \begin{center} \begin{small} \begin{sc} \resizebox{.82\textwidth}{!}{% \begin{tabular}{llccc} \toprule[1pt]\midrule[0.3pt] SAD name & Measurement name & Physionet name & Rule & Risk score \\ \midrule[0.3pt] \textbf{ Renal Injury} & creatinine & Creatinine & >1.3 & 0.667 \\ & potassium & Potassium & >5.0 & 0.067 \\ & phosphorus & Phosphate & >4.5 & 0.067 \\ & bicarb (hco3) & HCO3 & >26 & 0.067 \\ & blood urea nitrogen (bun) & BUN & >20 & 0.133 \\ \cmidrule(l){2-5} \textbf{Electrolyte} & calcium & Calcium & >10.5 & 0.167 \\ \textbf{Imbalance} & chloride & Chloride & <98 or >106 & 0.667 \\ & magnesium & Magnesium & <1.6 & 0.167 \\ \cmidrule(l){2-5} \textbf{Oxygen Carrying} & hematocrit & Hct & <37 & 0.500 \\ \textbf{Dysfunction} & hemoglobin & Hgb & <12 & 0.500 \\ \cmidrule(l){2-5} \textbf{Shock} & base excess & BaseExcess & < $-$3 & 0.100 \\ & lactic acid & Lactate & >2.0 & 0.150 \\ & ph & pH & <7.32 & 0.750 \\ \cmidrule(l){2-5} \textbf{Diminished } & sbp cuff & SBP & <120 & 0.250 \\ \textbf{Cardiac Output} & dbp cuff & DBP & <80 & 0.250 \\ & map cuff & MAP & <65 & 0.500 \\ \cmidrule(l){2-5} \textbf{Coagulopathy} & partial prothrombin time (ptt) & PTT & >35 & 0.250 \\ & fibrinogen & Fibrinogen & <233 & 0.250 \\ & platelets & Platelets & <150,000 & 0.500 \\ \cmidrule(l){2-5} \textbf{Cholestasis} & bilirubin direct & Bilirubin direct & >0.3 & 0.100 \\ & bilirubin total & Bilirubin total & >1.0 & 0.500 \\ & alkaline phosphatase & Alkalinephos & >120 & 0.400 \\ \cmidrule(l){2-5} \textbf{Hepatocellular Injury} & aspartate aminotransferase (ast) & AST & >40 & 1.000 \\ \cmidrule(l){2-5} \textbf{Oxygenation } & unassisted resp rate & Resp & >20 & 0.100 \\ \textbf{Dysfunction} & spo2 & O2Sat & <92 \% & 0.200 \\ & saturation of oxygen (sao2) & SaO2 & <92 \% & 0.200 \\ & end tidal co2 & EtCO2 & <35 or >45 & 0.100 \\ & fio2 & FiO2 & >21 \% & 0.300 \\ & partial pressure of carbon dioxide (paco2) & PaCO2 & <35 or >45 & 0.100 \\ \cmidrule(l){2-5} \textbf{Inflammation} & temperature & Temp & <36 or >38 & 0.400 \\ & pulse & HR & >90 & 0.100 \\ & glucose & Glucose & >125 & 0.100 \\ & white blood cell count & WBC & <4,000 or >12,000 & 0.400 \\ \midrule[0.3pt]\bottomrule[1pt] \end{tabular} } \end{sc} \end{small} \end{center} \vspace{-0.25in} \end{table} \vspace{-0.1in} \section{Data and Problem Set-up}\label{sec:background} \vspace{-0.05in} We start by presenting the data for sepsis prediction, which will motivate our model development. Data used for this analysis was a curated, publicly available data set from the 2019 Physionet challenge \citep{physionet2019}. The challenge data was sourced from patients admitted to the Intensive Care Unit (ICU) during their hospitalization and represented three categories of patient features: vital sign measurements, Laboratory (Lab) results, and demographic information. \vspace{-0.03in} { \it Vital Signs.} Vital signs in ICU environments are normally recorded at an hourly interval and include \texttt{HR, O2Sat, Temp, SBP, MAP, DBP, Resp} (see Table~\ref{table:node_construction} for their full measurement names). Among the blood pressure measurements (\texttt{SBP}, \texttt{DBP}, and \texttt{MAP}), we only keep \texttt{MAP} in our study since \texttt{MAP} = (\texttt{SBP} + 2\texttt{DBP})$/3$. \vspace{-0.03in} { \it Lab Values.} Lab tests are most commonly collected once every 24 hours; however, this collection frequency may change based on the severity of a patient's illness. In addition to individual Lab values, we also use the count of the Lab tests over the past 6 hours as a proxy to represent the severity of a patient's illness (i.e., more severe disease results in more tests being ordered). \vspace{-0.03in} { \it Sepsis Associated Derangements (SADs).} Thresholds representing breaks between normal and deranged physiology are identified utilizing already established criteria \citep{ABIM_ref_range}. We condense different measurements (containing both vital signs and Lab results) into a binary variable as an indicator of physiologic derangements seen preceding and during sepsis (see column ``SAD name'' in Table~\ref{table:node_construction}). { \it Demographic information.} Demographic features remain constant throughout hospitalization. The examined data set contains both age and sex. Here, the vital signs (regularly sampled) and raw Lab values (irregularly sampled) are exogenous variables, whereas SAD indicators are endogenous. The irregularly sampled series will be handled via forwarding filling. Our primary interest is to study all exogenous and endogenous series' effects on endogenous series and construct (Granger causal) graph/network over endogenous series. \vspace{-0.1in} \section{Discrete Hawkes Networks} \vspace{-0.05in} \subsection{Formulation} Given $N_1$ observed sequences of binary SADs over a time horizon $T$: $\{y_1^{(i)},\dots,y_T^{(i)}\}$, $i = 1,\dots,N_1$. We also observe both continuous and discrete-valued time series $\{x_1^{(i)},\dots,x_T^{(i)}\}, i = 1,\dots,N_2$, which can correspond to vital signs and Lab test counts, and demographic variables $(z_1,\dots,z_{N_3})$. In the following, we will refer to each SAD variable as a node since it corresponds to a node in the Granger causal graph. To model the mutual inter-dependence among the variables, we consider a generalized linear model (GLM), which closely resembles the intensity function of Hawkes point process \citep{hawkes1971point,hawkes1971spectra,hawkes1974cluster}. For the $i$-th node variable ($i = 1,\dots,N_1$), at time step $t \ (t = 2,\dots,T)$, we assume: \vspace{-0.1in} \begin{align}\label{eq:hawkes_model} \PP \Big( & y_t^{(i)} =1 \Big\| \cH_{t-1} \Big) = g\Bigg(\nu_i + \sum_{j = 1}^{N_3} \gamma_{ij} z_j \\ & + \sum_{\tau = 1}^{t-1} \bigg( \sum_{j = 1}^{N_2} \beta_{ij} x_{t-\tau}^{(j)} e^{-\Tilde{R}_{ij} \tau} + \sum_{j = 1}^{N_1} \alpha_{ij} y_{t-\tau}^{(j)} e^{-R_{ij} \tau}\bigg)\Bigg), \nonumber \end{align} where $\cH_t$ denotes the past observation up to time $t$ and $g: \RR \rightarrow [0,1]$ is a link function. For example, $g$ can be non-linear, such as sigmoid link function $g(x) = 1/(1+e^{-x})$; also, it can be linear $g(x) = x$ on domain $x \in [0,1] \subset \RR$. {\it Non-linear Granger causal graph.} By the definition of Granger causality in non-linear model \citep{tank2018neural}, matrix $A = (\alpha_{ij}) \in \RR^{N_1 \times N_1}$ represents the causal graph structure over $N_1$ SAD nodes. To be precise, $j$-th SAD does NOT Granger cause $i$-th SAD if $\alpha_{ij} = 0$. {\it Connection to Hawkes process.} For $i$-th SAD node variable, $\alpha_{ij}$ and $\beta_{ij}$ represent the magnitude of triggering effect of $j$-th SAD node variable and continuous variable to it. This effect decays exponentially fast with exponent characterized by $R_{ij}$ and $\Tilde{R}_{ij}$. $\gamma_{ij}$'s represent the influence of demographics and contribute to baseline intensity togerther with $\nu_i$. Note that the above model can be viewed as a discretized version of (non-linear) Hawkes process network with exponential triggering function \citep{wang2020uncertainty}; other methods in learning Discrete Hawkes Network include \citet{xu2016learning,achab2017uncovering}, we do not dig deeper in this direction since it is out of the scope of this work. \vspace{-0.1in} \subsection{Estimation} \vspace{-0.05in} In this section, we will leverage a recently developed technique \citep{juditsky2019signal,juditsky2020convex}, which estimates the parameters of the generalized linear model by solving stochastic monotone variational inequality (VI), to develop a statistically principled method to estimate the parameters of Discrete Hawkes Network and infer the Granger causal graph topology. {\it Preliminaries.} To begin with, we make reasonable simplification by assuming finite memory depth $d$ for both continuous and binary observations. Let $w_{t-d}^{t-1}$ denote the observation from $t-d$ to $t-1$: $\big(1,z_1,\dots,z_{N_3},x_{t-1}^{(1)},\dots,x_{t-d}^{(1)},\dots,x_{t-1}^{(N_2)},\dots,x_{t-d}^{(N_2)},y_{t-1}^{(1)},$ $\dots,y_{t-d}^{(1)},\dots,y_{t-1}^{(N_1)},\dots,y_{t-d}^{(N_1)}\big)^{ \mathrm{\scriptscriptstyle T} },$ where superscript $^{ \mathrm{\scriptscriptstyle T} }$ denotes matrix transpose. Since we only consider finite memory depth for binary observation, we could use one single parameter $\alpha_{ij\tau} := \alpha_{ij} \exp\{-R_{ij} \tau\}$ (similarly, $\beta_{ij\tau} := \beta_{ij} \exp\{-\Tilde{R}_{ij} \tau\}$) to represent the triggering effect with exponential decay. We rewrite \eqref{eq:hawkes_model} into: for $i = 1,\dots,N_1,$ \vspace{-0.06in} \begin{equation}\label{eq:model} \PP\left(y_t^{(i)}=1 \Big\| w_{t-d}^{t-1} \right) = g\left((w_{t-d}^{t-1})^{ \mathrm{\scriptscriptstyle T} } \theta_i\right), \quad t = d+1,\dots,T, \end{equation} where $\theta_i \in \RR^N$ ($N = 1+N _3+dN_2+dN_1$) is the parameter to be estimated: $\theta_i = (\nu_i,\gamma_{i1},\dots,\gamma_{iN_3},\beta_{i11},\dots,\beta_{i1d},$ $\beta_{iN_21},\dots,\beta_{iN_2d},\alpha_{i11},\dots,\alpha_{i1d},\alpha_{iN_11},\dots,\alpha_{iN_1d})^{ \mathrm{\scriptscriptstyle T} }.$ This parameter summarizes the influence from all variables to node $i$ and could be estimated independently from the remaining $N_1-1$ parameters. {\it Granger Causality.} We can see \eqref{eq:model} is actually a generalized linear version of Vector Autoregressive (VAR) model. Therefore, we say $j$-th node series $\{y^{(j)}_t\}$ (or vital sign series $\{x^{(j)}_t\}$) Granger-causes $i$-th node series $\{y_t^{(i)}\}$ if $\alpha_{ij\tau} \not= 0$ (or $\beta_{ij\tau} \not= 0$) for some $\tau \in \{1,\dots,d\}$. {\it Estimation with variational inequality.} Denote the observation by $W_{T}:=(w_{1-d}^{0},\dots,w_{T-d+1}^{T}) \in \RR^{(T+1) \times N}$, where variables observed at time step $1-d,\dots,0$ are viewed as given history. We assume parameter $\theta_i$ is constrained in a convex compact set $\theta_i \in \Theta_i \subset \RR^N$, then, for $i = 1,\dots,N_1$, we use the weak solution to the following variational inequality as the estimator $\hat \theta_i$: \vspace{-0.15in} \begin{equation} \text {find } \hat \theta_i \in \Theta_i:\langle F_{ W_{T}}^{(i)}(\theta), \theta-\hat \theta_i\rangle \geq 0, \ \forall \theta \in \Theta_i, \label{VI_1}\tag{{VI}$[ F_{W_{T}}^{(i)}, \Theta_i]$} \end{equation} \vspace{-0.1in} where $F_{W_{T}}^{(i)}(\theta_i)$ is the empirical vector field and defined as: \vspace{-0.3in} $$F_{W_{T}}^{(i)}(\theta_i) := \frac{1}{T} \sum_{t=1}^T w_{t-d}^{t-1} \left( g\left((w_{t-d}^{t-1})^{ \mathrm{\scriptscriptstyle T} } \theta_i\right) - y_t^{(i)} \right).$$ \vspace{-0.2in} \paragraph{Remarks.} (i) The intuition behind this method is straightforward. Let's consider the global counterpart of the above vector field, whose root is the unknown ground truth $\theta_{0,i}$, \vspace{-0.25in} \begin{align} F^{(i)}(\theta_i) :=& \EE_{(w,y^{(i)})} \left[w \left( g\left(w^{ \mathrm{\scriptscriptstyle T} } \theta_i\right) - y^{(i)} \right)\right] \\ =& \EE_{(w,y^{(i)})} \left[w \left( g\left(w^{ \mathrm{\scriptscriptstyle T} } \theta_i\right) - g\left(w^{ \mathrm{\scriptscriptstyle T} } \theta_{0,i}\right) \right)\right]. \end{align} \vspace{-0.1in} Although we cannot access this global counterpart, by solving the empirical one \ref{VI_1} we could approximate the ground truth very well. We will show how well this approximation would be in the next section. (ii) Least Square Estimation for Linear VAR model and Maximum Likelihood Estimation for logistic regression model are both special cases of our proposed VI estimates. One can see detailed derivations in Appendix~\ref{appendix:eg}. \vspace{-0.1in} \section{Non-asymptotic Performance Guarantees} \vspace{-0.05in} In this section, we show the VI estimate will eventually converge to a very small neighborhood of the ground truth. Besides, we will derive a linear program (LP) based confidence interval (CI) of parameters $\theta_i$'s. {\it Non-asymptotic bound on estimation error.} To begin with, we state two necessary model assumptions: \begin{assumption}\label{assumption:vector_field} The link function $g(\cdot)$ is continuous and monotone, and the vector field $G(\theta) = \EE_w[wg(w^{ \mathrm{\scriptscriptstyle T} }\theta)]$ is well defined (and therefore monotone along with $g$). Moreover, $g$ is differentiable and has uniformly bounded first order derivative $m_g \leq \|g'\|\leq M_g$ for $0<m_g\leq M_g$. \end{assumption} \begin{assumption}\label{assumption:observation} The observations (static, binary and continuous) are bounded almost surly: $\exists M_w>0$ such that at any time step $t$, we have $\norm{w_{t-d}^{t-1}}_\infty \leq M_w$ with probability one. \end{assumption} We define an auxiliary vector field defined as $\Tilde{F}_{W_{T}}^{(i)}(\theta_i) := \frac{1}{T} \sum_{t=1}^T w_{t-d}^{t-1} \left( g\left((w_{t-d}^{t-1})^{ \mathrm{\scriptscriptstyle T} } \theta_i\right) - g\left((w_{t-d}^{t-1})^{ \mathrm{\scriptscriptstyle T} } \theta_{0,i}\right) \right).$ This vector field changes the constant term in ${F}_{W_{T}}^{(i)}(\theta_i)$ to make sure its unique root/weak solution to corresponding VI is the unknown ground truth $\theta_{0,i}$. Recall that $\hat \theta_i$ is the root of ${F}_{W_{T}}^{(i)}(\theta_i)$. Then, we will bound the difference between $\hat \theta_i$ and $\theta_{0,i}$ via the difference between ${F}_{W_{T}}^{(i)}(\theta_i)$ and $\Tilde{F}_{W_{T}}^{(i)}(\theta_i)$: $$\Delta^{(i)} := {F}_{W_{T}}^{(i)}(\theta_i) - \Tilde{F}_{W_{T}}^{(i)}(\theta_i) = {F}_{W_{T}}^{(i)}(\theta_{0,i}).$$ \begin{proposition}\label{lma:bound_delta} Under Assumptions~\ref{assumption:vector_field} and \ref{assumption:observation}, for $i = 1,\dots,N_1$, $\forall \ \varepsilon \in (0,1)$, with probability at least $1-\varepsilon$, the difference between the empirical and auxiliary vector field $\Delta^{(i)}$ can be bounded as follows: \begin{equation}\label{eq:bound_inf} \norm{\Delta^{(i)}}_\infty \leq M_w \sqrt{{\log(2N/\varepsilon)}/{T}} \end{equation} Moreover, this implies \begin{equation}\label{eq:bound_l2} \norm{\Delta^{(i)}}_2 \leq M_w \sqrt{N{\log(2N/\varepsilon)}/{T}}. \end{equation} \end{proposition} \textbf{Remark.} The proof leverages the concentration property for martingales. Similar results could also be found in \citet{juditsky2020convex,wei2021inferring}. We defer its proof to Appendix~\ref{appendix:proof}. We want to remark that further improvement can be achieved by Bernstein inequality (as in \citet{juditsky2020convex}), but the rate remains the same. \begin{theorem}[Upper bound on $\norm{\hat \theta_i - \theta_{0,i}}_2$]\label{thm:upper_err_bound} Under Assumptions~\ref{assumption:vector_field} and \ref{assumption:observation}, for $i = 1,\dots,N_1$ and any $\varepsilon \in (0,1)$, with probability at least $1-\varepsilon$, the $\ell_2$ distance between ground truth $\theta_{0,i}$ and $\hat \theta_i$, which is weak solution to \ref{VI_1}, can be upper bounded as follows : $$\norm{\hat \theta_i - \theta_{0,i}}_2 \leq \frac{M_w}{m_g \lambda_1} \sqrt{\frac{N\log (2N/\varepsilon)}{T }},$$ where where $\lambda_1$ is the smallest eigenvalue of $\mathbb{W}_{1:T} = \sum_{t=1}^T w_{t-d}^{t-1}(w_{t-d}^{t-1})^{ \mathrm{\scriptscriptstyle T} }/T$. \end{theorem} \textbf{Remarks.} (i) The above theorem is an extension to the general link function case of Theorem 1 \citep{juditsky2020convex}, where they only sketched the proof without giving further details; we defer the detailed proof to Appendix~\ref{appendix:proof}. (ii) As pointed out in \citet{juditsky2020convex}, $\mathbb{W}_{1:T} \in \RR^{N \times N}$ will be full rank when $T$ is sufficiently large, i.e., with high probability, $\lambda_1$ will be a positive constant. {\it Linear Program-based confidence interval.} As pointed out in section II.E \citep{juditsky2020convex}, for general non-linear link function $g$, it would be hard to separate $\theta_i$ from $\sum_{t=1}^T w_{t-d}^{t-1} g\left((w_{t-d}^{t-1})^{ \mathrm{\scriptscriptstyle T} } \theta_i\right)/T$. First, we derive a CI for linear link function case via a more precise data-driven bound for $F_{W_{T}}^{(i)}(\theta_i)\in \RR^N$ as \citet{juditsky2020convex} did in Lemma 2 (see its proof in Appendix~\ref{appendix:CI}): \begin{proposition}[Confidence interval for linear transform of $\theta_i$ for linear link function case]\label{prop:CI} Under Assumptions~\ref{assumption:vector_field} and \ref{assumption:observation}, for $i = 1,\dots,N_1$, and every $s > 1$, the following holds with probability at least $1-2N\{s[\log((s-1)T)+2] + 2\} e^{1-s}$: $$\theta_\ell[W_T,s;i] \leq a^{ \mathrm{\scriptscriptstyle T} } \theta_i \leq \theta_u[W_T,s;i], \quad \forall a \in \RR^N,$$where $\theta_\ell[W_T,s;i]$ and $\theta_u[W_T,s;i]$ are defined in \eqref{eq:CI_lower}, \eqref{eq:CI_upper}. \end{proposition} This CI is obtained by solving LPs \eqref{eq:CI_lower} and \eqref{eq:CI_upper}. For general non-linear link function $g$, since it is typically constrained in a compact subset to satisfy Assumption~\ref{assumption:vector_field} (see Example~\ref{eg:logistic} in Appendix~\ref{appendix:eg}), we can obtain linear bounds on the non-linear link function and then repeat the above techniques to obtain similar CI; details on this generalization can be found in Appendix~\ref{appendix:CI}. \vspace{-0.15in} \section{Synthetic Data Experiments} \vspace{-0.05in} In this section, we demonstrate the performance of our proposed model using a simple toy example. We fit the Granger causal graph over 5 binary node variables with sigmoid non-linear link function. We present the true network topology in first two figures in Figure~\ref{fig:simu_topo} and report the estimated topology via Discrete Hawkes Network in the last two figures in Figure~\ref{fig:simu_topo}. Further details, such as synthetic data generation process, are deferred to Appendix~\ref{appendix:num_simu}. \begin{figure}[!htp] \vspace{-0.1in} \centerline{ \includegraphics[width = 0.12\textwidth]{fig_num_simu/illus.pdf} \includegraphics[width = 0.12\textwidth]{fig_num_simu/exp1_true.png} \includegraphics[width = 0.12\textwidth]{fig_num_simu/exp1_n_500.png} \includegraphics[width = 0.12\textwidth]{fig_num_simu/exp1_n_5k.png} } \vspace{-0.1in} \caption{From left to right: true network topology (blue indicates positive effect and red indicates negative effect), true adjacency matrix, estimated Discrete Hawkes Network with $T = 500$ and $T = 5000$.} \label{fig:simu_topo} \centerline{ \includegraphics[width = 0.24\textwidth]{fig_num_simu/traj_3.pdf} \includegraphics[width = 0.24\textwidth]{fig_num_simu/loglog_3.pdf} } \vspace{-0.1in} \caption{Left: Trajectory for $\ell_2$ norm of estimation error and its data-driven bound. Right: log-log plot of estimation error and its bound; this shows that our bound is sharp in rate.} \label{fig:traj} \vspace{-0.05in} \end{figure} \begin{figure}[!htp] \vspace{-0.1in} \centerline{ \includegraphics[width = 0.25\textwidth,trim={4cm 0 2.8cm 0},clip]{fig/CI_graph/TP_thres_0.15_CI_new.pdf} \includegraphics[width = 0.25\textwidth,trim={4cm 0 2.8cm 0},clip]{fig/CI_graph/TP_thres_0.15_CI_old.pdf} \includegraphics[width = 0.25\textwidth,trim={4cm 0 2.8cm 0},clip]{fig/CI_graph/err_thres_0.15_CI_new.pdf} \includegraphics[width = 0.25\textwidth,trim={4cm 0 2.8cm 0},clip]{fig/CI_graph/err_thres_0.15_CI_old.pdf} } \vspace{-0.1in} \caption{From left to right: bootstrap network topology (1) with feature selection using TP rate for CV; (2) without feature selection using TP rate for CV; (3) with feature selection using classification error for CV; (4) without feature selection using classification error for CV. We only show edges whose weights are greater than 0.15. Color blue indicates positive effect whereas red indicates negative effect.}\label{fig:network_structure_CI_thres} \vspace{0.15in} \centerline{ \includegraphics[width = 0.25\textwidth,trim={4cm 0 2.8cm 0},clip]{fig/CI_graph/TP_CI_new.pdf} \includegraphics[width = 0.25\textwidth,trim={4cm 0 2.8cm 0},clip]{fig/CI_graph/TP_CI_old.pdf} \includegraphics[width = 0.25\textwidth,trim={4cm 0 2.8cm 0},clip]{fig/CI_graph/err_CI_new.pdf} \includegraphics[width = 0.25\textwidth,trim={4cm 0 2.8cm 0},clip]{fig/CI_graph/err_CI_old.pdf} } \vspace{-0.1in} \caption{From left to right: non-thresholding bootstrap network topology (1) with feature selection using TP rate for CV; (2) without feature selection using TP rate for CV; (3) with feature selection using classification error for CV; (4) without feature selection using classification error for CV. Color blue indicates positive effect whereas red indicates negative effect. The criterion for cross validation is true positive rate (left) and classification error (right).}\label{fig:network_structure_CI} \vspace{-0.15in} \end{figure} Since this network is sparse, we also impose $\ell_1$ penalty and the results are deferred to Figure~\ref{fig:simu_topo_l1}. From both figures, we can observe that when trajectory is long enough, we can faithfully recover the true network topology. Most importantly, we study the trajectories of the $\ell_2$ norm of the estimation error and the data-driven bound. Here, the data-driven bound requires us to calculate $\lambda_1$ and $m_g$ from the data. Since we consider simple binary r.v.s in our toy example, $M_w$ is one. We plot the trajectory for a particular node in Figure~\ref{fig:traj}. The results for the rest of the nodes are deferred to Figure~\ref{fig:traj_additional} in Appendix~\ref{appendix:num_simu}. From both figures (especially the slope in the log-log plot), we observe that our data-driven bound is sharp in rate, though the constant could be loose. This constant could be further improved by using Bernstein's inequality instead of Azuma's inequality, as commented in remark of Proposition~\ref{lma:bound_delta}. \vspace{-0.15in} \section{Real Data Experiments} \vspace{-0.05in} In Experiment 1, nodes in the network are constructed based on well-known, measurable, physiologic relationships in the human body. This expert-driven approach is subsequently compared to a purely data-driven model for identifying possible clusters of inpatient data in Experiment 2. \vspace{-0.1in} \subsection{Experiment 1}\label{subsec:exp1} \vspace{-0.05in} In the first experiment, we aim to learn network topology over nodes which are constructed based on known physiologic relationships. { \it Feature construction.} As previously described, vital sign measurements were condensed into single features represented by summary statistics (i.e., maximum, minimum, mean) of the past 6 hours, creating a total of 12 distinct representations of a patient's vital signs. A count of total Lab tests over the past 6 hours was used as a proxy for patient acuity and was also incorporated as a feature. SAD nodes were created by grouping all 34 Lab measurements into ten nodes (see Table~\ref{table:node_construction}), representative of common physiologic derangements seen in sepsis. Moreover, instead of constructing a sequence of binary variables for each node, we assigned a risk score at each time, indicating the severity of the SAD. However, when a variable (i.e., node) was used as the response during modeling, it was treated as binary by applying indicator function $\mathbf{1}_{\{y > 0\}}$. { \it Sub-group analysis.} To simplify model development, we carried out a sub-group analysis and excluded demographic features from the model. We used sex $= 0$ (female) and age $>60$ sub-group in the following to demonstrate our method, which contained 5,222 patients in the Physionet data set. {\it Model fitting.} The primary outcome of interest was sepsis, which necessitated the addition of an $11$-th binary time series called ``SepsisLabel'' to our data. This resulted in a total of $N_1 = 11$ nodes in our network. Using each of those $N_1$ variables as responses (recall that risk scores were binarized when used as a response) and the rest as features, we fitted our proposed model with sigmoid link function with hyperparameter being the number of training iterations and performed forward feature selection. The primary cross-validation (CV) criterion for both feature selection and hyperparameter tuning was the True Positive (TP) rate (classification accuracy for positive samples); we also compared classification error and AUC. TP rate was chosen because in a clinical setting, particularly as it pertains to sepsis, greater importance is placed on not missing the disease (i.e., maintaining a high sensitivity) as opposed to producing a false alert. \begin{table}[!htp] \vspace{-0.15in} \caption{Coefficients for Discrete Hawkes Network. For each node, from left to right, and from the first row to the second row, the order of feature follows the order in forwarding selection.}\label{table:model_coeff} \vspace{-0.15in} \begin{center} \begin{small} \begin{sc} \resizebox{1\textwidth}{!}{% \begin{tabular}{lcccccc} \toprule[1pt]\midrule[0.3pt] \textbf{ Renal Injury} & Oxygen Carrying Dysfunction & Diminished Cardiac Output & Oxygenation Dysfunction & Shock & Inflammation \\ (TP rate = 0.724) & 0.355 & 0.025 & 0.086 & 0.097 & 0.057 \\ \cmidrule(l){2-6} & Coagulopathy & Cholestasis \\ & 0.067 & 0.179 \\ \midrule \textbf{Electrolyte Imbalance} & Oxygen Carrying Dysfunction & Coagulopathy & HR (max) & Sepsis & Oxygenation Dysfunction \\ (TP rate = 0.705)& 0.330 & 0.261 & 0.016 & 0.065 & 0.073 \\ \cmidrule(l){2-6} & Inflammation \\ & 0.071\\ \midrule \textbf{Oxygen Carrying Dysfunction} & Renal Injury & Coagulopathy & Electrolyte Imbalance & Diminished Cardiac Output & Shock \\ (TP rate = 0.703) & 0.287 & 0.431 & 0.513 & 0.174 & -0.038 \\ \cmidrule(l){2-6} & Oxygenation Dysfunction & O2Sat min \\ & 0.039 & 0.139\\ \midrule \textbf{Shock} & Inflammation & Diminished Cardiac Output & HR (max) & Coagulopathy & Renal Injury \\ (TP rate = 0.673) & 0.088 & 0.234 & 0.324 & 0.350 & 0.190 \\ \cmidrule(l){2-6} & Electrolyte Imbalance & Oxygenation Dysfunction & ICULOS\\ & 0.294 & 0.148 & 0.097 \\ \midrule \textbf{Diminished Cardiac Output} & Electrolyte Imbalance & Shock & Inflammation & Hepatocellular Injury & Oxygen Carrying Dysfunction \\ (TP rate = 0.622) & 0.086 & 0.117 & 0.013 & 0.085 & 0.233 \\ \cmidrule(l){2-6} & Resp mean & Temp max\\ & -0.041 & 0.077\\ \midrule \textbf{Coagulopathy} & Hepatocellular Injury & Oxygen Carrying Dysfunction & Shock & Cholestasis & Sepsis \\ (TP rate = 0.632) & 0.173 & 0.211 & 0.238 & 0.215 & 0.019 \\ \cmidrule(l){2-6} & Electrolyte Imbalance & Renal Injury & HR (max) \\ & 0.259 & 0.144 & 0.020\\ \midrule \textbf{Cholestasis} & Shock & Hepatocellular Injury & HR (mean) & Renal Injury & Coagulopathy \\ (TP rate = 0.677)&-0.002 & 0.864 & 0.127 & 0.295 & 0.397 \\ \cmidrule(l){2-6} & Inflammation & Sepsis & ICULOS & Oxygenation Dysfunction\\ & -0.002 & 0.048 & 0.324 & 0.089\\ \midrule \textbf{Hepatocellular Injury} & Inflammation & Oxygen Carrying Dysfunction & Shock & Sepsis & Diminished Cardiac Output \\ (TP rate = 0.619) & 0.060 & 0.170 & 0.063 & 0.088 & 0.043 \\ \cmidrule(l){2-6} & Coagulopathy & MAP (min) & O2Sat min & Renal Injury \\ & 0.434 & 0.063 & 0.008 & 0.262 \\ \midrule \textbf{Oxygenation Dysfunction} & Sepsis & Inflammation & Resp (mean) & Shock & Diminished Cardiac Output \\ (TP rate = 0.780)& 0.093 & 0.047 & 2.538 & 0.699 & 0.237 \\ \cmidrule(l){2-6} & MAP min & Hepatocellular Injury\\ & 0.060 & 0.111\\ \midrule \textbf{Inflammation} & Sepsis & HR (max) & Renal Injury & Oxygenation Dysfunction & Shock \\ (TP rate = 0.710)& 0.099 & 1.597& 0.117 & 0.119 & 0.176 \\ \midrule \textbf{Sepsis} & HR (mean) & ICULOS& Renal Injury& Inflammation& Electrolyte Imbalance \\ (TP rate = 0.768)& 0.174& 0.722& 0.509& 0.165& 0.200 \\ \cmidrule(l){2-6} & Diminished Cardiac Output& Resp (min) & Coagulopathy\\ &0.387& 0.458& -0.104\\ \midrule[0.3pt]\bottomrule[1pt] \end{tabular} } \end{sc} \end{small} \end{center} \vspace{-0.3in} \end{table} \vspace{-0.1in} \paragraph{\it Comparison to XGBoost.} During the forward selection process, the TP rate goes from around 0.6 up to final 0.768 whereas the TP rate for using all features and subset selection based on random forest feature importance remain below 0.7. Our model achieve comparable performance (TP rate = 0.77 and AUC = 0.70) to sophisticated and commonly used prediction algorithm XGBoost (TP rate = 0.73 and AUC = 0.85). Due to space limitation, we defer further details such as the training procedure to Appendix~\ref{appendix:training_details}. {\it Results and interpretation.} As previously discussed, nodes were created by a clinician to identify the distinct types of measurable, physiologic change that accompanies sepsis-related illness (i.e., SAD nodes); however, the clinician did not determine the relationship amongst the SAD nodes. Rather, these relationships were an output of model training. Both { Table~\ref{table:model_coeff}} and { Figure~\ref{fig:new_net_structure}} illustrate a compelling network of SAD nodes that follow closely with known and expected causal relationships in sepsis-related illness. For example, the finding that Diminished Cardiac Output strongly promotes sepsis events or that Shock strongly promotes Coagulopathy are well-appreciated relationships. The primary outcome of interest for this work was sepsis; still, as demonstrated in {Table~\ref{table:model_coeff}}, the causal relationship between any node pair can be estimated, giving clinician users insight into the probability of observing subsequent SADs after sepsis. {\it Bootstrap confidence intervals.} We also performed uncertainty quantification via bootstrap. We determined the existence of an edge in the network based on the $90\%$ bootstrap confidence interval (CI), i.e., we assigned zero weight to that edge if the CI contains zero; otherwise, we used the median of the bootstrap samples as the weight. The resulting network topology is reported below in left two graphs in Figure~\ref{fig:network_structure_CI_thres}. Meanwhile, we also used classification error as the CV criterion to infer the network topology in right two graphs in Figure~\ref{fig:network_structure_CI_thres}. We applied hard thresholding on the network topology to improve legibility by only keeping directed edges whose absolute weights are greater than $0.15$. The networks in left graph in Figure~\ref{fig:network_structure_CI_thres} help to elucidate which relationships are most important in the network, which is an essential aspect of interpretability. The network with forward selection shows a high level of influence by the Diminished Cardiac Output and Shock nodes. This is not surprising as both of these SADs are known to cause organ injury. The network that does not use forward selection has identified relationships that suggest certain SADs actually have an inhibitory effect. While there are possible explanations for these inhibitory effects, they are not commonly known or expected from a physiologic perspective. Overall, the network that employees forward feature selection demonstrates a more meaningful series of relationships consistent with known physiologic responses to sepsis. \begin{table}[!htp] \vspace{-0.15in} \caption{Data-driven cluster by Hierarchical Blockmodelling.}\label{table:measurement_clsutering} \begin{center} \begin{small} \begin{sc} \resizebox{0.95\textwidth}{!}{% \begin{tabular}{ccl} \toprule[1pt]\midrule[0.3pt] 1st-level cluster & 2nd-level cluster & Measurement physionet name \\ \midrule[0.3pt] \textbf{A} & A1 & Creatinine , Potassium , HCO3 , Magnesium , Bilirubin total , WBC;\\ \cmidrule(l){2-3} & A2 & Phosphate , BUN , Chloride , Hct , Hgb , Platelets , Glucose ;\\ \midrule[0.3pt] \textbf{B} & B1 & Calcium , BaseExcess , SaO2 , PaCO2 ;\\ \cmidrule(l){2-3} & B2 & Lactate , pH , DBP , O2Sat ;\\ \cmidrule(l){2-3} &B3& SBP , PTT , Temp ;\\ \cmidrule(l){2-3} &NA& MAP , Fibrinogen , Bilirubin direct , Alkalinephos , AST , Resp , EtCO2 , FiO2 , HR , SepsisLabel \\ \midrule[0.3pt]\bottomrule[1pt] \end{tabular} } \end{sc} \end{small} \end{center} \vspace{-0.25in} \end{table} We evaluated classification performance utilizing two separate CV metrics: TP rate (left two panels in Figure~\ref{fig:network_structure_CI_thres}) and classification error (right two panels in Figure~\ref{fig:network_structure_CI_thres}). Both approaches produce networks that demonstrate many conserved features, however, use of TP rate seems to place greater emphasis on clinically relevant relationships. For example the first graph (counting from left to right) in Figure~\ref{fig:network_structure_CI_thres} (i.e. maximizing TP rate with forward feature selection) shows greater involvement of the Renal node and slight differences in edge weights when compared to the third graph in Figure~\ref{fig:network_structure_CI_thres} (i.e. minimizing classification error). The same is also observed in the second and fourth graphs of Figure~\ref{fig:network_structure_CI_thres}, where forward feature selection is not used. For example maximizing TP rate seems to place more weight shock to cholestasis relationship which correlates with a well known clinical relationship. Ultimately maximizing TP during CV produces graphs that not only have a higher sensitivity for sepsis, but also seem to make more sense clinically. To better elucidate the subtle relationships between nodes we also plot the non-thresholding version of Figure~\ref{fig:network_structure_CI_thres}. In Figure~\ref{fig:network_structure_CI} the effect of not performing feature selection becomes evident as we can see numerous red edges indicating a inhibitory relationship between SAD nodes. From a physiologic perspective one would not normally expect a SAD to inhibit another SAD. While there could be unappreciated physiologic relationships or biases in the data that explain such an inhibitory relationship, these inhibitory relationships disappear (as seen in the first and third graphs in Figure~\ref{fig:network_structure_CI}) with feature selection suggesting that they are not meaningful and should be eliminated. The elimination of inhibitory relationships further highlights the importance of feature selection. \vspace{-0.1in} \subsection{Experiment 2} \vspace{-0.05in} In the second experiment, we assumed there was no prior information regarding the nature of the network and instead re-grouped the 34 measurements in Table~\ref{table:node_construction} using a purely data-driven method. Here, we propose two approaches to perform the measurement clustering: (i) Hierarchical clustering based on correlation matrix and symmetrized Hawkes Network; (ii) Blockmodelling based on asymmetric Hawkes Network. Due to space limitation, we focus on approach (ii) here and defer details of approach (i) to Appendix~\ref{appendix:data_cls}. {\it Blockmodelling based on asymmetric Discrete Hawkes Network.} We constructed 34 binary time series and provided a label ``$1$'' if the Lab test was reported out AND the Lab result was abnormal based on the rules in Table~\ref{table:node_construction}. We define clusters using a stochastic block model: for any two clusters $V_i$ and $V_j$ and any two nodes $a,b \in V_i$; then there is approximately the same number of in-edges (respectively out edges) connecting $a$ to nodes in $V_j$ and of in-edges (respectively out edges) connecting $b$ to nodes in $V_j$. Identifying clusters from asymmetric adjacency matrix is called blockmodelling \citep{holland1983stochastic,wang1987stochastic}. We apply a spectral algorithm for blockmodelling \citep{sussman2012consistent}. Further details of this algorithm and the training procedure can be found in Appendix~\ref{appendix:blockmodelling}. We report the clusters in Table~\ref{table:measurement_clsutering} and the fitted topology in Figure~\ref{fig:blockmodelling}. \begin{wrapfigure}{r}{0.2\textwidth} \vspace{-0.25in} \subfigure{\includegraphics[scale=0.3]{fig/network_cls/blk.pdf}} \vspace{-0.15in} \caption{Estimated topology via Blockmodelling.} \label{fig:blockmodelling} \vspace{-0.1in} \end{wrapfigure} Based on Hierarchical Blockmodeling, we identify five blocks/clusters and the associated network topology among them. Analysis of the first level suggests a predominantly renal-inflammatory axis in Group A with values like \texttt{Creatinine, BUN, Phosphate, WBC} being important, and a cardio-pulmonary axis in Group B with values like \texttt{SaO2, O2Sat, SBP, Temp} being important. Inside of Group A, we see derangements following known patterns that demonstrate renal injury (A1), promoting electrolyte imbalances (A2). Similarly, we see in Group B that reduced blood pressure and fevers (B3) promote aberrations in oxygenation and acid/base equilibrium (B2) (a frequent association in sepsis). For demonstration purposes, this Hierarchical Blockmodel created the adjacency matrix using a threshold of 0.15; however, this could be lowered to identify a higher number of clusters and relationships. While single nodes are grouped together to form a cluster, it does not necessarily mean there is a correlation within the cluster (unless there is a self-directed edge (e.g., A2). Instead, the composite effect of nodes within a cluster promotes dysfunction in the nodes of other clusters to which it is connected. \vspace{-0.1in} \section{Conclusion}\label{sec:discussion} \vspace{-0.05in} Motivated by sepsis prediction, we present a highly interpretable model for Granger causal graph based on generalized linear model (GLM), a computationally efficient procedure for model estimation with performance guarantees, and a bootstrap procedure for estimation uncertainty quantification. Our experimental results, both synthetic data and real data experiments, demonstrate that the good performance is achievable with our proposed method compared to the state-of-the-art black-box algorithms. Developing a full, interpretable, causal graph that is capable of facilitating real-world clinical decision-making would require the analysis of a larger cohort of patients from multiple health systems with a more robust set of demographic data. \newpage \bibliographystyle{icml2022} \section{Introduction} \vspace{-0.1in} Continuous, automated surveillance systems that incorporate machine learning models are becoming increasingly common in healthcare environments. These models can capture temporally dependent changes across multiple patient variables and can enhance a clinician's situational awareness by providing an early warning alarm of an impending adverse event. Among those adverse events, we are particularly interested in sepsis, which is a life-threatening medical condition contributing to one in five deaths globally \citep{world2020global} and stands as one of the most important cases for automated in-hospital surveillance. Sepsis is formally defined as life-threatening organ dysfunction caused by a dysregulated host response to infection \citep{singer2016third}. Delays in recognizing sepsis and initiating appropriate treatment can adversely impact patient outcomes. In a recent study of adult sepsis patients, each hour of delayed treatment was associated with higher risk-adjusted in-hospital mortality (odds ratio, 1.04 per hour) \citep{seymourTimeTreatmentMortality2017}. It stands to reason that early recognition of the physiologic aberrations preceding sepsis would afford clinicians more time to intervene and may contribute to improving outcomes and reducing costs. Many machine learning methods have been developed to predict the onset of sepsis, utilizing data from the electronic medical record (EMR) \citep{fleuren2020machine}. A recent sepsis prediction competition \citep{reyna2019early} demonstrated both the popularity and robust performance of XGBoost models \citep{du2019automated,zabihi2019sepsis,yang2020explainable}; meanwhile, Deep Neural Networks \citep{shashikumarDeepAISEInterpretableRecurrent2021} are also commonly used. However, most approaches offer an alert adjudicator very little information pertaining to the reasons for the alert/prediction, leading many to refer to them as ``black box'' techniques. Thus, model predictions related to disease identification, particularly for complex diseases, still need to be adjudicated (i.e., interpreted) by a clinician before further action (i.e., treatment) can be initiated. Among the aforementioned works, \citet{yang2020explainable} provided one of the best attempts at identifying causality for their models' predictions by reporting feature importance at a global level for all patients; still, this does not convey which features were most important in arriving at a given prediction for an individual patient. The common lack of interpretability of many clinical models, particularly those related to sepsis, suggests a strong need for principled methods (with theoretical guarantee) to study the interactions among time series in medical settings. \begin{wrapfigure}{r}{0.5\textwidth} \vspace{-0.3in} \subfigure{\includegraphics[scale = 0.3]{fig/network_graph/new_network.pdf}} \vspace{-0.1in} \caption{Granger causal graph over endogenous Sepsis Associated Derangement (SAD) indicators obtained via Discrete Hawkes Network with forward feature selection.} \label{fig:new_net_structure} \vspace{-0.1in} \end{wrapfigure} One approach to obtain interpretable predictive models for sepsis is to consider its syndromic nature --- there is often a constellation of different physiologic derangements that can combine to create the condition. Figure~\ref{fig:new_net_structure} shows a series of different nodes representing these types of physiologic derangements. For example, a clinical adjudicator may be more inclined to arrive at a concordant opinion regarding sepsis if they know that the alert was caused by the combined effects from the Renal Injury and Diminished Cardiac Output nodes. Likewise, this same adjudicator might be less inclined to corroborate an alert on a different patient if the main contributing cause was from Electrolyte Imbalance alone. In modeling relationships between nodes and their effect on sepsis, a natural approach is through {\it Granger causal graphs}, which analyze the interactions among time series. A popular approach to capture Granger causal graph is the Linear Vector Autoregressive (VAR) model \citep{lutkepohl2005new}. However, it has been recognized that traditional time series models such as VAR have many limitations, including linearity and assuming continuous-valued observations \citep{shojaie2021granger}. In addition, the observations can be both continuous and categorical-valued in many real applications, including medical data. Moreover, the traditional time series model such as VAR assumes that the observations are synchronous and indexed by integers. In the medical setting, the observations can be both discrete and continuous-valued, and they can also be asynchronous and sampled with different frequencies. For example, vital signs are recorded regularly, whereas laboratory (lab) tests are only ordered when clinically necessary; thus, this cannot be simply formulated into a missing data problem In this paper, we present a new Granger causal graph based on the generalized linear model (GLM) to handle observations that are (i) asynchronous and (ii) mixed type (real-valued, integer-valued, binary, or categorical valued). The model estimation is achieved by solving a monotone operator variation inequality problem, a general convex optimization problem. This approach also enables us to establish performance guarantees via recent advances in optimization \citep{juditsky2019signal,juditsky2020convex}. In particular, we develop (i) a non-asymptotic upper bound on estimation error verified by numerical examples and (ii) quantifiable uncertainty by establishing confidence interval for the estimated graph structure by solving a linear program. We demonstrate via real data experiments that our proposed GLM with forward-feature selection can achieve comparable performance to a powerful method such as XGBoost. Moreover, our learned Granger causal graph is highly interpretable, thus making the future adoption of these models to conduct continuous surveillance of high-risk patients by clinicians much more likely. Here, we demonstrate the effectiveness of our approach in learning a Granger causal graph over Sepsis Associated Derangements (SADs), but it can be generalized to other applications with similar requirements. {\textbf{Related work. }} Recent advancements on the Granger causal graph mainly focus on non-linear dynamics and tackling high-dimensionality via regularization: the former includes applying a separable matrix-valued kernel \citep{sindhwani2012scalable} and neural networks \citep{tank2018neural} to learn non-linear Granger causality; other approaches address the high-dimensionality caused by viewing all series as endogenous. Techniques include group Lasso \citep{bolstad2011causal,basu2015network} and nuclear norm regularization \citep{basu2019low}. Another notable work \citep{nicholson2017varx} modeled endogenous and exogenous variables separately (instead of treating all series endogenous) and used different penalties on endogenous and exogenous variables to learn the sparse graph structure. Our method closely resembles \citet{nicholson2017varx} in the following sense: part of features comes from direct observations and is treated exogenous (e.g., vital signs and lab test results), whereas the remaining SADs are derived from the first part and viewed as endogenous. We also want to emphasize that, even though our model is stationary and becomes a Markov process when we only consider one-step memory, it is different from Markov Chain because we avoid defining the state space. This is beneficial since (1) the state space is enormous since each state is a binary representation of whether or not each node variable is ``on''; (2) learning a smaller (latent) state-space from data \citep{alaa2017learning} would sacrifice the interpretability of the model. Recently, \citet{kim2011granger} initiated the study of inferring Granger causality for multivariate Hawkes Processes (MHP), i.e., Hawkes network. Notable contributions includes leveraging alternating direction method of multipliers to infer the low-rank structure in mutual excitation matrix \citep{zhou2013learning} applying expectation–maximization (EM) algorithm with various constraint \citep{xu2016learning,chen2022learning,ide2021cardinality} and leveraging powerful neural networks (NN) \citep{zhang2020cause} to infer the Granger causal graph. Our model is different from the aforementioned method in the following aspects: (1) Theoretically speaking, guarantee is largely missing for Neural Network (NN) and EM based methods --- EM only maximizes a lower bound on log-likelihood and could converge to a local solution, let alone NN method. Moreover, EM is NOT scalable due to its quadratic complexity in the number of events. (2) Practically speaking, our model handles {\it multiple short time series sequences} (most patients have short ICU stays and the measurements are recorded hourly), whereas aforementioned methods dealing with one long point process sequence cannot be easily reformulated to handle our target dataset. Nevertheless, we will numerically compare one theoretically sound gradient-based method \citep{wang2020uncertainty} and one NN-based method \citep{khanna2019economy} that share similar problem formulation with our method in Section~\ref{sec:exp}. Last but not least, irregularity in time series literature has been extensively studied. For example, \citet{bahadori2012granger} proposed a $\ell_1$-regularized linear AR model to infer the granger causality, where the influence from past irregular observations is in a weighted form specified by the occurrence/observed time; \citet{tank2017interpretable} applied Kalman filtering-smoothing algorithm to evaluate the expectation involving the unobserved samples given the observed ones in the Em algorithm to learn a VAR model from mixed-frequency time series. More recent contributions leveraged powerful NNs to handle this irregularity. \citet{shukla2019interpolation} applied NNs to output regularly sampled interpolants, which can serve as inputs of subsequent tasks; other NN-based methods, e.g., \citet{che2018recurrent}, can by-pass this middle interpolation step and directly take irregular time series as input to complete the final task. For more on NN-based method for irregular time series, we refer readers to \citet{weerakody2021review}. As a comparison, the missingness/irregularity in our dataset carries meaning itself --- an absence of lab test represents the clinician's belief that this patient does not have related illness. Thus, it can be handled with well-known physiological patterns that precede sepsis and condensed into binary node variables in our Granger causal graph. Moreover, we also explore a data-driven method to validate the node formation. \vspace{-0.2in} \section{Sepsis Associated Derangements}\label{sec:background} \vspace{-0.05in} We start by presenting the data for sepsis prediction, which will motivate our model development. Data used for this analysis was a curated, publicly available data set from the 2019 Physionet challenge \citep{physionet2019}. The challenge data was sourced from patients admitted to the Intensive Care Unit (ICU) during their hospitalization and represented three categories of patient features: demographic information, vital sign measurements and Laboratory (Lab) results. { \it Demographic information} remains constant throughout hospitalization. The examined data set contains both age and sex. { \it Vital Signs} in ICU environments are normally recorded at an hourly interval and include \texttt{HR, O2Sat, Temp, SBP, MAP, DBP, Resp} (see Table~\ref{table:node_construction} for their full measurement names). { \it Lab Values} are results of Lab tests, which are most commonly collected once every 24 hours; however, this collection frequency may change based on the severity of a patient's illness. { \it Construction of Sepsis Associated Derangements (SADs).} The missingness in regularly sampled vital signs and irregularly sampled lab values carries different meaning --- the missing vital signs are rare and random, and therefore it can be treated by standard imputation method; however, the absence of a lab test shows indicates the clinician's belief of no sign of corresponding disease whereas the result of a taken lab test remains effective for a short period of time. To incorporate such information, we leverage the thresholds, which represent breaks between normal and deranged physiology and \begin{wraptable}{r}{0.56\textwidth} \vspace{-0.2in} \caption{SAD construction via medical knowledge.}\label{table:node_construction} \vspace{-0.05in} \begin{center} \begin{small} \begin{sc} \resizebox{.55\textwidth}{!}{% \begin{tabular}{llccc} \toprule[1pt]\midrule[0.3pt] SAD name & Measurement name & Physionet name & Rule & Risk score \\ \midrule[0.3pt] \textbf{ Renal Injury} & creatinine & Creatinine & >1.3 & 0.667 \\ & potassium & Potassium & >5.0 & 0.067 \\ & phosphorus & Phosphate & >4.5 & 0.067 \\ & bicarb & HCO3 & >26 & 0.067 \\ & blood urea nitrogen & BUN & >20 & 0.133 \\ \cmidrule(l){2-5} \textbf{Electrolyte} & calcium & Calcium & >10.5 & 0.167 \\ \textbf{Imbalance} & chloride & Chloride & <98 or >106 & 0.667 \\ & magnesium & Magnesium & <1.6 & 0.167 \\ \cmidrule(l){2-5} \textbf{Oxygen Carrying} & hematocrit & Hct & <37 & 0.500 \\ \textbf{Dysfunction} & hemoglobin & Hgb & <12 & 0.500 \\ \cmidrule(l){2-5} \textbf{Shock} & base excess & BaseExcess & < $-$3 & 0.100 \\ & lactic acid & Lactate & >2.0 & 0.150 \\ & ph & pH & <7.32 & 0.750 \\ \cmidrule(l){2-5} \textbf{Diminished } & sbp cuff & SBP & <120 & 0.250 \\ \textbf{Cardiac Output} & dbp cuff & DBP & <80 & 0.250 \\ & map cuff & MAP & <65 & 0.500 \\ \cmidrule(l){2-5} \textbf{Coagulopathy} & partial prothrombin time & PTT & >35 & 0.250 \\ & fibrinogen & Fibrinogen & <233 & 0.250 \\ & platelets & Platelets & <150,000 & 0.500 \\ \cmidrule(l){2-5} \textbf{Cholestasis} & bilirubin direct & Bilirubin direct & >0.3 & 0.100 \\ & bilirubin total & Bilirubin total & >1.0 & 0.500 \\ & alkaline phosphatase & Alkalinephos & >120 & 0.400 \\ \cmidrule(l){2-5} \textbf{Hepatocellular Injury} & aspartate aminotransferase & AST & >40 & 1.000 \\ \cmidrule(l){2-5} \textbf{Oxygenation } & unassisted resp rate & Resp & >20 & 0.100 \\ \textbf{Dysfunction} & spo2 & O2Sat & <92 \% & 0.200 \\ & saturation of $O_2$ & SaO2 & <92 \% & 0.200 \\ & end tidal $CO_2$ & EtCO2 & <35 or >45 & 0.100 \\ & fio2 & FiO2 & >21 \% & 0.300 \\ & partial pressure of $CO_2$ & PaCO2 & <35 or >45 & 0.100 \\ \cmidrule(l){2-5} \textbf{Inflammation} & temperature & Temp & <36 or >38 & 0.400 \\ & pulse & HR & >90 & 0.100 \\ & glucose & Glucose & >125 & 0.100 \\ & white blood cell count & WBC & <4,000 or >12,000 & 0.400 \\ \midrule[0.4pt]\bottomrule[1pt] \end{tabular} } \end{sc} \end{small} \end{center} \vspace{-0.2in} \end{wraptable} are identified utilizing already established criteria \citep{ABIM_ref_range}, to condense different measurements (containing both vital signs and Lab results) into a binary variable as an indicator of physiologic derangements seen preceding and during sepsis (see column ``SAD name'' in Table~\ref{table:node_construction}). Here, we apply forward filling to impute missing vital signs and construct SADs based on imputed vital signs and raw lab values. Then, we use imputed vital signs and SADs as inputs to fit a Granger causal graph over SADs on a sub-cohort of patients determined by demographic variables. \vspace{-0.1in} \section{Discrete Hawkes Networks} \vspace{-0.05in} \subsection{Formulation} Consider $N_1$ observed sequences of binary SADs over a time horizon $T$: $\{y_1^{(i)},\dots,y_T^{(i)}\}$, $i = 1,\dots,N_1$. We also observe both continuous and discrete-valued time series $\{x_1^{(i)},\dots,x_T^{(i)}\}, i = 1,\dots,N_2$, which correspond to vital signs as well as Lab test counts, and demographic variables $(z_1,\dots,z_{N_3})$. In the following, we will refer to each SAD variable as a node since it corresponds to a node in the Granger causal graph. To model the mutual inter-dependence among the variables, we consider a generalized linear model (GLM), which closely resembles the intensity function of Hawkes point process \citep{hawkes1971point,hawkes1971spectra,hawkes1974cluster}. For the $i$-th node variable ($i = 1,\dots,N_1$), at time step $t \ (t = 2,\dots,T)$, we assume: \begin{equation}\label{eq:hawkes_model} \PP \Big( y_t^{(i)} =1 \Big\| \cH_{t-1} \Big) = g\Bigg(\nu_i + \sum_{j = 1}^{N_3} \gamma_{ij} z_j + \sum_{\tau = 1}^{t-1} \bigg( \sum_{j = 1}^{N_2} \beta_{ij} x_{t-\tau}^{(j)} e^{-\Tilde{R}_{ij} \tau} + \sum_{j = 1}^{N_1} \alpha_{ij} y_{t-\tau}^{(j)} e^{-R_{ij} \tau}\bigg)\Bigg), \end{equation} where $\cH_t$ denotes the past observation up to time $t$ and $g: \RR \rightarrow [0,1]$ is a link function. For example, $g$ can be non-linear, such as sigmoid link function $g(x) = 1/(1+e^{-x})$; also, it can be linear $g(x) = x$ on domain $x \in [0,1] \subset \RR$. {\it Non-linear Granger causal graph.} By the definition of Granger causality in non-linear model \citep{tank2018neural}, matrix $A = (\alpha_{ij}) \in \RR^{N_1 \times N_1}$ represents the causal graph structure over $N_1$ SAD nodes. To be precise, $j$-th SAD does NOT Granger cause $i$-th SAD if $\alpha_{ij} = 0$. {\it Connection to multivariate Hawkes process (MHP).} For $i$-th SAD node variable, $\alpha_{ij}$ and $\beta_{ij}$ represent the magnitude of triggering effect of $j$-th SAD node variable and continuous variable to it. This effect decays exponentially fast with exponent characterized by $R_{ij}$ and $\Tilde{R}_{ij}$. $\gamma_{ij}$'s represent the influence of demographics and contribute to baseline intensity togerther with $\nu_i$. Thus, the above model can be viewed as a discretized version of (non-linear) MHP with exponential triggering function \citep{xu2016learning,wang2020uncertainty}. \vspace{-0.1in} \subsection{Estimation} \vspace{-0.05in} In this section, we will leverage a recently developed technique \citep{juditsky2019signal,juditsky2020convex}, which estimates the parameters of the generalized linear model by solving stochastic monotone variational inequality (VI), to develop a statistically principled method to estimate the parameters of Discrete Hawkes Network and infer the Granger causal graph topology. {\it Preliminaries.} To begin with, we make reasonable simplification by assuming finite memory depth $d$ for both continuous and binary observations. Let $w_{t-d}^{t-1}$ denote the observation from $t-d$ to $t-1$: $\big(1,z_1,\dots,z_{N_3},x_{t-1}^{(1)},\dots,x_{t-d}^{(1)},\dots,x_{t-1}^{(N_2)},\dots,x_{t-d}^{(N_2)},y_{t-1}^{(1)},$ $\dots,y_{t-d}^{(1)},\dots,y_{t-1}^{(N_1)},\dots,y_{t-d}^{(N_1)}\big)^{ \mathrm{\scriptscriptstyle T} },$ where superscript $^{ \mathrm{\scriptscriptstyle T} }$ denotes matrix transpose. Since we only consider finite memory depth for binary observation, we could use one single parameter $\alpha_{ij\tau} := \alpha_{ij} \exp\{-R_{ij} \tau\}$ (similarly, $\beta_{ij\tau} := \beta_{ij} \exp\{-\Tilde{R}_{ij} \tau\}$) to represent the triggering effect with exponential decay. We rewrite \eqref{eq:hawkes_model} into: \begin{equation}\label{eq:model} \PP\left(y_t^{(i)}=1 \Big\| w_{t-d}^{t-1} \right) = g\left((w_{t-d}^{t-1})^{ \mathrm{\scriptscriptstyle T} } \theta_i\right), \quad i = 1,\dots,N_1, \quad t = d+1,\dots,T, \end{equation} where $\theta_i \in \RR^N$ ($N = 1+N _3+dN_2+dN_1$) is the parameter to be estimated: $\theta_i = (\nu_i,\gamma_{i1},\dots,\gamma_{iN_3},\beta_{i11},\dots,\beta_{i1d},$ $\beta_{iN_21},\dots,\beta_{iN_2d},\alpha_{i11},\dots,\alpha_{i1d},\alpha_{iN_11},\dots,\alpha_{iN_1d})^{ \mathrm{\scriptscriptstyle T} }.$ This parameter summarizes the influence from all variables to node $i$ and could be estimated independently from the remaining $N_1-1$ parameters. {\it Granger Causality.} We can see \eqref{eq:model} is actually a generalized version of Vector Autoregressive (VAR) model. Therefore, we say $j$-th node series $\{y^{(j)}_t\}$ (or vital sign series $\{x^{(j)}_t\}$) Granger-causes $i$-th node series $\{y_t^{(i)}\}$ if $\alpha_{ij\tau} \not= 0$ (or $\beta_{ij\tau} \not= 0$) for some $\tau \in \{1,\dots,d\}$. {\it Estimation with variational inequality.} Denote the observation by $W_{T}:=(w_{1-d}^{0},\dots,w_{T-d+1}^{T}) \in \RR^{(T+1) \times N}$, where variables observed at time step $1-d,\dots,0$ are viewed as given history. We assume parameter $\theta_i$ is constrained in a convex compact set $\theta_i \in \Theta_i \subset \RR^N$, then, for $i = 1,\dots,N_1$, we use the weak solution to the following variational inequality as the estimator $\hat \theta_i$: \vspace{-0.15in} \begin{equation} \text {find } \hat \theta_i \in \Theta_i:\langle F_{ W_{T}}^{(i)}(\theta), \theta-\hat \theta_i\rangle \geq 0, \ \forall \theta \in \Theta_i, \label{VI_1}\tag{{VI}$[ F_{W_{T}}^{(i)}, \Theta_i]$} \end{equation} \vspace{-0.1in} where $\langle \cdot \rangle$ represents the standard inner product in Euclidean space and $F_{W_{T}}^{(i)}(\theta_i)$ is the empirical vector field: \vspace{-0.35in} $$F_{W_{T}}^{(i)}(\theta_i) := \frac{1}{T} \sum_{t=1}^T w_{t-d}^{t-1} \left( g\left((w_{t-d}^{t-1})^{ \mathrm{\scriptscriptstyle T} } \theta_i\right) - y_t^{(i)} \right).$$ \vspace{-0.2in} \paragraph{Remarks.} (i) The feasible region $\Theta_i$ makes sure the assumptions (which are introduced later in next section) are satisfied and is defined differently in different problems; see two examples (with definitions) in Appendix~\ref{appendix:eg}. (ii) The intuition behind this method is straightforward. Let's consider the global counterpart of the above vector field, whose root is the unknown ground truth $\theta_{0,i}$, \vspace{-0.25in} \begin{align} F^{(i)}(\theta_i) :=& \EE_{(w,y^{(i)})} \left[w \left( g\left(w^{ \mathrm{\scriptscriptstyle T} } \theta_i\right) - y^{(i)} \right)\right] \\ =& \EE_{(w,y^{(i)})} \left[w \left( g\left(w^{ \mathrm{\scriptscriptstyle T} } \theta_i\right) - g\left(w^{ \mathrm{\scriptscriptstyle T} } \theta_{0,i}\right) \right)\right]. \end{align} \vspace{-0.1in} Although we cannot access this global counterpart, by solving the empirical one \ref{VI_1} we could approximate the ground truth very well. We next show how well this approximation can be. \vspace{-0.1in} \subsection{Non-asymptotic performance guarantees} \vspace{-0.05in} In this section, we show the VI estimate will eventually converge to a very small neighborhood of the ground truth. Besides, we will derive a linear program (LP) based confidence interval (CI) of parameters $\theta_i$'s. Due to space limitation, we defer the Ci to Appendix~\ref{appendix:CI}. To begin with, we state two necessary model assumptions: \begin{assumption}\label{assumption:vector_field} The link function $g(\cdot)$ is continuous and monotone, and the vector field $G(\theta) = \EE_w[wg(w^{ \mathrm{\scriptscriptstyle T} }\theta)]$ is well defined (and therefore monotone along with $g$). Moreover, $g$ is differentiable and has uniformly bounded first order derivative $m_g \leq \|g'\|\leq M_g$ for $0<m_g\leq M_g$. \end{assumption} \begin{assumption}\label{assumption:observation} The observations (static, binary and continuous) are bounded almost surly: $\exists M_w>0$ such that at any time step $t$, we have $\norm{w_{t-d}^{t-1}}_\infty \leq M_w$ with probability one. \end{assumption} We define an auxiliary vector field $\Tilde{F}_{W_{T}}^{(i)}(\theta_i) := \frac{1}{T} \sum_{t=1}^T w_{t-d}^{t-1} \left( g\left((w_{t-d}^{t-1})^{ \mathrm{\scriptscriptstyle T} } \theta_i\right) - g\left((w_{t-d}^{t-1})^{ \mathrm{\scriptscriptstyle T} } \theta_{0,i}\right) \right).$ This vector field changes the constant term in ${F}_{W_{T}}^{(i)}(\theta_i)$ to make sure its unique root/weak solution to corresponding VI is the unknown ground truth $\theta_{0,i}$. Recall that $\hat \theta_i$ is the root of ${F}_{W_{T}}^{(i)}(\theta_i)$. Then, we will bound the difference between $\hat \theta_i$ and $\theta_{0,i}$ via the difference between ${F}_{W_{T}}^{(i)}(\theta_i)$ and $\Tilde{F}_{W_{T}}^{(i)}(\theta_i)$: $$\Delta^{(i)} := {F}_{W_{T}}^{(i)}(\theta_i) - \Tilde{F}_{W_{T}}^{(i)}(\theta_i) = {F}_{W_{T}}^{(i)}(\theta_{0,i}).$$ \begin{proposition}\label{lma:bound_delta} Under Assumptions~\ref{assumption:vector_field} and \ref{assumption:observation}, for $i = 1,\dots,N_1$, $\forall \ \varepsilon \in (0,1)$, with probability at least $1-\varepsilon$, the difference between the empirical and auxiliary vector field $\Delta^{(i)}$ can be bounded as follows: \vspace{-0.1in} \begin{equation}\label{eq:bound_inf} \norm{\Delta^{(i)}}_\infty \leq M_w \sqrt{{\log(2N/\varepsilon)}/{T}} \end{equation} Moreover, this implies \begin{equation}\label{eq:bound_l2} \norm{\Delta^{(i)}}_2 \leq M_w \sqrt{N{\log(2N/\varepsilon)}/{T}}. \end{equation} \end{proposition} The proof of Proposition~\ref{lma:bound_delta} leverages the concentration property of martingales. Similar results could also be found in \citet{juditsky2020convex,wei2021inferring}. We defer its proof to Appendix~\ref{appendix:proof}. We want to remark that improvement can be achieved by Bernstein inequality, but the rate remains the same This proposition enables us to prove the following non-asymptotic estimation error bound: \begin{theorem}[Upper bound on $\norm{\hat \theta_i - \theta_{0,i}}_2$]\label{thm:upper_err_bound} Under Assumptions~\ref{assumption:vector_field} and \ref{assumption:observation}, for $i = 1,\dots,N_1$ and any $\varepsilon \in (0,1)$, with probability at least $1-\varepsilon$, the $\ell_2$ distance between ground truth $\theta_{0,i}$ and $\hat \theta_i$, which is weak solution to \ref{VI_1}, can be upper bounded as follows: \vspace{-0.05in} $$\norm{\hat \theta_i - \theta_{0,i}}_2 \leq \frac{M_w}{m_g \lambda_1} \sqrt{\frac{N\log (2N/\varepsilon)}{T }},$$ \vspace{-0.05in}where where $\lambda_1$ is the smallest eigenvalue of $\mathbb{W}_{1:T} = \sum_{t=1}^T w_{t-d}^{t-1}(w_{t-d}^{t-1})^{ \mathrm{\scriptscriptstyle T} }/T$. \end{theorem} The above theorem is an extension to the general link function case of Theorem 1 \citep{juditsky2020convex}, where they only sketched the proof without giving further details; we defer the detailed proof to Appendix~\ref{appendix:proof}. Moreover, as pointed out in \citet{juditsky2020convex}, $\mathbb{W}_{1:T} \in \RR^{N \times N}$ will be full rank when $T$ is sufficiently large, i.e., with high probability, $\lambda_1$ will be a positive constant. \vspace{-0.15in} \section{Synthetic Data Experiments}\label{sec:exp} \vspace{-0.1in} In this section, we demonstrate the performance of our proposed model via some simple toy examples. {\it Demonstration of consistency.} We fit the Granger causal graph over 5 binary node variables with sigmoid non-linear link function. We present the true network topology in first two figures in Figure~\ref{fig:simu_topo} \begin{wrapfigure}{r}{0.5\textwidth} \vspace{-0.15in} \centerline{ \includegraphics[width = 0.5\textwidth]{ICML2022_resp_fig/exp0.png} } \vspace{-0.1in} \caption{From left to right: true adjacency matrix, estimated Discrete Hawkes Network with $T = 500$ and $T = 5000$.} \label{fig:simu_topo} \centerline{ \includegraphics[width = 0.24\textwidth]{fig_num_simu/traj_3.pdf} \includegraphics[width = 0.24\textwidth]{fig_num_simu/loglog_3.pdf} } \vspace{-0.1in} \caption{Left: Trajectory for $\ell_2$ norm of estimation error and its data-driven bound. Right: log-log plot of estimation error and its bound; this shows that our bound is sharp in rate.} \label{fig:traj} \vspace{-0.2in} \end{wrapfigure} and report the estimated topology via Discrete Hawkes Network in the last two figures in Figure~\ref{fig:simu_topo}. Further details, such as synthetic data generation process, are deferred to Appendix~\ref{appendix:num_simu}. Since this network is sparse, we also impose $\ell_1$ penalty and the results are deferred to Figure~\ref{fig:simu_topo_l1} in Appendix~\ref{appendix:num_simu}. From both figures, we can observe that when trajectory is long enough, we can faithfully recover the true network topology. Most importantly, we study the trajectories of the $\ell_2$ norm of the estimation error and the data-driven bound. Here, the data-driven bound requires us to calculate $\lambda_1$ and $m_g$ from the data. Since we consider simple binary r.v.s in our toy example, $M_w$ is one. We plot the trajectory for a particular node in Figure~\ref{fig:traj}. The results for the rest of the nodes are deferred to Figure~\ref{fig:traj_additional} in Appendix~\ref{appendix:num_simu}. From both figures (especially the slope in the log-log plot), we observe that our data-driven bound is sharp in rate, though the constant could be loose. This constant could be further improved by using Bernstein's inequality instead of Azuma's inequality, as commented in remark of Proposition~\ref{lma:bound_delta}. {\it Comparison to existing methods.} We compare methods: \texttt{\textcircled{\small 1}} Proposed VI method, \texttt{\textcircled{\small 2}} Gradient method \citep{wang2020uncertainty}, and \texttt{\textcircled{\small 3}} NN method \citep{khanna2019economy}, under \begin{wrapfigure}{r}{0.75\textwidth} \vspace{-0.2in} {\includegraphics[scale = 0.31]{ICML2022_resp_fig/exp1.png}} \vspace{-0.22in} \caption{Heatmap of estimated adjacency matrices. The error vector on the top of each figure corresponds to (L1 Error; Support Recovery Error after proper thresholding; Weighted Support Recovery).}\label{fig:syn_exp1} \vspace{-0.2in} \end{wrapfigure} two different data generating processes: \texttt{Setting 1}: MHP with exponential kernel and \texttt{Setting 2}: Proposed model with sigmoid link. Further details can be found in Appendix~\ref{appendix:num_simu}. True adjacency matrices $A = (\alpha_{ij})$ are visualized in 1, 2, 3, 4-(a) respectively in Figure~\ref{fig:syn_exp1}. The major weakness of \texttt{\textcircled{\small 2}} and \texttt{\textcircled{\small 3}} is that they are unable to model inhibiting effect with negative $\alpha_{ij}$'s (e.g., proper medication lowers the chance of poor health status). We apply log-barrier method in \textcircled{\small 2}, i.e., we add penalty $p(b) = \sum_{i} \log(\lambda_i(t_i) - b)$ to the log-likelihood ($\lambda_i(t_i)$ is the intensity of event $i$ occurring at time $t_i$ and $b$ is hyperparameter) to make sure the intensity will not be negative. We report the fitted adjacency matrices in Figure~\ref{fig:syn_exp1}. We observe that: (1) Under correct model specification, all methods faithfully recover $A$ (1-(d), 2-(b, c), 3-(d), 4-(b, c)). (2) Our method \texttt{\textcircled{\small 1}} recovers the true pattern of $A$ even under model mis-specification (see support recovery error in 1-(b, c), 3-(b, c)) whereas \texttt{\textcircled{\small 2}} fails to do so (2-(d), 4-(d)). (3) As a powerful non-parametric method, \texttt{\textcircled{\small 3}} also roughly recovers the true pattern (1, 2-(e)); its major weakness is that it cannot model negative $\alpha_{ij}$'s. Besides, the log-barrier modification enables gradient-based method to further model inhibiting effect in Hawkes network (3-(d)). \vspace{-0.15in} \section{Real Data Experiments} \vspace{-0.15in} In Experiment 1, nodes in the network are constructed based on well-known, measurable, physiologic relationships in the human body. This expert-driven approach is subsequently compared to a purely data-driven model for identifying possible clusters of inpatient data in Experiment 2. \vspace{-0.1in} \paragraph{Experiment 1.} Now, we aim to recover the network topology over SADs constructed in Section~\ref{sec:background} { \it Feature construction.} As previously described, vital sign measurements were condensed into single features represented by summary statistics (i.e., maximum, minimum, mean) of the past 6 hours, creating a total of 12 distinct representations of a patient's vital signs. A count of total Lab tests over the past 6 hours was used as a proxy for patient acuity and was also incorporated as a feature. SAD nodes were created by grouping all 34 Lab measurements into ten nodes (see Table~\ref{table:node_construction}), representative of common physiologic derangements seen in sepsis. Moreover, instead of constructing a sequence of binary variables for each node, we assigned a risk score at each time, indicating the severity of the SAD. However, when a variable (i.e., node) was used as the response during modeling, it was treated as binary by applying indicator function $\mathbf{1}_{\{y > 0\}}$. { \it Sub-group analysis.} To simplify model development, we carried out a sub-group analysis and excluded demographic features from the model. We used sex $= 0$ (female) and age $>60$ sub-group in the following to demonstrate our method, which contained 5,222 patients in the Physionet data set. {\it Model fitting.} The primary outcome of interest was sepsis, which necessitated the addition of an $11$-th binary time series called ``SepsisLabel'' to our data. This resulted in a total of $N_1 = 11$ nodes in our network. Using each of those $N_1$ variables as responses (recall that risk scores were binarized when used as a response) and the rest as features, we fitted our proposed model with sigmoid link function with hyperparameter being the number of training iterations and performed forward feature selection. The primary cross-validation (CV) criterion for both feature selection and hyperparameter tuning was the True Positive (TP) rate (classification accuracy for positive samples); we also compared classification error and AUC. TP rate was chosen because in a clinical setting, particularly as it pertains to sepsis, greater importance is placed on not missing the disease (i.e., maintaining a high sensitivity) as opposed to producing a false alert. \vspace{-0.15in} \paragraph{\it Comparison to XGBoost.} During the forward selection, the TP rate goes from around 0.6 up to final 0.768 whereas the TP rate for using all features and subset selection based on random forest feature importance remain below 0.7. Our model achieve comparable performance (TP rate = 0.77 and AUC = 0.70) to sophisticated and commonly used prediction algorithm XGBoost (TP rate = 0.73 and AUC = 0.85), which outperformed other methods in the Challenge \citep{physionet2019}. Due to space limitation, we defer further details such as the training procedure to Appendix~\ref{appendix:training_details}. {\it Results and interpretation.} As previously discussed, nodes were created by a clinician to identify the distinct types of measurable, physiologic change that accompanies sepsis-related illness (i.e., SAD nodes); however, the clinician did not determine the relationship amongst the SAD nodes. Rather, these relationships were an output of model training. Both { Table~\ref{table:model_coeff} (deferred to Appendix~\ref{appendix:training_details} )} and { Figure~\ref{fig:new_net_structure}} illustrate a compelling network of SAD nodes that follow closely with known and expected causal relationships in sepsis-related illness. For example, the finding that Diminished Cardiac Output strongly promotes sepsis events or that Shock strongly promotes Coagulopathy are well-appreciated relationships. The primary outcome of interest for this work was sepsis; still, as demonstrated in {Table~\ref{table:model_coeff}}, the causal relationship between any node pair can be estimated, giving clinician users insight into the probability of observing subsequent SADs after sepsis. {\it Bootstrap confidence intervals.} We also performed uncertainty quantification via bootstrap. We determined the existence of an edge in the network based on the $90\%$ bootstrap confidence interval (CI), i.e., we assigned zero weight to that edge if the CI contains zero; otherwise, we used the median of the bootstrap samples as the weight. The resulting network topology is reported below in left two graphs in Figure~\ref{fig:network_structure_CI_thres}. Meanwhile, we also used classification error as the CV criterion to infer the network topology in right two graphs in Figure~\ref{fig:network_structure_CI_thres}. We applied hard thresholding on the network topology to improve legibility by only keeping directed edges with absolute weights greater than $.15$. \begin{figure}[!htp] \vspace{-0.1in} \centerline{ \includegraphics[width = 0.25\textwidth,trim={4cm 0 2.8cm 0},clip]{fig/CI_graph/TP_thres_0.15_CI_new.pdf} \includegraphics[width = 0.25\textwidth,trim={4cm 0 2.8cm 0},clip]{fig/CI_graph/TP_thres_0.15_CI_old.pdf} \includegraphics[width = 0.25\textwidth,trim={4cm 0 2.8cm 0},clip]{fig/CI_graph/err_thres_0.15_CI_new.pdf} \includegraphics[width = 0.25\textwidth,trim={4cm 0 2.8cm 0},clip]{fig/CI_graph/err_thres_0.15_CI_old.pdf} } \vspace{-0.1in} \caption{From left to right: bootstrap network topology (1) with feature selection using TP rate for CV; (2) without feature selection using TP rate for CV; (3) with feature selection using classification error for CV; (4) without feature selection using classification error for CV. We only show edges with weights greater than $.15$. Color blue and red indicate positive and negative effect, respectively.}\label{fig:network_structure_CI_thres} \centerline{ \includegraphics[width = 0.25\textwidth,trim={4cm 0 2.8cm 0},clip]{fig/CI_graph/TP_CI_new.pdf} \includegraphics[width = 0.25\textwidth,trim={4cm 0 2.8cm 0},clip]{fig/CI_graph/TP_CI_old.pdf} \includegraphics[width = 0.25\textwidth,trim={4cm 0 2.8cm 0},clip]{fig/CI_graph/err_CI_new.pdf} \includegraphics[width = 0.25\textwidth,trim={4cm 0 2.8cm 0},clip]{fig/CI_graph/err_CI_old.pdf} } \vspace{-0.1in} \caption{From left to right: non-thresholding bootstrap network topology (1) with feature selection using TP rate for CV; (2) without feature selection using TP rate for CV; (3) with feature selection using classification error for CV; (4) without feature selection using classification error for CV. Color blue indicates positive effect whereas red indicates negative effect. The criterion for cross validation is true positive rate (left) and classification error (right).}\label{fig:network_structure_CI} \vspace{-0.15in} \end{figure} The networks in left graph in Figure~\ref{fig:network_structure_CI_thres} help to elucidate which relationships are most important in the network, which is an essential aspect of interpretability. The network with forward selection shows a high level of influence by the Diminished Cardiac Output and Shock nodes. This is not surprising as both of these SADs are known to cause organ injury. The network that does not use forward selection has identified relationships that suggest certain SADs actually have an inhibitory effect. While there are possible explanations for these inhibitory effects, they are not commonly known or expected from a physiologic perspective. Overall, the network that employees forward feature selection demonstrates a more meaningful series of relationships consistent with known physiologic responses to sepsis. We evaluated classification performance utilizing two separate CV metrics: TP rate (left two panels in Figure~\ref{fig:network_structure_CI_thres}) and classification error (right two panels in Figure~\ref{fig:network_structure_CI_thres}). Both approaches produce networks that demonstrate many conserved features, however, use of TP rate seems to place greater emphasis on clinically relevant relationships. For example the first graph (counting from left to right) in Figure~\ref{fig:network_structure_CI_thres} (i.e. maximizing TP rate with forward feature selection) shows greater involvement of the Renal node and slight differences in edge weights when compared to the third graph in Figure~\ref{fig:network_structure_CI_thres} (i.e. minimizing classification error). The same is also observed in the second and fourth graphs of Figure~\ref{fig:network_structure_CI_thres}, where forward feature selection is not used. For example maximizing TP rate seems to place more weight shock to cholestasis relationship which correlates with a well known clinical relationship. Ultimately maximizing TP during CV produces graphs that not only have a higher sensitivity for sepsis, but also seem to make more sense clinically. To better elucidate the subtle relationships between nodes we also plot the non-thresholding version of Figure~\ref{fig:network_structure_CI_thres}. In Figure~\ref{fig:network_structure_CI} the effect of not performing feature selection becomes evident as we can see numerous red edges indicating a inhibitory relationship between SAD nodes. From a physiologic perspective one would not normally expect a SAD to inhibit another SAD. While there could be unappreciated physiologic relationships or biases in the data that explain such an inhibitory relationship, these inhibitory relationships disappear (as seen in the first and third graphs in Figure~\ref{fig:network_structure_CI}) with feature selection suggesting that they are not meaningful and should be eliminated. The elimination of inhibitory relationships further highlights the importance of feature selection. \paragraph{Experiment 2.} Now, we assumed there was no prior information regarding the nature of the network and instead re-grouped the 34 measurements in Table~\ref{table:node_construction} via data-driven method. Here, we propose two approaches to perform the measurement clustering: (i) Hierarchical clustering based on correlation matrix and symmetrized Hawkes Network; (ii) Blockmodelling based on asymmetric Hawkes Network. Due to space limitation, we defer details of approach (i) to Appendix~\ref{appendix:data_cls}. {\it Blockmodelling based on asymmetric Discrete Hawkes Network.} We constructed 34 binary time series and provided a label ``$1$'' if the Lab test was reported out AND the Lab result was abnormal based on \begin{wraptable}{r}{0.75\textwidth} \vspace{-0.2in} \caption{Data-driven cluster by Hierarchical Blockmodelling.}\label{table:measurement_clsutering} \vspace{-0.05in} \begin{center} \begin{small} \begin{sc} \resizebox{0.73\textwidth}{!}{% \begin{tabular}{ccl} \toprule[1pt]\midrule[0.3pt] 1st-level cluster & 2nd-level cluster & Measurement physionet name \\ \midrule[0.3pt] \textbf{A} & A1 & Creatinine , Potassium , HCO3 , Magnesium , Bilirubin total , WBC;\\ \cmidrule(l){2-3} & A2 & Phosphate , BUN , Chloride , Hct , Hgb , Platelets , Glucose ;\\ \midrule[0.3pt] \textbf{B} & B1 & Calcium , BaseExcess , SaO2 , PaCO2 ;\\ \cmidrule(l){2-3} & B2 & Lactate , pH , DBP , O2Sat ;\\ \cmidrule(l){2-3} &B3& SBP , PTT , Temp ;\\ \cmidrule(l){2-3} &NA& MAP , Fibrinogen , Bilirubin direct , Alkalinephos , AST , Resp , EtCO2 , FiO2 , HR , SepsisLabel \\ \midrule[0.3pt]\bottomrule[1pt] \end{tabular} } \end{sc} \end{small} \end{center} \vspace{-0.25in} \end{wraptable} the rules in Table~\ref{table:node_construction}. We define clusters using a stochastic block model: for any two clusters $V_i$ and $V_j$ and any two nodes $a,b \in V_i$; then there is approximately the same number of in-edges (respectively out edges) connecting $a$ to nodes in $V_j$ and of in-edges (respectively out edges) connecting $b$ to nodes in $V_j$. Identifying clusters from asymmetric adjacency matrix is called blockmodelling \citep{holland1983stochastic,wang1987stochastic}. We apply a spectral algorithm for blockmodelling \citep{sussman2012consistent}. Further details of this algorithm and the training procedure can be found in Appendix~\ref{appendix:blockmodelling}. We report the clusters in Table~\ref{table:measurement_clsutering} and the fitted topology in Figure~\ref{fig:blockmodelling}. \begin{wrapfigure}{r}{0.2\textwidth} \vspace{-0.45in} \subfigure{\includegraphics[scale=0.3]{fig/network_cls/blk.pdf}} \vspace{-0.15in} \caption{Estimated topology via Blockmodelling.} \label{fig:blockmodelling} \vspace{-0.1in} \end{wrapfigure} Based on Hierarchical Blockmodeling, we identify five blocks/clusters and the associated network topology among them. Analysis of the first level suggests a predominantly renal-inflammatory axis in Group A with values like \texttt{Creatinine, BUN, Phosphate, WBC} being important, and a cardio-pulmonary axis in Group B with values like \texttt{SaO2, O2Sat, SBP, Temp} being important. Inside of Group A, we see derangements following known patterns that demonstrate renal injury (A1), promoting electrolyte imbalances (A2). Similarly, we see in Group B that reduced blood pressure and fevers (B3) promote aberrations in oxygenation and acid/base equilibrium (B2) (a frequent association in sepsis). For demonstration purposes, this Hierarchical Blockmodel created the adjacency matrix using a threshold of 0.15; however, this could be lowered to identify a higher number of clusters and relationships. While single nodes are grouped together to form a cluster, it does not necessarily mean there is a correlation within the cluster (unless there is a self-directed edge (e.g., A2). Instead, the composite effect of nodes within a cluster promotes dysfunction in the nodes of other clusters to which it is connected. \vspace{-0.15in} \section{Discussion}\label{sec:discussion} \vspace{-0.1in} It is important to appreciate that many of the Lab tests that serve as a data source for our analysis are collected at the direction of a clinician, meaning there is an inherent component of suspicion associated with each Lab test. The important effects that drive suspicion and compel the ordering of tests may not be captured in our data and, subsequently, our network. Additionally, our cohort was limited to a specific subset of patients in order to reduce the number of data elements and make analysis more tractable, but it is commonly recognized that there are demographic features and co-existing medical conditions that affect how patients respond to sepsis. These unobserved features may also alter some of the findings for our network. { It is also important to appreciate that we accepted the consequence of increased false alarms (i.e. False Positives) in order to maximize our sensitivity. In clinical settings high false alarm rates may decrease clinical satisfaction and lead to alarm fatigue or disuse.} Nevertheless, both synthetic and real data experimental results serve as a demonstration that good performance is achievable with our proposed method. The development of a full and interpretable Granger causal graph that is capable of facilitating real-world clinical decision-making would require the analysis of a larger cohort of patients from multiple health systems with a more robust set of demographic data. An interpretable model like the one we have proposed offers some protection against the aforementioned limitations by allowing a clinician to combine their own knowledge about a patient with the findings of the model resulting in more informed decisions about a patient's health status. Last but not least, methodology-wise speaking, it is worth of exploring interesting topics such as connecting this newly developed VI approach with a principled variable section selection method (e.g., group Lasso) as well as exploring the theoretical guarantee behind it. \newpage \bibliographystyle{plainnat} \section{Introduction} \vspace{-0.1in} Automated surveillance tools aimed at identifying a patient's deterioration inside the hospital are becoming more common and stand to enhance a clinician's situational awareness; however, model predictions related to disease identification, particularly for complex diseases, still need to be adjudicated (i.e., interpreted) by a clinician before further action (i.e., treatment) can be initiated. Sepsis is a life-threatening medical condition contributing to one in five deaths globally \citep{world2020global} and exists as one of the most important cases for automated in-hospital surveillance. Sepsis is formally defined as life-threatening organ dysfunction caused by a dysregulated host response to infection \citep{singer2016third}. Delays in recognizing sepsis and initiating appropriate treatment can adversely impact patient outcomes. In a recent study of adult sepsis patients, each hour of delayed treatment was associated with higher risk-adjusted in-hospital mortality (odds ratio, 1.04 per hour) \citep{seymourTimeTreatmentMortality2017}. It stands to reason that early recognition of the physiologic aberrations preceding sepsis would afford clinicians more time to intervene and may contribute to improving outcomes and reducing costs. A number of machine learning methods have been developed to predict the onset of sepsis utilizing data from the electronic medical record (EMR) \citep{fleuren2020machine}. A recent sepsis prediction competition \citep{reyna2019early} demonstrated both the popularity and robust performance of XGBoost models \citep{du2019automated,zabihi2019sepsis,yang2020explainable}; meanwhile, Deep Neural Networks \citep{shashikumarDeepAISEInterpretableRecurrent2021} are also commonly used. Regrettably, most approaches offer an alert adjudicator very little information pertaining to the reason for the alert/prediction, leading many to refer to them as ``black box'' techniques. Among the aforementioned works, \citet{yang2020explainable} provided one of the best attempts at identifying causality for their models' predictions by reporting feature importance at a global level for all patients; however, this does not convey which features were most important in arriving at a given prediction for an individual patient. The common lack of interpretability of many clinical models, particularly those related to sepsis, suggests that a principled method (with theoretical guarantee) to study the interactions among time series in medical settings is underdeveloped. \begin{wrapfigure}{r}{0.5\textwidth} \vspace{-0.3in} \subfigure{\includegraphics[scale = 0.3]{fig/network_graph/new_network.pdf}} \vspace{-0.1in} \caption{Granger causal graph over endogenous Sepsis Associated Derangement (SAD) indicators obtained via discrete Hawkes network with forward feature selection.} \label{fig:new_net_structure} \vspace{-0.1in} \end{wrapfigure} Granger causal graphs, which analyze interactions among time series defined by association, avoid this limitation and afford a clinical adjudicator the ability to understand why an alert was made. The syndromic nature of sepsis means that there is a constellation of different physiologic derangements that can combine to create the condition. As evidenced in Figure~\ref{fig:new_net_structure}, a series of different nodes representing these types of physiologic derangements has been created. The relationships between nodes and their effect on sepsis are explained via generalized linear models (GLM), providing insight into what ``caused'' the alert. For example, a clinical adjudicator might be more inclined to arrive at a concordant opinion regarding sepsis if they were informed that the alert was caused by the combined effects from the Renal Injury and Diminished Cardiac Output nodes. Likewise, this same adjudicator might be less inclined to corroborate an alert on a different patient if the main contributing cause was from Electrolyte Imbalance alone. Linear Vector Autoregressive (VAR) model is the most popular method in studying the Granger causal graph among multiple time series \citep{lutkepohl2005new}. However, it has been pointed out by a recent survey study \citep{shojaie2021granger} that this approach suffers from assumptions such as linearity and continuous-valued series, since the real-data, which can be both continuous- and categorical-valued, usually exhibits complex dynamics; another flaw of classic linear VAR model is unscalability to high-dimension, which arises when one tries to identify all series as endogenous, since it is hard to check if we have all relevant information at hand in practice. In this work, we adopt a generalized linear model (GLM) approach for binary time series — spatio-temporal Bernoulli process \citep{juditsky2019signal,juditsky2020convex} — and generalize it to handle both continuous- and discrete-valued as well as regularly and irregularly sampled time series and learn a Granger causal graph over Sepsis Associated Derangements (SADs). We perform forward feature selection to remove redundant information and increase the signal-noise ratio. We demonstrate via real data experiments that our proposed GLM coupled with forward feature selection can achieve comparable performance to a powerful method such as XGBoost. One novel aspect of this work comes from the real underlying problem: we build a {\it highly interpretable} model from {\it mixed-type series}. The prioritization of interpretability considers the needs of the end-users, namely clinicians. This consideration of real-world constraints makes future adoption of these models much more likely for those conducting continuous surveillance of high-risk patients. In the medical setting, the observations can be both discrete and continuous-valued and sampled with different frequencies. For example, vital signs are recorded regularly, whereas laboratory (lab) tests are only ordered when clinically necessary; thus, this cannot be simply formulated into a missing data problem. Moreover, what separates our method from the classic linear VAR time series is the generalization to non-linear dynamics and a novel stochastic monotone variational inequality-based estimator. Most importantly, we develop a non-asymptotic upper bound on estimation error AND a Linear Program-based confidence interval for graph structure for arbitrary monotone (non-linear) link function for our proposed method. {\textbf{Related work. }} Recent developments on the Granger causal graph mainly focus on non-linear dynamics and tackling high-dimensionality via regularization: the former includes applying a separable matrix-valued kernel \citep{sindhwani2012scalable} and neural networks \citep{tank2018neural} to learn non-linear Granger causality; other approaches address the issue of high-dimensionality caused by viewing all series as endogenous. Techniques include group Lasso \citep{bolstad2011causal,basu2015network} and nuclear norm regularization \citep{basu2019low}. Another notable work \citep{nicholson2017varx} modeled endogenous and exogenous variables separately (instead of treating all series endogenous) and used different penalties on endogenous and exogenous variables to learn the sparse graph structure. We should mention that our method closely resembles \citet{nicholson2017varx}: part of features comes from direct observations and is treated exogenous (e.g., vital signs and Lab test results), whereas the remaining SADs are derived from the first part and viewed as endogenous. \vspace{-0.15in} \section{Problem set-up and proposed model} \vspace{-0.1in} \subsection{Mixed-type series}\label{sec:background} \vspace{-0.1in} Data used for this analysis was a curated, publicly available data set from the 2019 Physionet challenge \citep{physionet2019}. The challenge data was sourced from patients admitted to the Intensive Care Unit (ICU) during their hospitalization and represented three categories of patient features: vital sign measurements, Laboratory (Lab) results, and demographic information. \vspace{-0.03in} { \it Vital Signs.} Vital signs in ICU environments are normally recorded at an hourly interval and include \texttt{HR, O2Sat, Temp, SBP, MAP, DBP, Resp} (see Table~\ref{table:node_construction} for their full measurement names). Among the blood pressure measurements (\texttt{SBP}, \texttt{DBP}, and \texttt{MAP}), we only keep \texttt{MAP} in our study since \texttt{MAP} = (\texttt{SBP} + 2\texttt{DBP})$/3$. \vspace{-0.03in} { \it Lab Values.} Lab tests are most commonly collected once every 24 hours; however, this collection frequency may change based a the severity of a patient's illness. In addition to individual Lab values, we also use the count of the Lab tests over the past 6 hours as a proxy to represent the severity of a patient's illness (i.e., more severe disease results in more tests being ordered). \vspace{-0.03in} { \it Sepsis Associated Derangements (SADs).} Thresholds representing breaks between normal and deranged physiology are identified utilizing already establish criteria \citep{ABIM_ref_range}. We condense different measurements (containing both vital signs and Lab results) into a binary variable as an indicator of physiologic derangements seen preceding and during sepsis (see column ``SAD name'' in Table~\ref{table:node_construction}). \begin{table}[!htp] \vspace{-0.1in} \caption{SAD construction based on thresholding exogenous observations via medical knowledge.}\label{table:node_construction} \vspace{-0.25in} \begin{center} \begin{small} \begin{sc} \resizebox{1\textwidth}{!}{% \begin{tabular}{llccc} \toprule[1pt]\midrule[0.3pt] SAD name & Measurement name & Physionet name & Rule & Risk score \\ \midrule[0.3pt] \textbf{ Renal Injury} & creatinine & Creatinine & >1.3 & 0.667 \\ & potassium & Potassium & >5.0 & 0.067 \\ & phosphorus & Phosphate & >4.5 & 0.067 \\ & bicarb (hco3) & HCO3 & >26 & 0.067 \\ & blood urea nitrogen (bun) & BUN & >20 & 0.133 \\ \cmidrule(l){2-5} \textbf{Electrolyte} & calcium & Calcium & >10.5 & 0.167 \\ \textbf{Imbalance} & chloride & Chloride & <98 or >106 & 0.667 \\ & magnesium & Magnesium & <1.6 & 0.167 \\ \cmidrule(l){2-5} \textbf{Oxygen Carrying} & hematocrit & Hct & <37 & 0.500 \\ \textbf{Dysfunction} & hemoglobin & Hgb & <12 & 0.500 \\ \cmidrule(l){2-5} \textbf{Shock} & base excess & BaseExcess & < $-$3 & 0.100 \\ & lactic acid & Lactate & >2.0 & 0.150 \\ & ph & pH & <7.32 & 0.750 \\ \cmidrule(l){2-5} \textbf{Diminished } & sbp cuff & SBP & <120 & 0.250 \\ \textbf{Cardiac Output} & dbp cuff & DBP & <80 & 0.250 \\ & map cuff & MAP & <65 & 0.500 \\ \cmidrule(l){2-5} \textbf{Coagulopathy} & partial prothrombin time (ptt) & PTT & >35 & 0.250 \\ & fibrinogen & Fibrinogen & <233 & 0.250 \\ & platelets & Platelets & <150,000 & 0.500 \\ \cmidrule(l){2-5} \textbf{Cholestasis} & bilirubin direct & Bilirubin direct & >0.3 & 0.100 \\ & bilirubin total & Bilirubin total & >1.0 & 0.500 \\ & alkaline phosphatase & Alkalinephos & >120 & 0.400 \\ \cmidrule(l){2-5} \textbf{Hepatocellular Injury} & aspartate aminotransferase (ast) & AST & >40 & 1.000 \\ \cmidrule(l){2-5} \textbf{Oxygenation } & unassisted resp rate & Resp & >20 & 0.100 \\ \textbf{Dysfunction} & spo2 & O2Sat & <92 \% & 0.200 \\ & saturation of oxygen (sao2) & SaO2 & <92 \% & 0.200 \\ & end tidal co2 & EtCO2 & <35 or >45 & 0.100 \\ & fio2 & FiO2 & >21 \% & 0.300 \\ & partial pressure of carbon dioxide (paco2) & PaCO2 & <35 or >45 & 0.100 \\ \cmidrule(l){2-5} \textbf{Inflammation} & temperature & Temp & <36 or >38 & 0.400 \\ & pulse & HR & >90 & 0.100 \\ & glucose & Glucose & >125 & 0.100 \\ & white blood cell count & WBC & <4,000 or >12,000 & 0.400 \\ \midrule[0.3pt]\bottomrule[1pt] \end{tabular} } \end{sc} \end{small} \end{center} \vspace{-0.2in} \end{table} { \it Demographics.} Demographic features remain constant throughout hospitalization. The examined data set contains both age and sex. \begin{wrapfigure}{r}{0.6\textwidth} \subfigure{\includegraphics[scale = 0.4]{fig/mixed_data_type.pdf}} \vspace{-0.1in} \end{wrapfigure} Here, the vital signs (regularly sampled) and raw Lab values (irregularly sampled) are exogenous variables, whereas SAD indicators are endogenous. The irregularly sampled series will be handled via forwarding filling. Our primary interest is to study all exogenous and endogenous series' effects on endogenous series and construct (Granger causal) graph/network over endogenous series. \vspace{-0.1in} \subsection{Discrete Hawkes network} \vspace{-0.1in} {\it Model formulation.} Suppose we observe $N_1$ sequences of binary SADs on time horizon $T$: $\{y_1^{(i)},\dots,y_T^{(i)}\}$, $i = 1,\dots,N_1$; we also observe both continuous- and discrete-valued time series $\{x_1^{(i)},\dots,x_T^{(i)}\}, i = 1,\dots,N_2$, which are vital signs and Lab test counts, and demographic variables $(z_1,\dots,z_{N_3})$. In the following, we will call each of those SADs a node variable since it corresponds to a node in the Granger causal graph. With such a model at hand, we can better understand the dynamics within the human body, and most importantly, alert the clinicians to the potential causes and complications of an identified SAD. To model the mutual excitation among those series, we propose a generalized linear model, which closely resembles the intensity function of Hawkes point process \citep{hawkes1971point,hawkes1971spectra,hawkes1974cluster}. For $i$-th node variable ($i = 1,\dots,N_1$), at time step $t \ (t = 2,\dots,T)$, we assume: \begin{equation}\label{eq:hawkes_model} \PP\left(y_t^{(i)}=1 \Big\| \cH_{t-1} \right) = g\left(\nu_i + \sum_{j = 1}^{N_3} \gamma_{ij} z_j + \sum_{\tau = 1}^{t-1} \sum_{j = 1}^{N_2} \beta_{ij} x_{t-\tau}^{(j)} e^{-\Tilde{R}_{ij} \tau} + \sum_{\tau = 1}^{t-1} \sum_{j = 1}^{N_1} \alpha_{ij} y_{t-\tau}^{(j)} e^{-R_{ij} \tau}\right), \end{equation} where $\cH_t$ denotes the past observation up to time $t$ and $g: \RR \rightarrow [0,1]$ is a link function. For example, $g$ can be non-linear, such as sigmoid link function $g(x) = 1/(1+e^{-x})$; also, it can be linear $g(x) = x$, which should be restricted on domain $[0,1] \subset \RR$. {\it Non-linear Granger causal graph.} By the definition of Granger causality in non-linear model \citep{tank2018neural}, we know that matrix $A = (\alpha_{ij}) \in \RR^{N_1 \times N_1}$ represents the causal graph structure over $N_1$ SAD nodes. To be precise, we say $j$-th SAD does NOT Granger cause $i$-th SAD if $\alpha_{ij} = 0$. {\it Connection to Hawkes process.} For $i$-th SAD node variable, $\alpha_{ij}$ and $\beta_{ij}$ represent the magnitude of triggering effect of $j$-th SAD node variable and continuous variable to it. This effect decays exponentially fast with exponent characterized by $R_{ij}$ and $\Tilde{R}_{ij}$. $\gamma_{ij}$'s represent the influence of demographics and contribute to baseline intensity togerther with $\nu_i$. Note that the above model can be viewed as a discretized version of (non-linear) Hawkes process network with exponential triggering function \citep{wang2020uncertainty}; other methods in learning Hawkes network include \citet{xu2016learning,achab2017uncovering}, we do not dig deeper in this direction since it is out of the scope of this work. \vspace{-0.15in} \section{Parameter estimation with variational inequality} \vspace{-0.1in} In this section, we will leverage a recently developed technique \citep{juditsky2019signal,juditsky2020convex}, which estimates the parameters of the generalized linear model by solving stochastic monotone variational inequality (VI), to develop a statistically principled method to estimate the parameters of discrete Hawkes network and infer the Granger causal graph topology. {\it Preliminaries.} To begin with, we make reasonable simplification by assuming finite memory depth $d$ for both continuous and binary observations. Let $w_{t-d}^{t-1}$ denote the observation from $t-d$ to $t-1$: $$\left(1,z_1,\dots,z_{N_3},x_{t-1}^{(1)},\dots,x_{t-d}^{(1)},\dots,x_{t-1}^{(N_2)},\dots,x_{t-d}^{(N_2)},y_{t-1}^{(1)},\dots,y_{t-d}^{(1)},\dots,y_{t-1}^{(N_1)},\dots,y_{t-d}^{(N_1)}\right)^{ \mathrm{\scriptscriptstyle T} },$$ where superscript $^{ \mathrm{\scriptscriptstyle T} }$ denotes matrix transpose. Since we only consider finite memory depth for binary observation, we could use one single parameter $\alpha_{ij\tau} := \alpha_{ij} \exp\{-R_{ij} \tau\}$ (similarly, $\beta_{ij\tau} := \beta_{ij} \exp\{-\Tilde{R}_{ij} \tau\}$) to represent the triggering effect with exponential decay. We rewrite \eqref{eq:hawkes_model} into \begin{equation}\label{eq:model} \PP\left(y_t^{(i)}=1 \Big\| w_{t-d}^{t-1} \right) = g\left((w_{t-d}^{t-1})^{ \mathrm{\scriptscriptstyle T} } \theta_i\right), \quad t = d+1,\dots,T, \ i = 1,\dots,N_1, \end{equation} where $\theta_i \in \RR^N$ ($N = 1+N _3+dN_2+dN_1$) is the parameter to be estimated: $$\theta_i = \left(\nu_i,\gamma_{i1},\dots,\gamma_{iN_3},\beta_{i11},\dots,\beta_{i1d},\beta_{iN_21},\dots,\beta_{iN_2d},\alpha_{i11},\dots,\alpha_{i1d},\alpha_{iN_11},\dots,\alpha_{iN_1d}\right)^{ \mathrm{\scriptscriptstyle T} }.$$ This parameter summarizes the influence from all variables to node $i$ and could be estimated independently from the remaining $N_1-1$ parameters. {\it Granger Causality.} We can see \eqref{eq:model} is actually a generalized linear version of Vector Autoregressive (VAR) model. Therefore, we say $j$-th node series $\{y^{(j)}_t\}$ (or vital sign series $\{x^{(j)}_t\}$) Granger-causes $i$-th node series $\{y_t^{(i)}\}$ if $\alpha_{ij\tau} \not= 0$ (or $\beta_{ij\tau} \not= 0$) for some $\tau \in \{1,\dots,d\}$. {\it Estimation method.} Denote the observation by $W_{T}:=(w_{1-d}^{0},\dots,w_{T-d+1}^{T}) \in \RR^{(T+1) \times N}$, where variables observed at time step $1-d,\dots,0$ are viewed as given history. We assume parameter $\theta_i$ is constrained in a convex compact set $\theta_i \in \Theta_i \subset \RR^N$, then, for $i = 1,\dots,N_1$, we use the weak solution to the following variational inequality as the estimator $\hat \theta_i$: \vspace{-0.1in} \begin{equation} \text { find } \hat \theta_i \in \Theta_i:\langle F_{ W_{T}}^{(i)}(\theta), \theta-\hat \theta_i\rangle \geq 0, \quad \forall \theta \in \Theta_i, \label{VI_1}\tag{{VI}$[ F_{W_{T}}^{(i)}, \Theta_i]$} \end{equation} \vspace{-0.1in} where $F_{W_{T}}^{(i)}(\theta_i)$ is the empirical vector field and defined as follows: \vspace{-0.2in} $$F_{W_{T}}^{(i)}(\theta_i) := \frac{1}{T} \sum_{t=1}^T w_{t-d}^{t-1} \left( g\left((w_{t-d}^{t-1})^{ \mathrm{\scriptscriptstyle T} } \theta_i\right) - y_t^{(i)} \right).$$ \vspace{-0.2in} \paragraph{Remarks.} (i) The intuition behind this method is straightforward. Let's consider the global counterpart of the above vector field, whose root/weak solution is the unknown ground truth $\theta_i^{\text{\rm true}}$, \vspace{-0.15in} $$F^{(i)}(\theta_i) := \EE_{(w,y^{(i)})} \left[w \left( g\left(w^{ \mathrm{\scriptscriptstyle T} } \theta_i\right) - y^{(i)} \right)\right] = \EE_{(w,y^{(i)})} \left[w \left( g\left(w^{ \mathrm{\scriptscriptstyle T} } \theta_i\right) - g\left(w^{ \mathrm{\scriptscriptstyle T} } \theta_i^{\text{\rm true}}\right) \right)\right].$$ \vspace{-0.1in} Although we cannot access this global counterpart, by solving the empirical one \ref{VI_1} we could approximate the ground truth very well. We will show how well this approximation would be in the next section. (ii) Least Square Estimation for Linear VAR model and Maximum Likelihood Estimation for logistic regression model are both special cases of our proposed VI estimates; detailed derivations are deferred to Appendix~\ref{appendix:eg}. \vspace{-0.15in} \section{Non-asymptotic error bound and confidence interval} \vspace{-0.1in} Now, we show the VI estimate will eventually converge to a very small neighborhood of the ground truth. Besides, we will derive a linear program (LP) based confidence interval (CI) of parameters $\theta_i$'s. {\it Non-asymptotic bound on estimation error.} To begin with, we state two necessary model assumptions: \begin{assumption}\label{assumption:vector_field} The link function $g(\cdot)$ is continuous and monotone, and the vector field $G(\theta) = \EE_w[wg(w^{ \mathrm{\scriptscriptstyle T} }\theta)]$ is well defined (and therefore monotone along with $g$). Moreover, $g$ is differentiable and has uniformly bounded first order derivative $m_g \leq \|g'\|\leq M_g$ for positive constants $m_g, M_g$. \end{assumption} \begin{assumption}\label{assumption:observation} The observations (static, binary and continuous) are bounded almost surly: there exists $M_w>0$ such that at any time step $t$, we have $\norm{w_{t-d}^{t-1}}_\infty \leq M_w$ with probability one. \end{assumption} We will use an auxiliary vector field defined as follows: \vspace{-0.15in} $$\Tilde{F}_{W_{T}}^{(i)}(\theta_i) := \frac{1}{T} \sum_{t=1}^T w_{t-d}^{t-1} \left( g\left((w_{t-d}^{t-1})^{ \mathrm{\scriptscriptstyle T} } \theta_i\right) - g\left((w_{t-d}^{t-1})^{ \mathrm{\scriptscriptstyle T} } \theta_i^{\text{\rm true}}\right) \right).$$ \vspace{-0.1in} This vector field changes the constant term in ${F}_{W_{T}}^{(i)}(\theta_i)$ to make sure its unique root/weak solution to corresponding VI is the unknown ground truth $\theta_i^{\text{\rm true}}$. Recall that $\hat \theta_i$ is the root of ${F}_{W_{T}}^{(i)}(\theta_i)$. Then, we will bound the difference between $\hat \theta_i$ and $\theta_i^{\text{\rm true}}$ via the difference between ${F}_{W_{T}}^{(i)}(\theta_i)$ and $\Tilde{F}_{W_{T}}^{(i)}(\theta_i)$: $$\Delta^{(i)} := {F}_{W_{T}}^{(i)}(\theta_i) - \Tilde{F}_{W_{T}}^{(i)}(\theta_i) = {F}_{W_{T}}^{(i)}(\theta_i^{\text{\rm true}}).$$ \begin{lemma}\label{lma:bound_delta} Under Assumptions~\ref{assumption:vector_field} and \ref{assumption:observation}, for $i = 1,\dots,N_1$, $\forall \ \varepsilon \in (0,1)$, with probability at least $1-\varepsilon$, the difference between the empirical and auxiliary vector field $\Delta^{(i)}$ can be bounded as follows: \begin{equation}\label{eq:bound_inf} \norm{\Delta^{(i)}}_\infty \leq M_w \sqrt{{\log(2N/\varepsilon)}/{T}} \end{equation} Moreover, this implies \begin{equation}\label{eq:bound_l2} \norm{\Delta^{(i)}}_2 \leq M_w \sqrt{N{\log(2N/\varepsilon)}/{T}}. \end{equation} \end{lemma} The proof of the above lemma leverages the concentration property for martingales. Similar results could also be found in \citet{juditsky2020convex,wei2021inferring}. We defer its proof to Appendix~\ref{appendix:proof}.We want to remark that further improvement on this bound can be achieved by Bernstein inequality (as \citet{juditsky2020convex} did), but the order will remain the same. \begin{theorem}[Upper bound on $\norm{\hat \theta_i - \theta_i^{\text{\rm true}}}_2$]\label{thm:upper_err_bound} Under Assumptions~\ref{assumption:vector_field} and \ref{assumption:observation}, for $i = 1,\dots,N_1$ and any $\varepsilon \in (0,1)$, with probability at least $1-\varepsilon$, the $\ell_2$ distance between ground truth $\theta_i^{\text{\rm true}}$ and $\hat \theta_i$, which is weak solution to \ref{VI_1}, can be upper bounded as follows : $$\norm{\hat \theta_i - \theta_i^{\text{\rm true}}}_2 \leq \frac{M_w}{m_g \lambda_1} \sqrt{\frac{N\log (2N/\varepsilon)}{T }},$$ where where $\lambda_1$ is the smallest eigenvalue of $\mathbb{W}_{1:T} = \sum_{t=1}^T w_{t-d}^{t-1}(w_{t-d}^{t-1})^{ \mathrm{\scriptscriptstyle T} }/T$. \end{theorem} \textbf{Remarks.} (i) The above theorem is an extension to the general link function case of Theorem 1 \citep{juditsky2020convex}, where they only sketched the proof without giving further details; we defer the detailed proof to Appendix~\ref{appendix:proof}. (ii) As pointed out in \citet{juditsky2020convex}, $\mathbb{W}_{1:T} \in \RR^{N \times N}$ will be full rank when $T$ is sufficiently large, i.e., with high probability, $\lambda_1$ will be a positive constant. {\it Linear Program-based confidence interval.} As pointed out in section II.E \citep{juditsky2020convex}, for general non-linear link function $g$, it would be hard to separate $\theta_i$ from $\sum_{t=1}^T w_{t-d}^{t-1} g\left((w_{t-d}^{t-1})^{ \mathrm{\scriptscriptstyle T} } \theta_i\right)/T$. First, we derive a CI for linear link function case via a more precise data-driven bound for $F_{W_{T}}^{(i)}(\theta_i)\in \RR^N$ as \citet{juditsky2020convex} did in Lemma 2 (see its proof in Appendix~\ref{appendix:CI}): \begin{proposition}[Confidence interval for linear transform of $\theta_i$ for linear link function case]\label{prop:CI} Under Assumptions~\ref{assumption:vector_field} and \ref{assumption:observation}, for $i = 1,\dots,N_1$, and every $s > 1$, the following holds with probability at least $1-2N\{s[\log((s-1)T)+2] + 2\} e^{1-s}$: $$\theta_\ell[W_T,s;i] \leq a^{ \mathrm{\scriptscriptstyle T} } \theta_i \leq \theta_u[W_T,s;i], \quad \forall a \in \RR^N,$$where $\theta_\ell[W_T,s;i]$ and $\theta_u[W_T,s;i]$ are defined in \eqref{eq:CI_lower} and \eqref{eq:CI_upper}, respectively. \end{proposition} This CI is obtained by solving LPs \eqref{eq:CI_lower} and \eqref{eq:CI_upper}. For general non-linear link function $g$, since it is typically constrained in a compact subset to satisfy Assumption~\ref{assumption:vector_field} (see Example~\ref{eg:logistic} in Appendix~\ref{appendix:eg}), we can obtain linear bounds on the non-linear link function and then repeat the above techniques to obtain similar CI; details on this generalization can be found in Appendix~\ref{appendix:CI}. \vspace{-0.15in} \section{Real data experiments} \vspace{-0.1in} In Experiment 1, nodes in the network are constructed by a clinician based on well-known, measurable, physiologic relationships in the human body. This expert-driven approach is subsequently compared to a purely data-driven model for identifying possible clusters of inpatient data in Experiment 2. \vspace{-0.1in} \subsection{Experiment 1: network topology based on known physiologic relationships}\label{subsec:exp1} \vspace{-0.1in} { \it Feature construction.} As previously described, vital sign measurements were condensed into single features represented by summary statistics (i.e., maximum, minimum, mean) of the past 6 hours, creating a total of 12 distinct representations of a patient's vital signs. A count of total Lab tests over the past 6 hours was used as a proxy for patient acuity and was also incorporated as a feature. SAD nodes were created by grouping all 34 Lab measurements into ten nodes (see Table~\ref{table:node_construction}) representative of common physiologic derangements seen in sepsis. Moreover, instead of constructing a sequence of binary variables for each node, we assigned a risk score at each time, indicating the severity of the SAD. However, when a variable (i.e., node) was used as the response during modeling, it was treated as binary by applying indicator function $\mathbf{1}_{\{y > 0\}}$. { \it Sub-group analysis.} To simplify model development, we carried out a sub-group analysis and excluded demographic features from the model. We used sex $= 0$ (female) and age $>60$ sub-group in the following to demonstrate our method, which contained 5,222 patients in the Physionet data set. {\it Model fitting.} The primary outcome of interest was sepsis, which necessitated the addition of an $11$-th binary time series called ``SepsisLabel'' to our data. This resulted in a total of $N_1 = 11$ nodes in our network. Using each of those $N_1$ variables as responses (recall that risk scores were binarized when used as a response) and the rest as features, we performed forward feature selection and fitted logistic regression models with hyperparameter being the number of training iterations. The primary cross-validation criterion for both feature selection and hyperparameter tuning was the True Positive (TP) rate (classification accuracy for positive samples); we also compared classification error and AUC. TP rate was chosen because in a clinical setting, particularly as it pertains to sepsis, greater importance is placed on not missing the disease (i.e., maintaining a high sensitivity) as opposed to producing a false alert. We defer further details of the training procedure to Appendix~\ref{appendix:training_details}. {\it Results and interpretation.} As previously discussed, nodes were created by a clinician to identify the distinct types of measurable, physiologic change that accompanies sepsis-related illness (i.e., SAD nodes); however, the clinician did not determine the relationship amongst the SAD nodes. Rather, these relationships were an output of model training. Both { Table~\ref{table:model_coeff}} and { Figure~\ref{fig:new_net_structure}} illustrate a compelling network of SAD nodes that follow closely with known and expected causal relationships in sepsis-related illness. For example, the finding that Diminished Cardiac Output strongly promotes sepsis events or that Shock strongly promotes Coagulopathy are well-appreciated relationships. The primary outcome of interest for this work was sepsis; still, as demonstrated in {Table~\ref{table:model_coeff}}, the causal relationship between any node pair can be estimated, giving clinician users insight into the probability of observing subsequent SADs after sepsis. \begin{table}[!htp] \vspace{-0.15in} \caption{Coefficients for discrete Hawkes network. For each node, from left to right, and from the first row to the second row, the order of feature follows the order in forwarding selection.}\label{table:model_coeff} \vspace{-0.15in} \begin{center} \begin{small} \begin{sc} \resizebox{1\textwidth}{!}{% \begin{tabular}{lcccccc} \toprule[1pt]\midrule[0.3pt] \textbf{ Renal Injury} & Oxygen Carrying Dysfunction & Diminished Cardiac Output & Oxygenation Dysfunction & Shock & Inflammation \\ (TP rate = 0.724) & 0.355 & 0.025 & 0.086 & 0.097 & 0.057 \\ \cmidrule(l){2-6} & Coagulopathy & Cholestasis \\ & 0.067 & 0.179 \\ \midrule \textbf{Electrolyte Imbalance} & Oxygen Carrying Dysfunction & Coagulopathy & HR (max) & Sepsis & Oxygenation Dysfunction \\ (TP rate = 0.705)& 0.330 & 0.261 & 0.016 & 0.065 & 0.073 \\ \cmidrule(l){2-6} & Inflammation \\ & 0.071\\ \midrule \textbf{Oxygen Carrying Dysfunction} & Renal Injury & Coagulopathy & Electrolyte Imbalance & Diminished Cardiac Output & Shock \\ (TP rate = 0.703) & 0.287 & 0.431 & 0.513 & 0.174 & -0.038 \\ \cmidrule(l){2-6} & Oxygenation Dysfunction & O2Sat min \\ & 0.039 & 0.139\\ \midrule \textbf{Shock} & Inflammation & Diminished Cardiac Output & HR (max) & Coagulopathy & Renal Injury \\ (TP rate = 0.673) & 0.088 & 0.234 & 0.324 & 0.350 & 0.190 \\ \cmidrule(l){2-6} & Electrolyte Imbalance & Oxygenation Dysfunction & ICULOS\\ & 0.294 & 0.148 & 0.097 \\ \midrule \textbf{Diminished Cardiac Output} & Electrolyte Imbalance & Shock & Inflammation & Hepatocellular Injury & Oxygen Carrying Dysfunction \\ (TP rate = 0.622) & 0.086 & 0.117 & 0.013 & 0.085 & 0.233 \\ \cmidrule(l){2-6} & Resp mean & Temp max\\ & -0.041 & 0.077\\ \midrule \textbf{Coagulopathy} & Hepatocellular Injury & Oxygen Carrying Dysfunction & Shock & Cholestasis & Sepsis \\ (TP rate = 0.632) & 0.173 & 0.211 & 0.238 & 0.215 & 0.019 \\ \cmidrule(l){2-6} & Electrolyte Imbalance & Renal Injury & HR (max) \\ & 0.259 & 0.144 & 0.020\\ \midrule \textbf{Cholestasis} & Shock & Hepatocellular Injury & HR (mean) & Renal Injury & Coagulopathy \\ (TP rate = 0.677)&-0.002 & 0.864 & 0.127 & 0.295 & 0.397 \\ \cmidrule(l){2-6} & Inflammation & Sepsis & ICULOS & Oxygenation Dysfunction\\ & -0.002 & 0.048 & 0.324 & 0.089\\ \midrule \textbf{Hepatocellular Injury} & Inflammation & Oxygen Carrying Dysfunction & Shock & Sepsis & Diminished Cardiac Output \\ (TP rate = 0.619) & 0.060 & 0.170 & 0.063 & 0.088 & 0.043 \\ \cmidrule(l){2-6} & Coagulopathy & MAP (min) & O2Sat min & Renal Injury \\ & 0.434 & 0.063 & 0.008 & 0.262 \\ \midrule \textbf{Oxygenation Dysfunction} & Sepsis & Inflammation & Resp (mean) & Shock & Diminished Cardiac Output \\ (TP rate = 0.780)& 0.093 & 0.047 & 2.538 & 0.699 & 0.237 \\ \cmidrule(l){2-6} & MAP min & Hepatocellular Injury\\ & 0.060 & 0.111\\ \midrule \textbf{Inflammation} & Sepsis & HR (max) & Renal Injury & Oxygenation Dysfunction & Shock \\ (TP rate = 0.710)& 0.099 & 1.597& 0.117 & 0.119 & 0.176 \\ \midrule \textbf{Sepsis} & HR (mean) & ICULOS& Renal Injury& Inflammation& Electrolyte Imbalance \\ (TP rate = 0.768)& 0.174& 0.722& 0.509& 0.165& 0.200 \\ \cmidrule(l){2-6} & Diminished Cardiac Output& Resp (min) & Coagulopathy\\ &0.387& 0.458& -0.104\\ \midrule[0.3pt]\bottomrule[1pt] \end{tabular} } \end{sc} \end{small} \end{center} \vspace{-0.25in} \end{table} {\it Bootstrap confidence intervals.} We also performed uncertainty quantification via bootstrap. We determined the existence of an edge in the network based on the $90\%$ bootstrap confidence interval (CI), i.e., we assigned zero weight to that edge if the CI contains zero; otherwise, we used the median of the bootstrap samples as the weight. The resulting network topology is reported below in Figure~\ref{fig:tp_network_structure_CI_thres}. Meanwhile, we also used classification error as the CV criterion to infer the network topology in Figure~\ref{fig:err_network_structure_CI_thres}. We applied hard thresholding on the network topology to improve legibility by only keeping directed edges whose absolute weights are greater than $0.15$. For the complete network topology (without hard thresholding), one can see Figures~\ref{fig:old_network_structure_CI} and \ref{fig:new_network_structure_CI} in Appendix~\ref{appendix:add_exp}. The networks in Figure~\ref{fig:tp_network_structure_CI_thres} help to elucidate which relationships are most important in the network, which is an essential aspect of interpretability. The network with forward selection shows a high level of influence by the Diminished Cardiac Output and Shock nodes. This is not surprising as both of these SADs are known to cause organ injury. The network that does not use forward selection has identified relationships that suggest certain SADs actually have an inhibitory effect. While there are possible explanations for these inhibitory effects, they are not commonly known or expected from a physiologic perspective. Overall, the network that employees forward feature selection demonstrates a more meaningful series of relationships consistent with known physiologic responses to sepsis. \begin{figure}[!htp] \vspace{-0.05in} \centerline{ \includegraphics[width = 0.4\textwidth,trim={4cm 0 2.8cm 0},clip]{fig/CI_graph/TP_thres_0.15_CI_new.pdf} \hspace{0.1in} \includegraphics[width = 0.4\textwidth,trim={4cm 0 2.8cm 0},clip]{fig/CI_graph/TP_thres_0.15_CI_old.pdf} } \vspace{-0.1in} \caption{Bootstrap network topology with (left) and without (right) feature selection. We only keep (directed) edge with absolute weight greater than 0.15. The blue (directed) edge indicates a positive effect, whereas the red indicates a negative effect. The cross-validation criterion is TP rate.} \label{fig:tp_network_structure_CI_thres} \vspace{-0.25in} \end{figure} \vspace{-0.1in} \subsection{Experiment 2: data-driven measurement clustering and network topology} \vspace{-0.1in} In our second experiment, we assumed there was no prior information regarding the nature of the network and instead re-grouped the 34 measurements in Table~\ref{table:node_construction} using a purely data-driven method. We constructed 34 binary time series and provided a label ``$1$'' if the Lab test was reported out AND the Lab result was abnormal based on the rules in Table~\ref{table:node_construction}. {\it Hierarchical clustering based on ``distance'' matrix.} Analysis of the similarity among measurements begins with the construction of a correlation matrix including all 34 measurements in Figure~\ref{fig:dist_mat}. In this case, correlation occurs when both variables are found to be abnormal. For example, one can see that when \texttt{Creatinine} is abnormal, it likely that \texttt{BUN} and \texttt{Phosphate} would also be abnormal based on the correlation matrix. This correlation and many of the others in the table like this are commonly found in sepsis patients. \begin{wrapfigure}{r}{0.64\textwidth} \vspace{-0.2in} \centerline{ \includegraphics[width = 0.3\textwidth]{fig/data_exploration/cor_mat.png} \hspace{0.15in} \includegraphics[width = 0.3\textwidth]{fig/network_cls/hawkes_network_raw.png} } \vspace{-0.1in} \caption{Correlation matrix (left) and adjacency matrix for discrete Hawkes network (right).} \label{fig:dist_mat} \vspace{-0.15in} \end{wrapfigure} We can view the correlation as statistical distance. Since larger correlation indicates smaller ``distance'', we used the element-wise inverse of the correlation matrix as the distance matrix. Here we grouped those measurements based on positive correlation; for those with negative or zero correlation, we treated them as though they are very far away from each other and assigned a large constant as the distance. Then, we can apply (hierarchical) clustering to obtain the clusters. The resulting clusters are plotted in Figure~\ref{fig:Hierarchical_clustering}. \begin{figure}[!htp] \vspace{-0.05in} \centerline{ \includegraphics[width = 0.5\textwidth]{fig/network_cls/corr_cls.png} \includegraphics[width = 0.5\textwidth]{fig/network_cls/sym+h_cls+ward_2.png} } \vspace{-0.1in} \caption{Hierarchical clustering based on correlation (left) and discrete Hawkes network (right).} \label{fig:Hierarchical_clustering} \vspace{-0.05in} \end{figure} Similar to the fitting procedure above, we fitted our proposed discrete Hawkes network model on those 34 binary time series to construct a directed graph. We plot the adjacency matrix in Figure~\ref{fig:dist_mat}. Here, the adjacency matrix is asymmetric, which makes it difficult to perform clustering. This asymmetric adjacency matrix $A$ can be symmetrized by using $A_{sym} = A + A^{ \mathrm{\scriptscriptstyle T} }$. Then we can apply the same method as we did for the correlation matrix above to complete the (hierarchical) clustering. The result is plotted in Figure~\ref{fig:Hierarchical_clustering}. Both approaches for clustering patient features (i.e., via simple correlation and via a discrete Hawkes network) produce nodes that share similarity with the SAD nodes derived by a clinical expert in Experiment 1. For example, in Figure~\ref{fig:Hierarchical_clustering} we see a cluster that includes the measurements: \texttt{Lactate, PaCO2, BaseExcess, pH} which commonly become deranged during shock. While these measurements do occur together on a common Lab panel (i.e., they are often collected simultaneously), this doesn't necessarily imply that their derangements would be similarly correlated as this label panel has many permutations of derangement caused by different non-sepsis disease processes. It is more reasonable to consider that the data-driven clustering methods are independently identifying clinically relevant SADs. While the simple correlation approach identifies concomitant relationships (i.e., two things happening together), it does not consider a time-dependent, causal relationship the way the Hawkes network does. This important distinction is appreciated when considering the two maps in Figure~\ref{fig:Hierarchical_clustering}. The Hawkes process develops nodes that have close intra-node relationships that are very clearly separated from other clusters. In contrast, the inter-node distances tend to be less pronounced in the correlation-based hierarchical clustering method. {\it Blockmodelling based on asymmetric Hawkes network.} In this approach, we define clusters using a stochastic block model: for any two clusters $V_i$ and $V_j$ and any two nodes $a,b \in V_i$; then there is approximately the same number of in-edges (respectively out edges) connecting $a$ to nodes in $V_j$ and of in-edges (respectively out edges) connecting $b$ to nodes in $V_j$. Identifying clusters from asymmetric adjacency matrix is called blockmodelling \citep{holland1983stochastic,wang1987stochastic}. We introduce a spectral algorithm for blockmodelling \citep{sussman2012consistent} in Appendix~\ref{appendix:blockmodelling}. This algorithm has hyperparameters $K$ (number of clusters/blocks) and $d$ (top $d$ eigenvectors are kept in the spectral decomposition). Since it only deals with unweighted directed graphs, we construct the unweighted adjacency matrix by thresholding with $0.15$ as we did before. By applying the spectral algorithm recursively, we get hierarchical blockmodels and report the results in Figure~\ref{fig:blockmodelling}. \begin{figure}[!htp] \vspace{-0.15in} \centerline{ \includegraphics[width = 0.45\textwidth]{fig/network_cls/blockmodelling.png} \hspace{0.15in} \includegraphics[width = 0.45\textwidth]{fig/network_cls/blk.pdf} } \vspace{-0.05in} \caption{Left: Hierarchical Blockmodeling (hyperparameter under each plot). We chose the smallest $d$ such that the explained variance ratio is at least $95\%$. Right: the resulting network topology.} \label{fig:blockmodelling} \vspace{-0.1in} \end{figure} Based on Hierarchical Blockmodeling, we identify five blocks/clusters and the associated network topology among them. Analysis of the first level suggests a predominantly renal-inflammatory axis in Group A with values like \texttt{Creatinine, BUN, Phosphate, WBC} being important, and a cardio-pulmonary axis in Group B with values like \texttt{SaO2, O2Sat, SBP, Temp} being important. Inside of Group A, we see derangements following known patterns that demonstrate renal injury (A1) promoting electrolyte imbalances (A2). Similarly, we see in Group B that reduced blood pressure and fevers (B3) promote aberrations in oxygenation and acid/base equilibrium (B2) (a frequent association in sepsis). For demonstration purposes, this Hierarchical Blockmodel created the adjacency matrix using a threshold of 0.15; however, this could be lowered to identify a higher number of clusters and relationships. While single nodes are grouped together to form a cluster, it does not necessarily mean there is a correlation within the cluster (unless there is a self-directed edge (e.g., A2). Instead, the composite effect of nodes within a cluster promote dysfunction in the nodes of other clusters to which it is connected. \begin{table}[H] \vspace{-0.05in} \caption{Data-driven cluster based on Hierarchical Blockmodelling.}\label{table:measurement_clsutering} \vspace{-0.15in} \begin{center} \begin{small} \begin{sc} \resizebox{1\textwidth}{!}{% \begin{tabular}{ccl} \toprule[1pt]\midrule[0.3pt] 1st-level cluster & 2nd-level cluster & Measurement physionet name \\ \midrule[0.3pt] \textbf{A} & A1 & Creatinine , Potassium , HCO3 , Magnesium , Bilirubin total , WBC;\\ \cmidrule(l){2-3} & A2 & Phosphate , BUN , Chloride , Hct , Hgb , Platelets , Glucose ;\\ \midrule[0.3pt] \textbf{B} & B1 & Calcium , BaseExcess , SaO2 , PaCO2 ;\\ \cmidrule(l){2-3} & B2 & Lactate , pH , DBP , O2Sat ;\\ \cmidrule(l){2-3} &B3& SBP , PTT , Temp ;\\ \cmidrule(l){2-3} &NA& MAP , Fibrinogen , Bilirubin direct , Alkalinephos , AST , Resp , EtCO2 , FiO2 , HR , SepsisLabel \\ \midrule[0.3pt]\bottomrule[1pt] \end{tabular} } \end{sc} \end{small} \end{center} \vspace{-0.2in} \end{table} \newpage \bibliographystyle{plainnat} \section{Introduction} Automated surveillance tools aimed at identifying a patient's deterioration inside the hospital are becoming more common and stand to enhance a clinician's situational awareness; however, model predictions related to disease identification, particularly for complex diseases, still need to be adjudicated (i.e., interpreted) by a clinician before further action (i.e., treatment) can be initiated. Sepsis is a life-threatening medical condition contributing to one in five deaths globally \citep{world2020global} and exists as one of the most important cases for automated in-hospital surveillance. Sepsis is formally defined as life-threatening organ dysfunction caused by a dysregulated host response to infection \citep{singer2016third}. Delays in recognizing sepsis and initiating appropriate treatment can adversely impact patient outcomes. In a recent study of adult sepsis patients, each hour of delayed treatment was associated with higher risk-adjusted in-hospital mortality (odds ratio, 1.04 per hour) \citep{seymourTimeTreatmentMortality2017}. It stands to reason that early recognition of the physiologic aberrations preceding sepsis would afford clinicians more time to intervene and may contribute to improving outcomes and reducing costs. A number of machine learning methods have been developed to predict the onset of sepsis utilizing data from the electronic medical record (EMR) \citep{fleuren2020machine}. A recent sepsis prediction competition \citep{reyna2019early} demonstrated both the popularity and robust performance of XGBoost models \citep{du2019automated,zabihi2019sepsis,yang2020explainable}; meanwhile, Deep Neural Networks \citep{shashikumarDeepAISEInterpretableRecurrent2021} are also commonly used. Regrettably, most approaches offer an alert adjudicator very little information pertaining to the reason for the alert/prediction, leading many to refer to them as ``black box'' techniques. Among the aforementioned works, \citet{yang2020explainable} provided one of the best attempts at identifying causality for their models' predictions by reporting feature importance at a global level for all patients; however, this does not convey which features were most important in arriving at a given prediction for an individual patient. The common lack of interpretability of many clinical models, particularly those related to sepsis, suggests that a principled method (with theoretical guarantee) to study the interactions among time series in medical settings is underdeveloped. \begin{figure}[!htp] \centerline{ \includegraphics[width = 0.6\textwidth]{fig/network_graph/new_network.pdf} } \caption{Granger Causal graph over endogenous Sepsis Associated Derangement (SAD) indicators obtained via discrete Hawkes network with forward feature selection.} \label{fig:new_net_structure} \end{figure} Granger causal graphs, which analyze interactions among time series defined by association, avoid this limitation and afford a clinical adjudicator the ability to understand why an alert was made. The syndromic nature of sepsis means that there is a constellation of different physiologic derangements that can combine to create the condition. As evidenced in Figure~\ref{fig:new_net_structure}, a series of different nodes representing these types of physiologic derangements has been created. The relationships between nodes and their effect on sepsis are explained via generalized linear models (GLM), providing insight into what ``caused'' the alert. For example, a clinical adjudicator might be more inclined to arrive at a concordant opinion regarding sepsis if they were informed that the alert was caused by the combined effects from the Renal Injury and Diminished Cardiac Output nodes. Likewise, this same adjudicator might be less inclined to corroborate an alert on a different patient if the main contributing cause was from Electrolyte Imbalance alone. Linear Vector Autoregressive (VAR) model is the most popular method in studying the Granger causal graph among multiple time series \citep{lutkepohl2005new}. However, it has been pointed out by a recent survey study \citep{shojaie2021granger} that this approach suffers from assumptions such as linearity and continuous-valued series, since the real-data, which can be both continuous- and categorical-valued, usually exhibits complex dynamics; another flaw of classic linear VAR model is unscalability to high-dimension, which arises when one tries to identify all series as endogenous, since it is hard to check if we have all relevant information at hand in practice. In this work, we adopt a generalized linear model (GLM) approach for binary time series — spatio-temporal Bernoulli process \citep{juditsky2019signal,juditsky2020convex} — and generalize it to handle both continuous- and discrete-valued as well as regularly and irregularly sampled time series and learn a Granger causal graph over Sepsis Associated Derangements (SADs). We perform forward feature selection to remove redundant information and increase the signal-noise ratio. We demonstrate via real data experiments that our proposed GLM coupled with forward feature selection can achieve comparable performance to a powerful method such as XGBoost. One novel aspect of this work comes from the real underlying problem: we build a {\it highly interpretable} model from {\it mixed-type series}. The prioritization of interpretability considers the needs of the end-users, namely clinicians. This consideration of real-world constraints makes future adoption of these models much more likely for those conducting continuous surveillance of high-risk patients. In the medical setting, the observations can be both discrete and continuous-valued and sampled with different frequencies. For example, vital signs are recorded regularly, whereas laboratory (lab) tests are only ordered when clinically necessary; thus, this cannot be simply formulated into a missing data problem. Moreover, what separates our method from the classic linear VAR time series is the generalization to non-linear dynamics and a novel stochastic monotone variational inequality-based estimator. Most importantly, we develop a non-asymptotic upper bound on estimation error AND a Linear Program-based confidence interval for graph structure for arbitrary monotone (non-linear) link function for our proposed method. {\textbf{Related work. }} Recent developments on the Granger causal graph mainly focus on non-linear dynamics and tackling high-dimensionality via regularization: the former includes applying a separable matrix-valued kernel \citep{sindhwani2012scalable} and neural networks \citep{tank2018neural} to learn non-linear Granger causality; other approaches address the issue of high-dimensionality caused by viewing all series as endogenous. Techniques include group Lasso \citep{bolstad2011causal,basu2015network} and nuclear norm regularization \citep{basu2019low}. Another notable work \citep{nicholson2017varx} modeled endogenous and exogenous variables separately (instead of treating all series endogenous) and used different penalties on endogenous and exogenous variables to learn the sparse graph structure. We should mention that our method closely resembles \citet{nicholson2017varx}: part of features comes from direct observations and is treated exogenous (e.g., vital signs and Lab test results), whereas the remaining SADs are derived from the first part and viewed as endogenous. \section{Problem set-up and proposed model} \subsection{Mixed-type series}\label{sec:background} Data used for this analysis was a curated, publicly available data set from the 2019 Physionet challenge \citep{physionet2019}. The challenge data was sourced from patients admitted to the Intensive Care Unit (ICU) during their hospitalization and represented three categories of patient features: vital sign measurements, Laboratory (Lab) results, and demographic information. { \it Vital Signs.} Vital signs in ICU environments are normally recorded at an hourly interval and include \texttt{HR, O2Sat, Temp, SBP, MAP, DBP, Resp} (see Table~\ref{table:node_construction} for their full measurement names). Among the blood pressure measurements (\texttt{SBP}, \texttt{DBP}, and \texttt{MAP}), we only keep \texttt{MAP} in our study since \texttt{MAP} = (\texttt{SBP} + 2\texttt{DBP})$/3$. { \it Lab Values.} Lab tests are most commonly collected once every 24 hours; however, this collection frequency may change based a the severity of a patient's illness. In addition to individual Lab values, we also use the count of the Lab tests over the past 6 hours as a proxy to represent the severity of a patient's illness (i.e., more severe disease results in more tests being ordered). { \it Sepsis Associated Derangements (SADs).} Thresholds representing breaks between normal and deranged physiology are identified utilizing already establish criteria \citep{ABIM_ref_range}. We condense different measurements (containing both vital signs and Lab results) into a binary variable as an indicator of physiologic derangements seen preceding and during sepsis (see column ``SAD name'' in Table~\ref{table:node_construction}). \begin{table}[!htp] \caption{SAD construction based on thresholding exogenous observations via medical knowledge.}\label{table:node_construction} \begin{center} \begin{small} \begin{sc} \resizebox{1\textwidth}{!}{% \begin{tabular}{llccc} \toprule[1pt]\midrule[0.3pt] SAD name & Measurement name & Physionet name & Rule & Risk score \\ \midrule[0.3pt] \textbf{ Renal Injury} & creatinine & Creatinine & >1.3 & 0.667 \\ & potassium & Potassium & >5.0 & 0.067 \\ & phosphorus & Phosphate & >4.5 & 0.067 \\ & bicarb (hco3) & HCO3 & >26 & 0.067 \\ & blood urea nitrogen (bun) & BUN & >20 & 0.133 \\ \cmidrule(l){2-5} \textbf{Electrolyte} & calcium & Calcium & >10.5 & 0.167 \\ \textbf{Imbalance} & chloride & Chloride & <98 or >106 & 0.667 \\ & magnesium & Magnesium & <1.6 & 0.167 \\ \cmidrule(l){2-5} \textbf{Oxygen Carrying} & hematocrit & Hct & <37 & 0.500 \\ \textbf{Dysfunction} & hemoglobin & Hgb & <12 & 0.500 \\ \cmidrule(l){2-5} \textbf{Shock} & base excess & BaseExcess & < $-$3 & 0.100 \\ & lactic acid & Lactate & >2.0 & 0.150 \\ & ph & pH & <7.32 & 0.750 \\ \cmidrule(l){2-5} \textbf{Diminished } & sbp cuff & SBP & <120 & 0.250 \\ \textbf{Cardiac Output} & dbp cuff & DBP & <80 & 0.250 \\ & map cuff & MAP & <65 & 0.500 \\ \cmidrule(l){2-5} \textbf{Coagulopathy} & partial prothrombin time (ptt) & PTT & >35 & 0.250 \\ & fibrinogen & Fibrinogen & <233 & 0.250 \\ & platelets & Platelets & <150,000 & 0.500 \\ \cmidrule(l){2-5} \textbf{Cholestasis} & bilirubin direct & Bilirubin direct & >0.3 & 0.100 \\ & bilirubin total & Bilirubin total & >1.0 & 0.500 \\ & alkaline phosphatase & Alkalinephos & >120 & 0.400 \\ \cmidrule(l){2-5} \textbf{Hepatocellular Injury} & aspartate aminotransferase (ast) & AST & >40 & 1.000 \\ \cmidrule(l){2-5} \textbf{Oxygenation } & unassisted resp rate & Resp & >20 & 0.100 \\ \textbf{Dysfunction} & spo2 & O2Sat & <92 \% & 0.200 \\ & saturation of oxygen (sao2) & SaO2 & <92 \% & 0.200 \\ & end tidal co2 & EtCO2 & <35 or >45 & 0.100 \\ & fio2 & FiO2 & >21 \% & 0.300 \\ & partial pressure of carbon dioxide (paco2) & PaCO2 & <35 or >45 & 0.100 \\ \cmidrule(l){2-5} \textbf{Inflammation} & temperature & Temp & <36 or >38 & 0.400 \\ & pulse & HR & >90 & 0.100 \\ & glucose & Glucose & >125 & 0.100 \\ & white blood cell count & WBC & <4,000 or >12,000 & 0.400 \\ \midrule[0.3pt]\bottomrule[1pt] \end{tabular} } \end{sc} \end{small} \end{center} \end{table} { \it Demographics.} Demographic features remain constant throughout hospitalization. The examined data set contains both age and sex. \begin{wrapfigure}{r}{0.6\textwidth} \subfigure{\includegraphics[scale = 0.4]{fig/mixed_data_type.pdf}} \end{wrapfigure} Here, the vital signs (regularly sampled) and raw Lab values (irregularly sampled) are exogenous variables, whereas SAD indicators are endogenous. The irregularly sampled series will be handled via forwarding filling. Our primary interest is to study all exogenous and endogenous series' effects on endogenous series and construct (Granger causal) graph/network over endogenous series. \subsection{Discrete Hawkes network} $$\{y_1^{(i)},\dots,y_T^{(i)}\}, \quad i = 1,\dots,d.$$ \begin{equation} \PP\left(y_t^{(i)}=1 \Big\| x_{t-w}^{t-1} \right) = g\left((x_{t-w}^{t-1})^{ \mathrm{\scriptscriptstyle T} } \theta_i\right), \quad t = w+1,\dots,T, \quad i = 1,\dots,d, \end{equation} where \begin{align} x_{t-w}^{t-1} &= \left(1,y_{t-1}^{(1)},\dots,y_{t-w}^{(1)},\dots,y_{t-1}^{(d)},\dots,y_{t-w}^{(d)}\right)^{ \mathrm{\scriptscriptstyle T} } \in \RR^{1+wd}, \\ \theta_i &= \left(\alpha_{i0},\alpha_{i11},\dots,\alpha_{i1d},\alpha_{iN_11},\dots,\alpha_{iN_1d}\right)^{ \mathrm{\scriptscriptstyle T} } \in \RR^{1+wd}. \end{align} We solve the following VI \begin{equation} \text { find } \hat \theta_i \in \Theta_i:\langle F^{(i)}(\theta), \theta-\hat \theta_i\rangle \geq 0, \quad \forall \theta \in \Theta_i, \end{equation} where $F^{(i)}(\theta_i)$ is the empirical vector field and defined as follows: $$F^{(i)}(\theta_i) := \frac{1}{T-w} \sum_{t=w+1}^T x_{t-w}^{t-1} \left( g\left((x_{t-w}^{t-1})^{ \mathrm{\scriptscriptstyle T} } \theta_i\right) - y_t^{(i)} \right).$$ {\it Model formulation.} Suppose we observe $N_1$ sequences of binary SADs on time horizon $T$: $\{y_1^{(i)},\dots,y_T^{(i)}\}$, $i = 1,\dots,N_1$; we also observe both continuous- and discrete-valued time series $\{x_1^{(i)},\dots,x_T^{(i)}\}, i = 1,\dots,N_2$, which are vital signs and Lab test counts, and demographic variables $(z_1,\dots,z_{N_3})$. In the following, we will call each of those SADs a node variable since it corresponds to a node in the Granger causal graph. With such a model at hand, we can better understand the dynamics within the human body, and most importantly, alert the clinicians to the potential causes and complications of an identified SAD. To model the mutual excitation among those series, we propose a generalized linear model, which closely resembles the intensity function of Hawkes point process \citep{hawkes1971point,hawkes1971spectra,hawkes1974cluster}. For $i$-th node variable ($i = 1,\dots,N_1$), at time step $t \ (t = 2,\dots,T)$, we assume: \begin{equation}\label{eq:hawkes_model} \PP\left(y_t^{(i)}=1 \Big\| \cH_{t-1} \right) = g\left(\nu_i + \sum_{j = 1}^{N_3} \gamma_{ij} z_j + \sum_{\tau = 1}^{t-1} \sum_{j = 1}^{N_2} \beta_{ij} x_{t-\tau}^{(j)} e^{-\Tilde{R}_{ij} \tau} + \sum_{\tau = 1}^{t-1} \sum_{j = 1}^{N_1} \alpha_{ij} y_{t-\tau}^{(j)} e^{-R_{ij} \tau}\right), \end{equation} where $\cH_t$ denotes the past observation up to time $t$ and $g: \RR \rightarrow [0,1]$ is a link function. For example, $g$ can be non-linear, such as sigmoid link function $g(x) = 1/(1+e^{-x})$; also, it can be linear $g(x) = x$, which should be restricted on domain $[0,1] \subset \RR$. {\it Non-linear Granger causal graph.} By the definition of Granger causality in non-linear model \citep{tank2018neural}, we know that matrix $A = (\alpha_{ij}) \in \RR^{N_1 \times N_1}$ represents the causal graph structure over $N_1$ SAD nodes. To be precise, we say $j$-th SAD does NOT Granger cause $i$-th SAD if $\alpha_{ij} = 0$. {\it Connection to Hawkes process.} For $i$-th SAD node variable, $\alpha_{ij}$ and $\beta_{ij}$ represent the magnitude of triggering effect of $j$-th SAD node variable and continuous variable to it. This effect decays exponentially fast with exponent characterized by $R_{ij}$ and $\Tilde{R}_{ij}$. $\gamma_{ij}$'s represent the influence of demographics and contribute to baseline intensity togerther with $\nu_i$. Note that the above model can be viewed as a discretized version of (non-linear) Hawkes process network with exponential triggering function \citep{wang2020uncertainty}; other methods in learning Hawkes network include \citet{xu2016learning,achab2017uncovering}, we do not dig deeper in this direction since it is out of the scope of this work. \section{Parameter estimation with variational inequality} In this section, we will leverage a recently developed technique \citep{juditsky2019signal,juditsky2020convex}, which estimates the parameters of the generalized linear model by solving stochastic monotone variational inequality (VI), to develop a statistically principled method to estimate the parameters of discrete Hawkes network and infer the Granger causal graph topology. {\it Preliminaries.} To begin with, we make reasonable simplification by assuming finite memory depth $d$ for both continuous and binary observations. Let $w_{t-d}^{t-1}$ denote the observation from $t-d$ to $t-1$: $$\left(1,z_1,\dots,z_{N_3},x_{t-1}^{(1)},\dots,x_{t-d}^{(1)},\dots,x_{t-1}^{(N_2)},\dots,x_{t-d}^{(N_2)},y_{t-1}^{(1)},\dots,y_{t-d}^{(1)},\dots,y_{t-1}^{(N_1)},\dots,y_{t-d}^{(N_1)}\right)^{ \mathrm{\scriptscriptstyle T} },$$ where superscript $^{ \mathrm{\scriptscriptstyle T} }$ denotes matrix transpose. Since we only consider finite memory depth for binary observation, we could use one single parameter $\alpha_{ij\tau} := \alpha_{ij} \exp\{-R_{ij} \tau\}$ (similarly, $\beta_{ij\tau} := \beta_{ij} \exp\{-\Tilde{R}_{ij} \tau\}$) to represent the triggering effect with exponential decay. We rewrite \eqref{eq:hawkes_model} into \begin{equation}\label{eq:model} \PP\left(y_t^{(i)}=1 \Big\| w_{t-d}^{t-1} \right) = g\left((w_{t-d}^{t-1})^{ \mathrm{\scriptscriptstyle T} } \theta_i\right), \quad t = d+1,\dots,T, \ i = 1,\dots,N_1, \end{equation} where $\theta_i \in \RR^N$ ($N = 1+N _3+dN_2+dN_1$) is the parameter to be estimated: $$\theta_i = \left(\nu_i,\gamma_{i1},\dots,\gamma_{iN_3},\beta_{i11},\dots,\beta_{i1d},\beta_{iN_21},\dots,\beta_{iN_2d},\alpha_{i11},\dots,\alpha_{i1d},\alpha_{iN_11},\dots,\alpha_{iN_1d}\right)^{ \mathrm{\scriptscriptstyle T} }.$$ This parameter summarizes the influence from all variables to node $i$ and could be estimated independently from the remaining $N_1-1$ parameters. {\it Granger Causality.} We can see \eqref{eq:model} is actually a generalized linear version of Vector Autoregressive (VAR) model. Therefore, we say $j$-th node series $\{y^{(j)}_t\}$ (or vital sign series $\{x^{(j)}_t\}$) Granger-causes $i$-th node series $\{y_t^{(i)}\}$ if $\alpha_{ij\tau} \not= 0$ (or $\beta_{ij\tau} \not= 0$) for some $\tau \in \{1,\dots,d\}$. {\it Estimation method.} Denote the observation by $W_{T}:=(w_{1-d}^{0},\dots,w_{T-d+1}^{T}) \in \RR^{(T+1) \times N}$, where variables observed at time step $1-d,\dots,0$ are viewed as given history. We assume parameter $\theta_i$ is constrained in a convex compact set $\theta_i \in \Theta_i \subset \RR^N$, then, for $i = 1,\dots,N_1$, we use the weak solution to the following variational inequality as the estimator $\hat \theta_i$: \begin{equation} \text { find } \hat \theta_i \in \Theta_i:\langle F_{ W_{T}}^{(i)}(\theta), \theta-\hat \theta_i\rangle \geq 0, \quad \forall \theta \in \Theta_i, \label{VI_1}\tag{{VI}$[ F_{W_{T}}^{(i)}, \Theta_i]$} \end{equation} where $F_{W_{T}}^{(i)}(\theta_i)$ is the empirical vector field and defined as follows: $$F_{W_{T}}^{(i)}(\theta_i) := \frac{1}{T} \sum_{t=1}^T w_{t-d}^{t-1} \left( g\left((w_{t-d}^{t-1})^{ \mathrm{\scriptscriptstyle T} } \theta_i\right) - y_t^{(i)} \right).$$ \paragraph{Remarks.} (i) The intuition behind this method is straightforward. Let's consider the global counterpart of the above vector field, whose root/weak solution is the unknown ground truth $\theta_i^{\text{\rm true}}$, $$F^{(i)}(\theta_i) := \EE_{(w,y^{(i)})} \left[w \left( g\left(w^{ \mathrm{\scriptscriptstyle T} } \theta_i\right) - y^{(i)} \right)\right] = \EE_{(w,y^{(i)})} \left[w \left( g\left(w^{ \mathrm{\scriptscriptstyle T} } \theta_i\right) - g\left(w^{ \mathrm{\scriptscriptstyle T} } \theta_i^{\text{\rm true}}\right) \right)\right].$$ Although we cannot access this global counterpart, by solving the empirical one \ref{VI_1} we could approximate the ground truth very well. We will show how well this approximation would be in the next section. (ii) Least Square Estimation for Linear VAR model and Maximum Likelihood Estimation for logistic regression model are both special cases of our proposed VI estimates; detailed derivations are deferred to Appendix~\ref{appendix:eg}. \section{Non-asymptotic error bound and confidence interval} Now, we show the VI estimate will eventually converge to a very small neighborhood of the ground truth. Besides, we will derive a linear program (LP) based confidence interval (CI) of parameters $\theta_i$'s. {\it Non-asymptotic bound on estimation error.} To begin with, we state two necessary model assumptions: \begin{assumption}\label{assumption:vector_field} The link function $g(\cdot)$ is continuous and monotone, and the vector field $G(\theta) = \EE_w[wg(w^{ \mathrm{\scriptscriptstyle T} }\theta)]$ is well defined (and therefore monotone along with $g$). Moreover, $g$ is differentiable and has uniformly bounded first order derivative $m_g \leq \|g'\|\leq M_g$ for positive constants $m_g, M_g$. \end{assumption} \begin{assumption}\label{assumption:observation} The observations (static, binary and continuous) are bounded almost surly: there exists $M_w>0$ such that at any time step $t$, we have $\norm{w_{t-d}^{t-1}}_\infty \leq M_w$ with probability one. \end{assumption} We will use an auxiliary vector field defined as follows: $$\Tilde{F}_{W_{T}}^{(i)}(\theta_i) := \frac{1}{T} \sum_{t=1}^T w_{t-d}^{t-1} \left( g\left((w_{t-d}^{t-1})^{ \mathrm{\scriptscriptstyle T} } \theta_i\right) - g\left((w_{t-d}^{t-1})^{ \mathrm{\scriptscriptstyle T} } \theta_i^{\text{\rm true}}\right) \right).$$ This vector field changes the constant term in ${F}_{W_{T}}^{(i)}(\theta_i)$ to make sure its unique root/weak solution to corresponding VI is the unknown ground truth $\theta_i^{\text{\rm true}}$. Recall that $\hat \theta_i$ is the root of ${F}_{W_{T}}^{(i)}(\theta_i)$. Then, we will bound the difference between $\hat \theta_i$ and $\theta_i^{\text{\rm true}}$ via the difference between ${F}_{W_{T}}^{(i)}(\theta_i)$ and $\Tilde{F}_{W_{T}}^{(i)}(\theta_i)$: $$\Delta^{(i)} := {F}_{W_{T}}^{(i)}(\theta_i) - \Tilde{F}_{W_{T}}^{(i)}(\theta_i) = {F}_{W_{T}}^{(i)}(\theta_i^{\text{\rm true}}).$$ \begin{lemma}\label{lma:bound_delta} Under Assumptions~\ref{assumption:vector_field} and \ref{assumption:observation}, for $i = 1,\dots,N_1$, $\forall \ \varepsilon \in (0,1)$, with probability at least $1-\varepsilon$, the difference between the empirical and auxiliary vector field $\Delta^{(i)}$ can be bounded as follows: \begin{equation}\label{eq:bound_inf} \norm{\Delta^{(i)}}_\infty \leq M_w \sqrt{{\log(2N/\varepsilon)}/{T}} \end{equation} Moreover, this implies \begin{equation}\label{eq:bound_l2} \norm{\Delta^{(i)}}_2 \leq M_w \sqrt{N{\log(2N/\varepsilon)}/{T}}. \end{equation} \end{lemma} The proof of the above lemma leverages the concentration property for martingales. Similar results could also be found in \citet{juditsky2020convex,wei2021inferring}. We defer its proof to Appendix~\ref{appendix:proof}.We want to remark that further improvement on this bound can be achieved by Bernstein inequality (as \citet{juditsky2020convex} did), but the order will remain the same. \begin{theorem}[Upper bound on $\norm{\hat \theta_i - \theta_i^{\text{\rm true}}}_2$]\label{thm:upper_err_bound} Under Assumptions~\ref{assumption:vector_field} and \ref{assumption:observation}, for $i = 1,\dots,N_1$ and any $\varepsilon \in (0,1)$, with probability at least $1-\varepsilon$, the $\ell_2$ distance between ground truth $\theta_i^{\text{\rm true}}$ and $\hat \theta_i$, which is weak solution to \ref{VI_1}, can be upper bounded as follows : $$\norm{\hat \theta_i - \theta_i^{\text{\rm true}}}_2 \leq \frac{M_w}{m_g \lambda_1} \sqrt{\frac{N\log (2N/\varepsilon)}{T }},$$ where where $\lambda_1$ is the smallest eigenvalue of $\mathbb{W}_{1:T} = \sum_{t=1}^T w_{t-d}^{t-1}(w_{t-d}^{t-1})^{ \mathrm{\scriptscriptstyle T} }/T$. \end{theorem} \textbf{Remarks.} (i) The above theorem is an extension to the general link function case of Theorem 1 \citep{juditsky2020convex}, where they only sketched the proof without giving further details; we defer the detailed proof to Appendix~\ref{appendix:proof}. (ii) As pointed out in \citet{juditsky2020convex}, $\mathbb{W}_{1:T} \in \RR^{N \times N}$ will be full rank when $T$ is sufficiently large, i.e., with high probability, $\lambda_1$ will be a positive constant. {\it Linear Program-based confidence interval.} As pointed out in section II.E \citep{juditsky2020convex}, for general non-linear link function $g$, it would be hard to separate $\theta_i$ from $\sum_{t=1}^T w_{t-d}^{t-1} g\left((w_{t-d}^{t-1})^{ \mathrm{\scriptscriptstyle T} } \theta_i\right)/T$. First, we derive a CI for linear link function case via a more precise data-driven bound for $F_{W_{T}}^{(i)}(\theta_i)\in \RR^N$ as \citet{juditsky2020convex} did in Lemma 2 (see its proof in Appendix~\ref{appendix:CI}): \begin{proposition}[Confidence interval for linear transform of $\theta_i$ for linear link function case]\label{prop:CI} Under Assumptions~\ref{assumption:vector_field} and \ref{assumption:observation}, for $i = 1,\dots,N_1$, and every $s > 1$, the following holds with probability at least $1-2N\{s[\log((s-1)T)+2] + 2\} e^{1-s}$: $$\theta_\ell[W_T,s;i] \leq a^{ \mathrm{\scriptscriptstyle T} } \theta_i \leq \theta_u[W_T,s;i], \quad \forall a \in \RR^N,$$where $\theta_\ell[W_T,s;i]$ and $\theta_u[W_T,s;i]$ are defined in \eqref{eq:CI_lower} and \eqref{eq:CI_upper}, respectively. \end{proposition} This CI is obtained by solving LPs \eqref{eq:CI_lower} and \eqref{eq:CI_upper}. For general non-linear link function $g$, since it is typically constrained in a compact subset to satisfy Assumption~\ref{assumption:vector_field} (see Example~\ref{eg:logistic} in Appendix~\ref{appendix:eg}), we can obtain linear bounds on the non-linear link function and then repeat the above techniques to obtain similar CI; details on this generalization can be found in Appendix~\ref{appendix:CI}. \section{Real data experiments} In Experiment 1, nodes in the network are constructed by a clinician based on well-known, measurable, physiologic relationships in the human body. This expert-driven approach is subsequently compared to a purely data-driven model for identifying possible clusters of inpatient data in Experiment 2. \subsection{Exp. 1: network topology based on known physiologic relationships}\label{subsec:exp1} { \it Feature construction.} As previously described, vital sign measurements were condensed into single features represented by summary statistics (i.e., maximum, minimum, mean) of the past 6 hours, creating a total of 12 distinct representations of a patient's vital signs. A count of total Lab tests over the past 6 hours was used as a proxy for patient acuity and was also incorporated as a feature. SAD nodes were created by grouping all 34 Lab measurements into ten nodes (see Table~\ref{table:node_construction}) representative of common physiologic derangements seen in sepsis. Moreover, instead of constructing a sequence of binary variables for each node, we assigned a risk score at each time, indicating the severity of the SAD. However, when a variable (i.e., node) was used as the response during modeling, it was treated as binary by applying indicator function $\mathbf{1}_{\{y > 0\}}$. { \it Sub-group analysis.} To simplify model development, we carried out a sub-group analysis and excluded demographic features from the model. We used sex $= 0$ (female) and age $>60$ sub-group in the following to demonstrate our method, which contained 5,222 patients in the Physionet data set. {\it Model fitting.} The primary outcome of interest was sepsis, which necessitated the addition of an $11$-th binary time series called ``SepsisLabel'' to our data. This resulted in a total of $N_1 = 11$ nodes in our network. Using each of those $N_1$ variables as responses (recall that risk scores were binarized when used as a response) and the rest as features, we performed forward feature selection and fitted logistic regression models with hyperparameter being the number of training iterations. The primary cross-validation criterion for both feature selection and hyperparameter tuning was the True Positive (TP) rate (classification accuracy for positive samples); we also compared classification error and AUC. TP rate was chosen because in a clinical setting, particularly as it pertains to sepsis, greater importance is placed on not missing the disease (i.e., maintaining a high sensitivity) as opposed to producing a false alert. We defer further details of the training procedure to Appendix~\ref{appendix:training_details}. {\it Results and interpretation.} As previously discussed, nodes were created by a clinician to identify the distinct types of measurable, physiologic change that accompanies sepsis-related illness (i.e., SAD nodes); however, the clinician did not determine the relationship amongst the SAD nodes. Rather, these relationships were an output of model training. Both { Table~\ref{table:model_coeff}} and { Figure~\ref{fig:new_net_structure}} illustrate a compelling network of SAD nodes that follow closely with known and expected causal relationships in sepsis-related illness. For example, the finding that Diminished Cardiac Output strongly promotes sepsis events or that Shock strongly promotes Coagulopathy are well-appreciated relationships. The primary outcome of interest for this work was sepsis; still, as demonstrated in {Table~\ref{table:model_coeff}}, the causal relationship between any node pair can be estimated, giving clinician users insight into the probability of observing subsequent SADs after sepsis. \begin{table}[!htp] \vspace{-0.15in} \caption{Coefficients for discrete Hawkes network. For each node, from left to right, and from the first row to the second row, the order of feature follows the order in forwarding selection.}\label{table:model_coeff} \vspace{-0.1in} \begin{center} \begin{small} \begin{sc} \resizebox{1\textwidth}{!}{% \begin{tabular}{lcccccc} \toprule[1pt]\midrule[0.3pt] \textbf{ Renal Injury} & Oxygen Carrying Dysfunction & Diminished Cardiac Output & Oxygenation Dysfunction & Shock & Inflammation \\ (TP rate = 0.724) & 0.355 & 0.025 & 0.086 & 0.097 & 0.057 \\ \cmidrule(l){2-6} & Coagulopathy & Cholestasis \\ & 0.067 & 0.179 \\ \midrule \textbf{Electrolyte Imbalance} & Oxygen Carrying Dysfunction & Coagulopathy & HR (max) & Sepsis & Oxygenation Dysfunction \\ (TP rate = 0.705)& 0.330 & 0.261 & 0.016 & 0.065 & 0.073 \\ \cmidrule(l){2-6} & Inflammation \\ & 0.071\\ \midrule \textbf{Oxygen Carrying Dysfunction} & Renal Injury & Coagulopathy & Electrolyte Imbalance & Diminished Cardiac Output & Shock \\ (TP rate = 0.703) & 0.287 & 0.431 & 0.513 & 0.174 & -0.038 \\ \cmidrule(l){2-6} & Oxygenation Dysfunction & O2Sat min \\ & 0.039 & 0.139\\ \midrule \textbf{Shock} & Inflammation & Diminished Cardiac Output & HR (max) & Coagulopathy & Renal Injury \\ (TP rate = 0.673) & 0.088 & 0.234 & 0.324 & 0.350 & 0.190 \\ \cmidrule(l){2-6} & Electrolyte Imbalance & Oxygenation Dysfunction & ICULOS\\ & 0.294 & 0.148 & 0.097 \\ \midrule \textbf{Diminished Cardiac Output} & Electrolyte Imbalance & Shock & Inflammation & Hepatocellular Injury & Oxygen Carrying Dysfunction \\ (TP rate = 0.622) & 0.086 & 0.117 & 0.013 & 0.085 & 0.233 \\ \cmidrule(l){2-6} & Resp mean & Temp max\\ & -0.041 & 0.077\\ \midrule \textbf{Coagulopathy} & Hepatocellular Injury & Oxygen Carrying Dysfunction & Shock & Cholestasis & Sepsis \\ (TP rate = 0.632) & 0.173 & 0.211 & 0.238 & 0.215 & 0.019 \\ \cmidrule(l){2-6} & Electrolyte Imbalance & Renal Injury & HR (max) \\ & 0.259 & 0.144 & 0.020\\ \midrule \textbf{Cholestasis} & Shock & Hepatocellular Injury & HR (mean) & Renal Injury & Coagulopathy \\ (TP rate = 0.677)&-0.002 & 0.864 & 0.127 & 0.295 & 0.397 \\ \cmidrule(l){2-6} & Inflammation & Sepsis & ICULOS & Oxygenation Dysfunction\\ & -0.002 & 0.048 & 0.324 & 0.089\\ \midrule \textbf{Hepatocellular Injury} & Inflammation & Oxygen Carrying Dysfunction & Shock & Sepsis & Diminished Cardiac Output \\ (TP rate = 0.619) & 0.060 & 0.170 & 0.063 & 0.088 & 0.043 \\ \cmidrule(l){2-6} & Coagulopathy & MAP (min) & O2Sat min & Renal Injury \\ & 0.434 & 0.063 & 0.008 & 0.262 \\ \midrule \textbf{Oxygenation Dysfunction} & Sepsis & Inflammation & Resp (mean) & Shock & Diminished Cardiac Output \\ (TP rate = 0.780)& 0.093 & 0.047 & 2.538 & 0.699 & 0.237 \\ \cmidrule(l){2-6} & MAP min & Hepatocellular Injury\\ & 0.060 & 0.111\\ \midrule \textbf{Inflammation} & Sepsis & HR (max) & Renal Injury & Oxygenation Dysfunction & Shock \\ (TP rate = 0.710)& 0.099 & 1.597& 0.117 & 0.119 & 0.176 \\ \midrule \textbf{Sepsis} & HR (mean) & ICULOS& Renal Injury& Inflammation& Electrolyte Imbalance \\ (TP rate = 0.768)& 0.174& 0.722& 0.509& 0.165& 0.200 \\ \cmidrule(l){2-6} & Diminished Cardiac Output& Resp (min) & Coagulopathy\\ &0.387& 0.458& -0.104\\ \midrule[0.3pt]\bottomrule[1pt] \end{tabular} } \end{sc} \end{small} \end{center} \end{table} {\it Bootstrap confidence intervals.} We also performed uncertainty quantification via bootstrap. We determined the existence of an edge in the network based on the $90\%$ bootstrap confidence interval (CI), i.e., we assigned zero weight to that edge if the CI contains zero; otherwise, we used the median of the bootstrap samples as the weight. The resulting network topology is reported below in Figure~\ref{fig:tp_network_structure_CI_thres}. Meanwhile, we also used classification error as the CV criterion to infer the network topology in Figure~\ref{fig:err_network_structure_CI_thres}. We applied hard thresholding on the network topology to improve legibility by only keeping directed edges whose absolute weights are greater than $0.15$. For the complete network topology (without hard thresholding), one can see Figures~\ref{fig:old_network_structure_CI} and \ref{fig:new_network_structure_CI} in Appendix~\ref{appendix:add_exp}. The networks in Figure~\ref{fig:tp_network_structure_CI_thres} help to elucidate which relationships are most important in the network, which is an essential aspect of interpretability. The network with forward selection shows a high level of influence by the Diminished Cardiac Output and Shock nodes. This is not surprising as both of these SADs are known to cause organ injury. The network that does not use forward selection has identified relationships that suggest certain SADs actually have an inhibitory effect. While there are possible explanations for these inhibitory effects, they are not commonly known or expected from a physiologic perspective. Overall, the network that employees forward feature selection demonstrates a more meaningful series of relationships consistent with known physiologic responses to sepsis. \begin{figure}[!htp] \centerline{ \includegraphics[width = 0.4\textwidth,trim={4cm 0 2.8cm 0},clip]{fig/CI_graph/TP_thres_0.15_CI_new.pdf} \hspace{0.1in} \includegraphics[width = 0.4\textwidth,trim={4cm 0 2.8cm 0},clip]{fig/CI_graph/TP_thres_0.15_CI_old.pdf} } \caption{Bootstrap network topology with (left) and without (right) feature selection. We only keep (directed) edge with absolute weight greater than 0.15. The blue (directed) edge indicates a positive effect, whereas the red indicates a negative effect. The cross-validation criterion is TP rate.} \label{fig:tp_network_structure_CI_thres} \end{figure} \subsection{Exp. 2: data-driven measurement clustering and network topology} In our second experiment, we assumed there was no prior information regarding the nature of the network and instead re-grouped the 34 measurements in Table~\ref{table:node_construction} using a purely data-driven method. We constructed 34 binary time series and provided a label ``$1$'' if the Lab test was reported out AND the Lab result was abnormal based on the rules in Table~\ref{table:node_construction}. \begin{figure}[!htp] \centerline{ \includegraphics[width = 0.4\textwidth]{fig/data_exploration/cor_mat.png} \hspace{0.15in} \includegraphics[width = 0.4\textwidth]{fig/network_cls/hawkes_network_raw.png} } \caption{Correlation matrix (left) and adjacency matrix for discrete Hawkes network (right).} \label{fig:dist_mat} \end{figure} {\it Hierarchical clustering based on ``distance'' matrix.} Analysis of the similarity among measurements begins with the construction of a correlation matrix including all 34 measurements in Figure~\ref{fig:dist_mat}. In this case, correlation occurs when both variables are found to be abnormal. For example, one can see that when \texttt{Creatinine} is abnormal, it likely that \texttt{BUN} and \texttt{Phosphate} would also be abnormal based on the correlation matrix. This correlation and many of the others in the table like this are commonly found in sepsis patients. We can view the correlation as statistical distance. Since larger correlation indicates smaller ``distance'', we used the element-wise inverse of the correlation matrix as the distance matrix. Here we grouped those measurements based on positive correlation; for those with negative or zero correlation, we treated them as though they are very far away from each other and assigned a large constant as the distance. Then, we can apply (hierarchical) clustering to obtain the clusters. The resulting clusters are plotted in Figure~\ref{fig:Hierarchical_clustering}. \begin{figure}[!htp] \centerline{ \includegraphics[width = 0.5\textwidth]{fig/network_cls/corr_cls.png} \includegraphics[width = 0.5\textwidth]{fig/network_cls/sym+h_cls+ward_2.png} } \caption{Hierarchical clustering based on correlation (left) and discrete Hawkes network (right).} \label{fig:Hierarchical_clustering} \end{figure} Similar to the fitting procedure above, we fitted our proposed discrete Hawkes network model on those 34 binary time series to construct a directed graph. We plot the adjacency matrix in Figure~\ref{fig:dist_mat}. Here, the adjacency matrix is asymmetric, which makes it difficult to perform clustering. This asymmetric adjacency matrix $A$ can be symmetrized by using $A_{sym} = A + A^{ \mathrm{\scriptscriptstyle T} }$. Then we can apply the same method as we did for the correlation matrix above to complete the (hierarchical) clustering. The result is plotted in Figure~\ref{fig:Hierarchical_clustering}. Both approaches for clustering patient features (i.e., via simple correlation and via a discrete Hawkes network) produce nodes that share similarity with the SAD nodes derived by a clinical expert in Experiment 1. For example, in Figure~\ref{fig:Hierarchical_clustering} we see a cluster that includes the measurements: \texttt{Lactate, PaCO2, BaseExcess, pH} which commonly become deranged during shock. While these measurements do occur together on a common Lab panel (i.e., they are often collected simultaneously), this doesn't necessarily imply that their derangements would be similarly correlated as this label panel has many permutations of derangement caused by different non-sepsis disease processes. It is more reasonable to consider that the data-driven clustering methods are independently identifying clinically relevant SADs. While the simple correlation approach identifies concomitant relationships (i.e., two things happening together), it does not consider a time-dependent, causal relationship the way the Hawkes network does. This important distinction is appreciated when considering the two maps in Figure~\ref{fig:Hierarchical_clustering}. The Hawkes process develops nodes that have close intra-node relationships that are very clearly separated from other clusters. In contrast, the inter-node distances tend to be less pronounced in the correlation-based hierarchical clustering method. {\it Blockmodelling based on asymmetric Hawkes network.} In this approach, we define clusters using a stochastic block model: for any two clusters $V_i$ and $V_j$ and any two nodes $a,b \in V_i$; then there is approximately the same number of in-edges (respectively out edges) connecting $a$ to nodes in $V_j$ and of in-edges (respectively out edges) connecting $b$ to nodes in $V_j$. Identifying clusters from asymmetric adjacency matrix is called blockmodelling \citep{holland1983stochastic,wang1987stochastic}. We introduce a spectral algorithm for blockmodelling \citep{sussman2012consistent} in Appendix~\ref{appendix:blockmodelling}. This algorithm has hyperparameters $K$ (number of clusters/blocks) and $d$ (top $d$ eigenvectors are kept in the spectral decomposition). Since it only deals with unweighted directed graphs, we construct the unweighted adjacency matrix by thresholding with $0.15$ as we did before. By applying the spectral algorithm recursively, we get hierarchical blockmodels and report the results in Figure~\ref{fig:blockmodelling}. \begin{figure}[!htp] \centerline{ \includegraphics[width = 0.45\textwidth]{fig/network_cls/blockmodelling.png} \hspace{0.15in} \includegraphics[width = 0.45\textwidth]{fig/network_cls/blk.pdf} } \caption{Left: Hierarchical Blockmodeling (hyperparameter under each plot). We chose the smallest $d$ such that the explained variance ratio is at least $95\%$. Right: the resulting network topology.} \label{fig:blockmodelling} \end{figure} Based on Hierarchical Blockmodeling, we identify five blocks/clusters and the associated network topology among them. Analysis of the first level suggests a predominantly renal-inflammatory axis in Group A with values like \texttt{Creatinine, BUN, Phosphate, WBC} being important, and a cardio-pulmonary axis in Group B with values like \texttt{SaO2, O2Sat, SBP, Temp} being important. Inside of Group A, we see derangements following known patterns that demonstrate renal injury (A1) promoting electrolyte imbalances (A2). Similarly, we see in Group B that reduced blood pressure and fevers (B3) promote aberrations in oxygenation and acid/base equilibrium (B2) (a frequent association in sepsis). For demonstration purposes, this Hierarchical Blockmodel created the adjacency matrix using a threshold of 0.15; however, this could be lowered to identify a higher number of clusters and relationships. While single nodes are grouped together to form a cluster, it does not necessarily mean there is a correlation within the cluster (unless there is a self-directed edge (e.g., A2). Instead, the composite effect of nodes within a cluster promote dysfunction in the nodes of other clusters to which it is connected. \begin{table}[H] \caption{Data-driven cluster based on Hierarchical Blockmodelling.}\label{table:measurement_clsutering} \vspace{-0.1in} \begin{center} \begin{small} \begin{sc} \resizebox{1\textwidth}{!}{% \begin{tabular}{ccl} \toprule[1pt]\midrule[0.3pt] 1st-level cluster & 2nd-level cluster & Measurement physionet name \\ \midrule[0.3pt] \textbf{A} & A1 & Creatinine , Potassium , HCO3 , Magnesium , Bilirubin total , WBC;\\ \cmidrule(l){2-3} & A2 & Phosphate , BUN , Chloride , Hct , Hgb , Platelets , Glucose ;\\ \midrule[0.3pt] \textbf{B} & B1 & Calcium , BaseExcess , SaO2 , PaCO2 ;\\ \cmidrule(l){2-3} & B2 & Lactate , pH , DBP , O2Sat ;\\ \cmidrule(l){2-3} &B3& SBP , PTT , Temp ;\\ \cmidrule(l){2-3} &NA& MAP , Fibrinogen , Bilirubin direct , Alkalinephos , AST , Resp , EtCO2 , FiO2 , HR , SepsisLabel \\ \midrule[0.3pt]\bottomrule[1pt] \end{tabular} } \end{sc} \end{small} \end{center} \vspace{-0.1in} \end{table} \section{Discussion}\label{sec:discussion} We develop a model to infer non-linear Granger causality from mixed-type of irregularly sampled time-series, and leverage a recently developed stochastic variational inequality (VI) approach to estimate the model parameters. We conduct a non-asymptotic theoretical analysis and demonstrate the good performance of our proposed method coupled with heuristic forward feature selection via real data experiments. Future work includes connecting this newly developed VI approach with a principled subsection selection method (e.g., group Lasso). It is important to appreciate that many of the Lab tests that serve as a data source for our analysis are collected at the direction of a clinician, meaning there is an inherent component of suspicion associated with each Lab test. The important effects that drive suspicion and compel the ordering of tests may not be captured in our data and, subsequently, our network. Additionally, our cohort was limited to a specific subset of patients in order to reduce the number of data elements and make analysis more tractable, but it is commonly recognized that there are demographic features and co-existing medical conditions that affect how patients respond to sepsis. These unobserved features may also alter some of the findings for our network. { It is also important to appreciate that we accepted the consequence of increased false alarms (i.e. False Positives) in order to maximize our sensitivity. In clinical settings high false alarm rates may decrease clinical satisfaction and lead to alarm fatigue or disuse.} In summary, our experimental results serve as a demonstration that good performance is achievable with our proposed method. The development of a full, interpretable, causal graph capable of facilitating real-world clinical decision-making would require the analysis of a larger cohort of patients from multiple health systems with a more robust set of demographic data. An interpretable model like the one we have proposed offers some protection against the aforementioned limitations by allowing a clinician to combine their own knowledge about a patient with the findings of the model resulting in more informed decisions about a patient's health status. \newpage \bibliographystyle{plainnat} \section{Introduction} However, model predictions related to disease identification, particularly for complex diseases, still need to be adjudicated (i.e., interpreted) by a clinician before further action (i.e., treatment) can be initiated. Automated surveillance tools aimed at identifying hospitalized patients' deterioration conditions are becoming more common and stand to enhance a clinician's situational awareness. We are particularly interested in sepsis prediction, which is a life-threatening medical condition contributing to one in five deaths globally \citep{world2020global} and stands as one of the most important cases for automated in-hospital surveillance. Sepsis is formally defined as life-threatening organ dysfunction caused by a dysregulated host response to infection \citep{singer2016third}. Delays in recognizing sepsis and initiating appropriate treatment can adversely impact patient outcomes. In a recent study of adult sepsis patients, each hour of delayed treatment was associated with higher risk-adjusted in-hospital mortality (odds ratio, 1.04 per hour) \citep{seymourTimeTreatmentMortality2017}. It stands to reason that early recognition of the physiologic aberrations preceding sepsis would afford clinicians more time to intervene and may contribute to improving outcomes and reducing costs. A number of machine learning methods have been developed to predict the onset of sepsis utilizing data from the electronic medical record (EMR) \citep{fleuren2020machine}. A recent sepsis prediction competition \citep{reyna2019early} demonstrated both the popularity and robust performance of XGBoost models \citep{du2019automated,zabihi2019sepsis,yang2020explainable}; meanwhile, Deep Neural Networks \citep{shashikumarDeepAISEInterpretableRecurrent2021} are also commonly used. Regrettably, most approaches offer an alert adjudicator very little information pertaining to the reason for the alert/prediction, leading many to refer to them as ``black box'' techniques. Among the aforementioned works, \citet{yang2020explainable} provided one of the best attempts at identifying causality for their models' predictions by reporting feature importance at a global level for all patients; however, this does not convey which features were most important in arriving at a given prediction for an individual patient. The common lack of interpretability of many clinical models, particularly those related to sepsis, suggests that a principled method (with theoretical guarantee) to study the interactions among time series in medical settings is underdeveloped. \begin{figure}[!htp] \centerline{ \includegraphics[width = 0.45\textwidth]{fig/network_graph/new_network.pdf} } \vspace{-0.1in} \caption{Granger Causal graph over endogenous Sepsis Associated Derangement (SAD) indicators obtained via discrete Hawkes network with forward feature selection.} \label{fig:new_net_structure} \vspace{-0.1in} \end{figure} Granger causal graphs, which analyze interactions among time series defined by association, avoid this limitation and afford a clinical adjudicator the ability to understand why an alert was made. The syndromic nature of sepsis means that there is a constellation of different physiologic derangements that can combine to create the condition. As evidenced in Figure~\ref{fig:new_net_structure}, a series of different nodes representing these types of physiologic derangements has been created. The relationships between nodes and their effect on sepsis are explained via generalized linear models (GLM), providing insight into what ``caused'' the alert. For example, a clinical adjudicator might be more inclined to arrive at a concordant opinion regarding sepsis if they were informed that the alert was caused by the combined effects from the Renal Injury and Diminished Cardiac Output nodes. Likewise, this same adjudicator might be less inclined to corroborate an alert on a different patient if the main contributing cause was from Electrolyte Imbalance alone. Linear Vector Autoregressive (VAR) model is the most popular method in studying the Granger causal graph among multiple time series \citep{lutkepohl2005new}. However, it has been pointed out by a recent survey study \citep{shojaie2021granger} that this approach suffers from assumptions such as linearity and continuous-valued series, since the real-data, which can be both continuous- and categorical-valued, usually exhibits complex dynamics; another flaw of classic linear VAR model is unscalability to high-dimension, which arises when one tries to identify all series as endogenous, since it is hard to check if we have all relevant information at hand in practice. In this work, we adopt a generalized linear model (GLM) approach for binary time series — spatio-temporal Bernoulli process \citep{juditsky2019signal,juditsky2020convex} — and generalize it to handle both continuous- and discrete-valued as well as regularly and irregularly sampled time series and learn a Granger causal graph over Sepsis Associated Derangements (SADs). We perform forward feature selection to remove redundant information and increase the signal-noise ratio. We demonstrate via real data experiments that our proposed GLM coupled with forward feature selection can achieve comparable performance to a powerful method such as XGBoost. One novel aspect of this work comes from the real underlying problem: we build a {\it highly interpretable} model from {\it mixed-type series}. The prioritization of interpretability considers the needs of the end-users, namely clinicians. This consideration of real-world constraints makes future adoption of these models much more likely for those conducting continuous surveillance of high-risk patients. In the medical setting, the observations can be both discrete and continuous-valued and sampled with different frequencies. For example, vital signs are recorded regularly, whereas laboratory (lab) tests are only ordered when clinically necessary; thus, this cannot be simply formulated into a missing data problem. Moreover, what separates our method from the classic linear VAR time series is the generalization to non-linear dynamics and a novel stochastic monotone variational inequality-based estimator. Most importantly, we develop a non-asymptotic upper bound on estimation error AND a Linear Program-based confidence interval for graph structure for arbitrary monotone (non-linear) link function for our proposed method. {\textbf{Related work. }} Recent developments on the Granger causal graph mainly focus on non-linear dynamics and tackling high-dimensionality via regularization: the former includes applying a separable matrix-valued kernel \citep{sindhwani2012scalable} and neural networks \citep{tank2018neural} to learn non-linear Granger causality; other approaches address the issue of high-dimensionality caused by viewing all series as endogenous. Techniques include group Lasso \citep{bolstad2011causal,basu2015network} and nuclear norm regularization \citep{basu2019low}. Another notable work \citep{nicholson2017varx} modeled endogenous and exogenous variables separately (instead of treating all series endogenous) and used different penalties on endogenous and exogenous variables to learn the sparse graph structure. We should mention that our method closely resembles \citet{nicholson2017varx}: part of features comes from direct observations and is treated exogenous (e.g., vital signs and Lab test results), whereas the remaining SADs are derived from the first part and viewed as endogenous. \vspace{-0.1in} \section{Problem Set-up and Proposed Model} \vspace{-0.05in} \begin{table}[!htp] \vspace{-0.15in} \caption{SAD construction based on thresholding exogenous observations via medical knowledge.}\label{table:node_construction} \begin{center} \begin{small} \begin{sc} \resizebox{.8\textwidth}{!}{% \begin{tabular}{llccc} \toprule[1pt]\midrule[0.3pt] SAD name & Measurement name & Physionet name & Rule & Risk score \\ \midrule[0.3pt] \textbf{ Renal Injury} & creatinine & Creatinine & >1.3 & 0.667 \\ & potassium & Potassium & >5.0 & 0.067 \\ & phosphorus & Phosphate & >4.5 & 0.067 \\ & bicarb (hco3) & HCO3 & >26 & 0.067 \\ & blood urea nitrogen (bun) & BUN & >20 & 0.133 \\ \cmidrule(l){2-5} \textbf{Electrolyte} & calcium & Calcium & >10.5 & 0.167 \\ \textbf{Imbalance} & chloride & Chloride & <98 or >106 & 0.667 \\ & magnesium & Magnesium & <1.6 & 0.167 \\ \cmidrule(l){2-5} \textbf{Oxygen Carrying} & hematocrit & Hct & <37 & 0.500 \\ \textbf{Dysfunction} & hemoglobin & Hgb & <12 & 0.500 \\ \cmidrule(l){2-5} \textbf{Shock} & base excess & BaseExcess & < $-$3 & 0.100 \\ & lactic acid & Lactate & >2.0 & 0.150 \\ & ph & pH & <7.32 & 0.750 \\ \cmidrule(l){2-5} \textbf{Diminished } & sbp cuff & SBP & <120 & 0.250 \\ \textbf{Cardiac Output} & dbp cuff & DBP & <80 & 0.250 \\ & map cuff & MAP & <65 & 0.500 \\ \cmidrule(l){2-5} \textbf{Coagulopathy} & partial prothrombin time (ptt) & PTT & >35 & 0.250 \\ & fibrinogen & Fibrinogen & <233 & 0.250 \\ & platelets & Platelets & <150,000 & 0.500 \\ \cmidrule(l){2-5} \textbf{Cholestasis} & bilirubin direct & Bilirubin direct & >0.3 & 0.100 \\ & bilirubin total & Bilirubin total & >1.0 & 0.500 \\ & alkaline phosphatase & Alkalinephos & >120 & 0.400 \\ \cmidrule(l){2-5} \textbf{Hepatocellular Injury} & aspartate aminotransferase (ast) & AST & >40 & 1.000 \\ \cmidrule(l){2-5} \textbf{Oxygenation } & unassisted resp rate & Resp & >20 & 0.100 \\ \textbf{Dysfunction} & spo2 & O2Sat & <92 \% & 0.200 \\ & saturation of oxygen (sao2) & SaO2 & <92 \% & 0.200 \\ & end tidal co2 & EtCO2 & <35 or >45 & 0.100 \\ & fio2 & FiO2 & >21 \% & 0.300 \\ & partial pressure of carbon dioxide (paco2) & PaCO2 & <35 or >45 & 0.100 \\ \cmidrule(l){2-5} \textbf{Inflammation} & temperature & Temp & <36 or >38 & 0.400 \\ & pulse & HR & >90 & 0.100 \\ & glucose & Glucose & >125 & 0.100 \\ & white blood cell count & WBC & <4,000 or >12,000 & 0.400 \\ \midrule[0.3pt]\bottomrule[1pt] \end{tabular} } \end{sc} \end{small} \end{center} \vspace{-0.2in} \end{table} \subsection{Mixed-type series}\label{sec:background} \vspace{-0.05in} Data used for this analysis was a curated, publicly available data set from the 2019 Physionet challenge \citep{physionet2019}. The challenge data was sourced from patients admitted to the Intensive Care Unit (ICU) during their hospitalization and represented three categories of patient features: vital sign measurements, Laboratory (Lab) results, and demographic information. \vspace{-0.03in} { \it Vital Signs.} Vital signs in ICU environments are normally recorded at an hourly interval and include \texttt{HR, O2Sat, Temp, SBP, MAP, DBP, Resp} (see Table~\ref{table:node_construction} for their full measurement names). Among the blood pressure measurements (\texttt{SBP}, \texttt{DBP}, and \texttt{MAP}), we only keep \texttt{MAP} in our study since \texttt{MAP} = (\texttt{SBP} + 2\texttt{DBP})$/3$. \vspace{-0.03in} { \it Lab Values.} Lab tests are most commonly collected once every 24 hours; however, this collection frequency may change based a the severity of a patient's illness. In addition to individual Lab values, we also use the count of the Lab tests over the past 6 hours as a proxy to represent the severity of a patient's illness (i.e., more severe disease results in more tests being ordered). \vspace{-0.03in} { \it Sepsis Associated Derangements (SADs).} Thresholds representing breaks between normal and deranged physiology are identified utilizing already establish criteria \citep{ABIM_ref_range}. We condense different measurements (containing both vital signs and Lab results) into a binary variable as an indicator of physiologic derangements seen preceding and during sepsis (see column ``SAD name'' in Table~\ref{table:node_construction}). { \it Demographics.} Demographic features remain constant throughout hospitalization. The examined data set contains both age and sex. Here, the vital signs (regularly sampled) and raw Lab values (irregularly sampled) are exogenous variables, whereas SAD indicators are endogenous. The irregularly sampled series will be handled via forwarding filling. Our primary interest is to study all exogenous and endogenous series' effects on endogenous series and construct (Granger causal) graph/network over endogenous series. \begin{figure}[!htp] \vspace{-0.1in} \centerline{ \subfigure{\includegraphics[scale = 0.4]{fig/mixed_data_type.pdf}} } \vspace{-0.2in} \end{figure} \vspace{-0.1in} \subsection{Discrete Hawkes network} \vspace{-0.05in} {\it Model formulation.} Suppose we observe $N_1$ sequences of binary SADs on time horizon $T$: $\{y_1^{(i)},\dots,y_T^{(i)}\}$, $i = 1,\dots,N_1$; we also observe both continuous- and discrete-valued time series $\{x_1^{(i)},\dots,x_T^{(i)}\}, i = 1,\dots,N_2$, which are vital signs and Lab test counts, and demographic variables $(z_1,\dots,z_{N_3})$. In the following, we will call each of those SADs a node variable since it corresponds to a node in the Granger causal graph. With such a model at hand, we can better understand the dynamics within the human body, and most importantly, alert the clinicians to the potential causes and complications of an identified SAD. To model the mutual excitation among those series, we propose a generalized linear model, which closely resembles the intensity function of Hawkes point process \citep{hawkes1971point,hawkes1971spectra,hawkes1974cluster}. For $i$-th node variable ($i = 1,\dots,N_1$), at time step $t \ (t = 2,\dots,T)$, we assume: \begin{align}\label{eq:hawkes_model} \PP \Big(y_t^{(i)} &=1 \Big\| \cH_{t-1} \Big) = g\Bigg(\nu_i + \sum_{j = 1}^{N_3} \gamma_{ij} z_j \\ & + \sum_{\tau = 1}^{t-1} \bigg( \sum_{j = 1}^{N_2} \beta_{ij} x_{t-\tau}^{(j)} e^{-\Tilde{R}_{ij} \tau} + \sum_{j = 1}^{N_1} \alpha_{ij} y_{t-\tau}^{(j)} e^{-R_{ij} \tau}\bigg)\Bigg), \nonumber \end{align} where $\cH_t$ denotes the past observation up to time $t$ and $g: \RR \rightarrow [0,1]$ is a link function. For example, $g$ can be non-linear, such as sigmoid link function $g(x) = 1/(1+e^{-x})$; also, it can be linear $g(x) = x$, which should be restricted on domain $[0,1] \subset \RR$. {\it Non-linear Granger causal graph.} By the definition of Granger causality in non-linear model \citep{tank2018neural}, we know that matrix $A = (\alpha_{ij}) \in \RR^{N_1 \times N_1}$ represents the causal graph structure over $N_1$ SAD nodes. To be precise, we say $j$-th SAD does NOT Granger cause $i$-th SAD if $\alpha_{ij} = 0$. {\it Connection to Hawkes process.} For $i$-th SAD node variable, $\alpha_{ij}$ and $\beta_{ij}$ represent the magnitude of triggering effect of $j$-th SAD node variable and continuous variable to it. This effect decays exponentially fast with exponent characterized by $R_{ij}$ and $\Tilde{R}_{ij}$. $\gamma_{ij}$'s represent the influence of demographics and contribute to baseline intensity togerther with $\nu_i$. Note that the above model can be viewed as a discretized version of (non-linear) Hawkes process network with exponential triggering function \citep{wang2020uncertainty}; other methods in learning Hawkes network include \citet{xu2016learning,achab2017uncovering}, we do not dig deeper in this direction since it is out of the scope of this work. \section{Proposed Estimation Method} In this section, we will leverage a recently developed technique \citep{juditsky2019signal,juditsky2020convex}, which estimates the parameters of the generalized linear model by solving stochastic monotone variational inequality (VI), to develop a statistically principled method to estimate the parameters of discrete Hawkes network and infer the Granger causal graph topology. {\it Preliminaries.} To begin with, we make reasonable simplification by assuming finite memory depth $d$ for both continuous and binary observations. Let $w_{t-d}^{t-1}$ denote the observation from $t-d$ to $t-1$: $\big(1,z_1,\dots,z_{N_3},x_{t-1}^{(1)},\dots,x_{t-d}^{(1)},\dots,x_{t-1}^{(N_2)},\dots,x_{t-d}^{(N_2)},y_{t-1}^{(1)},$ $\dots,y_{t-d}^{(1)},\dots,y_{t-1}^{(N_1)},\dots,y_{t-d}^{(N_1)}\big)^{ \mathrm{\scriptscriptstyle T} },$ where superscript $^{ \mathrm{\scriptscriptstyle T} }$ denotes matrix transpose. Since we only consider finite memory depth for binary observation, we could use one single parameter $\alpha_{ij\tau} := \alpha_{ij} \exp\{-R_{ij} \tau\}$ (similarly, $\beta_{ij\tau} := \beta_{ij} \exp\{-\Tilde{R}_{ij} \tau\}$) to represent the triggering effect with exponential decay. We rewrite \eqref{eq:hawkes_model} into: for $i = 1,\dots,N_1,$ \vspace{-0.06in} \begin{equation}\label{eq:model} \PP\left(y_t^{(i)}=1 \Big\| w_{t-d}^{t-1} \right) = g\left((w_{t-d}^{t-1})^{ \mathrm{\scriptscriptstyle T} } \theta_i\right), \quad t = d+1,\dots,T, \end{equation} where $\theta_i \in \RR^N$ ($N = 1+N _3+dN_2+dN_1$) is the parameter to be estimated: $\theta_i = (\nu_i,\gamma_{i1},\dots,\gamma_{iN_3},\beta_{i11},\dots,\beta_{i1d},$ $\beta_{iN_21},\dots,\beta_{iN_2d},\alpha_{i11},\dots,\alpha_{i1d},\alpha_{iN_11},\dots,\alpha_{iN_1d})^{ \mathrm{\scriptscriptstyle T} }.$ This parameter summarizes the influence from all variables to node $i$ and could be estimated independently from the remaining $N_1-1$ parameters. {\it Granger Causality.} We can see \eqref{eq:model} is actually a generalized linear version of Vector Autoregressive (VAR) model. Therefore, we say $j$-th node series $\{y^{(j)}_t\}$ (or vital sign series $\{x^{(j)}_t\}$) Granger-causes $i$-th node series $\{y_t^{(i)}\}$ if $\alpha_{ij\tau} \not= 0$ (or $\beta_{ij\tau} \not= 0$) for some $\tau \in \{1,\dots,d\}$. {\it Parameter estimation with variational inequality.} Denote the observation by $W_{T}:=(w_{1-d}^{0},\dots,w_{T-d+1}^{T}) \in \RR^{(T+1) \times N}$, where variables observed at time step $1-d,\dots,0$ are viewed as given history. We assume parameter $\theta_i$ is constrained in a convex compact set $\theta_i \in \Theta_i \subset \RR^N$, then, for $i = 1,\dots,N_1$, we use the weak solution to the following variational inequality as the estimator $\hat \theta_i$: \vspace{-0.15in} \begin{equation} \text {find } \hat \theta_i \in \Theta_i:\langle F_{ W_{T}}^{(i)}(\theta), \theta-\hat \theta_i\rangle \geq 0, \ \forall \theta \in \Theta_i, \label{VI_1}\tag{{VI}$[ F_{W_{T}}^{(i)}, \Theta_i]$} \end{equation} \vspace{-0.1in} where $F_{W_{T}}^{(i)}(\theta_i)$ is the empirical vector field and defined as follows: \vspace{-0.3in} $$F_{W_{T}}^{(i)}(\theta_i) := \frac{1}{T} \sum_{t=1}^T w_{t-d}^{t-1} \left( g\left((w_{t-d}^{t-1})^{ \mathrm{\scriptscriptstyle T} } \theta_i\right) - y_t^{(i)} \right).$$ \vspace{-0.2in} \paragraph{Remarks.} (i) The intuition behind this method is straightforward. Let's consider the global counterpart of the above vector field, whose root is the unknown ground truth $\theta_i^{\text{\rm true}}$, \vspace{-0.25in} \begin{align} F^{(i)}(\theta_i) :=& \EE_{(w,y^{(i)})} \left[w \left( g\left(w^{ \mathrm{\scriptscriptstyle T} } \theta_i\right) - y^{(i)} \right)\right] \\ =& \EE_{(w,y^{(i)})} \left[w \left( g\left(w^{ \mathrm{\scriptscriptstyle T} } \theta_i\right) - g\left(w^{ \mathrm{\scriptscriptstyle T} } \theta_i^{\text{\rm true}}\right) \right)\right]. \end{align} \vspace{-0.1in} Although we cannot access this global counterpart, by solving the empirical one \ref{VI_1} we could approximate the ground truth very well. We will show how well this approximation would be in the next section. (ii) Least Square Estimation for Linear VAR model and Maximum Likelihood Estimation for logistic regression model are both special cases of our proposed VI estimates; detailed derivations are deferred to Appendix~\ref{appendix:eg}. \vspace{-0.05in} \section{Real Data Experiments} \vspace{-0.05in} In Experiment 1, nodes in the network are constructed by a clinician based on well-known, measurable, physiologic relationships in the human body. This expert-driven approach is subsequently compared to a purely data-driven model for identifying possible clusters of inpatient data in Experiment 2. \begin{figure}[!htp] \vspace{-0.1in} \centerline{ \includegraphics[width = 0.25\textwidth,trim={4cm 0 2.8cm 0},clip]{fig/CI_graph/TP_thres_0.15_CI_new.pdf} \includegraphics[width = 0.25\textwidth,trim={4cm 0 2.8cm 0},clip]{fig/CI_graph/TP_thres_0.15_CI_old.pdf} \includegraphics[width = 0.25\textwidth,trim={4cm 0 2.8cm 0},clip]{fig/CI_graph/err_thres_0.15_CI_new.pdf} \includegraphics[width = 0.25\textwidth,trim={4cm 0 2.8cm 0},clip]{fig/CI_graph/err_thres_0.15_CI_old.pdf} } \vspace{-0.1in} \caption{From left to right: bootstrap network topology (1) with feature selection using TP rate for CV; (2) without feature selection using TP rate for CV; (3) with feature selection using classification error for CV; (4) without feature selection using classification error for CV. We only keep (directed) edge with weight (logistic coefficient) whose absolute value is greater than 0.15. The blue (directed) edge indicates a positive effect whereas the red indicates a negative effect.}\label{fig:network_structure_CI_thres} \vspace{0.1in} \centerline{ \includegraphics[width = 0.25\textwidth,trim={4cm 0 2.8cm 0},clip]{fig/CI_graph/TP_CI_new.pdf} \includegraphics[width = 0.25\textwidth,trim={4cm 0 2.8cm 0},clip]{fig/CI_graph/TP_CI_old.pdf} \includegraphics[width = 0.25\textwidth,trim={4cm 0 2.8cm 0},clip]{fig/CI_graph/err_CI_new.pdf} \includegraphics[width = 0.25\textwidth,trim={4cm 0 2.8cm 0},clip]{fig/CI_graph/err_CI_old.pdf} } \vspace{-0.1in} \caption{From left to right: non-thresholding bootstrap network topology (1) with feature selection using TP rate for CV; (2) without feature selection using TP rate for CV; (3) with feature selection using classification error for CV; (4) without feature selection using classification error for CV. The blue (directed) edge indicates a positive effect whereas the red indicates a negative effect. The criterion for cross validation is true positive rate (left) and classification error (right).}\label{fig:network_structure_CI} \vspace{-0.1in} \end{figure} \vspace{-0.1in} \subsection{Experiment 1: network topology based on known physiologic relationships}\label{subsec:exp1} \vspace{-0.05in} { \it Feature construction.} As previously described, vital sign measurements were condensed into single features represented by summary statistics (i.e., maximum, minimum, mean) of the past 6 hours, creating a total of 12 distinct representations of a patient's vital signs. A count of total Lab tests over the past 6 hours was used as a proxy for patient acuity and was also incorporated as a feature. SAD nodes were created by grouping all 34 Lab measurements into ten nodes (see Table~\ref{table:node_construction}) representative of common physiologic derangements seen in sepsis. Moreover, instead of constructing a sequence of binary variables for each node, we assigned a risk score at each time, indicating the severity of the SAD. However, when a variable (i.e., node) was used as the response during modeling, it was treated as binary by applying indicator function $\mathbf{1}_{\{y > 0\}}$. { \it Sub-group analysis.} To simplify model development, we carried out a sub-group analysis and excluded demographic features from the model. We used sex $= 0$ (female) and age $>60$ sub-group in the following to demonstrate our method, which contained 5,222 patients in the Physionet data set. {\it Model fitting.} The primary outcome of interest was sepsis, which necessitated the addition of an $11$-th binary time series called ``SepsisLabel'' to our data. This resulted in a total of $N_1 = 11$ nodes in our network. Using each of those $N_1$ variables as responses (recall that risk scores were binarized when used as a response) and the rest as features, we performed forward feature selection and fitted logistic regression models with hyperparameter being the number of training iterations. The primary cross-validation criterion for both feature selection and hyperparameter tuning was the True Positive (TP) rate (classification accuracy for positive samples); we also compared classification error and AUC. TP rate was chosen because in a clinical setting, particularly as it pertains to sepsis, greater importance is placed on not missing the disease (i.e., maintaining a high sensitivity) as opposed to producing a false alert. We defer further details of the training procedure to Appendix~\ref{appendix:training_details}. {\it Results and interpretation.} As previously discussed, nodes were created by a clinician to identify the distinct types of measurable, physiologic change that accompanies sepsis-related illness (i.e., SAD nodes); however, the clinician did not determine the relationship amongst the SAD nodes. Rather, these relationships were an output of model training. Both { Table~\ref{table:model_coeff}} and { Figure~\ref{fig:new_net_structure}} illustrate a compelling network of SAD nodes that follow closely with known and expected causal relationships in sepsis-related illness. For example, the finding that Diminished Cardiac Output strongly promotes sepsis events or that Shock strongly promotes Coagulopathy are well-appreciated relationships. The primary outcome of interest for this work was sepsis; still, as demonstrated in {Table~\ref{table:model_coeff}}, the causal relationship between any node pair can be estimated, giving clinician users insight into the probability of observing subsequent SADs after sepsis. \begin{table}[!htp] \vspace{-0.15in} \caption{Coefficients for discrete Hawkes network. For each node, from left to right, and from the first row to the second row, the order of feature follows the order in forwarding selection.}\label{table:model_coeff} \vspace{-0.1in} \begin{center} \begin{small} \begin{sc} \resizebox{1\textwidth}{!}{% \begin{tabular}{lcccccc} \toprule[1pt]\midrule[0.3pt] \textbf{ Renal Injury} & Oxygen Carrying Dysfunction & Diminished Cardiac Output & Oxygenation Dysfunction & Shock & Inflammation \\ (TP rate = 0.724) & 0.355 & 0.025 & 0.086 & 0.097 & 0.057 \\ \cmidrule(l){2-6} & Coagulopathy & Cholestasis \\ & 0.067 & 0.179 \\ \midrule \textbf{Electrolyte Imbalance} & Oxygen Carrying Dysfunction & Coagulopathy & HR (max) & Sepsis & Oxygenation Dysfunction \\ (TP rate = 0.705)& 0.330 & 0.261 & 0.016 & 0.065 & 0.073 \\ \cmidrule(l){2-6} & Inflammation \\ & 0.071\\ \midrule \textbf{Oxygen Carrying Dysfunction} & Renal Injury & Coagulopathy & Electrolyte Imbalance & Diminished Cardiac Output & Shock \\ (TP rate = 0.703) & 0.287 & 0.431 & 0.513 & 0.174 & -0.038 \\ \cmidrule(l){2-6} & Oxygenation Dysfunction & O2Sat min \\ & 0.039 & 0.139\\ \midrule \textbf{Shock} & Inflammation & Diminished Cardiac Output & HR (max) & Coagulopathy & Renal Injury \\ (TP rate = 0.673) & 0.088 & 0.234 & 0.324 & 0.350 & 0.190 \\ \cmidrule(l){2-6} & Electrolyte Imbalance & Oxygenation Dysfunction & ICULOS\\ & 0.294 & 0.148 & 0.097 \\ \midrule \textbf{Diminished Cardiac Output} & Electrolyte Imbalance & Shock & Inflammation & Hepatocellular Injury & Oxygen Carrying Dysfunction \\ (TP rate = 0.622) & 0.086 & 0.117 & 0.013 & 0.085 & 0.233 \\ \cmidrule(l){2-6} & Resp mean & Temp max\\ & -0.041 & 0.077\\ \midrule \textbf{Coagulopathy} & Hepatocellular Injury & Oxygen Carrying Dysfunction & Shock & Cholestasis & Sepsis \\ (TP rate = 0.632) & 0.173 & 0.211 & 0.238 & 0.215 & 0.019 \\ \cmidrule(l){2-6} & Electrolyte Imbalance & Renal Injury & HR (max) \\ & 0.259 & 0.144 & 0.020\\ \midrule \textbf{Cholestasis} & Shock & Hepatocellular Injury & HR (mean) & Renal Injury & Coagulopathy \\ (TP rate = 0.677)&-0.002 & 0.864 & 0.127 & 0.295 & 0.397 \\ \cmidrule(l){2-6} & Inflammation & Sepsis & ICULOS & Oxygenation Dysfunction\\ & -0.002 & 0.048 & 0.324 & 0.089\\ \midrule \textbf{Hepatocellular Injury} & Inflammation & Oxygen Carrying Dysfunction & Shock & Sepsis & Diminished Cardiac Output \\ (TP rate = 0.619) & 0.060 & 0.170 & 0.063 & 0.088 & 0.043 \\ \cmidrule(l){2-6} & Coagulopathy & MAP (min) & O2Sat min & Renal Injury \\ & 0.434 & 0.063 & 0.008 & 0.262 \\ \midrule \textbf{Oxygenation Dysfunction} & Sepsis & Inflammation & Resp (mean) & Shock & Diminished Cardiac Output \\ (TP rate = 0.780)& 0.093 & 0.047 & 2.538 & 0.699 & 0.237 \\ \cmidrule(l){2-6} & MAP min & Hepatocellular Injury\\ & 0.060 & 0.111\\ \midrule \textbf{Inflammation} & Sepsis & HR (max) & Renal Injury & Oxygenation Dysfunction & Shock \\ (TP rate = 0.710)& 0.099 & 1.597& 0.117 & 0.119 & 0.176 \\ \midrule \textbf{Sepsis} & HR (mean) & ICULOS& Renal Injury& Inflammation& Electrolyte Imbalance \\ (TP rate = 0.768)& 0.174& 0.722& 0.509& 0.165& 0.200 \\ \cmidrule(l){2-6} & Diminished Cardiac Output& Resp (min) & Coagulopathy\\ &0.387& 0.458& -0.104\\ \midrule[0.3pt]\bottomrule[1pt] \end{tabular} } \end{sc} \end{small} \end{center} \vspace{-0.15in} \end{table} {\it Bootstrap confidence intervals.} We also performed uncertainty quantification via bootstrap. We determined the existence of an edge in the network based on the $90\%$ bootstrap confidence interval (CI), i.e., we assigned zero weight to that edge if the CI contains zero; otherwise, we used the median of the bootstrap samples as the weight. The resulting network topology is reported below in left two graphs in Figure~\ref{fig:network_structure_CI_thres}. Meanwhile, we also used classification error as the CV criterion to infer the network topology in right two graphs in Figure~\ref{fig:network_structure_CI_thres}. We applied hard thresholding on the network topology to improve legibility by only keeping directed edges whose absolute weights are greater than $0.15$. The networks in left graph in Figure~\ref{fig:network_structure_CI_thres} help to elucidate which relationships are most important in the network, which is an essential aspect of interpretability. The network with forward selection shows a high level of influence by the Diminished Cardiac Output and Shock nodes. This is not surprising as both of these SADs are known to cause organ injury. The network that does not use forward selection has identified relationships that suggest certain SADs actually have an inhibitory effect. While there are possible explanations for these inhibitory effects, they are not commonly known or expected from a physiologic perspective. Overall, the network that employees forward feature selection demonstrates a more meaningful series of relationships consistent with known physiologic responses to sepsis. We evaluated classification performance utilizing two separate CV metrics: TP rate (left two panels in Figure~\ref{fig:network_structure_CI_thres}) and classification error (right two panels in Figure~\ref{fig:network_structure_CI_thres}). Both approaches produce networks that demonstrate many conserved features, however, use of TP rate seems to place greater emphasis on clinically relevant relationships. For example the first graph (counting from left to right) in Figure~\ref{fig:network_structure_CI_thres} (i.e. maximizing TP rate with forward feature selection) shows greater involvement of the Renal node and slight differences in edge weights when compared to the third graph in Figure~\ref{fig:network_structure_CI_thres} (i.e. minimizing classification error). The same is also observed in the second and fourth graphs of Figure~\ref{fig:network_structure_CI_thres}, where forward feature selection is not used. For example maximizing TP rate seems to place more weight shock to cholestasis relationship which correlates with a well known clinical relationship. Ultimately maximizing TP during CV produces graphs that not only have a higher sensitivity for sepsis, but also seem to make more sense clinically. To better elucidate the subtle relationships between nodes we also plot the non-thresholding version of Figure~\ref{fig:network_structure_CI_thres}. In Figure~\ref{fig:network_structure_CI} the effect of not performing feature selection becomes evident as we can see numerous red edges indicating a inhibitory relationship between SAD nodes. From a physiologic perspective one would not normally expect a SAD to inhibit another SAD. While there could be unappreciated physiologic relationships or biases in the data that explain such an inhibitory relationship, these inhibitory relationships disappear (as seen in the first and third graphs in Figure~\ref{fig:network_structure_CI}) with feature selection suggesting that they are not meaningful and should be eliminated. The elimination of inhibitory relationships further highlights the importance of feature selection. \vspace{-0.05in} \subsection{Experiment 2: data-driven measurement clustering and network topology} \vspace{-0.05in} In our second experiment, we assumed there was no prior information regarding the nature of the network and instead re-grouped the 34 measurements in Table~\ref{table:node_construction} using a purely data-driven method. We constructed 34 binary time series and provided a label ``$1$'' if the Lab test was reported out AND the Lab result was abnormal based on the rules in Table~\ref{table:node_construction}. {\it Hierarchical clustering based on ``distance'' matrix.} Analysis of the similarity among measurements begins with the construction of a correlation matrix including all 34 measurements in Figure~\ref{fig:dist_mat}. In this case, correlation occurs when both variables are found to be abnormal. For example, one can see that when \texttt{Creatinine} is abnormal, it likely that \texttt{BUN} and \texttt{Phosphate} would also be abnormal based on the correlation matrix. This correlation and many of the others in the table like this are commonly found in sepsis patients. \begin{figure}[!htp] \centerline{ \includegraphics[width = 0.22\textwidth]{fig/data_exploration/cor_mat.png} \hspace{0.1in} \includegraphics[width = 0.22\textwidth]{fig/network_cls/hawkes_network_raw.png} } \vspace{-0.1in} \caption{Correlation matrix (left) and adjacency matrix for discrete Hawkes network (right).} \label{fig:dist_mat} \vspace{-0.05in} \end{figure} We can view the correlation as statistical distance. Since larger correlation indicates smaller ``distance'', we used the element-wise inverse of the correlation matrix as the distance matrix. Here we grouped those measurements based on positive correlation; for those with negative or zero correlation, we treated them as though they are very far away from each other and assigned a large constant as the distance. Then, we can apply (hierarchical) clustering to obtain the clusters. The resulting clusters are plotted in Figure~\ref{fig:Hierarchical_clustering_corr}. \begin{figure}[!htp] \vspace{-0.05in} \centerline{ \includegraphics[width = 0.5\textwidth]{fig/network_cls/corr_cls.png}} \vspace{-0.1in} \caption{Hierarchical clustering based on correlation matrix.} \label{fig:Hierarchical_clustering_corr} \vspace{-0.15in} \end{figure} Similar to the fitting procedure above, we fitted our proposed discrete Hawkes network model on those 34 binary time series to construct a directed graph. We plot the adjacency matrix in Figure~\ref{fig:dist_mat}. Here, the adjacency matrix is asymmetric, which makes it difficult to perform clustering. This asymmetric adjacency matrix $A$ can be symmetrized by using $A_{sym} = A + A^{ \mathrm{\scriptscriptstyle T} }$. Then we can apply the same method as we did for the correlation matrix above to complete the (hierarchical) clustering. The result is plotted in Figure~\ref{fig:Hierarchical_clustering_hawkes}. \begin{figure}[!htp] \vspace{-0.05in} \centerline{\includegraphics[width = 0.5\textwidth]{fig/network_cls/sym+h_cls+ward_2.png}} \vspace{-0.1in} \caption{Hierarchical clustering based on symmetrized discrete Hawkes network.} \label{fig:Hierarchical_clustering_hawkes} \vspace{-0.1in} \end{figure} Both approaches for clustering patient features (i.e., via simple correlation and via a discrete Hawkes network) produce nodes that share similarity with the SAD nodes derived by a clinical expert in Experiment 1. For example, in Figure~\ref{fig:Hierarchical_clustering_hawkes} we see a cluster that includes the measurements: \texttt{Lactate, PaCO2, BaseExcess, pH} which commonly become deranged during shock. While these measurements do occur together on a common Lab panel (i.e., they are often collected simultaneously), this doesn't necessarily imply that their derangements would be similarly correlated as this label panel has many permutations of derangement caused by different non-sepsis disease processes. It is more reasonable to consider that the data-driven clustering methods are independently identifying clinically relevant SADs. While the simple correlation approach identifies concomitant relationships (i.e., two things happening together), it does not consider a time-dependent, causal relationship the way the Hawkes network does. This important distinction is appreciated when considering the two maps in Figures~\ref{fig:Hierarchical_clustering_corr} and \ref{fig:Hierarchical_clustering_hawkes}. The Hawkes process develops nodes that have close intra-node relationships that are very clearly separated from other clusters. In contrast, the inter-node distances tend to be less pronounced in the correlation-based hierarchical clustering method. \begin{table}[!htp] \vspace{-0.15in} \caption{Data-driven cluster based on Hierarchical Blockmodelling.}\label{table:measurement_clsutering} \begin{center} \begin{small} \begin{sc} \resizebox{0.8\textwidth}{!}{% \begin{tabular}{ccl} \toprule[1pt]\midrule[0.3pt] 1st-level cluster & 2nd-level cluster & Measurement physionet name \\ \midrule[0.3pt] \textbf{A} & A1 & Creatinine , Potassium , HCO3 , Magnesium , Bilirubin total , WBC;\\ \cmidrule(l){2-3} & A2 & Phosphate , BUN , Chloride , Hct , Hgb , Platelets , Glucose ;\\ \midrule[0.3pt] \textbf{B} & B1 & Calcium , BaseExcess , SaO2 , PaCO2 ;\\ \cmidrule(l){2-3} & B2 & Lactate , pH , DBP , O2Sat ;\\ \cmidrule(l){2-3} &B3& SBP , PTT , Temp ;\\ \cmidrule(l){2-3} &NA& MAP , Fibrinogen , Bilirubin direct , Alkalinephos , AST , Resp , EtCO2 , FiO2 , HR , SepsisLabel \\ \midrule[0.3pt]\bottomrule[1pt] \end{tabular} } \end{sc} \end{small} \end{center} \vspace{-0.25in} \end{table} {\it Blockmodelling based on asymmetric Hawkes network.} In this approach, we define clusters using a stochastic block model: for any two clusters $V_i$ and $V_j$ and any two nodes $a,b \in V_i$; then there is approximately the same number of in-edges (respectively out edges) connecting $a$ to nodes in $V_j$ and of in-edges (respectively out edges) connecting $b$ to nodes in $V_j$. Identifying clusters from asymmetric adjacency matrix is called blockmodelling \citep{holland1983stochastic,wang1987stochastic}. We introduce a spectral algorithm for blockmodelling \citep{sussman2012consistent} in Appendix~\ref{appendix:blockmodelling}. This algorithm has hyperparameters $K$ (number of clusters/blocks) and $d$ (top $d$ eigenvectors are kept in the spectral decomposition). Since it only deals with unweighted directed graphs, we construct the unweighted adjacency matrix by thresholding with $0.15$ as we did before. By applying the spectral algorithm recursively, we get hierarchical blockmodels and report the results in Figure~\ref{fig:blockmodelling}. \begin{figure}[!htp] \vspace{-0.05in} \centerline{ \includegraphics[width = 0.25\textwidth]{fig/network_cls/blockmodelling.png}\includegraphics[width = 0.25\textwidth]{fig/network_cls/blk.pdf} } \vspace{-0.05in} \caption{Left: Hierarchical Blockmodeling (hyperparameter under each plot). We chose the smallest $d$ such that the explained variance ratio is at least $95\%$. Right: the resulting network topology.} \label{fig:blockmodelling} \vspace{-0.1in} \end{figure} Based on Hierarchical Blockmodeling, we identify five blocks/clusters and the associated network topology among them. Analysis of the first level suggests a predominantly renal-inflammatory axis in Group A with values like \texttt{Creatinine, BUN, Phosphate, WBC} being important, and a cardio-pulmonary axis in Group B with values like \texttt{SaO2, O2Sat, SBP, Temp} being important. Inside of Group A, we see derangements following known patterns that demonstrate renal injury (A1) promoting electrolyte imbalances (A2). Similarly, we see in Group B that reduced blood pressure and fevers (B3) promote aberrations in oxygenation and acid/base equilibrium (B2) (a frequent association in sepsis). For demonstration purposes, this Hierarchical Blockmodel created the adjacency matrix using a threshold of 0.15; however, this could be lowered to identify a higher number of clusters and relationships. While single nodes are grouped together to form a cluster, it does not necessarily mean there is a correlation within the cluster (unless there is a self-directed edge (e.g., A2). Instead, the composite effect of nodes within a cluster promote dysfunction in the nodes of other clusters to which it is connected. \vspace{-0.1in} \section{Discussion}\label{sec:discussion} \vspace{-0.05in} We develop a model to infer non-linear Granger causality from mixed-type of irregularly sampled time-series, and leverage a recently developed stochastic variational inequality (VI) approach to estimate the model parameters. We conduct a non-asymptotic theoretical analysis and demonstrate the good performance of our proposed method coupled with heuristic forward feature selection via real data experiments. Future work includes connecting this newly developed VI approach with a principled subsection selection method (e.g., group Lasso). It is important to appreciate that many of the Lab tests that serve as a data source for our analysis are collected at the direction of a clinician, meaning there is an inherent component of suspicion associated with each Lab test. The important effects that drive suspicion and compel the ordering of tests may not be captured in our data and, subsequently, our network. Additionally, our cohort was limited to a specific subset of patients in order to reduce the number of data elements and make analysis more tractable, but it is commonly recognized that there are demographic features and co-existing medical conditions that affect how patients respond to sepsis. These unobserved features may also alter some of the findings for our network. { It is also important to appreciate that we accepted the consequence of increased false alarms (i.e. False Positives) in order to maximize our sensitivity. In clinical settings high false alarm rates may decrease clinical satisfaction and lead to alarm fatigue or disuse.} In summary, our experimental results serve as a demonstration that good performance is achievable with our proposed method. The development of a full, interpretable, causal graph capable of facilitating real-world clinical decision-making would require the analysis of a larger cohort of patients from multiple health systems with a more robust set of demographic data. An interpretable model like the one we have proposed offers some protection against the aforementioned limitations by allowing a clinician to combine their own knowledge about a patient with the findings of the model resulting in more informed decisions about a patient's health status. \newpage \bibliographystyle{icml2021} \section{Introduction} \vspace{-0.1in} Continuous, automated surveillance systems that incorporate machine learning models are becoming increasingly common in healthcare environments. These models can capture temporally dependent changes across multiple patient variables and can enhance a clinician's situational awareness by providing an early warning alarm of an impending adverse event. Among those adverse events, we are particularly interested in sepsis, which is a life-threatening medical condition contributing to one in five deaths globally \citep{world2020global} and stands as one of the most important cases for automated in-hospital surveillance. Sepsis is formally defined as life-threatening organ dysfunction caused by a dysregulated host response to infection \citep{singer2016third}. Delays in recognizing sepsis and initiating appropriate treatment can adversely impact patient outcomes. In a recent study of adult sepsis patients, each hour of delayed treatment was associated with higher risk-adjusted in-hospital mortality (odds ratio, 1.04 per hour) \citep{seymourTimeTreatmentMortality2017}. It stands to reason that early recognition of the physiologic aberrations preceding sepsis would afford clinicians more time to intervene and may contribute to improving outcomes and reducing costs. Many machine learning methods have been developed to predict the onset of sepsis, utilizing data from the electronic medical record (EMR) \citep{fleuren2020machine}. A recent sepsis prediction competition \citep{reyna2019early} demonstrated both the popularity and robust performance of XGBoost models \citep{du2019automated,zabihi2019sepsis,yang2020explainable}; meanwhile, Deep Neural Networks \citep{shashikumarDeepAISEInterpretableRecurrent2021} are also commonly used. However, most approaches offer an alert adjudicator very little information pertaining to the reasons for the alert/prediction, leading many to refer to them as ``black box'' techniques. Thus, model predictions related to disease identification, particularly for complex diseases, still need to be adjudicated (i.e., interpreted) by a clinician before further action (i.e., treatment) can be initiated. Among the aforementioned works, \citet{yang2020explainable} provided one of the best attempts at identifying causality for their models' predictions by reporting feature importance at a global level for all patients; still, this does not convey which features were most important in arriving at a given prediction for an individual patient. The common lack of interpretability of many clinical models, particularly those related to sepsis, suggests a strong need for principled methods (with theoretical guarantee) to study the interactions among time series in medical settings. \begin{figure}[!htp] \centerline{ \includegraphics[width = 0.45\textwidth]{fig/network_graph/new_network.pdf} } \vspace{-0.15in} \caption{Granger Causal graph over endogenous Sepsis Associated Derangements (SADs) obtained via Discrete Hawkes Network with forward feature selection.} \label{fig:new_net_structure} \vspace{-0.3in} \end{figure} One approach to obtain interpretable predictive models for sepsis is to consider its syndromic nature --- there is often a constellation of different physiologic derangements that can combine to create the condition. Figure~\ref{fig:new_net_structure} shows a series of different nodes representing these types of physiologic derangements. For example, a clinical adjudicator may be more inclined to arrive at a concordant opinion regarding sepsis if they know that the alert was caused by the combined effects from the Renal Injury and Diminished Cardiac Output nodes. Likewise, this same adjudicator might be less inclined to corroborate an alert on a different patient if the main contributing cause was from Electrolyte Imbalance alone. In modeling relationships between nodes and their effect on sepsis, a natural approach is through {\it Granger causal (GC) graphs}, which analyze the interactions among time series. A popular approach to capture GC graph is the Linear Vector Autoregressive (VAR) model \citep{lutkepohl2005new}. However, it has been recognized that traditional time series models, e.g., VAR, have many limitations, including linearity and assuming continuous-valued observations \citep{shojaie2021granger}. In addition, the observations can be both continuous and categorical-valued in many real applications, including medical data. Moreover, the traditional time series model assumes that the observations are synchronous and indexed by integers. In the medical setting, the observations can be both discrete and continuous-valued, and they can also be asynchronous and sampled with different frequencies. For example, vital signs are recorded regularly, whereas laboratory (lab) tests are only ordered when clinically necessary; thus, this cannot be simply formulated into a missing data problem In this paper, we present a new GC graph based on the generalized linear model (GLM) to handle observations that are (i) asynchronous and (ii) mixed type (real-valued, integer-valued, binary, or categorical valued). The model estimation is achieved by solving a monotone operator variation inequality problem, a general convex optimization problem. This approach also enables us to establish performance guarantees via recent advances in optimization \citep{juditsky2019signal,juditsky2020convex}. In particular, we develop (i) a non-asymptotic upper bound on estimation error verified by numerical examples and (ii) quantifiable uncertainty by establishing confidence interval for the estimated graph structure by solving a linear program. We demonstrate via real data experiments that our proposed GLM with forward-feature selection can achieve comparable performance to a powerful method such as XGBoost. Moreover, our learned GC graph is highly interpretable, thus making the future adoption of these models to conduct continuous surveillance of high-risk patients by clinicians much more likely. Here, we demonstrate the effectiveness of our approach in learning a GC graph over Sepsis Associated Derangements (SADs), but it can be generalized to other applications with similar requirements. \vspace{-0.2in} \section{Sepsis Associated Derangements}\label{sec:background} \vspace{-0.05in} We start by presenting the data for sepsis prediction, which will motivate our model development. Data used for this analysis was a curated, publicly available data set from the 2019 Physionet challenge \citep{physionet2019}. The challenge data was sourced from patients admitted to the Intensive Care Unit (ICU) during their hospitalization and represented three categories of patient features: demographic information, vital sign measurements and Laboratory (Lab) results. {\it Demographic information} remains constant throughout hospitalization. The examined data set contains both age and sex. {\it Vital Signs} in ICU environments are normally recorded at an hourly interval and include \texttt{HR, O2Sat, Temp, SBP, MAP, DBP, Resp} (see Table~\ref{table:node_construction} for their full measurement names). {\it Lab Values} are results of Lab tests, which are most commonly collected once every 24 hours; however, this collection frequency may change based on the severity of a patient's illness. \noindent {\it Construction of Sepsis Associated Derangements (SADs).} The missingness in regularly sampled vital signs and irregularly sampled lab values carries different meaning --- the missing vital signs are rare and random, and therefore it can be treated by standard imputation method; however, the absence of a lab test shows indicates the clinician's belief of no sign of corresponding disease whereas the result of a taken lab test remains effective for a short period of time. To incorporate such information, we leverage the thresholds, which represent breaks between normal and deranged physiology and are identified utilizing already established criteria \citep{ABIM_ref_range}, to condense different measurements (containing both vital signs and Lab results) into a binary variable as an indicator of physiologic derangements seen preceding and during sepsis (see column ``SAD name'' in Table~\ref{table:node_construction} in the Appendix). Here, we apply forward filling to impute missing vital signs and construct SADs based on imputed vital signs and raw lab values. Then, we use imputed vital signs and SADs as inputs to fit a Granger causal (GC) graph over SADs on a sub-cohort of patients determined by demographic variables. \vspace{-0.2in} \section{Discrete Hawkes Networks} \vspace{-0.05in} \subsection{Formulation} Consider $N_1$ observed sequences of binary SADs over a time horizon $T$: $\{y_1^{(i)},\dots,y_T^{(i)}\}$, $i = 1,\dots,N_1$. We also observe both continuous and discrete-valued time series $\{x_1^{(i)},\dots,x_T^{(i)}\}, i = 1,\dots,N_2$, which correspond to vital signs as well as Lab test counts, and demographic variables $(z_1,\dots,z_{N_3})$. In the following, we will refer to each SAD variable as a node since it corresponds to a node in the GC graph. To model the mutual inter-dependence among the variables, we consider a generalized linear model (GLM), which closely resembles the intensity function of Hawkes point process \citep{hawkes1971point,hawkes1971spectra,hawkes1974cluster}. For the $i$-th node variable ($i = 1,\dots,N_1$), at time step $t \ (t = 2,\dots,T)$, we assume $\mathbb{P} ( y_t^{(i)} =1 \| \mathcal{H}_{t-1} )$ takes the following generalized linear form: \vspace{-0.25in} \begin{align}\label{eq:hawkes_model} &g\Bigg(\nu_i + \sum_{j = 1}^{N_3} \gamma_{ij} z_j + \sum_{\tau = 1}^{t-1} \bigg( \sum_{j = 1}^{N_2} \beta_{ij} x_{t-\tau}^{(j)} e^{-\Tilde{R}_{ij} \tau} \nonumber\\ &\quad\quad\quad\quad\quad\quad\quad\quad+ \sum_{j = 1}^{N_1} \alpha_{ij} y_{t-\tau}^{(j)} e^{-R_{ij} \tau}\bigg)\Bigg), \end{align} \vspace{-0.1in} \noindent where $\mathcal{H}_t$ denotes the past observation up to time $t$ and $g: \mathbb{R} \rightarrow [0,1]$ is a link function. For example, $g$ can be non-linear, such as sigmoid link function $g(x) = 1/(1+e^{-x})$; also, it can be linear $g(x) = x$ on domain $x \in [0,1] \subset \mathbb{R}$. {\it Non-linear Granger causal graph.} By the definition of Granger causality in non-linear model \citep{tank2018neural}, matrix $A = (\alpha_{ij}) \in \mathbb{R}^{N_1 \times N_1}$ represents the causal graph structure over $N_1$ SAD nodes. To be precise, $j$-th SAD does NOT Granger cause $i$-th SAD if $\alpha_{ij} = 0$. {\it Connection to multivariate Hawkes process (MHP).} For $i$-th SAD node variable, $\alpha_{ij}$ and $\beta_{ij}$ represent the magnitude of triggering effect of $j$-th SAD node variable and continuous variable to it. This effect decays exponentially fast with exponent characterized by $R_{ij}$ and $\Tilde{R}_{ij}$. $\gamma_{ij}$'s represent the influence of demographics and contribute to baseline intensity togerther with $\nu_i$. Thus, the above model can be viewed as a discretized version of (non-linear) MHP with exponential triggering function \vspace{-0.1in} \subsection{Estimation} \vspace{-0.05in} In this section, we will leverage a recently developed technique \citep{juditsky2019signal,juditsky2020convex}, which estimates the parameters of the generalized linear model by solving stochastic monotone variational inequality (VI), to develop a statistically principled method to estimate the parameters of Discrete Hawkes Network and infer the GC graph topology. {\it Preliminaries.} To begin with, we make reasonable simplification by assuming finite memory depth $d$ for both continuous and binary observations. Let $w_{t-d}^{t-1}$ denote the observation from $t-d$ to $t-1$: $\big(1,z_1,\dots,z_{N_3},x_{t-1}^{(1)},\dots,x_{t-d}^{(1)},\dots,x_{t-1}^{(N_2)},\dots,$ $x_{t-d}^{(N_2)},y_{t-1}^{(1)},\dots,y_{t-d}^{(1)},\dots,y_{t-1}^{(N_1)},\dots,y_{t-d}^{(N_1)}\big)^{ \mathrm{\scriptscriptstyle T} },$ where superscript $^{ \mathrm{\scriptscriptstyle T} }$ denotes matrix transpose. Since we only consider finite memory depth for binary observation, we could use one single parameter $\alpha_{ij\tau} := \alpha_{ij} \exp\{-R_{ij} \tau\}$ (similarly, $\beta_{ij\tau} := \beta_{ij} \exp\{-\Tilde{R}_{ij} \tau\}$) to represent the triggering effect with exponential decay. We rewrite \eqref{eq:hawkes_model} into: \begin{equation}\label{eq:model} \mathbb{P}\left(y_t^{(i)}=1 \Big\| w_{t-d}^{t-1} \right) = g\left((w_{t-d}^{t-1})^{ \mathrm{\scriptscriptstyle T} } \theta_i\right), \end{equation} where $\theta_i \in \mathbb{R}^N$ ($N = 1+N _3+dN_2+dN_1$) is the parameter to be estimated: $\theta_i = (\nu_i,\gamma_{i1},\dots,\gamma_{iN_3},\beta_{i11},\dots,\beta_{i1d},\beta_{iN_21},\dots,$ $\beta_{iN_2d},\alpha_{i11},\dots,\alpha_{i1d},\alpha_{iN_11},\dots,\alpha_{iN_1d})^{ \mathrm{\scriptscriptstyle T} }.$ This parameter summarizes the influence from all variables to node $i$ and could be estimated independently from the remaining $N_1-1$ parameters. {\it Granger Causality.} We can see \eqref{eq:model} is actually a generalized version of Vector Autoregressive (VAR) model. Therefore, we say $j$-th node series $\{y^{(j)}_t\}$ (or vital sign series $\{x^{(j)}_t\}$) Granger-causes $i$-th node series $\{y_t^{(i)}\}$ if $\alpha_{ij\tau} \not= 0$ (or $\beta_{ij\tau} \not= 0$) for some $\tau \in \{1,\dots,d\}$. {\it Estimation with VI.} Denote the observation by $W_{T}:=(w_{1-d}^{0},\dots,w_{T-d+1}^{T})$ $ \in \mathbb{R}^{(T+1) \times N}$, where variables observed at time step $1-d,\dots,0$ are viewed as given history. We assume parameter $\theta_i$ is constrained in a convex compact set $\theta_i \in \Theta_i \subset \mathbb{R}^N$, then, for $i = 1,\dots,N_1$, we use the weak solution to the following variational inequality as the estimator $\hat \theta_i$: \vspace{-0.25in} \begin{equation} \text {find } \hat \theta_i \in \Theta_i:\langle F_{ W_{T}}^{(i)}(\theta), \theta-\hat \theta_i\rangle \geq 0, \ \forall \theta \in \Theta_i, \label{VI_1}\tag{{VI}$[ F_{W_{T}}^{(i)}, \Theta_i]$} \end{equation} where $\langle \cdot \rangle$ represents the standard inner product in Euclidean space and $F_{W_{T}}^{(i)}(\theta_i)$ is the empirical vector field: \vspace{-0.2in} $$F_{W_{T}}^{(i)}(\theta_i) := \frac{1}{T} \sum_{t=1}^T w_{t-d}^{t-1} \left( g\left((w_{t-d}^{t-1})^{ \mathrm{\scriptscriptstyle T} } \theta_i\right) - y_t^{(i)} \right).$$ \vspace{-0.1in} \paragraph{Remarks.} (i) The feasible region $\Theta_i$ makes sure the assumptions (which are introduced later in next section) are satisfied and is defined differently in different problems; see two examples (with definitions) in Appendix~\ref{appendix:eg}. (ii) The intuition behind this method is straightforward. Let's consider the global counterpart of the above vector field, whose root is the unknown ground truth $\theta_{0,i}$, \vspace{-0.2in} \begin{align} F^{(i)}(\theta_i) :=& \mathbb{E}_{(w,y^{(i)})} \left[w \left( g\left(w^{ \mathrm{\scriptscriptstyle T} } \theta_i\right) - y^{(i)} \right)\right] \\ =& \mathbb{E}_{(w,y^{(i)})} \left[w \left( g\left(w^{ \mathrm{\scriptscriptstyle T} } \theta_i\right) - g\left(w^{ \mathrm{\scriptscriptstyle T} } \theta_{0,i}\right) \right)\right]. \end{align} Although we cannot access this global counterpart, by solving the empirical one \ref{VI_1} we could approximate the ground truth very well. We next show how well this approximation can be. \vspace{-0.1in} \subsection{Theoretical analysis} \vspace{-0.05in} In this section, we show the VI estimate will eventually converge to a very small neighborhood of the ground truth. Besides, we will derive a linear program (LP) based confidence interval (CI) of parameters $\theta_i$'s. Due to space limitation, we defer the CI to Appendix~\ref{appendix:CI}. To begin with, we state two necessary model assumptions: \paragraph{Assumption 1} The link function $g(\cdot)$ is continuous and monotone, and the vector field $G(\theta) = \mathbb{E}_w[wg(w^{ \mathrm{\scriptscriptstyle T} }\theta)]$ is well defined (and therefore monotone along with $g$). Moreover, $g$ is differentiable and has uniformly bounded first order derivative $m_g \leq \|g'\|\leq M_g$ for $0<m_g\leq M_g$. \paragraph{Assumption 2} The observations (static, binary and continuous) are bounded almost surly: $\exists M_w>0$ such that at any time step $t$, we have $\norm{w_{t-d}^{t-1}}_\infty \leq M_w$ with probability one. \vspace{-0.1in} \begin{figure}[htbp] {% \subfigure[{From left to right: true adjacency matrix, estimated Discrete Hawkes Network with $T = 500$ and $T = 5000$.} ]{\label{fig:simu_topo}% \includegraphics[width = 0.45\textwidth]{ICML2022_resp_fig/exp0.png} }% $ \ $ \subfigure[Left: Trajectory for $\ell_2$ norm of estimation error and its data-driven bound. Right: log-log plot of estimation error and its bound, which shows our bound is sharp in rate. ]{\label{fig:traj}% { \includegraphics[width = 0.25\textwidth]{fig_num_simu/traj_3.pdf} \includegraphics[width = 0.25\textwidth]{fig_num_simu/loglog_3.pdf} }} } \vspace{-0.15in} \caption{Demonstration of consistency} \vspace{-0.15in} \end{figure} We define an auxiliary vector field $\Tilde{F}_{W_{T}}^{(i)}(\theta_i) := \frac{1}{T} \sum_{t=1}^T w_{t-d}^{t-1}( g((w_{t-d}^{t-1})^{ \mathrm{\scriptscriptstyle T} } \theta_i) - g((w_{t-d}^{t-1})^{ \mathrm{\scriptscriptstyle T} } \theta_{0,i}) ).$ This vector field changes the constant term in ${F}_{W_{T}}^{(i)}(\theta_i)$ to make sure its unique root/weak solution to corresponding VI is the unknown ground truth $\theta_{0,i}$. Recall that $\hat \theta_i$ is the root of ${F}_{W_{T}}^{(i)}(\theta_i)$. Then, we will bound the difference between $\hat \theta_i$ and $\theta_{0,i}$ via the difference between ${F}_{W_{T}}^{(i)}(\theta_i)$ and $\Tilde{F}_{W_{T}}^{(i)}(\theta_i)$: \vspace{-0.2in} $$\Delta^{(i)} := {F}_{W_{T}}^{(i)}(\theta_i) - \Tilde{F}_{W_{T}}^{(i)}(\theta_i) = {F}_{W_{T}}^{(i)}(\theta_{0,i}).$$ \vspace{-0.1in} \begin{proposition}\label{lma:bound_delta} Under Assumptions~1 and 2, for $i = 1,\dots,N_1$, $\forall \ \varepsilon \in (0,1)$, with probability at least $1-\varepsilon$, the difference between the empirical and auxiliary vector field $\Delta^{(i)}$ can be bounded as follows: \vspace{-0.1in} \begin{equation}\label{eq:bound_inf} \norm{\Delta^{(i)}}_\infty \leq M_w \sqrt{{\log(2N/\varepsilon)}/{T}} \end{equation} Moreover, this implies \begin{equation}\label{eq:bound_l2} \norm{\Delta^{(i)}}_2 \leq M_w \sqrt{N{\log(2N/\varepsilon)}/{T}}. \end{equation} \end{proposition} The proof of Proposition~\ref{lma:bound_delta} leverages the concentration property of martingales. Similar results could also be found in \citet{juditsky2020convex,wei2021inferring}. We defer its proof to Appendix~\ref{appendix:proof}. We want to remark that improvement can be achieved by Bernstein inequality, but the rate remains the same. This proposition enables us to prove the following non-asymptotic estimation error bound: \begin{theorem}[Upper bound on $\norm{\hat \theta_i - \theta_{0,i}}_2$]\label{thm:upper_err_bound} Under Assumptions~1 and 2, for $i = 1,\dots,N_1$ and any $\varepsilon \in (0,1)$, with probability at least $1-\varepsilon$, the $\ell_2$ distance between ground truth $\theta_{0,i}$ and $\hat \theta_i$, which is weak solution to \ref{VI_1}, can be upper bounded as follows: \vspace{-0.1in} $$\norm{\hat \theta_i - \theta_{0,i}}_2 \leq \frac{M_w}{m_g \lambda_1} \sqrt{\frac{N\log (2N/\varepsilon)}{T }},$$ \vspace{-0.1in} \noindent where $\lambda_1$ is the smallest eigenvalue of $\mathbb{W}_{1:T} = \sum_{t=1}^T w_{t-d}^{t-1}(w_{t-d}^{t-1})^{ \mathrm{\scriptscriptstyle T} }/T$. \end{theorem} The above theorem is an extension to the general link function case of Theorem 1 \citep{juditsky2020convex}, where they only sketched the proof without giving further details; we defer the detailed proof to Appendix~\ref{appendix:proof}. Moreover, as pointed out in \citet{juditsky2020convex}, $\mathbb{W}_{1:T} \in \mathbb{R}^{N \times N}$ will be full rank when $T$ is sufficiently large, i.e., with high probability, $\lambda_1$ will be a positive constant. \vspace{-0.15in} \section{Numerical simulation}\label{sec:exp} \vspace{-0.1in} In this section, we demonstrate the performance of our proposed model via some simple toy examples. \begin{figure}[!htp] \centering \vspace{-0.1in} {\includegraphics[scale = 0.45]{ICML2022_resp_fig/exp1.png}} \vspace{-0.3in} \caption{Heatmap of estimated adjacency matrices. The error vector on the top of each figure corresponds to (L1 Error; Support Recovery Error after proper thresholding; Weighted Support Recovery).}\label{fig:syn_exp1} \vspace{-0.4in} \end{figure} \noindent {\it Demonstration of consistency.} We fit the GC graph over 5 binary node variables with sigmoid non-linear link function. We present the true network topology in first two figures in Figure~\ref{fig:simu_topo} and report the estimated topology via Discrete Hawkes Network in the last two figures in Figure~\ref{fig:simu_topo}. Further details, such as synthetic data generation process, are deferred to Appendix~\ref{appendix:num_simu}. Since this network is sparse, we also impose $\ell_1$ penalty and the results are deferred to Figure~\ref{fig:simu_topo_l1} in Appendix~\ref{appendix:num_simu}. From both figures, we can observe that when trajectory is long enough, we can faithfully recover the true network topology. Most importantly, we study the trajectories of the $\ell_2$ norm of the estimation error and the data-driven bound. Here, the data-driven bound requires us to calculate $\lambda_1$ and $m_g$ from the data. Since we consider simple binary r.v.s in our toy example, $M_w$ is one. We plot the trajectory for a particular node in Figure~\ref{fig:traj}. The results for the rest of the nodes are deferred to Figure~\ref{fig:traj_additional} in Appendix~\ref{appendix:num_simu}. From both figures (especially the slope in the log-log plot), we observe that our data-driven bound is sharp in rate, though the constant could be loose. This constant could be further improved by using Bernstein's inequality instead of Azuma's inequality (see remark of Proposition~\ref{lma:bound_delta}). \noindent {\it Comparison to existing methods.} We compare methods: \texttt{\textcircled{\small 1}} Proposed VI method, \texttt{\textcircled{\small 2}} Gradient method \citep{wang2020uncertainty}, and \texttt{\textcircled{\small 3}} NN method \citep{khanna2019economy}, under two different data generating processes: \texttt{Setting 1}: MHP with exponential kernel and \texttt{Setting 2}: Proposed model with sigmoid link. Further details can be found in Appendix~\ref{appendix:num_simu}. True adjacency matrices $A = (\alpha_{ij})$ are visualized in 1, 2, 3, 4-(a) respectively in Figure~\ref{fig:syn_exp1}. The major weakness of \texttt{\textcircled{\small 2}} and \texttt{\textcircled{\small 3}} is that they are unable to model inhibiting effect with negative $\alpha_{ij}$'s (e.g., proper medication lowers the chance of poor health status). We apply log-barrier method in \textcircled{\small 2}, i.e., we add penalty $p(b) = \sum_{i} \log(\lambda_i(t_i) - b)$ to the log-likelihood ($\lambda_i(t_i)$ is the intensity of event $i$ occurring at time $t_i$ and $b$ is hyperparameter) to make sure the intensity will not be negative. We report the fitted adjacency matrices in Figure~\ref{fig:syn_exp1}. We observe that: (1) Under correct model specification, all methods faithfully recover $A$ (1-(d), 2-(b, c), 3-(d), 4-(b, c)). (2) Our method \texttt{\textcircled{\small 1}} recovers the true pattern of $A$ even under model mis-specification (see support recovery error in 1-(b, c), 3-(b, c)) whereas \texttt{\textcircled{\small 2}} fails to do so (2-(d), 4-(d)). (3) As a powerful non-parametric method, \texttt{\textcircled{\small 3}} also roughly recovers the true pattern (1, 2-(e)); its major weakness is that it cannot model negative $\alpha_{ij}$'s. Besides, the log-barrier modification enables gradient-based method to further model inhibiting effect in Hawkes network (3-(d)). \vspace{-0.15in} \section{Real Data Experiments} \vspace{-0.15in} In Experiment 1, nodes in the network are constructed based on well-known, measurable, physiologic relationships in the human body. This expert-driven approach is subsequently compared to a purely data-driven model for identifying possible clusters of inpatient data in Experiment 2. Due to space limitation, we defer the results of Experiment 2 to Appendix~\ref{appendix:blockmodelling}. Now, we aim to recover the network topology over SADs constructed in Section~\ref{sec:background} \noindent {\it Feature construction.} As previously described, vital sign measurements were condensed into single features represented by summary statistics (i.e., maximum, minimum, mean) of the past 6 hours, creating a total of 12 distinct representations of a patient's vital signs. A count of total Lab tests over the past 6 hours was used as a proxy for patient acuity and was also incorporated as a feature. SAD nodes were created by grouping all 34 Lab measurements into ten nodes (see Table~\ref{table:node_construction}), representative of common physiologic derangements seen in sepsis. Moreover, instead of constructing a sequence of binary variables for each node, we assigned a risk score at each time, indicating the severity of the SAD. However, when a variable (i.e., node) was used as the response during modeling, it was treated as binary by applying indicator function $\mathbf{1}_{\{y > 0\}}$. \noindent {\it Sub-group analysis.} To simplify model development, we carried out a sub-group analysis and excluded demographic features from the model. We used sex $= 0$ (female) and age $>60$ sub-group in the following to demonstrate our method, which contained 5,222 patients in the Physionet data set. \noindent {\it Model fitting.} The primary outcome of interest was sepsis, which necessitated the addition of an $11$-th binary time series called ``SepsisLabel'' to our data. This resulted in a total of $N_1 = 11$ nodes in our network. Using each of those $N_1$ variables as responses (recall that risk scores were binarized when used as a response) and the rest as features, we fitted our proposed model with sigmoid link function with hyperparameter being the number of training iterations and performed forward feature selection. The primary cross-validation (CV) criterion for both feature selection and hyperparameter tuning was the True Positive (TP) rate (classification accuracy for positive samples); we also compared classification error and AUC. TP rate was chosen because in a clinical setting, particularly as it pertains to sepsis, greater importance is placed on not missing the disease (i.e., maintaining a high sensitivity) as opposed to producing a false alert. \vspace{-0.15in} \noindent \paragraph{\it Comparison to XGBoost.} During the forward selection, the TP rate goes from around 0.6 up to final 0.768 whereas the TP rate for using all features and subset selection based on random forest feature importance remain below 0.7. Our model achieve comparable performance (TP rate = 0.77 and AUC = 0.70) to sophisticated and commonly used prediction algorithm XGBoost (TP rate = 0.73 and AUC = 0.85), which outperformed other methods in the Challenge \citep{physionet2019}. Due to space limitation, we defer further details such as the training procedure to Appendix~\ref{appendix:training_details}. \noindent {\it Results and interpretation.} As previously discussed, nodes were created by a clinician to identify the distinct types of measurable, physiologic change that accompanies sepsis-related illness (i.e., SAD nodes); however, the clinician did not determine the relationship amongst the SAD nodes. Rather, these relationships were an output of model training. Both { Table~\ref{table:model_coeff} (deferred to Appendix~\ref{appendix:training_details} )} and { Figure~\ref{fig:new_net_structure}} illustrate a compelling network of SAD nodes that follow closely with known and expected causal relationships in sepsis-related illness. For example, the finding that Diminished Cardiac Output strongly promotes sepsis events or that Shock strongly promotes Coagulopathy are well-appreciated relationships. The primary outcome of interest for this work was sepsis; still, as demonstrated in {Table~\ref{table:model_coeff}}, the causal relationship between any node pair can be estimated, giving clinician users insight into the probability of observing subsequent SADs after sepsis. \noindent {\it Bootstrap confidence intervals.} We also performed uncertainty quantification via bootstrap. We determined the existence of an edge in the network based on the $90\%$ bootstrap confidence interval (CI), i.e., we assigned zero weight to that edge if the CI contains zero; otherwise, we used the median of the bootstrap samples as the weight. The resulting network topology is reported below in left two graphs in Figure~\ref{fig:network_structure_CI_thres}. Meanwhile, we also used classification error as the CV criterion to infer the network topology in right two graphs in Figure~\ref{fig:network_structure_CI_thres}. We applied hard thresholding on the network topology to improve legibility by only keeping directed edges with absolute weights greater than $.15$. The networks in left graph in Figure~\ref{fig:network_structure_CI_thres} help to elucidate which relationships are most important in the network, which is an essential aspect of interpretability. The network with forward selection shows a high level of influence by the Diminished Cardiac Output and Shock nodes. This is not surprising as both of these SADs are known to cause organ injury. The network that does not use forward selection has identified relationships that suggest certain SADs actually have an inhibitory effect. While there are possible explanations for these inhibitory effects, they are not commonly known or expected from a physiologic perspective. Overall, the network that employees forward feature selection demonstrates a more meaningful series of relationships consistent with known physiologic responses to sepsis. \begin{figure}[H] \vspace{-0.05in} \centerline{ \includegraphics[width = 0.125\textwidth,trim={4cm 0 2.8cm 0},clip]{fig/CI_graph/TP_thres_0.15_CI_new.pdf} \includegraphics[width = 0.125\textwidth,trim={4cm 0 2.8cm 0},clip]{fig/CI_graph/TP_thres_0.15_CI_old.pdf} \includegraphics[width = 0.125\textwidth,trim={4cm 0 2.8cm 0},clip]{fig/CI_graph/err_thres_0.15_CI_new.pdf} \includegraphics[width = 0.125\textwidth,trim={4cm 0 2.8cm 0},clip]{fig/CI_graph/err_thres_0.15_CI_old.pdf} } \vspace{-0.2in} \caption{From left to right: bootstrap network topology (1) with feature selection using TP rate for CV; (2) without feature selection using TP rate for CV; (3) with feature selection using classification error for CV; (4) without feature selection using classification error for CV. We only show edges with weights greater than $.15$. Color blue and red indicate positive and negative effect, respectively.}\label{fig:network_structure_CI_thres} \vspace{-0.25in} \end{figure} We evaluated classification performance utilizing two separate CV metrics: TP rate (left two panels in Figure~\ref{fig:network_structure_CI_thres}) and classification error (right two panels in Figure~\ref{fig:network_structure_CI_thres}). Both approaches produce networks that demonstrate many conserved features, however, use of TP rate seems to place greater emphasis on clinically relevant relationships. For example the first graph (counting from left to right) in Figure~\ref{fig:network_structure_CI_thres} (i.e. maximizing TP rate with forward feature selection) shows greater involvement of the Renal node and slight differences in edge weights when compared to the third graph in Figure~\ref{fig:network_structure_CI_thres} (i.e. minimizing classification error). The same is also observed in the second and fourth graphs of Figure~\ref{fig:network_structure_CI_thres}, where forward feature selection is not used. For example maximizing TP rate seems to place more weight shock to cholestasis relationship which correlates with a well known clinical relationship. Ultimately maximizing TP during CV produces graphs that not only have a higher sensitivity for sepsis, but also seem to make more sense clinically. \begin{figure}[!htp] \vspace{-0.05in} \centerline{ \includegraphics[width = 0.125\textwidth,trim={4cm 0 2.8cm 0},clip]{fig/CI_graph/TP_CI_new.pdf} \includegraphics[width = 0.125\textwidth,trim={4cm 0 2.8cm 0},clip]{fig/CI_graph/TP_CI_old.pdf} \includegraphics[width = 0.125\textwidth,trim={4cm 0 2.8cm 0},clip]{fig/CI_graph/err_CI_new.pdf} \includegraphics[width = 0.125\textwidth,trim={4cm 0 2.8cm 0},clip]{fig/CI_graph/err_CI_old.pdf} } \vspace{-0.2in} \caption{From left to right: non-thresholding bootstrap network topology (1) with feature selection using TP rate for CV; (2) without feature selection using TP rate for CV; (3) with feature selection using classification error for CV; (4) without feature selection using classification error for CV. Color blue indicates positive effect whereas red indicates negative effect. The criterion for cross validation is true positive rate (left) and classification error (right).}\label{fig:network_structure_CI} \vspace{-0.25in} \end{figure} To better elucidate the subtle relationships between nodes we also plot the non-thresholding version of Figure~\ref{fig:network_structure_CI_thres}. In Figure~\ref{fig:network_structure_CI} the effect of not performing feature selection becomes evident as we can see numerous red edges indicating a inhibitory relationship between SAD nodes. From a physiologic perspective one would not normally expect a SAD to inhibit another SAD. While there could be unappreciated physiologic relationships or biases in the data that explain such an inhibitory relationship, these inhibitory relationships disappear (as seen in the first and third graphs in Figure~\ref{fig:network_structure_CI}) with feature selection suggesting that they are not meaningful and should be eliminated. The elimination of inhibitory relationships further highlights the importance of feature selection. \newpage	{ "redpajama_set_name": "RedPajamaArXiv" }	4,863
Q: Why does "FileSystemUsage" metric for "Microsoft.Web/sites" always return zero? While answering Retrieve quota for Microsoft Azure App Service Storage, I stumbled upon the FileSystemUsage metric for Microsoft.Web/sites resource type. As per the documentation, this metric should return Percentage of filesystem quota consumed by the app.. However when I execute Metrics - List REST API operation (and also in the Metrics blade in Azure Portal) for my web app, the value is always returned as zero. I checked it against a number of web apps in my Azure Subscriptions and for all of them the result was zero. I am curious to know the reason for that. In contrast, if I execute App Service Plans - List Usages REST API operation, it returns me the correct value. For example, if my App Service Plan is S2, I get following response back: { "unit": "Bytes", "nextResetTime": "9999-12-31T23:59:59.9999999Z", "currentValue": 815899648, "limit": 536870912000,//500 GB (50 GB/instance x max 10 instances) "name": { "value": "FileSystemStorage", "localizedValue": "File System Storage" } }, Did I misunderstand FileSystemUsage for Web Apps? Would appreciate if someone can explain the purpose of this metric? If it is indeed what is documented, then why the API is returning zero value? A: This should be the default behavior, please check this doc Understand metrics: Note File System Usage is a new metric being rolled out globally, no data is expected unless your app is hosted in an App Service Environment. So currently this metric File System Usage should only be working on ASE.	{ "redpajama_set_name": "RedPajamaStackExchange" }	1,768
The following gives a glimpse into what bilingual education entails, and why it's generally thought of a controversial type of instruction. By the mid-1800s, there have been schools throughout the nation using German, Dutch, Czech, Spanish, Norwegian, French, and different languages, and lots of states had legal guidelines officially authorizing bilingual education. Globalisasi adalah suatu proses tatanan masyarakat yang tidak mengenal batas wilayah dan menghubungkan antara masyarakat di suatu negara dengan masyarakat di negara lain di seluruh dunia. Secondly, bilingual schooling might privilege one language over a learner's first language, resulting in a lack of cultural capital and a weakening of their first tradition identification. Proponents of bilingual training additionally argue that bilingualism in the United States is usually related to immigration and should maintain a stigma for those students who would profit by studying in bilingual lecture rooms. In Canada, immersion teaching programs are designed for native audio system of the majority language (English) to turn into proficient in a minority language (French), whereas heritage-language packages are implemented to assist native audio system of indigenous and immigrant languages turn out to be proficient in English. Leann Parker coordinated the conferences and edited the resulting sequence of five volumes, which supplied a nonetheless-useful conspectus of the state of analysis data. In Ireland, bilingual training is being implemented to restore the native language. If there are disadvantages to a bilingual education, these may be sociocultural relatively than cognitive. Furthermore, by sixth grade, the late-exit transitional bilingual training college students have been the only group catching up academically, in all content material areas, to their English-speaking friends; the opposite two teams were falling additional behind. Some schools offer bilingual applications, whereas others offer English as a Second Language (ESL) programs. It is a part of the Open Access Journal Movement so all the information is on the market on-line without cost.	{ "redpajama_set_name": "RedPajamaC4" }	4,983
module.exports = function(RED) { "use strict"; var http = require("http"); function assignmentFunction(node, msg, lat, lon, city, country, callback) { if (country && city) { node.country = country; node.city = city; } else if (lat && lon) { if (90 >= lat && lat >= -90) { node.lat = lat; } else { node.error("Invalid lat provided",msg); return; } if (180 >= lon && lon >= -180) { node.lon = lon; } else { node.error("Invalid lon provided",msg); return; } } callback(); } function weatherPoll(node, msg, callback) { //wipe clear the payload if it exists, or create it if it doesn't msg.payload = {}; msg.location = {}; var url; //If there is a value missing, the URL is not initialised. if (node.lat && node.lon) { url = "http://api.openweathermap.org/data/2.5/weather?lat=" + node.lat + "&lon=" + node.lon; } else if (node.city && node.country) { url = "http://api.openweathermap.org/data/2.5/weather?q=" + node.city + "," + node.country; } //If the URL is not initialised, there has been an error with the input data, //and a node.error is reported. if (url) { node.status({fill:"blue",shape:"dot",text:"requesting"}); http.get(url, function(res) { var weather = ""; res.on('data', function(d) { weather += d; }); res.on('end', function() { var jsun; try { jsun = JSON.parse(weather); } catch (e) { callback("The API call returned invalid JSON"); return; } if (jsun) { if (jsun.hasOwnProperty("weather") && jsun.hasOwnProperty("main")) { msg.data = jsun; msg.payload.weather = jsun.weather[0].main; msg.payload.detail = jsun.weather[0].description; msg.payload.tempk = jsun.main.temp; if (jsun.main.hasOwnProperty("temp")) { msg.payload.tempc = parseInt(10 * (Number(jsun.main.temp) - 273.2))/10; } msg.payload.humidity = jsun.main.humidity; msg.payload.maxtemp = jsun.main.temp_max; msg.payload.mintemp = jsun.main.temp_min; msg.payload.windspeed = jsun.wind.speed; msg.payload.winddirection = jsun.wind.deg; msg.payload.location = jsun.name; msg.payload.sunrise = jsun.sys.sunrise; msg.payload.sunset = jsun.sys.sunset; msg.payload.clouds = jsun.clouds.all; msg.location.lon = jsun.coord.lon; msg.location.lat = jsun.coord.lat; msg.location.city = jsun.name; msg.location.country = jsun.sys.country; if (jsun.hasOwnProperty("dt")) { msg.time = new Date(jsun.dt*1000); } msg.title = "Current Weather Information"; msg.description = "Current weather information at coordinates: " + msg.location.lat + ", " + msg.location.lon; msg.payload.description = ("The weather in " + jsun.name + " at coordinates: " + jsun.coord.lat + ", " + jsun.coord.lon + " is " + jsun.weather[0].main + " (" + jsun.weather[0].description + ")." ); callback(); } else { if (jsun.message === "Error: Not found city") { callback("Invalid city/country"); return; } else { callback(jsun.cod + " " + jsun.message); return; } } } }); }).on('error', function(e) { callback(e); return; }); node.status({}); } else { callback("Invalid location information provided"); } } function OpenWeatherMapInputNode(n) { RED.nodes.createNode(this, n); var node = this; this.repeat = 300000; this.interval_id = null; var previousdata = null; var city; var country; var lat; var lon; this.interval_id = setInterval( function() { node.emit("input",{}); }, this.repeat ); this.on('input', function(msg) { if (n.country && n.city) { country = n.country; city = n.city; } else if (n.lat && n.lon) { lat = n.lat; lon = n.lon; } assignmentFunction(node, msg, lat, lon, city, country, function() { weatherPoll(node, msg, function(err) { if (err) { node.error(err,msg); } else { var msgString = JSON.stringify(msg); if (msgString !== previousdata) { previousdata = msgString; node.send(msg); } } }); }); }); this.on("close", function() { if (this.interval_id !== null) { clearInterval(this.interval_id); } }); node.emit("input",{}); } function OpenWeatherMapQueryNode(n) { RED.nodes.createNode(this,n); var node = this; var city; var country; var lat; var lon; this.on('input', function(msg) { if (n.country && n.city) { country = n.country; city = n.city; } else if (n.lat && n.lon) { lat = n.lat; lon = n.lon; } else if (msg.location) { if (msg.location.lat && msg.location.lon) { lat = msg.location.lat; lon = msg.location.lon; } else if (msg.location.city && msg.location.country) { city = msg.location.city; country = msg.location.country; } } assignmentFunction(node, msg, lat, lon, city, country, function() { weatherPoll(node, msg, function(err) { if (err) { node.error(err,msg); } else { node.send(msg); } }); }); }); } RED.nodes.registerType("openweathermap",OpenWeatherMapQueryNode); RED.nodes.registerType("openweathermap in",OpenWeatherMapInputNode); };	{ "redpajama_set_name": "RedPajamaGithub" }	637
Manor Szolomon (héberül: מנור סולומון, Kfar Szaba, 1999. július 24. –) izraeli válogatott labdarúgó, az angol Fulham játékosa. Pályafutása Klubcsapatokban Pályafutását hazájában kezdte, ahol a Makkabi Petah Tikva csapatában mutatkozott be a felnőttek között. 2018 januárjában felkerült az Európai Labdarúgó-szövetség hivatalos honlapján közzétett "Európa 50 legígéretesebb labdarúgójának" listájára. Abban a szezonban a Izrael Makkabi Petah Tikva mind a 33 bajnoki mérkőzésén játéklehetőséget kapott és négy gólt ért el ezeken a találkozókon. 2016 és 2019 között hatvannnyolc alkalommal lépett pályára az izraeli élvonalban, ezalatt nyolcszor talált az ellenfelek kapujába. 2019 januárjában szerződtette az ukrán Premjer Ligában szereplő Sahtar Doneck. Szolomon öt évre szóló szerződést írt alá. Tétmérkőzésen 2019. február 14-én mutatkozott be a bányászváros csapatában az Eintracht Frankfurt ellen az Európa-ligában, nem egészen húsz évesen. Marlos helyén csereként állt be a találkozó 69. percében. A Premjer League-ben 2019. február 25-én debütált egy Olekszandrija elleni bajnokin Viktor Kovalenko cseréjeként. Tizenegy találkozón szerepelt a bajnokságban a szezon végéig, amikor bajnoki címet és kupagyőzelmet ünnepelhetett. A következő idényban a Bajnokok Ligájában is bemutatkozhatott, 2019. november 26-án pedig ő szerezte csapata gólját a Manchester City elleni 1–1-es döntetlen alkalmával. A 2019-20-as szezonban újból bajnok lett csapatával, húsz mérkőzésen háromszor volt eredményes és bejutottak az Európa-liga elődöntőjébe, ahol az Internazionale ejtette ki az ukrán csapatot. 2020. október 21-én a Real Madrid is eredményes volt csapata bravúros, idegenbeli 3–2-es győzelmekor. A válogatottban Többszörös utánpótlás-válogatott. 2015 és 2017 között az izraeli U17-es és U19-es válogatottakban húsz mérkőzést játszott és háromszor volt eredményes. 2017 és 2018 között az izraeli U21-es válogatott tagja. A felnőtt csapatban 2018 őszén, tizenkilenc éves korában mutatkozott be. Magánélete Kfar Szaba városában született, zsidó családban. Édesapja és édesanyja is testnevelő tanár. Szolgált az izraeli hadseregben. A labdarúgás alapjait a Hapóél Kfar Szaba utánpótlás akadémiáján sajátította el, kilencéves korában pedig a Makkabi Petah Tikvalabdarúgója lett. Középiskolai tanulmányait szülővárosában végezte, a Galii Gimnáziumban. Sikerei, díjai Sahtar Ukrán bajnok: 2018–19, 2019-20 Ukrán kupagyőztes: 2018–19 Jegyzetek 1999-ben született személyek Élő személyek Izraeli labdarúgók Labdarúgó-középpályások A Sahtar Doneck labdarúgói A Premjer Liha labdarúgói	{ "redpajama_set_name": "RedPajamaWikipedia" }	251
Q: how to get tables of an access db into a list box using c#? i needed to create a form in which i hav to browse and open mdb files ---> i did this part usin oprnfile dialogue! private void button1_Click(object sender, EventArgs e) { OpenFileDialog oDlg = new OpenFileDialog(); oDlg.Title = "Select MDB"; oDlg.Filter = "MDB (.Mdb)\|.mdb"; oDlg.RestoreDirectory = true; string dir = Environment.GetFolderPath(Environment.SpecialFolder.Desktop); oDlg.InitialDirectory = dir; DialogResult result = oDlg.ShowDialog(); if (result == DialogResult.OK) { textBox1.Text = oDlg.FileName.ToString(); } } *this is my code so far!!! now i need to make 3 list boxes!! 1st one to display the table names of the db! 2nd to to display field names when clicked on table name!!! 3rd to display attributes on fiels on clickin on it! v can edit the attribute values and on clickin of save button it should update the database!!! A: This class should get you the information you need. public static class DatabaseInfoCollector { public static System.Collections.Generic.List<string> GetTables(string file) { System.Data.DataTable tables; using(System.Data.OleDb.OleDbConnection connection = new System.Data.OleDb.OleDbConnection("Provider=Microsoft.Jet.OLEDB.4.0;Data Source=" + file)) { connection.Open(); tables = connection.GetOleDbSchemaTable(System.Data.OleDb.OleDbSchemaGuid.Tables,new object[]{null,null,null,"TABLE"}); } System.Collections.Generic.List<string> Tables = new System.Collections.Generic.List<string>(); for (int i = 0; i < tables.Rows.Count; i++) { Tables.Add(tables.Rows[i][2].ToString()); } return Tables; } public static System.Collections.Generic.List<string> GetColumnNames(string file, string table) { System.Data.DataTable dataSet = new System.Data.DataTable(); using(System.Data.OleDb.OleDbConnection connection = new System.Data.OleDb.OleDbConnection("Provider=Microsoft.Jet.OLEDB.4.0;Data Source=" + file)) { connection.Open(); System.Data.OleDb.OleDbCommand Command = new System.Data.OleDb.OleDbCommand("SELECT FROM " + table,connection); using(System.Data.OleDb.OleDbDataAdapter dataAdapter = new System.Data.OleDb.OleDbDataAdapter(Command)) { dataAdapter.Fill(dataSet); } } System.Collections.Generic.List<string> columns = new System.Collections.Generic.List<string>(); for(int i = 0; i < dataSet.Columns.Count; i ++) { columns.Add(dataSet.Columns[i].ColumnName); } return columns; } } Fill the tables list like this. System.Collections.Generic.List<string> Tables = DatabaseInfoCollector.GetTables(textBox1.Text); foreach(string table in Tables) { cboTable.Items.Add(table); } Fill the columns like this. System.Collections.Generic.List<string> Columns = DatabaseInfoCollector.GetColumnNames(textBox1.Text,cboTable.SelectedItem.ToString()); foreach(string column in Columns) { cboColumns.Items.Add(column); } You can also use this method to return a DataTable containing all kinds of information about each column. public static System.Data.DataTable GetSchemaData(string file) { System.Data.DataTable columns; using(System.Data.OleDb.OleDbConnection connection = new System.Data.OleDb.OleDbConnection("Provider=Microsoft.Jet.OLEDB.4.0;Data Source=" + file)) { connection.Open(); columns = connection.GetOleDbSchemaTable(System.Data.OleDb.OleDbSchemaGuid.Columns,new object[]{null,null,null,null}); } return columns; } A: Use the System.Data.OleDb.* classes to get the data from the access file. Example: //Create the OleDbConnection object //and associate it with our database using(OleDbConnection conn = new OleDbConnection( "PROVIDER=Microsoft.Jet.OLEDB.4.0;Data Source="+textBox1.Text)){ //Open the database connection conn.Open(); //Create an OleDbCommand object and //pass it the SQL read query and the connection to use OleDbCommand cmd = new OleDbCommand(sqlstr,conn); //Procure the OleDbDataReader object to browse the recordset OleDbDataReader rdr = cmd.ExecuteReader(); //Keep reading records in the forward direction while (rdr.Read()) { //Use one of the various methods available to read the data //Eg:- GetValue, GetValues, Item etc. . . . . . . } } A: Use System.Data.OleDb to open a connection with new OleDbConnection(connectionString). The connection string should be "Provider=Microsoft.Jet.OLEDB.4.0;Data Source=[PathToMDBFile]" var conn = new OleDbConnection(connectionString); var ds = new DataSet(); var adapter = new OleDbDataAdapter("SELECT Column1 FROM Table1", conn); conn.Open(); adapter.Fill(ds); conn.Close(); var value = ds.Tables[0].Rows[0]["Column1"].ToString(); That will get you the first value in the column named Column1	{ "redpajama_set_name": "RedPajamaStackExchange" }	5,953
<?xml version="1.0" encoding="utf-8"?> <manifest xmlns:android="http://schemas.android.com/apk/res/android" package="com.tum.ident" android:versionCode="1" android:versionName="0.61" > <uses-feature android:name="android.hardware.camera" android:required="false" /> <uses-feature android:name="android.hardware.camera.front" android:required="false" /> <uses-sdk android:minSdkVersion="9" android:targetSdkVersion="19"/> <uses-permission android:name="android.permission.RECEIVE_BOOT_COMPLETED" /> <uses-permission android:name="android.permission.GET_TASKS" /> <uses-permission android:name="android.permission.WAKE_LOCK" /> <uses-permission android:name="android.permission.ACCESS_WIFI_STATE"/> <uses-permission android:name="android.permission.WRITE_EXTERNAL_STORAGE" /> <uses-permission android:name="android.permission.CAMERA" /> <uses-permission android:name="android.permission.RECORD_AUDIO"/> <uses-permission android:name="android.permission.INTERNET"></uses-permission> <uses-permission android:name="android.permission.ACCESS_NETWORK_STATE"></uses-permission> <uses-permission android:name="android.permission.READ_PHONE_STATE"></uses-permission> <uses-permission android:name="android.permission.READ_CONTACTS"/> <uses-permission android:name="android.permission.BLUETOOTH" /> <uses-permission android:name="android.permission.BLUETOOTH_ADMIN" /> <uses-permission android:name="android.permission.READ_PHONE_STATE" /> <uses-permission android:name="android.permission.ACCESS_FINE_LOCATION" /> <uses-permission android:name="android.permission.ACCESS_COARSE_LOCATION"/> <uses-permission android:name="android.permission.GET_ACCOUNTS"></uses-permission> <uses-permission android:name="android.permission.AUTHENTICATE_ACCOUNTS"></uses-permission> <uses-permission android:name="android.permission.READ_CALL_LOG"></uses-permission> <uses-permission android:name="android.permission.READ_EXTERNAL_STORAGE"/> <uses-permission android:name="android.permission.CHANGE_WIFI_STATE" /> <uses-permission android:name="android.permission.BATTERY_STATS"/> <uses-permission android:name="android.permission.ACCESS_GPS" /> <uses-permission android:name="android.permission.ACCESS_LOCATION" /> <uses-permission android:name="com.google.android.providers.gsf.permission.READ_GSERVICES"></uses-permission> <application android:allowBackup="true" android:icon="@drawable/ic_launcher" android:label="@string/app_name" android:theme="@style/AppTheme" > <meta-data android:name="com.google.android.gms.version" android:value="@integer/google_play_services_version" /> <activity android:name="com.tum.ident.MainActivity" android:label="@string/app_name" > <intent-filter> <action android:name="android.intent.action.MAIN" /> <category android:name="android.intent.category.LAUNCHER" /> </intent-filter> </activity> <activity android:name="com.tum.ident.UpdateActivity" android:label="@string/app_name" > <intent-filter> <category android:name="android.intent.category.LAUNCHER" /> </intent-filter> </activity> <receiver android:name="com.tum.ident.broadcast.Broadcast" > <intent-filter> <action android:name="android.intent.action.BOOT_COMPLETED" /> </intent-filter> </receiver> <service android:name="com.tum.ident.IdentificationService" /> </application> </manifest>	{ "redpajama_set_name": "RedPajamaGithub" }	5,493
HomepageIMFBlog2019-01-16T14:33:34-05:00 IMFBlog2019-07-18T09:25:47-05:00July 17, 2019\| By Gita Gopinath Español, 中文, 日本語, Português Following the global financial crisis, overall current account surpluses and deficits fell sharply from about 6 percent of global GDP in 2007 to about 3.5 percent in 2013. (more…) Chart of the weekCorporate Tax Rates: How Low Can You Go By IMFBlog In life, two things are certain: death and taxes, the saying goes. (more…) Español, Português Over the past two decades, most of the changes in bilateral trade balances—the difference in the value of exports and imports between two countries—were explained by macroeconomic factors, according to IMF research. (more…) Tariff Shocks: The Role of Value Chains in Europe IMFBlog2019-07-03T15:32:46-05:00July 3, 2019\| By Raju Huidrom, Carlos Mulas-Granados, Laura Papi, and Emil Stavrev (Español, Português) The Czech Republic exports only a small number of cars and car parts directly to the United States, but it's likely to suffer significant economic damage if that country were to impose tariffs on auto imports. (more…) By Tobias Adrian, Rohit Goel and Fabio Natalucci The slope of the yield curve in the US has inverted in recent months, making long-term debt significantly cheaper than short-term debt. (more…) Chart of The WeekThe Price of Capital Goods and the Threat to Investment Over the past three decades, the prices of machinery and equipment have fallen sharply relative to overall prices. (more…) IMFBlog2019-06-27T09:37:18-05:00June 27, 2019\| By Tobias Adrian and Ceyla Pazarbasioglu From artificial intelligence to mobile applications, technology helps to increase your access to secure and efficient financial products and services. (more…) When Disaster Strikes: Preparing for Climate Change By Seán Nolan and Krishna Srinivasan Earlier this year, Cyclone Idai devastated Mozambique, Malawi, and Zimbabwe by leaving more than 1,000 people dead, thousands more missing, and damages in the billions. (more…) Chart of the WeekGrowing Through Education in Nigeria By Vivian Malta and Monique Newiak Our chart of the week, drawn from the IMF's 2019 economic health check for Nigeria, highlights substantial inequality in access to education between girls and boys, and between rich and poor. (more…) Chart of the WeekMapping the World's Financial Weak Spots Where will the next financial crisis come from? The short answer is: We don't know. We can, however, look for vulnerabilities in the system that, if left untreated, can develop into problems. (more…)	{ "redpajama_set_name": "RedPajamaCommonCrawl" }	4,448
\section{Introduction}\label{sec:Introduction} There are considerable interest in non-Hermitian operators and indefinite Hilbert space structures in quantum mechanics after the discovery that complex Hamiltonians possessing ${\cal PT}$-symmetry (the product of parity and time reversal) can have a real spectrum \cite{bendb}. The non-Hermitian and ${\cal PT}$-symmetric quantum theory has been successfully used in studies of mathematical physics, solid state physics, quantum field theory, optics, to mention a few (for a comprehensive literature, see \cite{ review, review2, review3} and references therein). The diversity of theoretical and experimental investigations call for clarification whether the ${\cal PT}$-symmetric quantum mechanics is a fundamental theory with physically acceptable predictions and conclusions. The primary requirement that a physically acceptable quantum theory should satisfy, is the reality of the spectrum and the associated conservation of probability. The latter is realized in conventional quantum mechanics by unitarity of the time evolution operator. In this regard, there have been considerable progress in understanding the spectral reality of ${\cal PT}$-symmetric Hamiltonian from establishing the corresponding sufficient conditions and by comparing pseudo-Hermiticity with ${\cal PT}$-symmetry \cite{ review, review2, review3, dorey, most}. The feature of the space of states necessary to define the probability was investigated. The disconcerting problem of the space of states appearing to be an indefinite metric space was subsequently resolved. One solution is based on the observation that self-consistent condition dictates that the space of states is not Hilbert space but Krein space \cite{gj,znj}. Another solution involves the introduction of the ``charge conjugation'' operator ${\cal C}$ and the resultant ${\cal CPT}$ inner product, providing a positive defined norm at the outset \cite{b1,b2}. The latter approach logically leads to a unitary time evolution. Thus, the requirement for a fundamental quantum theory, conservation of the probabilities for Hamiltonians with real spectra is satisfied. In order to be a fundamental physical theory, ${\cal PT}$-symmetric quantum mechanics should reproduce not only the spectrum reality and unitary but also the general conditions such as no-signaling principle. The no-signaling principle can be viewed as a realization of classical causality in quantum theory \cite{nosig, nosign1}. Another essential feature of the fundamental quantum theory is the violation of Bell inequalities that can be demonstrated as the deviation from the classical probabilistic result for the CHSH thought experiments \cite{cs,cs1,cs2}. In this regard, the no-signaling principle was analyzed in ${\cal PT}$-symmetric quantum mechanics and it is claimed that the principle is violated \cite{lee}. The conclusion, based on the calculation in the framework of conventional Hilbert space prescription, implies that ${\cal PT}$-symmetric quantum mechanics cannot be a fundamental theory. In this paper, based on the definition of probability via ${\cal CPT}$ inner product, we demonstrate that both no-signaling principle and the result of the CHSH experiment are reproduced by ${\cal PT}$-symmetric extension of quantum mechanics. Therefore, we reaffirm the consistency of ${\mathcal {PT}}$ symmetric quantum mechanics as a fundamental theory. The paper is organized as follows: in section II we give a brief review of a ${\cal CPT}$ inner product. We demonstrate on the example of a model Hamiltonian that in the space of states endowed with ${\cal CPT}$ inner product, the orthogonality of states is achieved, and the density matrix is diagonal. The orthogonality is the mathematical realization of the physical requirement, forbidding any state to have different eigenvalues simultaneously. In ${\cal PT}$-symmetric quantum mechanics, Hilbert space formalism fails to satisfy this condition. In section III, using ${\cal CPT}$ inner product prescription, we reexamine the no-signaling principle on the example of two separated observers sharing an entangled state. We illustrate that in both cases, when both observers are equipped with a a non-Hermitian ${\cal PT}$-symmetric Hamiltonians, or when one Hamiltonian is ${\cal PT}$-symmetric and other is Hermitian, the no-signaling principle is valid. The discrepancy between our results and those from \cite{lee} is attributed to using the different prescriptions for calculating the conditional probabilities. If one uses prescription dictated by ${\cal CPT}$ inner product, the no-signaling principle remains valid. Using ${\cal CPT}$ prescription, we also show that in ${\cal PT}$-symmetric quantum mechanics the measure of entanglement is invariant under unitary transformations, in analogous to the result obtained in conventional quantum mechanics. In section IV, we show that the quantumness, manifested by the CHSH experiment, is reproduced in ${\cal PT}$-symmetric quantum mechanics using ${\cal CPT}$ inner product. In the last section, we draw our conclusions. Expressions for the eigenfunctions of Hamiltonian for the composite system, density matrix, and the projection operators necessary for the derivation of our results, are given in Appendices. \section{ ${\mathcal CPT}$ inner product} It is well known that the physical requirement that it is impossible to measure simultaneously different eigenvalues \cite{landau,landau1} leads to the conclusion that the space of states of ${\cal PT}$-symmetric quantum mechanics is an indefinite metric space \cite{gj,znj}. The scalar product for two states $\psi_{\alpha}$ and $\psi_{\beta}$, identified with the transition amplitude, satisfying the requirement that it vanishes for the states with different eigenvalues, $E_{\alpha}\neq E_{\beta}$, is found to be \cite{gj,znj} \begin{equation} (\psi_{\alpha}\|\psi_{\beta})=({\cal PT}\psi_{\alpha})^{T}\,\psi_{\beta}\,=\,\int\,dx\,\psi_{\alpha}^{\star}(-x)\,\psi_{\beta}(x). \label{innerr} \end{equation} Throughout we consider the real-space independent case; all the results remain intact when wavefunctions depend on $x$. The linear space with indefinite metric described above satisfies the requirement that the transition amplitude between the states with different energies vanishes. Thus, the space equipped with the above scalar product serves as a space of states of ${\cal PT}$-symmetric quantum mechanics. In contrast, the traditional definition of the inner product, $\langle \psi_{\alpha}\|\psi_{\beta}\rangle=(\psi^{T}_{\alpha})^{\star}\,\psi_{\beta}$, violates the orthogonality of states with different eigenvalues. As such, Hilbert space cannot be the space of states for ${\cal PT}$-symmetric quantum mechanics. Probabilistic interpretation requires that the amplitude $(\psi_{\alpha}\|\psi_{\alpha})$ must be normalizable, which is not possible in Hilbert space prescription, since the inner product Eq. (\ref{innerr}) is not positively defined. This setback was overcomed by introducing an operator ${\cal C}$, which accounts for the negative sign of the norm defined from Eq. (\ref{innerr}). The inner product in ${\cal PT}$-symmetric quantum mechanics is defined as follows \cite{b1, b2} \begin{equation} \label{bbb} \langle\psi_{\alpha}\|\psi_{\beta}\rangle_{{\cal CPT}}=({\cal CPT}\psi_{\alpha})^{T}\,\psi_{\beta}. \end{equation} Linear operator ${\cal C}$ that measures the sign of norm (\ref{innerr}) is constructed in terms of the eigenfunctions of Hamiltonian $\psi_{n}$, $H\psi_{n}(x)\,=\,E_{n}\psi_{n}(x)$ \cite{b1}, \begin{equation} \label{CC1} {\cal C}=\sum_{n}\psi_{n}\otimes \psi_{n}^{T}, \end{equation} where ${\cal PT}$ symmetry is assumed not broken. Here $\otimes$ stands for the tensor product of vectors $\psi_{n}$. The norm associated with Eq. (\ref{CC1}) is positively-defined because it contributes additional factor of -1 when it is applied to the negative vectors $\psi^{-}$ whose ${\cal PT}$ norm is negative: $({\cal PT}\psi^{-})^{T}\,\psi^{-}<0$. In this way, ${\cal C}$ can be considered as the result of measurement of the sign of the inner product $(\psi\|\psi)$. The properties of ${\cal C}$ are similar to those of the charge conjugation operator in quantum field theory \cite{b1}. For the formal properties of operators with ${\cal C}$-symmetries, we refer to \cite{albe} for details. For ${\cal PT}$ and ${\cal CPT}$ frames on a Hilbert space for ${\cal PT}$ symmetric Hamiltonian see \cite{ciao}, \cite{ciao1}. We now demonstrate how ${\cal CPT}$ inner product prescription works for an example of exactly solvable non-Hermitian ${\cal PT}$-symmetrical Hamiltonian \cite{b1}: \begin{equation} \label{Ham} \fl H_{2\times 2}=s\left(\begin{array}{ccc} i\sin\alpha&1\\ 1&-i\sin\alpha \end{array}\right), \;{\cal P}=\left(\begin{array}{ccc} 0&1\\ 1&0 \end{array}\right),\;{\cal T}\left(\begin{array}{ccc} x\\ y \end{array}\right)=\left(\begin{array}{ccc} x^{\star}\\ y^{\star} \end{array}\right), \end{equation} where $x^{\star}$ is complex conjugate of $x$, $s$ and $\alpha$ are real parameters; $H_{2\times 2}$ is Hermitian when $\alpha=0$. The eigenvalues $E_{\pm}=\pm s\cos\alpha$ are real provided $\alpha<\pi/2$ \cite{b1}. The corresponding eigenfunctions of Hamiltonian (\ref{Ham}) are \begin{equation} \label{eigg1} \psi^{+} ={1\over\sqrt{2\cos\alpha}}\left( \begin{array}{ccc} e^{i\alpha/2}\\ e^{-i\alpha/2} \end{array}\right), \quad \psi^{-} ={1\over\sqrt{2\cos\alpha}}\left( \begin{array}{ccc} e^{-i\alpha/2}\\ -e^{i\alpha/2} \end{array}\right). \end{equation} According to Eq. (\ref{CC1}), the ${\cal C}$ operator is \begin{equation} \label{cop} {\cal C}\equiv \psi^{+}\otimes {\psi^{+}}^{T}+\psi^{-} \otimes {\psi^{-}}^{T}={1\over\cos\alpha}\left(\begin{array}{ccc}i\sin\alpha & 1\\ 1 & -i\sin\alpha \end{array}\right). \end{equation} It is straightforward to verify that ${\cal CPT}$ inner product satisfies requirements of the orthogonality and normalization: \begin{equation} \label{01} \langle\psi^{+}\|\psi^{-}\rangle_{{\cal CPT}}\,=\,0,\quad \\|\psi^{\pm}\\|^{2}\,=\,\langle\psi^{\pm}\|\psi^{\pm}\rangle_{{\cal CPT}}\,=\,1. \end{equation} Note that if one uses the Hilbert space formalism, the orthogonality condition is not satisfied. Instead of Eq. (\ref{01}), one now has: \begin{equation} \label{added} (\psi^{+})^{\star}\cdot \psi^-\,=\,\tan\alpha\neq 0. \end{equation} Density matrix defined in the space with ${\cal CPT}$ inner product is diagonal: \begin{equation} \label{dens} \fl \quad \quad\quad \rho\,=\,{1\over 2}\biggl(({\cal CPT}\psi^{+})\otimes {\psi^{+}}^{T}\,+\,({\cal CPT}\psi^{-})\otimes {\psi^{-}}^{T}\biggr)={1\over 2}\left( \begin{array}{ccc} 1& 0\\ 0 & 1 \end{array} \right). \end{equation} Thus, ${\cal CPT}$ inner product (\ref{innerr}) leads to physically acceptable results: a positively defined metric, orthonormality of eigenfunctions, and diagonal density matrix. We introduce an operator ${\cal C}^{\dagger}$ \begin{equation} \label{Cdagg} {\cal C}^{\dagger}\equiv {\cal TCT}. \end{equation} Since ${\cal T}^{2}=1$ and $[{\cal P},\,{\cal T}]=0$, transformations ${\cal CPT}$ and ${\cal C^{\dagger}P}$ result in a mutually complex conjugated wave functions. In terms of \begin{equation} \label{phi} \Phi\equiv {\cal C}^{\dagger}{\cal P}\,\psi, \end{equation} normalization and orthogonality conditions (\ref{01}) are written in a compact way \begin{equation} \label{fff} \langle\Phi^{\pm}\|\psi^{\pm}\rangle =1,\quad \langle\Phi^{\pm}\|\psi^{\mp}\rangle = 0, \end{equation} where the inner product $\langle \Phi\|\psi\rangle=\Phi^{\star}\,\psi^{T}$ formally coincides with the prescription of a Hilbert space. The normalized amplitude and the probability of transition from the state described by $\psi_{\alpha}$ to the state described by $\psi_{\beta}$ can be written as: \begin{equation} \label{caa} {\cal A}_{\alpha\beta}={\langle \Phi_{\alpha}\|\psi_{\beta}\rangle\over \sqrt{\langle \Phi_{\alpha}\|\psi_{\alpha}\rangle}\sqrt{\langle \Phi_{\beta}\|\psi_{\beta}\rangle}},\quad p_{\alpha\beta}=\left\| {\cal A}_{\alpha\beta}\right\|^{2};\quad 0\leq p_{\alpha\beta}\leq 1. \end{equation} Eqs. (\ref{fff} - \ref{caa}), along with the fact that in the space of states endowed by ${\mathcal CPT}$ inner product, the time evolution operator generated by a ${\mathcal PT}$ symmetric Hamiltonian is unitary \cite{b1}, present a self-consistent interpretation of ${\cal PT}$-symmetric quantum mechanics. \section{No-signaling principle in ${\mathcal PT}$ symmetric quantum mechanics} Besides satisfying requirements of the spectrum reality and the unitary time evolution, ${\mathcal PT}$ symmetric systems must meet other basic physical requirements to represent physically acceptable theory. One of such requirements is that they must satisfy the no-signaling principle: given system composed of two subsystems, Alice ($A$) and Bob ($B$), $A$ cannot communicate to $B$, unless $A$ transmits physical information to $B$ \cite{nosig}. It is well known that quantum mechanics satisfies the no-signaling principle \cite{nosig1}. The thought experiment may be set up as follows: $A$ and $B$ are at different locations and share non separable, entangled quantum state. $A$ is given a random message from a set of $N$ elements (the outcome of a measurement). $A$ and $B$ perform arbitrary quantum measurements, using their quantum state but without transmission of any physical information. According to the no-signaling principle, $B$ cannot obtain any information on message given to $A$. Regarding the probability distribution, quantum theory satisfies the no-signaling if $B$ cannot infer $A$'s message from outcomes. The no-signaling condition is formalized as the requirement that conditional probabilities satisfy the following relation \cite{nosig}: \begin{equation} \label{nosgdef} \sum_{a}P(a,\,b\|A,\,B)\,=\,P(b\|B), \end{equation} where $a$ and $b$ are outcomes of measurements $A$ and $B$, performed by Alice and Bob, respectively. $ A$ belongs to a set of possible measurements performed by Alice. If Eq. (\ref{nosgdef}) is not satisfied, then the no-signaling principle is violated. The validity of the no-signaling principle in ${\cal PT}$-symmetric quantum mechanics, and as a consequence, the status of ${\cal PT}$-symmetric quantum mechanics as a fundamental theory was recently questioned in \cite{lee,pati}. The thought experiment designed in \cite{lee} consists of two observers Alice and Bob share maximally entangled state $\|\psi_{0}\rangle = (\|00\rangle+\|11\rangle)/\sqrt{2}$. Alice has a ${\cal PT}$-symmetric non-Hermitian Hamiltonian $H_{2\times 2}$ as described by Eq. (\ref{Ham}), and does not interact with any subsystem on Bob's side. The total Hamiltonian describing the composite system is $H_{4\times 4}=H_{2\times 2}\otimes I_{2\times 2}$, where $I$ is the identity operator, chosen as the Hamiltonian for Bob. To examine the validity of the no-signaling principle in the set up described above we make use of similar prescription as for the $2\times 2$ case, normalizing the eigenfunctions based on ${\cal CPT}$ inner product $\langle \Phi_{j} \| \psi_{k}\rangle_{{\cal CPT}}$, in a full analogy with Eq. (\ref{phi}), with $\|\Phi_{j}\rangle$ being \begin{equation} \label{def1} \|\Phi_{j}\rangle\,\equiv\,{\cal C}^{\dag}_{4\times 4}{\cal P}_{4\times 4}\|\psi_{j}\rangle, \end{equation} where $j=1,\,2,\,3,\,4$, and the eigenfunctions of the total Hamiltonian $H_{4\times 4}$ are given in Appendix. In Eq. (\ref{def1}), operators ${\cal C}^{\dag}_{4\times 4}$ and ${\cal P}_{4\times 4}$ are defined as follows: \begin{equation} \label{stars} {\cal C}^{\dag}_{4\times 4}={\cal C}^{\dag}_{2\times 2}\otimes I_{2\times 2}, \; {\cal P}_{4\times 4}={\cal P}_{2\times 2}\otimes I_{2\times 2},\; {\cal P}_{2\times 2}=\left(\begin{array}{ccc}0 & 1\\ 1 & 0 \end{array}\right), \end{equation} and $\psi_{j}$ are eigenfunctions normalized with respect to ${\cal CPT}$ inner product $\langle \Phi_j \|\psi_{k}\rangle$. The eigenvalue equations are \begin{equation} \label{eigen} H_{4\times 4}\,\psi_{1,2}= s\cos\alpha\,\psi_{1,2},\; H_{4\times 4}\,\psi_{3,4} = -s\cos\alpha\,\psi_{3,4}, \end{equation} and ${\cal P}_{4\times 4}{\cal T}\psi_{j}=\psi_{j}$. The maximally entangled wave function $\psi_{0}$ that Alice and Bob share after the time evolution gives rise to two possible final outcomes \cite{lee} \begin{equation} \label{plus} \fl \quad \quad \quad \psi^{+}_{f}={1\over{\sqrt{2}\cos\alpha}}\left( \begin{array}{ccc} \sin\alpha\\ -i\\ -i\\ -\sin\alpha \end{array}\right), \quad \quad \psi^{-}_{f}={1\over{\sqrt{2}\cos\alpha}}\left( \begin{array}{ccc} -i\\ \sin\alpha\\ -\sin\alpha\\ -i \end{array}\right), \end{equation} where $\psi^{\pm}_{f}\equiv (U(\tau)A_{\pm}\otimes I)\,\psi_{0}$, $U(\tau)$ is the time evolution operator $U(\tau)\,=\,\exp(-iH_{2\times 2}\,\tau)$ \cite{time}, and $A_{\pm}$ are operators $I$ and $\sigma_{x}$ that Alice uses with respect to the information she wants to send via shared entangled wave function \cite{lee}. The evolution time $\tau$ is set to be $\tau=\pi/(E_+-E_-)$. The possible outcomes $a$ and $b$ are $+y$ or $-y$. Marginal joint probability, calculated in \cite{lee} using a Hilbert space prescription, results into expression depending on a parameter $\alpha$ in Alice's Hamiltonian \begin{equation} \label{lee23} \fl \quad \quad \sum_{a}P(a,\,b\|A,\,B)=\sum_{a=\pm y}\langle \psi^{\pm}_{f}\|(\|a\rangle\langle a \|\otimes \|b\rangle\langle b \|)\|\psi^{\pm}_{f}\rangle={(1\mp \sin\alpha)^{2}\over 2 (1+\sin^{2}\alpha)}. \end{equation} Eq. (\ref{lee23}) indicates that the Bob's outcomes probabilities depend on what measurement Alice performs, $A_{+}$ or $A_{-}$, which in turn implies the violation of the no-signaling principle. Note that it is straightforward to verify that $\psi_{j}$'s are not orthogonal with respect to Hilbert space inner product in that $\langle\psi_{j}\|\psi_{k}\rangle\neq\delta_{jk}$. By contrast, ${\cal CPT}$ inner product (\ref{fff}) satisfies the orthonormality condition \begin{equation} \label{33} \langle\Phi_{j}\|\psi_{k}\rangle=\delta_{jk}. \end{equation} The density matrix is defined the same way as in Eq. (\ref{dens}) and is diagonal \begin{equation} \label{dens2} \rho_{4\times 4}\,=\,{1\over 4}\sum^{4}_{j=1}\|\Phi_{j}\rangle\langle \psi_{j}\|,\quad(\rho_{4\times 4})_{ij}={\delta_{ij}\over 4}. \end{equation} The self-consistent way of formulating ${\cal PT}$-symmetric quantum mechanics requires that the transition between the states with different eigenvalues should vanish. The modulus of amplitude transiting into itself should be normalizable to one. The latter, in turn, defines the space of states as a linear space with ${\cal CPT}$, rather than Hilbert space inner product. In our case, when the quantum mechanical system contains subsystem whose dynamics is described by a ${\cal PT}$-symmetric Hamiltonian, the entangled wave function of the system belongs to the space with ${\cal CPT}$ inner product Eq. (\ref{innerr}). All the observables have to be calculated in this space. Thus, for the entangled states, in analogy to Eq. (\ref{def1}), we introduce $\|\Phi^{\pm}_{f}\rangle\equiv\,{\cal C^{\dag}}_{4\times 4}{\cal P}_{4\times 4}\|\psi^{\pm}_{f}\rangle$. We then have: \begin{equation} \label{final} \|\Phi^{+}_{f}\rangle={1\over \sqrt{2}}\left( \begin{array}{ccc} 0\\ -i\\ -i\\ 0 \end{array}\right),\quad \|\Phi^{-}_{f}\rangle={1\over \sqrt{2}}\left( \begin{array}{ccc} -i\\ 0\\ 0\\ -i \end{array}\right). \end{equation} Orthonormality conditions read as: \begin{equation} \label{inpr1} \langle \Phi^{\pm}_{f}\|\Phi^{\pm}_{f}\rangle = 1, \quad \langle \Phi^{\pm}_{f}\|\Phi^{\mp}_{f}\rangle = 0. \end{equation} We replace Eq. (\ref{lee23}), the expression for the marginal probabilities considered in \cite{lee}, by \begin{equation} \label{13} \langle \Phi^{\pm}_{f}\|(\|a\rangle\langle a \|\otimes \|b\rangle\langle b \|)\|\Phi^{\pm}_{f}\rangle, \end{equation} which respects the physical requirements such as positively defined probability, the orthogonality, and vanishing of the transition amplitude between different states. It is worth noting that the projectors $(\|a\rangle\langle a \|\otimes \|b\rangle\langle b \|)$ are Hermitian operators. To calculate the marginal probability of a composite system, we substitute $\|\psi^{\pm}_{f}\rangle$ by $\|\Phi^{\pm}_{f}\rangle$ in Eq. (\ref{lee23}) and insert the identity $I_{4 \times 4}\,=\,\sum_{j=1}^{4}\|\eta_{j}\rangle\langle \eta_{j}\|$, where $\|\eta_{j}\rangle$ are the eigenvectors of operator $\|a\rangle\langle a \|\otimes \|b\rangle\langle b\|$ that filter out the results of the possible outcomes. Then, it is straightforward to verify that \begin{eqnarray} \fl \quad \quad \sum_{a}P(a,\,b\|A,\,B)&=\sum_{j=1}^{4}\langle \Phi^{\pm}_{f}\|a\rangle\,\langle a \|\otimes \|b\rangle\langle b \,\|\eta_{j}\rangle\,\langle \eta_{j}\|\Phi^{\pm}_{f}\rangle\,=\\ \label{gd} &\sum_{a=\pm y} \langle \Phi^{\pm}_{f}\|a\rangle\,\langle a \|\otimes \|b\rangle\langle b \,\|\eta_{j=\pm y}\rangle\,\langle \eta_{= \pm y}\|\Phi^{\pm}_{f}\rangle\,=\,{1\over 2}. \end{eqnarray} As such, Eq. (\ref{gd}) does not contain the parameter $\alpha$. Thus, the no-signaling principle holds in ${\cal PT}$-symmetric quantum mechanics. The probabilities of Bob's outcomes do not depend on the measurements Alice performs. It is important to note that the calculated probability, Eq. (\ref{gd}), acquires $\Phi^{\pm}_{f}$ at both ends, which is simply attributed to the fact that the probability is the modular square of the amplitude. With the use of ${\cal CPT}$ prescription, the no-signaling principle is preserved. A straightforward calculation verifies the following \begin{equation} \label{gd2} \sum_{a} \langle \Phi^{\pm}_{f}\|a\rangle\,\langle a \|\otimes \|b\rangle\langle b\|\Phi^{\pm}_{f}\rangle\,=\,\sum_{b} \langle \Phi^{\pm}_{f}\|a\rangle\,\langle a \|\otimes \|b\rangle\langle b\|\Phi^{\pm}_{f}\rangle\,=\,{1\over 2}. \end{equation} The same procedure can be applied to the case when Bob also possesses ${\cal PT}$-symmetric Hamiltonian. The Hamiltonian described the corresponding system \begin{equation} \label{ham1} \fl\quad H=H_A(\alpha_A)\otimes H_B(\alpha_B),\;\; H_{A,\,B}(\alpha_{A,\,B})=s_{A,\,B}\left(\begin{array}{ccc}i\sin\alpha_{A,\,B} & 1\\ 1 & -i\sin\alpha_{A,\,B} \end{array}\right). \end{equation} Using eigenfunctions of Hamiltonian (\ref{ham1}) (see Appendix B) it is straightforward to show that the same result (\ref{gd2}) holds, demonstrating that the no-signaling is respected in this case as well. Therefore, no signaling is valid when either one or both Hamiltonians of a system comprised of two subsystems are non Hermitian and ${\cal PT}$-symmetric. We are now in a position to address an important issue concerning the conservation of entanglement under unitary transformations. It was stated \cite{pati} that in a two-component system, the measure of entanglement is changed due to the non-Hermiticity of the Hamiltonian (\ref{Ham}). The conclusion poses yet another serious challenge to a ${\cal PT}$-symmetric quantum mechanics since the measure of entanglement, among other general requirements, should be invariant under the local unitary transformations \cite{nosig,plan}. The measurement of entanglement $E$ is given by \cite{nosig,plan} \begin{equation} \label{e} E(\psi)=-tr_A(\rho_A\,\log\rho_A)=-tr_B(\rho_B\,\log\rho_B), \end{equation} where the reduced density matrices are defined as a partial traces: $\rho_A=tr_B(\|\psi\rangle\langle \psi\|)$ and $\rho_B=tr_A(\|\psi\rangle\langle \psi\|)$. In \cite{pati} prescription (\ref{e}) is applied to a bipartite system of Alice and Bob described above. According to \cite{pati}, starting from a maximally entangled state $\psi_{0} = (\|00\rangle+\|11\rangle)/\sqrt{2}$ and using Hilbert space definition for the reduced density matrix, after the time $\tau$, the density operator for Bob's subsystem is \begin{equation} \label{bobro} \rho_B\,=\,{1\over 2}\left(\begin{array}{ccc}1+\sin\alpha\cos\alpha & i\sin\alpha\\ -i\sin\alpha & 1-\sin\alpha\cos\alpha \end{array}\right). \end{equation} Entanglement measure $E$ is given by \begin{equation} \label{E} E=-\sum_{j}\lambda_{j}\log\lambda_{j}, \end{equation} where $\lambda_{j}$ are the eigenvalues of the density operator. The eigenvalues of (\ref{bobro}) are $\lambda_{\pm}=(1\pm\sqrt{1-\cos^{4}\alpha})/2$, so $-\sum_{j}\lambda_{j}\log\lambda_{j}$ depends on a non-Hermiticity parameter $\alpha$. After time $\tau$ entanglement measure is no longer unity, which implies that the maximally entangled state changes to a non-maximally entangled one. The violation of entanglement invariance, if true, would deprive ${\cal PT}$-symmetric quantum mechanics as a fundamental theory. Note that the reduced density operator appearing in the expression for the measure of entanglement (\ref{e}) is defined in \cite{pati} as $\rho_B=tr_A(\|\psi\rangle\langle \psi\|)$, calculated in the framework of the standard quantum theory. As stated above, the self-consistency of ${\cal PT}$-symmetric quantum mechanics is achieved when the space of states is a linear space equipped with ${\cal CPT}$ inner product in which the density matrix is defined by the prescription (\ref{dens}). ${\cal CPT}$ prescription leads to a physically acceptable result that the no-signaling principle is preserved. Therefore, as before, instead of the prescription $\|\psi\rangle\langle \psi\|$, we use $\|\psi\rangle\langle \Phi\|$, where $\Phi\equiv {\cal CPT}\psi$. Note that when $\psi$ is a pure state, the prescription $\rho=\|\psi\rangle\langle \psi\|$ does not lead to $\rho^2=\rho$ because of the non-orthogonality of $\langle\psi_i\|\psi_j\rangle$, while prescription $\rho=\|\psi\rangle\langle \Phi\|$ results in $\rho^2=\rho$. We calculate the density matrix using ${\cal CPT}$ inner product and obtain \begin{equation} \label{dens1} \fl \rho={1\over 2}\biggl(\|\psi^+\rangle\langle \Phi^+\|+\|\psi^-\rangle\langle \Phi^-\|\biggr)={1\over 4}\left( \begin{array}{cccc} 1 & {2i\sin\alpha\over \cos^{2}\alpha} & 0 & {1+\sin^{2}\alpha\over \cos^{2}\alpha}\\ {2i\sin\alpha\over \cos^{2}\alpha} & 1& {1+\sin^{2}\alpha\over \cos^{2}\alpha} & 0\\ 0& {1+\sin^{2}\alpha\over \cos^{2}\alpha} & 1& {2i\sin\alpha\over \cos^{2}\alpha}\\ {1+\sin^{2}\alpha\over \cos^{2}\alpha} & 0 & {2i\sin\alpha\over \cos^{2}\alpha}& 1 \end{array} \right) \end{equation} The reduced density operator for Bob, given by the partial trace of (\ref{dens1}) is \begin{equation} \label{dens2} \rho_B\,=\,{1\over 2}\left(\begin{array}{ccc}1 & 0\\ 0 & 1 \end{array}\right). \end{equation} In distinct of eigenvalues of density matrix (\ref{bobro}), latter calculated using Hilbert space prescription, the eigenvalues of matrix (\ref{dens2}) are $\lambda_+=\lambda_-=1/2$, and for the entanglement measure we obtain \begin{equation} \label{enta} E=\,-\lambda_+\log \lambda_+\,-\,\lambda_-\log \lambda_-\,=\,1. \end{equation} As a result, the entanglement measure remains invariant with regard to unitary transformations in ${\cal PT}$-symmetric quantum mechanics, contrary to claims in \cite{pati}, \cite{prent}. We demonstrated that both the no-signaling principle and entanglement measure invariance are respected in ${\cal PT}$-symmetric quantum mechanics when the space of states is the space endowed by the ${\cal CPT}$ inner product (\ref{bbb}). \section{THE CHSH game in ${\cal PT}$-symmetric quantum mechanics} The CHSH game, introduced by Clauser, Horne, Shimony and Holt \cite{cs}, is a Gedanken experiment devised to manifest the quantumness as the deviation from the classical physics. The CHSH game is used as a prototype of the Bell test \cite{cs, cs1, cbell}. The experiment is set up as a game where two players, Alice $A$ and Bob $B$, agree on a strategy before they are separated. Each of them receives as an input of a random bit $A,\,B \in (0,1)$ and in response they output a bit each $a,\,b \in (0,1)$. Players win the game when the parity of $a+b$ is equal to the product of $A$ and $B$, i.e. $a$ and $b$ have to be different from each other if $A=B=1$ and equal to each other for the other three possible combinations of $A$ and $B$. Evidently, if the players follow a classical strategy, only three of the four possible pairs of inputs $ (0,0), (0,1), (1,0), (1,1) $ can be satisfied simultaneously. In other words, players ought to agree beforehand that they both output the same bit independently from their input. As such, the maximum winning probability within the classical game is $3/4$, so \begin{equation} \label{bell0} P_{\mathrm{classical}}\,\leq\,0.75, \end{equation} which is Bell inequality for the CHSH game. In the quantum version of the game, Alice and Bob share an entangled state. Two qubits are separated and $A$ and $B$ measure their qubits depending on the inputs and then output the result of their measurements. Quantum mechanics states that when Alice and Bob start from the maximally entangled state \begin{equation} \|\psi_{0}\rangle={1\over \sqrt{2}}( \|00\rangle+\|11\rangle), \end{equation} the maximum winning probability in the quantum game is larger than $3/4$ by agreeing upon a strategy different from the classical one described above, \begin{equation} \label{bell1} P_{\mathrm{quant}}\,\leq\,\cos^2\biggl({\pi\over 8}\biggr)\approx 0.85, \end{equation} i.e. the Bell inequality (\ref{bell0}) is indeed violated \cite{cs,cbell}. In the following, we examine the quantum CHSH game in ${\cal PT}$-symmetric quantum mechanics. The goal is to check whether the Bell inequality is violated in ${\cal PT}$-symmetric quantum mechanics. We use the same procedure as in Hermitian quantum mechanics. Depending on their inputs, Alice and Bob measure their qubits in basis rotated by $0,\,\pi/4,\,\pi/8,\,-\pi/8$, respectively. This rotation is described as follows: when $A=0$, Alice measures in the standard basic $\|0\rangle$ and $\|1\rangle$ and when $A=1$, Alice measures in the $\pi/4$ rotated basis. Meanwhile Bob measures in the basis rotated by $\pi/8$ when $B=0$ and measures in the basis rotated by $-\pi/8$ when $B=1$. The relative angle between the basis vectors of Alice and Bob is $\pi/8$, $\pi/8$, $\pi/8$, and $3\pi/8$ for ($A$, $B$)=($0, 0$), ($0, 1$), ($1, 0$ and ($1, 1$), respectively. The wave function after the time evolution is \begin{equation} \|\psi^{AB}_{f}\rangle=(U_{\tau}(A)R_{A} \otimes U_{\tau}(B)R_{B})\|\psi_0\rangle, \end{equation} where $U_{\tau}$ is the time evolution operator, $R_{A}$ and $R_{B}$ are rotating operators along the basis vectors by angles $\theta_{A}$ and $\theta_{B}$, respectively. It is straightforward to verify that without using ${\cal CPT}$ inner product, i.e. if one calculates the marginal probability using $P(ab\|AB)=\langle\psi^{AB}_{f}\|(\|a\rangle\langle a \|\otimes \|b\rangle\langle b \|)\| \psi^{AB}_{f}\rangle$, the inequality (\ref{bell1}) is not reproduced. This conclusion is similar to the one when the no-signaling principle and entanglement measure were calculated for ${\cal PT}$-symmetric quantum mechanics using Hilbert space inner product. For calculation of probabilities, we use prescription (\ref{def1}) which for the time evolved entangled state results in: \begin{equation} \label{hohoho} \|\Phi^{AB}_{f}\rangle\equiv {\cal C^{\dagger}P}\|\psi^{AB}_{f}\rangle={1\over{\sqrt{2}}}\left( \begin{array}{ccc} -\cos(\theta_{A}-\theta_{B})\\ \sin(\theta_{A}-\theta_{B})\\ -\sin(\theta_{A}-\theta_{B})\\ \cos(\theta_{A}-\theta_{B}) \end{array}\right). \end{equation} Projectors for the measurement of four possible combinations of output bits $a$ and $b$ are $\|a\rangle\langle a\|\otimes \|b\rangle \langle b\|$, $a\in(0,1), b\in(0,1)$. Marginal probability calculated using ${\cal CPT}$ inner product is given by \begin{equation} P(ab\|AB)=\langle\Phi^{AB}_{f}\|(\|a\rangle\langle a \|\otimes \|b\rangle\langle b \|)\| \Phi^{AB}_{f}\rangle, \end{equation} and a straightforward calculation leads to \begin{equation} \label{ddd} P(ab\|AB)={1\over{2}}\biggl[\cos^2(\theta_{A}-\theta_{B})\delta_{ab}+\sin^2(\theta_{A}-\theta_{B})(1-\delta_{ab})\biggr]. \end{equation} The winning probability is calculated by summing up marginal probabilities for all possible outputs and inputs. Alice and Bob agree upon a quantum strategy that the difference between the angles is the same for all the combinations but when $A=B=1$. In other words, we have $\theta_{A}-\theta_{B}=\zeta$ for all cases but for $A=B=1$, $\theta_{A}-\theta_{B}=3\zeta$ \cite{cs}. Then, the winning probability is \begin{equation} \label{winn} P_{{\mathrm {quant}}}(\zeta)={1\over{4}}[3\cos^2\zeta\,+\,\sin^{2}(3\zeta)]. \end{equation} After optimization, we obtain that the winning probability has maximum at $\zeta=\pi/8$ and the maximum is $P^{{\mathrm {max}}}_{{\mathrm {quant}}}=P_{{\mathrm {quant}}}(\pi/8)=\cos^{2}(\pi/8)$. This is in conformity with the CHSH result (\ref{bell1}). Therefore, in ${\cal PT}$-symmetric quantum mechanics, the probability of winning in quantum CHSH experiment and thus the violation of Bell inequality are reproduced when for the space of states, the linear space equipped with ${\cal CPT}$ inner product is used. It is worth noting that from the Eq. (\ref{ddd}), it follows that $\sum_{a}P(ab\|AB)\,=\,1/2$, i.e. the condition for the no-signaling principle is satisfied. \section{Discussion} In this paper, we systematically evaluate the entanglement in ${\cal PT}$-symmetric quantum mechanics. The calculations are performed using ${\cal CPT}$ inner product prescription, which is important to rectify the fallacy of using Hilbert space inner product in ${\cal PT}$-symmetric quantum mechanics. Specifically, we demonstrate that the no-signaling principle is valid, the measure of the entanglement is invariant under the unitary transformation, and Bell inequality, presented in the framework of the CHSH experiment, is violated in conformity with results of the conventional quantum mechanics. Therefore, ${\cal PT}$-symmetric quantum mechanics can be a fundamental quantum theory, and offers a sensible description of nature. At this juncture, it is worth remarking that quantum entanglement plays a pivotal role in the discussion of the no-signaling principle. It is important to clarify the local and non-local correlations associated with quantum entanglement. If we use a separable, untangled initial state such as $\|00\rangle$ (a direct product of two bits), the system is referred to as local. If we use an initial entangled state such as $(\|00\rangle+\|11\rangle)$ the system is non-local and has a violation of the Bell inequality. We showed that in non-local ${\cal PT}$-symmetric systems the no-signaling principle is satisfied only when the physically accepted ${\cal CPT}$ inner product is used. If the initial state is untangled, separable state, the no-signaling principle is satisfied using either Hilbert-space or ${\cal CPT}$-inner product. In other words, in the framework of Hilbert metric, whether the no-signaling principle is violated depends on the existence of quantum entanglement. Using the ${\cal CPT}$ inner product removes this ambiguity: the no-signaling principle is satisfied in the cases of both local and non-local correlations, as well as for untangled or entangled states. Our findings pave the way to apply ${\cal PT}$-symmetric quantum correlations to a variety of quantum entangled systems such as quantum information theory, quantum computing, and materials theory. The extension of ${\cal PT}$-symmetric quantum mechanics to entangled systems allows for broad applications. After our work was completed we learned about recently published papers \cite{brody2}, \cite{znojill} that point to the inappropriate use of the Hilbert space metric in \cite {lee}. Here we demonstrate explicitly how to employ the ${\cal CPT}$ scheme to quantum probabilities. \section{ACKNOWLEDGEMENTS} This research was supported by National Science Foundation (Grant Nos. DMR-0934142 and HRD-1137751).	{ "redpajama_set_name": "RedPajamaArXiv" }	6,373
{"url":"https:\/\/stats.stackexchange.com\/questions\/375035\/can-the-covariance-matrix-in-a-gaussian-process-be-non-symmetric\/386542","text":"# Can the covariance matrix in a Gaussian Process be non-symmetric?\n\nI was watching a lecture on Gaussian Process and when the covariance matrix was introduced, the tutor explained that the matrix is $$(n \\times n)$$ because every point is covered twice - we include the information about the covariance of $$(x_1, x_2)$$ and about the covariance of $$(x_2, x_1)$$. She then said: that's because your covariance can vary in different directions.\n\nHow is it possible that the covariances can vary in different directions inside the GP covariance matrix? Could you give me an example of when that could be the case?\n\nUpdate:\n\nAfter giving it some thought, I realized that it is not $$cov(x_1, x_2)$$ or $$cov(x_2, x_1)$$ (as computed from the definition of covariance) that go into the GP covariance matrix, but instead (as was shown in the lecture as well), the covariance matrix is populated by a covariance kernel $$k(x, y)$$ that acts\/is interpreted as a covariance, but it is some function of the distance between $$x$$ and $$y$$.\n\nI could therefore imagine, that we might have a covariance kernel that is a function of $$(x - y)^p$$ where $$p$$ is an odd power. In such instance, it would indeed make $$k(x_1, x_2) \\neq k(x_2, x_1)$$. But would this be a valid kernel?\n\nCould you clarify if my thinking about the covariance kernel is reasonable? Could you explain if the covariance matrix in Gaussian Process can be non-symmetric? If yes, could you give an example of a dataset where it would make sense to make covariance different in different directions, i.e. where we would like $$k(x_1, x_2)$$ to be different from $$k(x_2, x_1)$$?\n\n\u2022 You are right, they are never different. The lady is wrong. \u2013\u00a0g g Nov 4 '18 at 17:11\n\u2022 I am giving it some thought and I have a possible explanation why it might make sense. The covariance matrix does not really contain $cov(x, y)$ but instead, it is populated by a function $k(x, y)$ that \"acts\" as a covariance (it is later interpreted as a covariance between $x$ and $y$, however, the function can indeed take a different value for $k(x, y)$ and $k(y, x)$). Since in the lecture it was said that the covariance kernel is a function of distance between $x$ and $y$, it might indeed make sense for kernels where there is $x - y$ raised to an odd power. Does my reasoning make sense? \u2013\u00a0camillejr Nov 4 '18 at 19:26\n\u2022 In a gaussian process, the matrix $K(x_1, x_2)$ is always used as a covariance matrix for a multivariate normal, hence, it must be symmetric. \u2013\u00a0InfProbSciX Nov 5 '18 at 10:12\n\u2022 @InfProb These comments appear to be applying two completely different senses of \"symmetric.\" The first sense is that $K(x_i,x_j)$ is a symmetric $n\\times n$ matrix. Specifically, $K(x_i,x_j)_{rs}=K(x_j,x_i)_{sr}$ for all $1\\le r,s\\le n.$ As you point out it must be, because it's a covariance matrix. The second sense--which I believe is the one used in this question--is that $K(x_i,x_j)=K(x_j,x_i)$ for all $i,j.$ This is decidedly not implied by the defining properties of a Gaussian process. \u2013\u00a0whuber Dec 19 '18 at 15:57\n\u2022 @whuber Could you please post an example of such an assymetric function? Don't kernel functions have to be symmetric as in this wikipedia article? \u2013\u00a0InfProbSciX Feb 1 at 9:34","date":"2019-08-19 06:17:51","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 13, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7594800591468811, \"perplexity\": 196.11194301451567}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-35\/segments\/1566027314667.60\/warc\/CC-MAIN-20190819052133-20190819074133-00135.warc.gz\"}"}	null	null
\section{Introduction} Quantum walks and quantum cellular automata are quantum lattice systems with a discrete step dynamics, which is reversible, and satisfies a causality constraint: In each step only finitely many neighboring cells contribute to the state change of a given cell. This leads to an interesting interplay between the conditions of reversibility (unitarity) and causality, which is the subject of this article. Starting point of the analysis is a simple intuition: for any connected group of cells in a one dimensional system as much ``quantum information'' as moves into the subsystem from the left has to move out at the other end. Moreover, this ``flow'' is a conserved quantity, in the sense that it remains constant over the spatial extent of the system. It can thus be determined locally at any point. Making this intuition precise, we associate with every such lattice system an \emph{index}, a quantity measuring the net flow of information. The index theory developed in this work completely resolves three, a priori very different, classification problems: (1) \emph{Find all locally computable invariants}. It is shown that there exists a ``crossover'' between two systems $S_1, S_2$ if and only if their indices coincide. More precisely, a crossover $S$ between $S_1$ and $S_2$ is a system which acts like $S_1$ on a negative half line $\{x\|x\leq a\}$ and like $S_2$ on a positive half line $\{x\|x\geq b\}$. Clearly, a locally computable invariant must assign the same value to two systems if there exists a crossover between them. It follows that any invariant is a function of the index. (2) \emph{Classify dynamics up to composition with local unitaries}. A natural way of constructing dynamics which respect both reversibility and causality is by concatenating layers of block unitaries. In every step, one would decompose the lattice into non-overlapping finite blocks and implement a unitary operation within every block. Such \emph{local unitary implementations} are conceptually related to the gate model of quantum information. Not every time evolution may be realized this way: a uniform right-shift of cells serves as the paradigmatic counter-example. We show that the systems with local implementations are precisely those with trivial index. Consequently, equivalence classes of dynamics modulo composition with block unitaries are labeled by their indices. (3) \emph{Determine the homotopy classes}. It is proved that two systems may be continuously deformed into each other (with a uniform bound on the causality properties along the connecting path) if and only if they have the same index. We will consider the above questions, and define indices, for two kinds of systems. {\em Quantum walks} are, on the one hand, the quantum analogs of classical random walks. On the other hand, they are discrete time analogs of a standard quantum particle ``hopping'' on a lattice according to a Hamiltonian which is a lattice version of the momentum operator $\mathrm{i}\partial_x$. The index defined for these systems is the same as a quantity called ``flow'' by Kitaev \cite{Kitaev}. Intuitively, this measures the mean speed of a quantum walk, expressed in units of ``state space dimensions shifted to the right per time step''. The mathematical background has been explored, in a more abstract setting, by Avron, Seiler and Simon \cite{Seiler}. Kitaev's work treated the first classification problem above. We will re-prove his results with an eye on generalizations to cellular automata, and will supply solutions to questions (2) and (3). Although the quantum walks seemed to be comparatively straightforward initially, the intuition gained from this case served us well in setting up the theory for the much more involved case of cellular automata. This allowed us to build an abstract index theory covering both cases with almost identical arguments (Sects.~\ref{sec:Gimp} and \ref{sec:Glci}). {\it Cellular automata} are characterized by the property that whatever state is possible in one cell (e.g., a superposition of empty/occupied) can be chosen independently for each cell. Expressed in terms of particles this means that we are necessarily looking at a ``gas'' system of possibly infinitely many particles. The basic definition of quantum cellular automata was given in \cite{qca}. On the one hand, the setting considered here is more restrictive than \cite{qca}, covering only one-dimensional systems. On the other hand, we are allowing for non-translationally invariant dynamics --- a strong generalization over the earlier paper. In fact, having completed the present work we feel that the translation invariance assumed in \cite{qca} was obscuring the fundamental interplay between reversibility and causality. Accordingly, we obtain here a stronger structure result, even though it is built on the same key ideas. Throughout, there is a strong interplay between local and global properties. For example, the following statement is an immediate consequence of our main Theorem~\ref{thmIndA}: If a nearest neighbor cellular automaton has somewhere a cell of dimension $n$, and somewhere else a cell of dimension $m$, coprime to $n$, then it can be globally implemented as a product of two partitioned unitary operations. Our paper is organized as follows: After giving two examples in Sect.~\ref{sec:ex}, We begin by a mathematical description of what we mean by quantum walks (Sect.~\ref{sec:Swalks}) and quantum cellular automata (Sect.~\ref{sec:Sautoms}). We then describe the notion of locally computable invariants, and why they should form an abelian group (Sect.~\ref{sec:Glci}). A similar general explanation of the notion of local implementation is given in Sect.\ref{sec:Gimp}. The detailed theory for quantum walks is in Sect.~\ref{sec:Iwalk}, and in Sect.~\ref{sec:Iauto} for cellular automata. This includes the proof that an index previously defined in the classical translationally invariant case \cite{Kari_index}, coincides with our index for this special case (Sect.~\ref{sec:CCA}). We close with an outlook on variants of index theory for either higher dimensional systems or automata with only approximate causality properties (Sect.~\ref{sec:out}). \section{Examples} \label{sec:ex} Before introducing the mathematical setting, we will illustrate the problems treated in this paper by giving two concrete examples. \subsection{Particle hopping on a ring} The simplest example is given by a single particle on a ring of $N$ sites arranged in a circle. More precisely, the Hilbert space we are considering is $\mathcal{C}^N$ with basis vectors $\{\ket{e_0}, \dots, \ket{e_{N-1}}\}$. The vector $\ket{e_i}$ is taken to represent a ``particle localized at position $i$''. One step of a reversible discrete-time dynamics is simply given by an arbitrary unitary $U\in U(\mathcal{C}^N)$. We will consider two such time evolutions $U_0, U_1$ defined with respect to the standard basis by \begin{equation} U_0: \ket{e_i} \mapsto \ket{e_i}, \qquad U_1: \ket{e_i} \mapsto \ket{e_{(i+1) \,\mathrm{mod}\,N}} \end{equation} respectively. The first unitary is the trivial evolution and the second one models a uniform movement of the particle with velocity one site per time step to the right. The physical interpretation of this simple model seems clear: we can think of a lattice version of a particle with one spatial degree of freedom, where we have introduced cyclic boundary conditions to get a simple, finite description. The causality property defining a quantum walk then expresses the physically reasonable assumptions that couplings are local and dynamics preserve locality. In this setting, it is natural to think of the time evolution as being generated by a Hamiltonian: $U_t = e^{\mathrm{i} t H}$. Such a Hamiltonian formula would allow us to extend the dynamics to arbitrary real times $t\in\mathcal{R}$. To recover $H$, we need to take a logarithm of $U_1$. This operation is of course not uniquely defined, but the ansatz \begin{equation}\label{eqn:fourierHopping} H=\sum_{k=0}^{N-1} \frac{k}{2\pi} \ket{f_k}\bra{f_k} \end{equation} in terms of the Fourier basis \begin{equation} \ket{f_k} = \frac{1}{\sqrt N} \sum_{j=0}^{N-1} e^{\frac{2 \pi \mathrm{i}}{N} k j} \end{equation} seems particularly appealing. It can easily be checked to be compatible with our previous definitions of $U_0$ and $U_1$. \begin{figure}\centering \includegraphics[width=.18\textwidth]{U0}\hspace{.2cm} \includegraphics[width=.18\textwidth]{U1}\hspace{.2cm} \includegraphics[width=.18\textwidth]{U2}\hspace{.2cm} \includegraphics[width=.18\textwidth]{U3}\hspace{.2cm} \includegraphics[width=.18\textwidth]{U4} \caption{Absolute value squared of a vector initially localized at site $6$ (of $10$) under the action of the time evolution $e^{\mathrm{i}tH}$ for $t\in\{0,.25,.5.,.75,1\}$. The Hamiltonian is given by Eq.~(\ref{eqn:fourierHopping}). The dynamics is not causal for non-integer values of $t$. \label{fig:fourierHopping} } \end{figure} Does this definition yield physically satisfactory dynamics for all times $t\in[0,1]$? Hardly. As demonstrated in Fig.~\ref{fig:fourierHopping}, a particle initially localized at site $6$ ($N=10$) will spread out over the entire ring during the interval $t\in[0,\frac12]$, and refocus to site $7$ during $t\in[\frac12, 1]$. Any sensible notion of ``causality'' is violated for non-integer values of $t$. Note that this contrasts with the time evolution generated by the momentum operator $H=\mathrm{i} \partial_x$ of a continuous-variable system. The latter fulfills $\big(e^{\mathrm{i}t H} \psi\big)(x) = \psi(x - t)$, thus preserving the localization properties of vectors $\psi\in L^2(\mathcal{R})$ for any $t\in\mathcal{R}$. The discussion immediately raises several questions: Is there a way to continuously interpolate between $U_0$ and $U_1$ while preserving causality? Our particular choice (\ref{eqn:fourierHopping}) for $H$ could have been unfortunate. Conceivably, there is a better-suited, potentially time-dependent Hamiltonian which does the job. More physically phrased: is it possible to discretize the spacial degrees of freedom, but not the temporal ones, of a free single particle, while respecting causality? (The answer is: no, this is not possible). Is there a simple way of deciding that the answer to the first question is negative? (Yes: the index of $U_0$ is $0$, the index of $U_1$ is $1$. The index is constant on connected components with uniformly bounded interaction length). Further questions we will answer include: Is there a ``gate-model'' implementation of $U_1$? More precisely, can I write $U_1$ in terms of a constant-depth sequence of unitary operations, each of which acts non-trivially only on a constant number of sites? (No). Can I engineer a large system on $N'\gg N$ sites, endowed with a global time evolution $U$, such that the restriction of $U$ to some region of contiguous sites looks like $U_0$ and the restriction of $U$ to some other region looks like $U_1$? (No). All these statements are made precise in Theorem~\ref{thmInd}. \subsection{Cluster state preparation} In this section, we consider $N$ spin-$1/2$ particles arranged on a circle. The Hilbert space of the system is $\mathcal{H} = \bigotimes_{i=1}^N \Cx^2$. In the previous example, it was clear what it meant for a state vector $\psi$ to be ``localized'' in some region $\Lambda\subset[1,N]$: namely this was the case if $\langle \psi\|e_i\rangle = 0$ for all $i\not\in\Lambda$. For state vectors on tensor product spaces, on the other hand, there seems to be no satisfactory notion of ``locality''. To circumvent this problem, we focus on observables instead. An observable $A\in\mathcal{B}(\mathcal{H})$ is localized in a region $\Lambda$ if $A$ acts like the identity on all tensor factors outside of $\Lambda$. Reversible dynamics on such a system is again represented by a unitary $U\in U(\mathcal{H})$. We use the symbol $\alpha$ to denote the action by conjugation of $U$ on observables: $A \mapsto \alpha(A)= U A U^$. Let $\{\sigma_x^{(i)}, \sigma_y^{(i)}, \sigma_z^{(i)}\}$ be the Pauli matrices acting on the $i$th spin. Since one can form a basis of $\mathcal{B}(\mathcal{H})$ from products of the Pauli matrices $\{\sigma_x^{(i)}, \sigma_z^{(i)}\}_{i=1}^N$ acting on single spins alone, it suffices to specify the effect of $\alpha$ on these $2 N$ matrices in order to completely determine the dynamics. For example, we can set \begin{eqnarray} \alpha(\sigma_x^{(i)}) &=& \sigma_z^{(i-1)}\otimes \sigma_x^{(i)}\otimes \sigma_z^{(i+1)}, \\ \alpha(\sigma_z^{(i)}) &=& \sigma_z^{(i)}. \end{eqnarray} It is a simple exercise to verify that the operators on the right hand side fulfill the same commutation relations as the $\{\sigma_x^{(i)}, \sigma_z^{(i)}\}$. This is sufficient to ensure that a unitary $U$ implementing the time evolution $\alpha$ actually exists. As in the previous example, we can ask more refined questions about $U$. For example: can we implement $U$ by a fixed-depth circuit of nearest-neighbor unitaries? Can one interpolate between $U$ and the trivial time evolution while keeping observables localized along the path? Is there a simple numerical invariant which would allow us to easily decide these questions? In this particular case an educated guess gives rise to affirmative answers to all these questions. Indeed, set \begin{equation} V_t^{(i, i+1)} = \left( \begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & e^{\mathrm{i} t \pi} \end{array} \right) \end{equation} with respect to the standard basis of the $i$th and $(i+1)$th spin. Define \begin{equation} U_t = \prod_{i=1}^N V_t^{(i,i+1)} \end{equation} (the product is well-defined because $V_t$ commutes with its translates, so the order in which the product is taken is immaterial). Then one checks that $\alpha$ corresponds to $U_1$, whereas $U_0$ is the trivial evolution. Clearly $U_t$ continuously interpolates between these two cases, and, by construction, does not increase the localization region of an observable by more than two sites. We note that $U_1$ is known in the quantum information literature as the interaction used to generate \emph{graph states} \cite{SchlingemannWerner,HeinEisertBriegel}. In Section~\ref{sec:Iauto}, we will set up a general theory for answering the questions posed above---including in cases where one is not so lucky to have an explicit parametrization in terms of gates at hand. \section{Systems}\label{sec:prelims}% \subsection{Quantum Walks}\label{sec:Swalks}% We consider a quantum system with a spatial degree of freedom $x\in{\mathbb Z}}\def\Nl{{\mathbb N}$, and at every site or ``cell'' $x$ a finite dimensional ``one-cell Hilbert space'' $\HH_x$. These spaces can be thought of as describing the internal states of the system as opposed to the external, spatial variables $x$. The Hilbert space of the system is \begin{equation}\label{dirsum} \HH=\bigoplus_{x=-\infty}^\infty \HH_x, \end{equation} The specification of the $\HH_x$ will be called a {\em cell structure}. We call a unitary operator $U$ on $\HH$ {\em causal}~{}\footnote{We are indebted to a referee who drew our attention to the inflationary use of the word ``local'' in our manuscript, where, among other things, quantum walks were called ``local'' unitaries. We changed this to ``causal'' for the crucial finite propagation property of walks and cellular automata. This is reminiscent of relativistic propagation in algebraic quantum field theory and in keeping with usage in signal processing (where $x$ would be time, and $x_-=x$). In quantum information it agrees with \cite{semilocal,ANW07}. The terminology disagrees with what some field theorists would probably say \cite{Wer87a}, and with \cite{qca}.}, % or a {\em quantum walk}, if, for any $x\in{\mathbb Z}}\def\Nl{{\mathbb N}$, there are some $x_-<x_+$ such that $\phi\in\HH_x\subset\HH$ implies $U\phi\in\bigoplus_{y=x_-}^{x_+}\HH_x$. We assume that $x_\pm$ are both non-decreasing as functions of $x$, and go to $\pm\infty$ when $x$ does. By $U_{yx}:\HH_x\to\HH_y$ we denote the block matrix corresponding to the direct sum (\ref{dirsum}), i.e. \begin{equation}\label{walklocal} U\bigoplus_x\phi_x=\bigoplus_y\sum_xU_{yx}\phi_x. \end{equation} The causality of $U$ implies that, for any $x$, only finitely many $y$ give non-zero summands. \sbsection{Grouping} The spatial variable $x$ of a walk and the internal degrees of freedom, described in $\HH_x$, are largely interchangeable. In one direction we can choose a basis $\ket{x,1}, \ldots, \ket{x,d}$ in some $\HH_x$, and replace the point $x$ by the sequence of points $(x,1), \ldots, (x,d)$, each with a one-dimensional space $\HH_{x,i}$ of internal states. Because in the above definition, we assumed that the spatial variable ranges over ${\mathbb Z}}\def\Nl{{\mathbb N}$, groupings have to be followed up by a relabeling of sites in the obvious way. In the other direction, we can ``fuse together'' several cells $x_1,\ldots,x_k$, getting a new cell $X$ with internal state space $\HH_X=\bigoplus_{i=1}^k\HH_i$. In either case it is clear how to adjust the neighborhood parameters $x_\pm$. Hence we can either regard our system as one without internal degrees of freedom, and Hilbert space $\HH=\ell^2({\mathbb Z}}\def\Nl{{\mathbb N})$. Typically this may involve some large neighborhoods $[x_-,x_+]$. Or else, we can group cells until we get a nearest neighborhood system, i.e., $x_\pm=x\pm1$, at the expense of having to deal with high-dimensional $\HH_x$. Most of these definitions and constructions are easily generalized to higher-dimensional lattices. It is therefore instructive to identify the feature which restricts our results to the one-dimensional case. Indeed, it lies in the fact that one can choose a partitioning into intervals $[a_i,b_i]\subset{\mathbb Z}}\def\Nl{{\mathbb N}$ such that the sites below $a_i$ and above $b_i$ interact only through the interval $[a_i,b_i]$. Formally, that is a consequence of demanding $\lim_{x\to\pm\infty}x_\pm=\pm\infty$. It is easy to see that such a separation need not be possible in a two-dimensional lattice, even if every cell has a finite neighborhood. In this more general setup, neighborhood relations up to regroupings may be described in terms of \emph{coarse geometry} \cite{coarse}, a theme we will not pursue here. \sbsection{Translationally invariant walks} The simplest way to define a cell structure is to choose a Hilbert space $\HH_0$, and to set $\HH_x\equiv\HH_0$ for all $x\in{\mathbb Z}}\def\Nl{{\mathbb N}$. We then have the unitary equivalence $\HH\cong\ell^2({\mathbb Z}}\def\Nl{{\mathbb N})\otimes\HH_0$. In that case we can define the {\em shift} operation $S$ and its powers by \begin{equation}\label{shift} S^n(\ket x\otimes\phi_0)=\ket{x+n}\otimes\phi_0. \end{equation} In this setting one frequently looks at translationally invariant walks, i.e., unitaries $U$ commuting with $S$. More generally, there might be some period $p$ such that $[U,S^p]=0$. Clearly, it is natural in this case to group $p$ consecutive cells, so that after grouping one gets a strictly translationally invariant walk. The space $\HH_0$ can then either be considered as an internal degree of freedom of a walking particle, or as a {\em coin} so that shift steps (possibly depending on the internal state) are alternated with unitary coin tosses ${\openone}\otimes C$. Translationally invariant systems will be treated in more detail in Sect.~\ref{sec:tiw}. \sbsection{Periodic boundary conditions} Since we are after a local theory of quantum walks, global aspects --- like the distinction between a walk on ${\mathbb Z}}\def\Nl{{\mathbb N}$ and a walk on a {\it large ring} of $M$ sites --- are secondary, as long as the interaction length $L=\max\abs{x_+-x_-}$ remains small in comparison with $M$. In fact, from any walk on a ring we can construct one on ${\mathbb Z}}\def\Nl{{\mathbb N}$ which locally looks the same. More formally, let the sites of the ring be labeled by the classes ${\mathbb Z}}\def\Nl{{\mathbb N}_M$ of integers modulo $M$, and identified with $\{0,\ldots,M-1\}$. Then we extend the cell structure by setting $\HH_{x+kM}=\HH_x$ for all $k\in{\mathbb Z}}\def\Nl{{\mathbb N}$. In order to extend the unitary $U$ on the ring to a walk $\widehat U$ on ${\mathbb Z}}\def\Nl{{\mathbb N}$ we set \begin{equation}\label{Uperiodic} \widehat U_{xy}=\left\lbrace \begin{array}{cl} 0& \quad \mbox{if }\ \|x-y\|>L \\ U_{x'y'} &\quad \mbox{if }\ \|x-y\|\leq L,\ x'\equiv x, y'\equiv y\ {\mathop{\rm mod}\nolimits} M. \end{array}\right. \end{equation} For the second line to be unambiguous, we require $2L<M$. To verify unitarity we need to compute \begin{equation}\label{UperiodicUnitary} \sum_y\widehat U_{xy}^\widehat U_{yz} =\sum_{y'}U_{x'y'}^U_{y'z'}, \end{equation} where we have assumed that $\|x-z\|\leq 2L$, because otherwise the left hand side is zero anyhow. Note that for each summation index $y$ only one class $y'\in{\mathbb Z}}\def\Nl{{\mathbb N}_M$ can occur in the sum on the right hand side. Moreover, every class $y'$ appears, although possibly with a zero contribution. But the sum on the right is $\delta_{x'z'}{\openone}_{x'}$, which together with a similar argument for $UU^$ proves the unitarity of $\widehat U$. From the point of view of index theory, the walk $U$ on the ring and $\widehat U$ on the line are the same. However, if we iterate $U$, the interaction length $(x_+-x_-)$ increases, and eventually non-zero matrix elements can occur anywhere in $U^n$. In this sense, the set of quantum walks on a ring does not form a group. This is the reason why the theory of walks on ${\mathbb Z}}\def\Nl{{\mathbb N}$ is more elegant and more complete. From now on we will therefore consider walks on ${\mathbb Z}}\def\Nl{{\mathbb N}$ only. \subsection{Cellular Automata}\label{sec:Sautoms}% Once again we consider a system in which a finite dimensional Hilbert space $\HH_x$ is associated with every site $x\in{\mathbb Z}}\def\Nl{{\mathbb N}$. However, rather than combining these in a direct sum, we take their tensor product. In plain English this means that, for any two sites $x,y$, rather than having a system of type $\HH_x$ at position $x$ {\it or} a system of type $\HH_y$ at position $y$, as in a quantum walk, we now have a system of type $\HH_x$ at position $x$ {\it and} a system of type $\HH_y$ at position $y$. In contrast to the infinite direct sum of Hilbert spaces, the infinite tensor product is not well-defined. Since we want to look at local properties, we could work with a ``potentially'' infinite product, i.e., some finite product with more factors added as needed in the course of an argument. But it is easier to work instead with the observable algebras $\AA_x$, equal to the operators on the Hilbert space $\HH_x$, or equivalently the algebra ${\mathcal M}_{d(x)}$, where $d(x)=\dim\HH_x$ (${\mathcal M}_d$ denotes the algebra of $d\times d$-matrices). In analogy to the definition for walks, we will refer to the specification of the algebras $\AA_x$ as the {\em cell structure}. For the observable algebras associated to sets $\Lambda\subset{\mathbb Z}}\def\Nl{{\mathbb N}$, we use the following notations: for finite $\Lambda$, $\AA(\Lambda)$ is the tensor product of all $\AA_x$ with $x\in\Lambda$. For $\Lambda_1\subset\Lambda_2$ we identify $\AA(\Lambda_1)$ with the subalgebra $\AA(\Lambda_1)\otimes {\openone}^{\Lambda_2\setminus\Lambda_1}\subset\AA(\Lambda_2)$. For infinite $\Lambda\subset{\mathbb Z}}\def\Nl{{\mathbb N}$ we denote by $\AA(\Lambda)$ the C-closure of the increasing family of finite dimensional algebras $\AA(\Lambda_f)$ for finite $\Lambda_f\subset\Lambda$, also called the quasi-local algebra \cite{BraRo}. In particular, the algebra of the whole chain is $\AA({\mathbb Z}}\def\Nl{{\mathbb N})$, sometimes abbreviated to $\AA$. A {\em cellular automaton} with cell structure $\{\AA_x\}_{x\in{\mathbb Z}}\def\Nl{{\mathbb N}}$ is an automorphism $\alpha$ of $\AA=\AA({\mathbb Z}}\def\Nl{{\mathbb N}))$ such that, for some functions $x\mapsto x_\pm$ as specified in Sect.~\ref{sec:Swalks}, each $\alpha(\AA_x)\subset\AA([x_-,x_+])$. Note that the restricted homomorphisms $\alpha_x:\AA_x\to\AA([x_-,x_+])$ uniquely determine $\alpha$, because every observable acting on a finite number of cells can be expanded into products of one-site observables. These {\em local rules} $\alpha_x$ have to satisfy the constraint that the algebras $\alpha_x(\AA_x)$ for different $x$ commute element-wise. In that case they uniquely determine an endomorphism $\alpha$. For examples and various construction methods for cellular automata we refer to \cite{qca}. Exactly as in the case of quantum walks we can group cells together for convenience. Whereas the dimensions for subcells add up for quantum walks ($\dim\bigoplus_{x\in\Lambda}\HH_x=\sum_{x\in\Lambda}\dim\HH_x$) we get $\AA(\Lambda)\cong{\mathcal M}_d$ with the product $d=\prod_{x\in\Lambda}d(x)$. By considering the time evolution of observables, we have implicitly chosen to work in the Heisenberg picture. The expectation value of the physical procedure ({\it i}) prepare a state $\rho$, ({\it ii}) run the automaton for $k$ time steps, ({\it iii}) measure an observable $A$ would thus be given by the expression $\rho(\alpha^k(A))$. Accordingly, we choose a convention for the {\em shift} on a chain with isomorphic cells, which at first seems inverted relative to the definition (\ref{shift}) for walks. We define it as the automorphism $\sigma$ with $\sigma(\AA_x)=\AA_{x-1}$, acting according to the assumed isomorphism of all the cell algebras. Thus if one prepares a certain state, it will be found shifted to the right after one step of $\sigma$, in accordance with (\ref{shift}) although in that case $U\HH_x=\HH_{x+1}$. \section{Local Implementability} \label{sec:Gimp} We have defined the causality properties of walks and cellular automata \emph{axiomatically}, i.e., as a condition on the input-output behavior of the maps $U$ and $\alpha$. Alternatively, one may take a \emph{constructive} approach. Here, one would list a set of operations that should certainly be included in the set of local dynamics, and refer to any given time evolution as being locally implementable if it can be represented as sequence of these basic building blocks. Both methods are equally valid, and in this section we will completely analyze their relation. From the axiomatic point of view this might be called a ``structure theorem'', whereas from the constructive point of view one would call it a ``characterization theorem''. In the case at hand, there is a natural choice of building blocks. Namely, we can partition the system into some subsets (``blocks'') of sites, and apply a unitary operation separately to each subsystem in the partition. (Note that the unitaries would be combined by a direct sum for walks and by a tensor product for cellular automata). For such maps the interplay between unitarity and causality is trivial: causality puts no constraint whatsoever on the choice of unitaries acting in each block. Moreover, it allows the overall operation to be resolved into a sequence of steps, in which one block operation is done after the other. This picture is close to the gate model of quantum computation~\cite{nc}: here each block unitary would correspond to one ``gate'' involving some subset of registers, so that these gates do not disturb each other. The fact that they can be executed in parallel is expressed by saying that these infinitely many gates nevertheless represent an operation of {\em logical depth 1}. For partitioned unitary operations the various block unitaries obviously commute. Commutation is really the essential feature if we want to resolve the overall time step into a sequence of block unitary steps. Indeed, consider a family of commuting unitaries $U_j$, each localized in a finite subset $\Lambda_j$ of some infinite lattice (not necessarily one-dimensional). We only need that the cover by the $\Lambda_j$ is locally finite, i.e., each point $x$ is contained in at most finitely many $\Lambda_j$. Then the product $\prod_j U_j$ implements a well-defined operation on localized elements. In the cellular automaton case (where localization just means $U_j\in\AA(\Lambda_j)$), we define the action on a local observable $A$ as \begin{equation}\label{communitary} \alpha(A)=\Bigl(\prod_j U_j^\Bigr)A \Bigl(\prod_j U_j\Bigr), \end{equation} with the understanding that both products range over the same index set, namely those $j$ for which $\Lambda_j$ meets the localization region of $A$. Here the products can be taken without regard to operator ordering, since we assumed that the $U_j$ commute. Including additional factors $U_j$ on both sides will not change $\alpha(A)$, since such factors can be ``commuted past'' all other $U_{j'},U_{j'}^$ and $A$ to meet the corresponding $U_j^$ and cancel. So the product is over {\it all} $j$, in the sense of a product over any sufficiently large finite set. Similar considerations apply for the case of walks on general lattices. Now if a QCA $\alpha$ is represented in the form (\ref{communitary}), we can also represent it as a product of partitioned operations: indeed, we only need to group the $U_j$ into families within which all $\Lambda_j$ are disjoint. The product of each family is obviously a partitioned unitary and under suitable uniformity conditions on the cover we only need a finite product of such partitioned operations to represent $\alpha$, typically $s+1$ factors, where $s$ is the spatial dimension of the lattice. Hence we consider the representation as a product of partitioned unitaries as essentially equivalent to the representation by commuting unitaries as in (\ref{communitary}). In either case we will say that the system is {\em locally implementable}. We now come to the basic result for implementing general walks or cellular automata by commuting unitaries --- provided we are allowed to enlarge the system. The key feature of these extensions is that they work in arbitrary (not necessarily one-dimensional) lattices and that the ancillary system is a copy of the system itself, on which we implement simultaneously the inverse operation. In the following result, we allow the underlying ``lattice'' $X$ to be any countable set. General neighborhood schemes are described as controlled sets in some coarse structure \cite{coarse}. For the present paper it suffices to describe causality in terms of a metric $d$ on $X$, of which we only assume that all balls ${\mathcal N}}\def\KK{{\mathcal K}_L(x)=\{y\|d(x,y)\leq L\}$ are finite sets. The causality condition for walks on $X$ is then that there is some ``interaction radius'' $L$ such that in (\ref{walklocal}) $U_{yx}=0$ for $d(x,y)>L$. Similarly, for QCAs, the causality condition reads $\alpha(\AA_x)\subset\AA({\mathcal N}}\def\KK{{\mathcal K}_L(x))$. For walks $U,V$ on the same lattice we simply write $U\oplus V$ for a walk with one-cell Hilbert spaces $\HH_x\oplus\KK_x$, where $\HH_x$ are the one-cell spaces for $U$ and $\KK_x$ those for $V$. This splits the total Hilbert space into $\HH\oplus\KK$, and $U\oplus V$ acts according to this direct sum. Similarly, we define the tensor product $\alpha\otimes\beta$ acting on two parallel systems combined in a tensor product. \begin{prop}\label{ANW} \hfill\break (1) For any quantum walk $U$, the walk $U\oplus U^$ is locally implementable. \hfill\break (2) For any cellular automaton $\alpha$, the automaton $\alpha\otimes\alpha^{-1}$ is locally implementable. \end{prop} \proof (1) We are considering a doubled system in which the one-cell Hilbert space at $x$ is $\HH_x\oplus\HH_x$. Let $S_x$ denote the unitary operator on the doubled system which swaps these two summands, and acts as the identity on the one-cell spaces of all other sites. Now consider the unitaries $$ T_x=(U^\oplus{\openone})S_x(U\oplus{\openone}). $$ These commute, because they are the images of the commuting transformations $S_x$ under the same unitary conjugation. Moreover, they are localized near $x$ by the causality properties postulated for $U$. Hence their infinite product defines a walk unitary, as discussed above. This unitary is $$ \prod_xT_x=(U^\oplus{\openone})S(U\oplus{\openone})=S({\openone}\oplus U^)(U\oplus{\openone})=S(U\oplus U^), $$ where we have used that $S=\prod_xS_x$ is just the global swap of the two system copies. Hence $U\oplus U^=(\prod_xS_x)(\prod_xT_x)$ is locally implemented. \par\noindent (2) Essentially the same idea works for cellular automata \cite{ANW07}. Again we consider the unitaries $S_x\in\AA_x\otimes\AA_x$, which swap the two tensor factors, so that $S_x(A_x\otimes B_x)=(B_x\otimes A_x)S_x$. Now consider the unitary elements $$ T_x=({\rm id}\otimes \alpha)[S_x].$$ Here we have written the arguments of an automorphism in brackets, to distinguish it from grouping parentheses, and thus eliminate a possible source of confusion in the coming computations. As images of a family of commuting unitaries under an automorphism, the $T_x$ are themselves a commuting family of unitaries. Moreover, they are localized in $\AA_x\otimes\AA_{{\mathcal N}}\def\KK{{\mathcal K}(x)}$. Hence they implement a cellular automaton $\beta$. We determine it by letting it act first on a localized element of the form $A_x\otimes{\openone}$ with $A_x\in\AA_x$. \begin{eqnarray}\nonumber% \beta[A_x\otimes{\openone}]&=&\Bigl(\prod_yT_y\Bigr)^\bigl(A_x\otimes{\openone}\bigr)\Bigl(\prod_yT_y\Bigr)\\ &=&({\rm id}\otimes \alpha)\Bigl[\prod_yS_y\Bigr]\ ({\rm id}\otimes \alpha)\Bigl[A_x\otimes{\openone}\Bigr]\ ({\rm id}\otimes \alpha)\Bigl[\prod_yS_y\Bigr] \nonumber\\ &=&({\rm id}\otimes \alpha)\Bigl[(\prod_yS_y)(A_x\otimes{\openone})(\prod_yS_y)\Bigr] \nonumber\\ &=&({\rm id}\otimes \alpha)[{\openone}\otimes A_x]={\openone}\otimes\alpha[A_x] \nonumber \end{eqnarray} A similar computation shows that $\beta[{\openone}\otimes \alpha[B_x]]=B_x\otimes{\openone}$. Since $\alpha$ is an automorphism, this is the same as $\beta[{\openone}\otimes B_x]=\alpha^{-1}[B_x]\otimes{\openone}$. Using the homomorphism property of $\beta$, we get for general localized elements $A,B$ that $\beta[A\otimes B]=\alpha^{-1}[B]\otimes\alpha[A]$. Hence following $\beta$ by a global swap (implemented by $\prod_xS_x$) we have implemented $\alpha\otimes\alpha^{-1}$ locally. \qed \section{The group of locally computable invariants} \label{sec:Glci} In this section we take up the idea of a {\it locally computable invariant} and show that, for either walks or automata, these invariants necessarily form an abelian group. The group multiplication reflects both the composition and the parallel application to a double chain. We postpone to later sections the question whether nontrivial invariants exist, i.e., at this stage it might well be that the group described here is trivial. Later on we will determine this group to be $({\mathbb Z}}\def\Nl{{\mathbb N},+)$ for quantum walks (see Sect.~\ref{sec:Iwalk})and $({\mathbb Q}}\def\Tw{{\mathbb T}_+,\cdot)$, the multiplicative group of positive fractions, for cellular automata (see Sect.~\ref{sec:Iauto}). In this section, in order not to double each step, we will describe the arguments for the case of walks, and just comment at the end on the necessary changes for the cellular automaton case. Suppose we have defined a property $\PP(U)$, which is defined for any quantum walk $U$, and which can be determined solely on the basis of a finite collection of the block matrices $U_{xy}$. More specifically, if we write the walk in nearest-neighbor form by grouping, we call a property $\PP(U)$ {\em locally computable} if we can compute it from the restriction of $U$ on any interval of length $\geq2$. The crucial part of this definition is, of course, that the result obtained in this way must be the same for any interval we may select for the computation, a property which we stress by calling $\PP$ a locally computable invariant. Suppose now that two walks $U_1$ and $U_2$ {\it share a patch}, in the sense that there is a long interval $[x_1,x_2]\subset{\mathbb Z}}\def\Nl{{\mathbb N}$, on which the Hilbert spaces $\HH_x$ for $x\in[x_1,x_2]$ have the same dimensions and, after the choice of a suitable isomorphism, the unitaries $U_1$ and $U_2$ restricted to these subspaces act in the same way. We assume that the interval is sufficiently long to determine $\PP$. Then local computability just means that we must have $\PP(U_1)=\PP(U_2)$. In other words, $\PP$ must be constant on each equivalence class of the relation of ``sharing a patch''. So the theory of locally computable invariants is really equivalent to characterizing the classes of the transitive hull of this relation: We will write $U_1\sim U_n$, if there is a chain of walks $U_1,U_2,\ldots,U_n$ such that, for all $i$, $U_i$ and $U_{i+1}$ share a patch. In contrast to the relation of sharing a patch, this equivalence relation no longer makes any requirements about the sizes of any one-cell Hilbert spaces in the walks $U_1$ and $U_n$. The most comprehensive locally computable property is now just the property of $U$ to belong to some equivalence class: all other locally computable properties are functions of this class. Our aim thus shifts to computing the set ${\mathcal J}$ of equivalence classes for ``$\sim$''. The equivalence class of a walk $U$ will be denoted by ${\mathop{\rm ind}\nolimits}\,(U)\in{\mathcal J}$, and called its (abstract) {\em index}. \sbsection{Triviality of locally implementable systems} Let us first make the connection to the questions of the previous section: suppose that a walk or automaton is locally implementable, i.e., the product of a collection of block partitioned unitaries. Compare this with a system in which all unitaries, whose localization intersects the positive half axis, are replaced by the identity. Clearly, this acts like the identity on all cells on the positive axis, and we can further modify the system by making it trivial ($0$-dimensional $\HH_x$ or $1$-dimensional algebras $\AA_x$) for $x>0$. Clearly these systems share a large patch (most of the negative axis), so they are equivalent. In other words, locally implementable systems have the same index as the identity on a trivial chain. \sbsection{Crossovers} A very useful fact about the relation $U_1\sim U_2$ is that it implies a prima facie much stronger relation: It is equivalent to the property that there is a ``crossover'' walk $U_c$, which coincides with $U_1$ on a negative half line $\{x\|x\leq a\}$ and coincides with $U_2$ on a positive half line $\{x\|x\geq b\}$. \proof Let us denote the relation just described by $U_1\approx U_2$. Then $U_1\approx U_2\Rightarrow U_1\sim U_2$, because $U_1$ and $U_2$ each share an infinite patch with $U_c$. In the converse direction, if $U_1$ and $U_2$ share a patch, we can define $U_c$ to be the walk whose one-cell Hilbert spaces $\HH_x$ are those of $U_1$ for $x$ to the left of the shared patch, and are those of $U_2$ for $x$ to the right of the shared patch. Similarly, we define the unitary $U_c$ to coincide with $U_1$ to the left and with $U_2$ on the right. On the shared patch we can choose either one, since the two walks coincide. Since the shared patch was assumed to be sufficiently long this does not lead to an ambiguity for either $U_c$ or $U_c^{-1}$. Hence $U_1\approx U_2$. In order to cover the case that $U_1$ and $U_2$ are linked by a chain in which any neighbors share a patch, we only need to prove that $U_1\approx U_2$ is a transitive relation. \begin{figure}\centering \includegraphics[width=8.5cm]{transit.eps} \caption{Combining a crossover from $U_1$ to $U_2$ with a crossover from $U_2$ to $U_3$ to obtain a crossover from $U_1$ to $U_3$. The shaded double chains can be fused to a single cell by Prop.~\ref{ANW}.} \label{fig:crosstrans} \end{figure} In order to prove transitivity, consider the walks $U_1,U_2,U_3$ with crossovers $U_{12}$ and $U_{23}$ as shown in Fig.~\ref{fig:crosstrans}. There we also included a copy of the inverse of $U_2$. We take the overall picture as a representation of the walk $U_{12}\oplus U_2^{-1}\oplus U_{23}$. Now consider the strands of $U_{12}$ and $U_2^{-1}$ to the right of the crossover region of $U_{12}$. Since $U_2\oplus U_2^{-1}$ is locally implementable by Prop.~\ref{ANW}, we can replace this pair of strands by a trivial system, still retaining a legitimate unitary operation for the rest. Similarly, we can fuse the strands of $U_{23}$ and $U_2^{-1}$ to the left of the crossover region of $U_{23}$ to nothing. This results in a unitary operator, which coincides with $U_1$ on a left half axis and with $U_3$ on a positive half axis, i.e., a crossover $U_{13}$. \qed \sbsection{Grouping} Suppose we regroup some finite collection of the cells. Clearly, this does not affect cells far away, and we immediately get a crossover. Hence the index does not change when regrouping cells, even if this is carried out in parallel. We will implicitly use this in the sequel by regrouping sites in whatever way is most convenient. \sbsection{Parallel chains} Define the direct sum $U\oplus V$ of walks as in the previous section. Then if $U_c$ (resp.\ $V_c$) is a crossover between $U_1$ and $U_2$ (resp.\ $V_1$ and $V_2$), $U_c\oplus V_c$ is obviously a crossover between $U_1\oplus V_1$ and $U_2\oplus V_2$. Hence the class ${\mathop{\rm ind}\nolimits}\,(U\oplus V)\in{\mathcal J}$ depends only on the equivalence classes of $U$ and $V$, and we can define an ``addition'' of indices by ${\mathop{\rm ind}\nolimits}\,(U)+{\mathop{\rm ind}\nolimits}\,(V)={\mathop{\rm ind}\nolimits}\,(U\oplus V)$. This addition is abelian, because there is a trivial crossover between $U\oplus V and V\oplus U$, just exchanging the summands on a half chain. Moreover, since an inverse is defined as $-{\mathop{\rm ind}\nolimits}\,(U)={\mathop{\rm ind}\nolimits}\,(U^)$ via Prop.~\ref{ANW}, we conclude that ${\mathcal J}$ becomes an abelian group. \sbsection{Products} Now suppose $U$ and $V$ are walks on the same cell structure, so that $UV$ makes sense. We claim that there is a crossover between $UV$ and $U\oplus V$. Hence we also get $${\mathop{\rm ind}\nolimits}\,(UV)={\mathop{\rm ind}\nolimits}\,(U\oplus V)={\mathop{\rm ind}\nolimits}\,(U)+{\mathop{\rm ind}\nolimits}\,(V).$$ Indeed, consider the cell structure on which $U\oplus V$ is defined, which has one-cell Hilbert spaces $\HH_x\oplus\HH_x$ at each site. Now let $S_+$ denote the unitary which acts as the swap on all $\HH_x\oplus\HH_x$ with $x>0$ and leaves the subspaces with $x\leq0$ unchanged. Then $(U\oplus{\openone})S_+({\openone}\oplus V)S_+$ is a crossover between $U\oplus V$ and $UV\oplus{\openone}\sim UV$. \sbsection{Modifications for cellular automata} The concept of crossovers and the arguments for the group structure can be taken over verbatim, with the replacements $U\mapsto\alpha$, $\HH_x\mapsto\AA_x$, $\oplus\mapsto\otimes$. Of course, the index group will also be different, and we will adopt the convention to write it multiplicatively. The product formula thus reads ${\mathop{\rm ind}\nolimits}\,(\alpha\beta)={\mathop{\rm ind}\nolimits}\,(\alpha\otimes\beta)={\mathop{\rm ind}\nolimits}\,(\alpha){\mathop{\rm ind}\nolimits}\,(\beta)$. \sbsection{Numerical representation and shift subgroups} To make the abstract theory of this section useful, one needs to establish an isomorphism of the index group with some explicitly known group. The natural way to do that is to identify {\it generators}, i.e., some particular walks which cannot be implemented locally, but are sufficient to generate arbitrary walks up to locally implementable factors. Although it is far from obvious at this point, it will turn out later that, for walks as well as for cellular automata, the role of generators is played by the shifts. Since there is only one kind of generators, it suffices to assign numbers as ``index values'' to the shifts to establish an isomorphism of the abstract index groups with groups of numbers. For walks, the shift was introduced in Sect.~\ref{sec:Swalks}. We denote by $S_d$ the shift on a system with $d$-dimensional internal degree of freedom ($\dim\HH_x=d$ for all $x$). Similarly, let $\sigma_d$ denote the shift automorphism on a chain with cell algebra ${\mathcal M}_d$. We tentatively demand \begin{equation}\label{shiftindW} {\mathop{\rm ind}\nolimits}\,(S_d)=d \end{equation} and, similarly, \begin{equation}\label{shiftindA} {\mathop{\rm ind}\nolimits}\,(\sigma_d)=d. \end{equation} This has to be consistent for shifts on parallel chains. Since $S_d\oplus S_e=S_{d+e}$ and $\sigma_d\otimes\sigma_e=\sigma_{d\cdot e}$, this requires that we take the indices of walks as a group of numbers under addition, and for the cellular automata as a group of numbers under multiplication. Indeed, we will show that the above formulas fix an isomorphism of the abstract index group ${\mathcal J}$ to $({\mathbb Z}}\def\Nl{{\mathbb N},+)$ for quantum walks, and to the group $({\mathbb Q}}\def\Tw{{\mathbb T}_+,\cdot)$ of positive fractions for cellular automata. \section{Index for quantum walks} \label{sec:Iwalk} \subsection{Pedestrian definition} The following is the basic definition of this chapter. To the best knowledge of the authors, it is due to Kitaev \cite{Kitaev}, who calls this quantity the {\em flow} of a walk $U$. \begin{defn}\label{defInd} For any walk $U$, we define the {\bf index} as \begin{equation}\label{defIndW} {\mathop{\rm ind}\nolimits}\, U=\sum_{x\geq0>y}\left(\mathop{\rm Tr}\nolimits (U_{xy})^U_{xy}-\mathop{\rm Tr}\nolimits (U_{yx})^U_{yx}\right). \end{equation} \end{defn} Note that the sum is finite by virtue of the definition of causal unitaries. Clearly, for the simple shift we get ${\mathop{\rm ind}\nolimits}\, S_1=1$, confirming Eq.~(\ref{shiftindW}). Of course, we will show presently that this quantity has all the properties of the abstract index discussed in the previous sections. However, from the definition given here it seems miraculous that such a quantity should be always an integer, and independent of the positioning of the cut. To see this it is better to rewrite this quantity in the following way. \subsection{Operator theoretic definition} We introduce the projection $P$ for the half axis $\{x\geq0\}$, i.e., the projection onto the subspace $\bigoplus_{x\geq0}\HH_x$. Then, for $\phi_x\in\HH_x$ and $\phi_y\in\HH_y$ we get \begin{equation} \bra{\phi_x} PU-UP\ket{\phi_y}=\left\lbrace \begin{array}{cl} 0 & x\geq0\ \mbox{and}\ y\geq0\\ -\bra{\phi_x}U_{xy}\ket{\phi_y} & x<0\ \mbox{and}\ y\geq0\\ \bra{\phi_x}U_{xy}\ket{\phi_y} & x\geq0\ \mbox{and}\ y<0\\ 0 & x<0\ \mbox{and}\ y<0 \end{array}\right. \end{equation} Hence, for any pair $(x,y)$ the commutator $[U,P]$ has just the signs used in the definition of the index, and we get \begin{equation}\label{indcomm} {\mathop{\rm ind}\nolimits}\, U=\mathop{\rm Tr}\nolimits U^[P,U]=\mathop{\rm Tr}\nolimits(U^PU-P) \end{equation} Note that for the the trace on the right hand side we cannot use linearity of the trace to write it as the difference of two (equal!) terms, because this would result in an indeterminate expression $\infty-\infty$. \subsection{Fundamental properties of the index for walks} \begin{thm}\label{thmInd}\ \begin{enumerate} \item ${\mathop{\rm ind}\nolimits}\, U$ is an integer for any walk $U$ \item ${\mathop{\rm ind}\nolimits}\, U$ is locally computable, and uniquely parameterizes the equivalence classes for the relation $\sim$ from Sect.~\ref{sec:Glci}, hence can be identified with the abstract index defined there. \item ${\mathop{\rm ind}\nolimits}\,(U_1\oplus U_2)={\mathop{\rm ind}\nolimits}\,(U_1)+{\mathop{\rm ind}\nolimits}\,(U_2)$, and, when $U_1$ and $U_2$ are defined on the same cell structure, ${\mathop{\rm ind}\nolimits}\,(U_1U_2)={\mathop{\rm ind}\nolimits}\,(U_1)+{\mathop{\rm ind}\nolimits}\,(U_2)$. Moreover, for the shift of $d$-dimensional cells: ${\mathop{\rm ind}\nolimits}\, S_d=d$. \item ${\mathop{\rm ind}\nolimits}\, U=0$ if and only if $U$ admits a ``local decoupling'', i.e. there is a unitary $V$, which acts like the identity on all but finitely many $\HH_x$, such that $UV$ is block diagonal with respect to the decomposition $\HH=\bigl(\bigoplus_{x\leq0}\HH_x\bigr)\oplus\bigl(\bigoplus_{x\geq1}\HH_x\bigr)$. \item ${\mathop{\rm ind}\nolimits}\, U=0$ if and only if it is locally implementable (see Sect.~\ref{sec:Gimp}). In this case it can be written as a product of just two partitioned unitaries. When $U$ is regrouped in nearest neighbor form, then the partitioned unitaries can be chosen to couple only pairs of nearest neighbors. \item ${\mathop{\rm ind}\nolimits}\, U_1={\mathop{\rm ind}\nolimits}\, U_0$ if and only if $U_0$ and $U_1$ lie in the same connected component, i.e., there is a norm continuous path $[0,1]\ni t\mapsto U_t$ of causal unitaries of uniformly bounded interaction length $L$ with the specified boundary values. \end{enumerate} \end{thm} \noindent The rest of this subsection is devoted to the proof of this result. According to Eq.~(\ref{indcomm}), the index is closely related to a difference of projections. If these were finite dimensional, we could just use linearity to get the difference of two integers. The following Lemma shows that the result is still an integer when the difference of the two projections has finite rank. Actually it is even sufficient for the difference to be trace class, and with a careful discussion of the trace, it is sufficient for the $\pm1$ eigenspaces of the difference to be finite dimensional \cite{Seiler}. Here we include the simple case sufficient for our purposes. \begin{lem}\label{finrank} Let $Q,P$ be orthogonal projections in a Hilbert space $\HH$, such that $Q-P$ has finite rank. Then \begin{enumerate} \item The range ${\mathcal R}}\def\HH{{\mathcal H}=(Q-P)\HH$ is an invariant subspace for both $Q$ and $P$. \item $\mathop{\rm Tr}\nolimits(Q-P)$ is an integer. \item There is a unitary operator $V$ such that $V\phi=\phi$ for all $\phi\perp(Q-P)\HH$, and such that $Q\geq V^PV$ or $Q\leq V^PV$. \item If $\mathop{\rm Tr}\nolimits(Q-P)=0$, the $V$ from the previous item satisfies $Q=V^PV$. \end{enumerate} \end{lem} \proof 1. follows from the identity $$Q(Q-P)=Q({\openone}-P)=(Q-P)({\openone}-P),$$ and its analogue for $P$. \\ 2. Clearly, we can evaluate the trace in a basis of ${\mathcal R}}\def\HH{{\mathcal H}$ since the basis elements from ${\mathcal R}}\def\HH{{\mathcal H}^\perp$ contribute only zeros. Since the restrictions of $Q$ and $P$ to ${\mathcal R}}\def\HH{{\mathcal H}$ are projections on a finite dimensional space, $$\mathop{\rm Tr}\nolimits(Q-P)=\mathop{\rm Tr}\nolimits_{\mathcal R}}\def\HH{{\mathcal H}(Q-P)=\mathop{\rm Tr}\nolimits_{\mathcal R}}\def\HH{{\mathcal H}(Q)-\mathop{\rm Tr}\nolimits_{\mathcal R}}\def\HH{{\mathcal H}(P)$$ is the difference of two natural numbers.\\ 3\&4. Obviously, we can find such a unitary on ${\mathcal R}}\def\HH{{\mathcal H}$ with the corresponding property for the restrictions of $Q$ and $P$ to ${\mathcal R}}\def\HH{{\mathcal H}$. We then extend $V$ to be the identity on ${\mathcal R}}\def\HH{{\mathcal H}^\perp$. When $\mathop{\rm Tr}\nolimits(Q-P)=0$, this $V$ is a unitary mapping from $Q{\mathcal R}}\def\HH{{\mathcal H}$ to $P{\mathcal R}}\def\HH{{\mathcal H}$. \qed \proof[of Theorem~\ref{thmInd}] None of the statements, or values of the index will change under grouping, except part of item 5, which requires nearest neighbor form. Therefore we will assume without loss that all walks are nearest neighbor. We will use Lemma~\ref{finrank} with $Q=U^PU$.\\ 1. This follows directly from Eq.~(\ref{indcomm}) and Lemma~\ref{finrank}, item 2. 2. Let $P'$ be the projection onto another half axis, say $x\geq x_0$. Then $P-P'$ is finite rank and hence $(U^PU-P)-(U^P'U-P')=P'-P-U^(P-P')U$ is the difference of two finite rank operators with equal trace. Hence the index does not depend on the cut position, and since formula~(\ref{defInd}) clearly involves only matrix elements at most 1 site from the cut, it is a locally computable invariant. It remains to be shown that it is a complete invariant, i.e., that ${\mathop{\rm ind}\nolimits}\, U_1={\mathop{\rm ind}\nolimits}\, U_2$ implies $U_1\sim U_2$ in the sense of Sect.~\ref{sec:Glci}. This will be done in connection with item 4 below. 3. This follows from Sect.~\ref{sec:Glci}. But a direct proof (for the product) is also instructive: $$(U_1U_2)^P(U_1U_2)-P=(U_2^PU_2-P)+U_2^(U_1^PU_1-P)U_2$$ is the sum of two finite rank operators, of which we can take the trace separately. 4. Apply Lemma~\ref{finrank}, item 3, to get $V$ with $P=V^(U^PU)V$, and hence $PUV=UVP$. The fact that $V-{\openone}$ vanishes on all but finitely many $\HH_x$ follows from its construction: $V-{\openone}$ vanishes on the complement of $(P-Q)\HH\subset\HH_{-1}\oplus\HH_0$, for the cut ``$-1\|0$'' used in Def.~\ref{defInd}. Note that this implies $V\sim{\openone}$, and also $UV\sim{\openone}$, since a unitary which has no matrix elements connecting $x\geq0$ and $x<0$ clearly allows a crossover with the identity. From the product formula for locally computable invariants we therefore get that ${\mathop{\rm ind}\nolimits}\, U=0$ implies $U\sim{\openone}$. Obviously, this extends to other values of the index: if ${\mathop{\rm ind}\nolimits}\, U_1={\mathop{\rm ind}\nolimits}\, U_2$ we have ${\mathop{\rm ind}\nolimits}\, U_1^U_2=0$, hence $U_1^U_2\sim{\openone}$ and hence $U_1\sim U_2$. This completes the proof of item 2.\\ 5\&6. These items each contain a trivial direction: We have already shown in Sect.~\ref{sec:Glci} that locally implementable walks have trivial index. Moreover, it is clear from Definition~\ref{defInd} that the index is a continuous function, and must hence be constant on each connected component. The non-trivial statement in 5.\ is that walks with trivial index are indeed implementable, and in 6.\ that walks with vanishing index can be connected to the identity (the rest then follows by multiplication). In either case, an explicit construction is required, and it will actually be the same one. So let $U=U_1$ be a walk ${\mathop{\rm ind}\nolimits}\, U=0$. Let $V_0$ denote the decoupling unitary for the cut $-1\|0$, obtained in the proof of item 4, and define similar unitaries $V_k$ for the cuts at $2k-1\|2k$ such that $UV_k$ has no non-zero matrix elements $(UV_k)_{xy}$ with $y<2k\leq x$. Let $H_k$ denote a hermitian operator located on the same subspaces as $V_k-{\openone}$, such that $V_k=\exp(iH_k)$. We will take all $H_k$ bounded in norm by the same constant ($\pi$ will do). Then since they live on orthogonal subspaces, their sum $H=\sum_kH_k$ is well-defined and also bounded. Now let $V(t)=\exp(itH)$, which is a norm continuous function of $t$, because $\norm H\leq\pi$. The endpoint $V(1)$ can also be defined by this product formula $V(1)=\prod_kV_k$, because on each subspace $\HH_{2k-1}\oplus\HH_{2k}$ only one these unitaries is different from ${\openone}$. Moreover, $UV(1)$ has no matrix elements $y<2k\leq x$ for any $k$, i.e., it is block diagonal for a decomposition of ${\mathbb Z}}\def\Nl{{\mathbb N}$ into pairs $\{2k,2k+1\}$. Now take a similar Hamiltonian path deforming each block in this matrix decomposition separately to the identity. Specifically, we take $W(0)={\openone}$ and $W(1)=UV(1)$. Then $t\mapsto W(t)V(t)^$ is a norm continuous path (although no longer a unitary group), with the endpoints ${\openone}$ and $U$. Moreover, each unitary $W(t)$ or $V(t)^$ is based on a partition into neighboring pairs so that, for no $t$, $W(t)V(t)^$ has any non-zero matrix element between sites with $\|x-y\|>2$. This proves the remaining statement in item 5 (for $t=1$), and also the statement about uniformly bounded neighborhoods in item 6. \qed \subsection{The translation invariant case} \label{sec:tiw}% Suppose that $U$ commutes with some power of the shift. It is then useful to group spaces $\HH_x$ into larger blocks to get commutation with the shift itself. That is, in this section we assume all $\HH_x\equiv\KK$ to be equal, and $U_{xy}=U_{x-y}$, where by a slight abuse of notation the single-index quantity $U_x$ is defined as $U_{x0}$. The width $L$ is the largest $x$ such that $U_x\neq0$ or $U_{-x}\neq0$. It is natural to diagonalize $U$ using the Fourier transform. We define ${\mathcal F}:\ell^2({\mathbb Z}}\def\Nl{{\mathbb N})\otimes\KK\to{\mathcal L}^2([-\pi,\pi])\otimes\KK$ by ${\mathcal F}(\Psi)(p)=\frac1{\sqrt{2\pi}}\sum_xe^{ipx}\Psi(x)$. This is to be read as a $\KK$-valued equation, where we use the natural identification of ${\mathcal L}^2([-\pi,\pi])\otimes\KK$ with the set of $\KK$-valued square integrable functions on $[-\pi,\pi]$. Similarly, we identify $\ell^2({\mathbb Z}}\def\Nl{{\mathbb N})\otimes\KK$ with the $\KK$-valued square summable sequences. Then ${\mathcal F} U{\mathcal F}^$ becomes the multiplication operator by the $p$-dependent matrix \begin{equation}\label{Uhat} \widehat U(p)=\sum_{x=-L}^L U_xe^{ipx}. \end{equation} Note that this is a Laurent polynomial in $e^{ip}$. The largest degree of $e^{ip}$ in the polynomial is $x_+-x$, which is constant by translation invariance. The lowest degree is $x-x_-$. Further, $\widehat U(p)$ must be a unitary operator on $\KK$ for every $p\in{\mathbb R}}\def\Cx{{\mathbb C}$. Taking these facts together, we conclude that both the determinant $\det\widehat U(p)=f(p)$ and its inverse $1/f(p)=\det\widehat U(p)^$ are Laurent polynomials as well. But this is only possible if $f$ is actually a monomial, say proportional to $\exp(inp)$ for some integer $n$. We claim that this $n$ is the index: \begin{prop} For a translation invariant walk, \begin{equation}\label{tiindexDet} \det\widehat U(p)=C e^{ip\ {\mathop{\rm ind}\nolimits}\,(U)}, \end{equation} for some phase constant $C$. \end{prop} As a simple example consider the shift on a chain with $\dim\HH_0=1$. We already noted after Definition~\ref{defInd} that this has index $1$. The corresponding $p$-dependent unitary is the number $\widehat U(p)=e^{ip}$, so this also gives index $1$. For unitaries acting on each site separately in the same way, we get agreement because ${\mathop{\rm ind}\nolimits}\, U=0$, and $\widehat U(p)$ is independent of $p$. Note also that both sides of \ref{tiindexDet} have the same behavior under composition and direct sums. This proves the formula for all walks which can be composed of shifts and sitewise rotations. Actually, {\it all} translationally invariant walks can be represented in this way \cite{Gao}, but we prefer to give a direct proof of the proposition without invoking this decomposition. \proof From Definition~\ref{defInd} we get \begin{eqnarray}\nonumber {\mathop{\rm ind}\nolimits}\, U &=& \sum_{x=0}^\infty\sum_{y=-\infty}^{-1}\mathop{\rm Tr}\nolimits\|U_{x-y}\|^2-\mathop{\rm Tr}\nolimits\|U_{y-x}\|^2 \\\nonumber &=& \sum_{n=-\infty}^\infty n\mathop{\rm Tr}\nolimits\|U_n\|^2 = \sum_{nm}\delta_{nm} n\mathop{\rm Tr}\nolimits(U_m^* U_n)\\\nonumber &=&\frac1{2\pi i}\int_{-\pi}^\pi\!\!dp\ \mathop{\rm Tr}\nolimits \Bigl(\widehat U(p)^* \frac{d\widehat U(p)}{dp}\Bigr)\nonumber \end{eqnarray} On the other hand, for any invertible matrix function $\widehat U$, $$\frac d{dp}\det\widehat U(p) =\det\widehat U(p)\ \mathop{\rm Tr}\nolimits\Bigl(\widehat U(p)^{-1}\frac{d\widehat U(p)}{dp}\Bigr).$$ Hence with $\det\widehat U(p)=\exp(ipn)$ the above integrand is actually constant equal to $in$, and ${\mathop{\rm ind}\nolimits}\,(U)=n$. \qed \begin{figure}\centering \psfrag{W}{$\omega_k(p)$} \psfrag{p}{$p$} \includegraphics[width=8cm]{wrapbands.eps} \caption{\label{fig:wind}Example for eigenvalues of $\widehat U(p)$, with $\dim\KK=3$, $L=5$, ${\mathop{\rm ind}\nolimits}\, U=-1$. In this case the spectrum is a single curve on the torus. The index can be computed by the signed number of crossings of any horizontal line, or as the sum of the derivatives of all branches.} \end{figure} The properties of a walk depend crucially on the properties of the eigenvalues $e^{i\omega_1(p)},\ldots,e^{i\omega_d(p)}$ of $\widehat U(p)$ (see Fig.~\ref{fig:wind}). Clearly, $p\mapsto\widehat U(p)$ is an analytic family of operators, so we can follow the eigenvalues as analytic curves \cite{Kato}. The derivatives of the eigenvalues determine the {\em group velocity}: Let $P_\alpha(p)$ be the eigenprojection of $\widehat U(p)$ belonging to the eigenvalue $\exp{i\omega_\alpha(p)}$. Then the group velocity operator can be written as \begin{equation}\label{groupVelo} G(p)=\lim_{t\to\infty}\frac1tX(t) =\sum_\alpha P_\alpha(p)\frac{d \omega_\alpha(p)}{d p}, \end{equation} where $X$ denotes the position operator, and at degenerate eigenvalues the projections $P_\alpha(p)$ have to be chosen appropriately, as dictated by analytic perturbation theory. The limit is in the strong resolvent sense. Hence the probability distribution for the selfadjoint operator $G$ in a state $\rho$ is equal to the asymptotic position distribution starting from $\rho$ in ``ballistic'' scaling\cite{TimeRandom}. In particular, when the internal state is unpolarised, i.e., when the initial state is of the form $\rho=\sigma\otimes{\openone}/d$, we find \cite{Kitaev} $$ \langle X(t)\rangle=\langle X(0)\rangle+ \frac td {\mathop{\rm ind}\nolimits}\,(U).$$ In this sense the index has direct relevance as a mean speed of the walk. It is, of course, suggestive to connect the topological properties of the eigenvalue curves in Fig.~\ref{fig:wind} with the index. In principle, these curves are allowed to cross each other. So in general, we have several branches of curves, which wind several times around the torus before closing. The number of curves and their winding numbers would appear to be a topological invariant, but this is not true because of the ``avoided crossing'' phenomenon, in which a small perturbation of the walk turns an eigenvalue crossing into a close encounter of two separate curves (suggested also at $p=1.6$ in Fig.~\ref{fig:wind}). Hence only the {\em sum of the winding numbers} is stable with respect to small perturbations, and this is indeed equal to ${\mathop{\rm ind}\nolimits}\, U$. To see this, note that at every $p$ the sum of the derivatives of all branches is equal to the index. Therefore the sum of the winding angles of the branches taken from $p=-\pi$ to $p=\pi$ is $2\pi\,{\mathop{\rm ind}\nolimits}\, U$. The winding angles of the closed curve components are just suitable sub-sums of this, and this partition is changed at avoided crossing points. We close this section by establishing a variant of the main theorem for the translationally invariant case. Of course, most of this follows by simply specializing. The only question which requires a new argument is whether the path connecting two translationally invariant walks can be chosen to go entirely through translationally invariant walks. This is established in the following proposition. \begin{prop} Let $U$ be a translationally invariant causal unitary with ${\mathop{\rm ind}\nolimits}\, U=0$. Then we can find a norm continuous path $t\mapsto U_t$ of translationally invariant causal unitaries of bounded width such that $U_0={\openone}$ and $U_1=U$. \end{prop} \proof We use the factorization theorem for ``paraunitary'' operators \cite{Gao} (see also \cite{Vogts}), which states that $\widehat U(p)$ can be written as a finite product $$ \widehat U(p)=V_0\prod_{k=1}^r \widehat W_{m_k}(p)\, V_k$$ of constant unitaries $V_k$ and the elementary causal unitaries $$ \widehat W_m(p)=\left(\begin{array}{cccc} e^{imp}&0&\cdots&0\\ 0&1&\cdots&0\\ \vdots&&\ddots&\vdots\\ 0&0&\cdots&1\end{array}\right) $$ As a quantum walk these corresponds to a shift of only the first internal state by $m$ positions, leaving all other internal states fixed. This walk has index $m$, and the product formula yields ${\mathop{\rm ind}\nolimits}\, U=\sum_km_k$. The maximal polynomial degree of any matrix element in $e^{\pm ip}$ depends on the localization region $[x_+,-x_-]$, and is clearly bounded by $L_{\rm max}=\sum_k\|m_k\|$. Hence we can contract the walk to ${\openone}$ by contracting each of the $V_k$ to ${\openone}$, never exceeding width $L_{\rm max}$ on the way. \qed \section{The index for cellular automata} \label{sec:Iauto} For cellular automata we proceed in analogy to the case of walks, i.e., by defining directly a locally computable quantity as the index ${\mathop{\rm ind}\nolimits}\,\alpha$ of a walk automorphism $\alpha$. We then establish that it is actually a complete locally computable invariant and, at the same time that it characterizes the connected components of QCAs. As a technical preparation we need some background on commutation properties of algebras spanning several cells. It is basically taken from \cite{qca}, and included here to make the presentation here self-contained. \subsection{Support algebras} For defining the index we need to find a quantitative characterization of ``how much'' of one cell ends up in another. To this end we introduce the notion of support algebras. Consider a subalgebra $\AA\subset{\mathcal B}_1\otimes{\mathcal B}_2$ of a tensor product. What is the position of $\AA$ relative to the tensor structure? Here we answer a relatively simple part of this question: which elements of ${\mathcal B}_1,{\mathcal B}_2$ are actually needed to build $\AA$? For the following Definition with Lemma, recall that $\AA'$ denotes the commutant $\{a\|\forall a_1\in\AA: [a,a_1]=0\}$. \begin{lem}\label{lem:spp} Let ${\mathcal B}_1$ and ${\mathcal B}_2$ be finite dimensional C-algebras, and $\AA\subset{\mathcal B}_1\otimes{\mathcal B}_2$ a subalgebra. Then \begin{enumerate} \item There is a smallest C-subalgebra ${\mathcal C}_1\subset{\mathcal B}_1$ such that $\AA\subset{\mathcal C}_1\otimes{\mathcal B}_2$. We call this the {\bf support algebra} of $\AA$ on ${\mathcal B}_1$, and denote it by ${\mathcal C}_1=\Spp(\AA,{\mathcal B}_1)$. \item Consider a basis $\{e_\mu\}\subset{\mathcal B}_2$, so that every $a\in\AA$ has a unique expansion $a=\sum_\mu a_\mu\otimes e_\mu$ with $a_\mu\in{\mathcal B}_1$. Then $\Spp(\AA,{\mathcal B}_1)$ is generated by all the elements $a_\mu$ arising in this way. \item The commutant of $\Spp(\AA,{\mathcal B}_1)$ in ${\mathcal B}_1$ is characterized as $\{b\in{\mathcal B}_1\|b\otimes{\openone}\in\AA'\}$. \end{enumerate} \end{lem} \proof We can pick out the terms $a_\mu$ by applying a suitable functional $\omega_\mu$ from the dual basis to the second factor, i.e., by applying the map ${\rm id}\otimes\omega_\mu:{\mathcal B}_1\otimes{\mathcal B}_2\to{\mathcal B}_1$, which takes $b_1\otimes b_2$ to $\omega_\mu(b_2)b_1$. Clearly, if $a\in{\mathcal C}_1\otimes{\mathcal B}_2$, so that $a$ can be expanded into simple tensors using only elements from ${\mathcal C}_1$ in the first factor, we find $a_\mu=(id\otimes\omega_\mu)(a)\in{\mathcal C}_1$. Hence the algebra described in item 2 must be contained in any ${\mathcal C}_1$ satisfying item 1. Since it also satisfies condition 1, we have identified the unique smallest ${\mathcal C}_1$. The characterization 3 follows by looking at commutators of the form $[b\otimes{\openone},a]$, and expanding $a$ as above. \qed This construction was introduced to the QI community by Zanardi \cite{Zanardi}, who applied it to the algebra generated by an interaction Hamiltonian, and consequently called it an ``interaction algebra''. Of course, we can apply the construction also to the second factor, so that \begin{equation}\label{a2Supp} \AA\subset \Spp(\AA,{\mathcal B}_1)\otimes \Spp(\AA,{\mathcal B}_2) \subset{\mathcal B}_1\otimes{\mathcal B}_2\;. \end{equation} The crucial fact we need about support algebras is that ``commutation of algebras with overlapping localization happens on the intersection''. More precisely, we have the following \begin{lem} \label{sppcomm} Let $\AA_1\subset{\mathcal B}_1\otimes{\mathcal B}_2$ and $\AA_2\subset{\mathcal B}_2\otimes{\mathcal B}_3$ be subalgebras such that $\AA_1\otimes{\openone}_3$ and ${\openone}_1\otimes\AA_2$ commute in ${\mathcal B}_1\otimes{\mathcal B}_2\otimes{\mathcal B}_3$. Then $\Spp(\AA_1,{\mathcal B}_2)$ and $\Spp(\AA_2,{\mathcal B}_2)$ commute in ${\mathcal B}_2$. \end{lem} \proof Pick bases $\{e_\mu\}\subset{\mathcal B}_1$ and $\{e'_\nu\}\subset{\mathcal B}_2$, and let $a\in\AA_1$ and $a'\in\AA_2$. Then we may expand uniquely: $a=\sum_\mu e_\mu\otimes a_\mu$ and $a'=\sum_\nu a'_\nu\otimes e'_\nu$. Then by assumption \begin{displaymath} 0=[a\otimes{\openone}_3,{\openone}_1\otimes a'] =\sum_{\mu\nu}e_\mu\otimes [a_\mu,a'_\nu]\otimes e'_\nu \;. \end{displaymath} Now since the elements $e_\mu\otimes e'_\nu$ are a basis of ${\mathcal B}_1\otimes{\mathcal B}_3$, this expansion is unique, so we must have $[a_\mu,a'_\nu]=0$ for all $\mu,\nu$. Clearly, this property also transfers to the algebras generated by the $a_\mu$ and $a'_\nu$, i.e., to the support algebras introduced in the Lemma. \qed \subsection{Defining the Index} \label{sec:Defindalpha} Now consider a cellular automaton $\alpha$ on a cell structure $\AA_x$. By regrouping, if necessary, we may assume that it has only nearest neighbor interactions. Now consider any two neighboring cells $\AA_{2x}\otimes\AA_{2x+1}$, and their image under $\alpha$, i.e., $$ \alpha\Bigl(\AA_{2x}\otimes\AA_{2x+1}\Bigr)\subset \Bigl(\AA_{2x-1}\otimes\AA_{2x}\Bigr)\otimes \Bigl(\AA_{2x+1}\otimes\AA_{2x+2}\Bigr).$$ We apply the support algebra construction to this inclusion, obtaining two algebras \begin{eqnarray}\label{RR2x} {\mathcal R}}\def\HH{{\mathcal H}_{2x}&=& \Spp\Bigl(\alpha\bigl(\AA_{2x}\otimes\AA_{2x+1}\bigr),\ \bigl(\AA_{2x-1}\otimes\AA_{2x}\bigr)\Bigr)\\ {\mathcal R}}\def\HH{{\mathcal H}_{2x+1}&=& \Spp\Bigl(\alpha\bigl(\AA_{2x}\otimes\AA_{2x+1}\bigr),\ \bigl(\AA_{2x+1}\otimes\AA_{2x+2}\bigr)\Bigr) \end{eqnarray} Intuitively, the algebras ${\mathcal R}}\def\HH{{\mathcal H}_y$ with even index become larger when information flows to the right, whereas the ones with odd index describe a flow to the left. Of course, this intuition will be made precise below, but at this stage one can at least check these statements for the shift: When $\alpha(\AA_y)=\AA_{y-1}$ (recall the convention made at the end of Sect.~\ref{sec:Sautoms}) we have ${\mathcal R}}\def\HH{{\mathcal H}_{2x}=\AA_{2x-1}\otimes\AA_{2x}$ and ${\mathcal R}}\def\HH{{\mathcal H}_{2x}=\Cx{\openone}$. This is to be contrasted with ${\mathcal R}}\def\HH{{\mathcal H}_y=\AA_y$ for the identity. Continuing with our construction, observe that by Lemma~\ref{sppcomm}, the subalgebras ${\mathcal R}}\def\HH{{\mathcal H}_{2x+1}$ and ${\mathcal R}}\def\HH{{\mathcal H}_{2x+2}$ commute in the algebra $\bigl(\AA_{2x+1}\otimes\AA_{2x+2}\bigr)$. Algebras ${\mathcal R}}\def\HH{{\mathcal H}_y$ which are further away commute anyhow, since they are contained in disjoint cells. We conclude that {\em all} ${\mathcal R}}\def\HH{{\mathcal H}_y$ commute. By definition of support algebras, $\alpha(\AA_{2x}\otimes\AA_{2x+1})\subset {\mathcal R}}\def\HH{{\mathcal H}_{2x}\otimes{\mathcal R}}\def\HH{{\mathcal H}_{2x+1}$, so that the algebras ${\mathcal R}}\def\HH{{\mathcal H}_x$ together generate an algebra containing $\alpha\AA({\mathbb Z}}\def\Nl{{\mathbb N})$. Because $\alpha$ is an automorphism, this is the same as $\AA({\mathbb Z}}\def\Nl{{\mathbb N})$. Now if any ${\mathcal R}}\def\HH{{\mathcal H}_x$ had a non-trivial center, i.e., if there were an element $X\in{\mathcal R}}\def\HH{{\mathcal H}_x$ commuting with all of ${\mathcal R}}\def\HH{{\mathcal H}_x$ but not a multiple of ${\openone}$, this $X$ would also be in the center of the entire quasi-local algebra $\AA({\mathbb Z}}\def\Nl{{\mathbb N})$. However, this center is known to be trivial \cite{BraRo}. We conclude that each ${\mathcal R}}\def\HH{{\mathcal H}_x$ must have trivial center, and hence be isomorphic to ${\mathcal M}_{r(x)}$ for some integer $r(x)$. Moreover, the inclusion noted at the beginning of this paragraph cannot be strict, since otherwise we would find an element in the relative commutant, which would once again be in the center $\alpha\AA({\mathbb Z}}\def\Nl{{\mathbb N})$. To summarize, we must have \begin{eqnarray}\label{AARReven} \alpha\bigl(\AA_{2x}\otimes\AA_{2x+1}\bigr) &=&{\mathcal R}}\def\HH{{\mathcal H}_{2x}\otimes{\mathcal R}}\def\HH{{\mathcal H}_{2x+1}, \\\mbox{hence}\qquad d(2x)d(2x+1)&=&r(2x)r(2x+1). \end{eqnarray} \begin{figure}\centering \psfrag{a}{\Large$\alpha$} \psfrag{i0}{$\AA_0$}\psfrag{r0}{${\mathcal R}}\def\HH{{\mathcal H}_0$} \psfrag{i1}{$\AA_1$}\psfrag{r1}{${\mathcal R}}\def\HH{{\mathcal H}_1$} \psfrag{i2}{$\AA_2$}\psfrag{r2}{${\mathcal R}}\def\HH{{\mathcal H}_2$} \psfrag{i3}{$\AA_3$}\psfrag{r3}{${\mathcal R}}\def\HH{{\mathcal H}_3$} \psfrag{i4}{$\AA_4$}\psfrag{r4}{${\mathcal R}}\def\HH{{\mathcal H}_4$} \psfrag{i5}{$\AA_5$}\psfrag{r5}{${\mathcal R}}\def\HH{{\mathcal H}_5$} \psfrag{i6}{$\AA_6$}\psfrag{r6}{${\mathcal R}}\def\HH{{\mathcal H}_6$} \includegraphics[width=8.5cm]{cells.eps} \caption{\label{fig:algebradims}Cell structure with support algebras. (Read top to bottom) If the width of cells is taken as log dimension, the index can be read off the slant in the boxes representing mapping by $\alpha$. } \end{figure} On the other hand, the commuting full matrix algebras ${\mathcal R}}\def\HH{{\mathcal H}_{2x+1}$ and ${\mathcal R}}\def\HH{{\mathcal H}_{2x+2}$ together span the tensor product isomorphic to ${\mathcal M}_{r(2x+1)r(2x+2)}$ inside $\bigl(\AA_{2x+1}\otimes\AA_{2x+2}\bigr)$. Again the inclusion cannot be strict, because otherwise the automorphism would not be onto. From this we get the second relation and dimension equation \begin{eqnarray}\label{AARRodd} {\mathcal R}}\def\HH{{\mathcal H}_{2x+1}\otimes{\mathcal R}}\def\HH{{\mathcal H}_{2x+2} &=&\AA_{2x+1}\otimes\AA_{2x+2}, \\\mbox{hence}\qquad r(2x+1)r(2x+2)&=&d(2x+1)d(2x+2).\nonumber \end{eqnarray} These relations are summarized pictorially in Fig.~\ref{fig:algebradims}. They give us the the first two equalities in \begin{equation}\label{dimtransfer} \frac{r(2x)}{d(2x)}=\frac{d(2x+1)}{r(2x+1)}=\frac{r(2x+2)}{d(2x+2)} \equiv {\mathop{\rm ind}\nolimits}\,\,\alpha.\nonumber \end{equation} In other words, this quantity is constant along the chain, and hence we are entitled to define it as the index ${\mathop{\rm ind}\nolimits}\, \alpha$. The even/odd asymmetry only comes from the construction, by which the even ${\mathcal R}}\def\HH{{\mathcal H}_{2x}$ describe a flow to the right (increasing $x$), and the odd ${\mathcal R}}\def\HH{{\mathcal H}_{2x+1}$ are associated with a flow to the left. By shifting the entire construction, we could switch the even/odd distinction, and define, for any $\AA_x$, both the ascending and the descending ${\mathcal R}}\def\HH{{\mathcal H}_x$. In any case, for the shift $\sigma_d$ of a $d$-dimensional chain we get $d(y)\equiv d$, $r(2x)=d^2$, and $r(2x-1)=1$, and hence ${\mathop{\rm ind}\nolimits}\,\sigma_d=d$, as announced in Eq.~(\ref{shiftindA}). It is part of the local computability property that we have a lot of freedom in choosing the cell structure for which we want to evaluate the index. Since one typically wants to use this freedom to simplify the computation, we will now summarize the constraints. It is clear that there are three subalgebras involved in the computation, playing the r\^ole of, say the above $\AA_0,\AA_1,\AA_2$ for determining ${\mathcal R}}\def\HH{{\mathcal H}_1$. Let us call these $\AA_L,\AA_M,\AA_R$ to emphasize that these algebras need not be part of the original cell structure, and we are free to choose them within certain limits. Let us start by fixing some algebra $\AA_M\cong{\mathcal M}_d$, a full matrix algebra contained in some local algebra, whose crucial property is to split the system: we must have an isomorphism of the total algebra with $\AA_{<M}\otimes\AA_M\otimes\AA_{>M}$, where the outer factors contain suitable infinite half chain algebras, and such that $$[\alpha(\AA_{<M}),\AA_{>M}]=[\alpha(\AA_{>M}),\AA_{<M}]=\{0\}.$$ Clearly, this imposes a a lower bound on the size of $\AA_M$ in terms of the interaction length of the automorphism. Now we choose finite dimensional matrix subalgebras $\AA_R\subset\AA_{>M}$ and $\AA_L\subset\AA_{<M}$ such that $\alpha(\AA_M)\subset\AA_L\otimes\AA_M\otimes\AA_R$. These three can be taken as part of a nearest neighbor cell structure, so that the above arguments give \begin{equation}\label{defIndA} \left.\begin{array}{rcl} \AA_M&\cong&{\mathcal M}_d\\ \Spp(\alpha(\AA_L\otimes\AA_M),\AA_M\otimes\AA_R)&\cong&{\mathcal M}_r \end{array}\right\rbrace \quad\Rightarrow {\mathop{\rm ind}\nolimits}\,\alpha=\frac dr \end{equation} Note that there is no harm in choosing $\AA_R$ larger than necessary: the support algebra, being the minimal algebra needed to build the tensor product, will simply not change. By a similar argument, we can choose $\AA_L$ too large without changing this support algebra. \subsection{Fundamental properties of the index for cellular automata} \begin{thm}\label{thmIndA}\ \begin{enumerate} \item ${\mathop{\rm ind}\nolimits}\,\alpha$ is a positive rational for every $\alpha$. When the automaton is regrouped in nearest neighbor form, both the numerator and the denominator of ${\mathop{\rm ind}\nolimits}\,\alpha$ in canceled form divide every cell dimension. \item ${\mathop{\rm ind}\nolimits}\,\alpha$ is locally computable, and uniquely characterizes the equivalence classes for the relation $\sim$ from Sect.~\ref{sec:Glci}. It can hence be identified with the abstract index defined there. \item ${\mathop{\rm ind}\nolimits}\,(\alpha\otimes\alpha')={\mathop{\rm ind}\nolimits}\,(\alpha){\mathop{\rm ind}\nolimits}\,(\alpha')$ and, when $\alpha$ and $\alpha'$ are defined on the same cell structure, ${\mathop{\rm ind}\nolimits}\,(\alpha\alpha')={\mathop{\rm ind}\nolimits}\,(\alpha){\mathop{\rm ind}\nolimits}\,(\alpha')$.\\ If, for some $y$, $\alpha(\AA((-\infty,y]))\subset\AA((-\infty,y]))$, then ${\mathop{\rm ind}\nolimits}\,\alpha\in\Nl$. \\ Moreover, for the shift of $d$-dimensional cells: ${\mathop{\rm ind}\nolimits}\, \sigma_d=d$. \item An automaton $\alpha$ has index 1 if and only if it can be implemented locally. In this case it can be written as a product of just two partitioned unitary automorphisms. If $\alpha$ is partitioned in nearest neighbor form, the partitioned automorphisms can be taken to couple pairs of nearest neighbors only. \item Two automata $\alpha_0,\alpha_1$ on the same cell structure have the same index if and only if they can be deformed to each other, i.e., there is a strongly continuous path $[0,1]\ni t\mapsto \alpha_t$ of automorphisms, all with the same neighborhoods, and with the specified boundary values. \end{enumerate} \end{thm} \proof (1,3)\ ${\mathop{\rm ind}\nolimits}\,\alpha\in{\mathbb Q}}\def\Tw{{\mathbb T}_+$ follows immediately from the construction in Sect.~\ref{sec:Defindalpha}, particularly Eq.~(\ref{dimtransfer}). Let ${\mathop{\rm ind}\nolimits}\,\alpha=\frac pq$ be the fraction in canceled form. Then, from this equation $p=nr(2x)$ and $q=nd(2x)$, where $n$ is the canceled factor. Hence $q$ divides $d(2x)$ and from the second fraction in (\ref{dimtransfer}) we find that $p$ divides $d(2x+1)$. By shifting the construction by one cell, we find the remaining divisibility statements. From Eq.~(\ref{dimtransfer}) we also get the product formulas 3. Suppose that $\alpha$ maps some left half chain in to itself. Then we choose a cell partition so that $y=2x+1$ in the setting of (\ref{RR2x}). Then ${\mathcal R}}\def\HH{{\mathcal H}_{2x+1}\subset\AA_{2x+1}$ and since these are full matrix algebras with the same unit, the quotient ${\mathop{\rm ind}\nolimits}\,\alpha=d_{2x+1}/r_{2x+1}$ in (\ref{dimtransfer}) is integer. The value for the shift was verified as an example after (\ref{dimtransfer}). (2,4,5) From Eq.~(\ref{dimtransfer}) local computability is obvious. From the general discussion in Sect.~\ref{sec:Glci} we also get that locally implementable $\alpha$ have ${\mathop{\rm ind}\nolimits}\,\alpha=1$. The hard part, which is needed to identify the abstract index with the concrete formula is the converse. For this the crucial step is the following claim: {\em Let $\alpha$ and $\alpha'$ be nearest neighbor cellular automata on the same cell structure and with the same index. Then there are unitaries $V_x\in\AA_x\otimes\AA_{x+1}$ such that the two locally implemented automorphisms \begin{eqnarray} \beta(A)&=&(\prod_xV_{2x-1})^A(\prod_xV_{2x-1}) \nonumber\\ \gamma(A)&=&(\prod_xV_{2x})^A(\prod_xV_{2x}) \nonumber \end{eqnarray} satisfy: $\alpha'\gamma=\beta\alpha$}. Before proving this claim, let us see how it implies the statements in the Theorem. By the general theory of Sect.~\ref{sec:Glci} locally implementable automorphisms $\beta,\gamma$ are $\sim$-equivalent to the identity, and $\alpha\sim\beta\alpha=\alpha'\gamma\sim\alpha'$. Hence equality of the indices as defined by (\ref{defIndA}) implies crossover equivalence, and hence the equality of all locally computable invariants. This proves item 2. The converse in item 4 follows by taking $\alpha'={\rm id}$, giving the local implementation $\alpha=\beta^{-1}\gamma$ of any index 1 automorphism $\alpha$. Finally, it is clear for item 5 that we can connect $\alpha$ and $\alpha'$ with the same index by the required continuous path: we just need to contract each unitary $V_x$ in $\beta,\gamma$ to the identity, to obtain a path $\alpha_t=\beta_t\alpha\gamma_t^{-1}$ with $\alpha_0=\alpha$ and $\alpha_1=\alpha'$. This path will not be continuous in the norm on automorphisms, i.e., we cannot make $\norm{\alpha_t-\alpha_s}$ small, since this would already fail for one-site operations $\alpha_t(A)=\Bigl(U_t^{\otimes\infty}\Bigr)^AU_t^{\otimes\infty}$ with $t\mapsto U_t$ norm continuous. However, for any finitely localized observable $A$, $t\mapsto \alpha_t(A)$ will be continuous in norm, which is the claim of strong continuity made in the Theorem. We remark that an important part of the proof of item 5 is missing at this point: We did not exclude the possibility that there are continuous paths linking automorphisms of different index. This will be achieved by Prop.~\ref{davidsformula}, an expression for the index which is manifestly continuous with respect to strongly continuous deformations. Now to prove the claim, let $\alpha$ and $\alpha'$ have the same cell structure and the same index. Then we carry out the construction of Sect.~\ref{sec:Defindalpha} for both automorphisms, resulting in some intermediate algebras ${\mathcal R}}\def\HH{{\mathcal H}_x$ and ${\mathcal R}}\def\HH{{\mathcal H}_x'$. Since the indices coincide, formula (\ref{dimtransfer}) demands that these are full matrix algebras of the same dimensions. For example, $$ {\mathcal R}}\def\HH{{\mathcal H}_{2x-1}\otimes{\mathcal R}}\def\HH{{\mathcal H}_{2x}=\AA_{2x-1}\otimes\AA_{2x}={\mathcal R}}\def\HH{{\mathcal H}_{2x-1}'\otimes{\mathcal R}}\def\HH{{\mathcal H}_{2x}'.$$ Clearly, there is a unitary operator $V_{2x-1}\in\AA_{2x-1}\otimes\AA_{2x}$ so that $V_{2x-1}^{\mathcal R}}\def\HH{{\mathcal H}_{y}V_{2x-1}={\mathcal R}}\def\HH{{\mathcal H}'_{y}$ for $y=2x$ and for $y=2x-1$. We can take all these unitaries together as implementing one partitioned automorphism $\beta(A)=(\prod_xV_{2x-1})^A(\prod_xV_{2x-1})$. By definition, it satisfies $\beta({\mathcal R}}\def\HH{{\mathcal H}_y)={\mathcal R}}\def\HH{{\mathcal H}'_y$ for all $y\in{\mathbb Z}}\def\Nl{{\mathbb N}$. Now consider the action of $\alpha$ and $\alpha'$ on $\AA_{2x}\otimes\AA_{2x+1}$. We now get two isomorphisms \begin{eqnarray}\nonumber \alpha':\AA_{2x}\otimes\AA_{2x+1}&\to&{\mathcal R}}\def\HH{{\mathcal H}'_{2x}\otimes{\mathcal R}}\def\HH{{\mathcal H}'_{2x+1} \quad\mbox{and}\\ \beta\alpha:\AA_{2x}\otimes\AA_{2x+1}&\to&{\mathcal R}}\def\HH{{\mathcal H}_{2x}\otimes{\mathcal R}}\def\HH{{\mathcal H}_{2x+1} \to{\mathcal R}}\def\HH{{\mathcal H}'_{2x}\otimes{\mathcal R}}\def\HH{{\mathcal H}'_{2x+1}. \nonumber \end{eqnarray} Hence $(\alpha')^{-1}\beta\alpha$ restricts to an automorphism of $\AA_{2x}\otimes\AA_{2x+1}$, and can therefore be implemented by a unitary $V_{2x}\in\AA_{2x}\otimes\AA_{2x+1}$. These unitaries together implement $\gamma$, and we get the desired equation $\alpha'\gamma=\beta\alpha$. \qed \subsection{Index for classical reversible automata} \label{sec:CCA} In this section, we will review a common notion of index for reversible classical cellular automata, and show that it coincides with our definition. In the context of this paper, a reversible classical cellular automaton can be defined as a particular case of a quantum cellular automaton. In each cell $\AA_x$ we single out a maximal abelian subalgebra ${\mathcal D}_x$. With respect to a suitable choice of basis, ${\mathcal D}_x$ is then the set of diagonal matrices. As a finite dimensional abelian algebra, we can regard ${\mathcal D}_x$ as the set of complex valued functions on a finite set ${\mathbb A}_x$, called the {\it alphabet} of the cell, which at the same time serves as the set of basis labels for the orthonormal basis in which ${\mathcal D}_x$ is diagonal. The global C-algebra of the classical system is then the infinite tensor product ${\mathcal D}({\mathbb Z}}\def\Nl{{\mathbb N})=\bigotimes_{x=-\infty}^\infty{\mathcal D}_x$. It is canonically isomorphic to the algebra of continuous functions on the compact cartesian product space ${\mathbb A}_{\mathbb Z}}\def\Nl{{\mathbb N}=\mathop\bigtimessym_{x=-\infty}^\infty{\mathbb A}_x$, also known as the space of infinite configurations. We use lower case letters such as $c$ for such configurations, and denote by $c(x)\in{\mathbb A}_x$ the configuration of the cell at $x$. Now let $\alpha$ be a QCA with the property that $\alpha({\mathcal D})\subset{\mathcal D}$. Then the restriction of $\alpha$ to ${\mathcal D}$ is an automorphism of ${\mathcal D}$, which must be of the form $(\alpha f)(c)=f(\Phi(c))$, where $\Phi$ is a homeomorphism on configurations. The causality conditions on $\alpha$ are readily expressed in terms of $\Phi$, and, together with analogous arguments for the inverses show that $\Phi$ is a reversible classical cellular automaton in the usual sense, apart from the requirement of translation invariance. There are some subtle points to note about the correspondence $\alpha\to\Phi$: \begin{itemize} \item Suppose that in the above argument we start from a general, not necessarily strictly causal automorphism $\alpha$ of the quasi-local algebra $\AA({\mathbb Z}}\def\Nl{{\mathbb N})$. We still get a continuous $\Phi$ on the compact space ${\mathbb A}_{\mathbb Z}}\def\Nl{{\mathbb N}$. By the definition of the product topology this means that the local configurations $\Phi(c)_x$ after the time step depend on only finitely many $c(y)$. In the translation invariant case this means that $\Phi$ is a cellular automaton with finite neighborhood. In fact, this argument is used to establish that the inverse of a reversibly cellular automaton also has a finite neighborhood. This is a rather surprising sharpening of the causality condition. However, we are appealing here to a highly non-constructive compactness argument, which gives no control on the size of the neighborhoods, or (barring translation invariance) on the uniformity of the neighborhoods. For example, we can apply it to a cellular automaton $\alpha$ on a 2D lattice, whose quasi-local C-algebra is isomorphic to that of a 1D automaton. Hence the condition of $\alpha$ being an automorphism is not strong enough to give a 1D automaton in the sense defined above. \item The mapping is onto, i.e., every classical reversible cellular automaton can be ``quantized''. The argument is very simple for finite lattices, e.g., a regular lattice with periodic boundary conditions: one labels the basis of a Hilbert space by the classical configurations. Then the classical automaton $\Phi$ is a permutation of the basis vectors, which can be interpreted as a unitary operator via $U_\Phi\ket c=\ket{\Phi(c)}$. Then for all observables we set $\alpha(A)=U_\Phi^AU_\Phi$. One needs to check that this transformation is causal in the quantum sense \cite{qca}, in particular that off-diagonal local operators that are finitely localized (i.e. localized on a finite number of cells) keep this property under the action of $\alpha$. Indeed one gets a bound on the quantum neighborhoods, which involves both the neighborhoods of $\Phi$ and the neighborhoods of $\Phi^{-1}$. The same computation provides a formula for $\alpha(A)$, for $A$ finitely localized, in terms of the classical rule, and this can be used to define $\alpha$ also for infinite lattices. We will not, however, make this explicit here. \item The mapping $\alpha\to\Phi$ is not injective. Indeed an ambiguity is inherent in the construction just described: we can choose different bases with the same diagonal operators $\kettbra a$ by choosing a phase for each basis vector. This amounts to changing $\alpha$ by an on-site unitary, which is certainly irrelevant for index purposes. But we can consider this more generally: suppose that two cellular automata $\alpha,\beta$ restrict to the same automorphism on the diagonal algebra ${\mathcal D}$. Then $\alpha\beta^{-1}$ leaves ${\mathcal D}$ point-wise fixed. In a finite lattice, so that $\alpha$ is unitarily implemented, the implementing unitary hence commutes with all elements of the maximally abelian algebra ${\mathcal D}$, hence must itself be diagonal. It is suggestive that this also holds in a localized form on the infinite lattice, so $\alpha\beta^{-1}$ would be a product of commuting unitaries and hence have trivial index. The following result builds on this intuition. \end{itemize} \begin{prop}\label{classicalfactor}% Suppose that $\alpha$ and $\beta$ be quantum cellular automata taking the diagonal algebra ${\mathcal D}$ into itself, with the same restriction to ${\mathcal D}$. Then ${\mathop{\rm ind}\nolimits}\,\alpha={\mathop{\rm ind}\nolimits}\,\beta$. \end{prop} Before coming to the proof of this proposition we single out two arguments of independent interest, each of which can be used to draw the main conclusion, without discussing in detail the structure of local phase factors. The first criterion uses the absence of propagation. The second uses the global transpose map $\Theta:\AA({\mathbb Z}}\def\Nl{{\mathbb N})\to{\mathbb Z}}\def\Nl{{\mathbb N}$. It is defined as the matrix transpose on each local algebra, in a basis in which ${\mathcal D}$ is diagonal. Since transposition is isometric, and consistent with the embeddings $A\mapsto A\otimes{\openone}$ it extends to the whole algebra. $\Theta$ is a linear anti-homomorphism (meaning $\Theta(AB)=\Theta(B)\Theta(A)$), and, for every automorphism $\alpha$, $\Theta\alpha\Theta$ is again an automorphism. \begin{lem} \begin{enumerate} \item Let $\alpha$ be a nearest neighbor cellular automaton such that, for some finite interval $[z_-,z_+]$ we have $\alpha^n\bigl(\AA([0,1])\bigr)\subset\AA([z_-,z_+])$ for all $n\in{\mathbb Z}}\def\Nl{{\mathbb N}$. Then ${\mathop{\rm ind}\nolimits}\,\alpha=1$. \item For any cellular automaton $\alpha$: ${\mathop{\rm ind}\nolimits}\,(\Theta\alpha\Theta)={\mathop{\rm ind}\nolimits}\,\alpha$. \end{enumerate} \end{lem} \proof 1. The index ${\mathop{\rm ind}\nolimits}\,\alpha^n$ can be expressed as a ratio of of subcell dimensions of $\AA([z_-,z_+])$, hence is uniformly bounded in $n$. But since ${\mathop{\rm ind}\nolimits}\,\alpha^n=({\mathop{\rm ind}\nolimits}\,\alpha)^n$ this implies ${\mathop{\rm ind}\nolimits}\,\alpha\leq1$. With the same argument for the inverse we get ${\mathop{\rm ind}\nolimits}\,\alpha\geq1$. 2. By assumption, the global transposition is made with respect to product basis, so that for a tensor product ${\mathcal B}={\mathcal B}_1\otimes{\mathcal B}_2$ of cells we get $\Theta_{\mathcal B}=\Theta_{{\mathcal B}_1}\otimes\Theta_{{\mathcal B}_2}$. We will drop the indices on $\Theta$ in the sequel. Then it is clear from the definition (Lemma~\ref{lem:spp}) that the support algebra construction behaves naturally under global transposition, i.e., we have $\Spp(\Theta\AA,\Theta{\mathcal B}_1)=\Theta\Spp(\AA,{\mathcal B}_1)$. Moreover, when ${\mathcal B}_1$ is a tensor product of cells we get $\Theta{\mathcal B}_1={\mathcal B}_1$. Hence in (\ref{RR2x}) we find for the automorphism $\widetilde\alpha=\Theta\alpha\Theta$: \begin{eqnarray} \widetilde{\mathcal R}}\def\HH{{\mathcal H}_{2x} &=& \Spp\Bigl(\Theta\alpha\Theta\bigl(\AA_{2x}\otimes\AA_{2x+1}\bigr),\ \bigl(\AA_{2x-1}\otimes\AA_{2x}\bigr)\Bigr) \nonumber\\ &=& \Spp\Bigl(\Theta\alpha\bigl(\AA_{2x}\otimes\AA_{2x+1}\bigr),\ \Theta\bigl(\AA_{2x-1}\otimes\AA_{2x}\bigr)\Bigr) \nonumber\\ &=& \Theta\Spp\Bigl(\alpha\bigl(\AA_{2x}\otimes\AA_{2x+1}\bigr),\ \bigl(\AA_{2x-1}\otimes\AA_{2x}\bigr)\Bigr)=\Theta{\mathcal R}}\def\HH{{\mathcal H}_{2x}. \nonumber \end{eqnarray} Since this has the same dimension as ${\mathcal R}}\def\HH{{\mathcal H}_{2x}$, we find from (\ref{dimtransfer}) that ${\mathop{\rm ind}\nolimits}\,(\Theta\alpha\Theta)={\mathop{\rm ind}\nolimits}\,\alpha$. \qed \proof[of Prop.~\ref{classicalfactor}] Due to the multiplication formula, we only need to consider the case that $\alpha$ is equal to the identity ($=\beta$) on ${\mathcal D}$. Consider any operator $A_x\in\AA_x$ in a single cell, and let $D_y\in{\mathcal D}_y$ be a diagonal element in another cell. Then $$\alpha(A_x)D_y=\alpha(A_x)\alpha(D_y)=\alpha(A_xD_y)=\alpha(D_yA_xD_y)=D_y\alpha(A_x).$$ Hence the finitely localized element $\alpha(A_x)$ commutes with all diagonal operators on the neighboring sites, and $\alpha(A_x)\in\AA_x\otimes\bigotimes_{y\neq x}{\mathcal D}_y$. This algebra is best seen as a direct sum of copies of $\AA_x$, labeled by configurations $c=\{c(y)\}$ with $c(y)\in{\mathbb A}_y$ of all cells $y\neq x$ in the localization region of $\alpha(\AA_x)$. A homomorphism of $\AA_x$ into this algebra splits into one homomorphism into each summand, which in turn is given by a unitary $U_x(c)$. Hence we can summarize the action of $\alpha$ on $\AA_x$ as \begin{equation} \alpha(A_x)=\sum_cU_x(c)^A_xU_x(c)\otimes P(c), \end{equation} where $P_c$ is the minimal projection of the diagonal algebra corresponding to $c$. We also know that diagonal elements of $\AA_x$ are fixed, so $U_x(c)$ is itself diagonal, say $U_x(c)\ket a=u(a,c)\ket a$. This leads to \begin{equation}\label{localphase} \alpha\bigl((\ketbra ab)_x\bigr)=\sum_c\frac{u(b,c)}{u(a,c)}\ (\ketbra ab)_x\otimes P(c). \end{equation} The commutation of $\alpha(\AA_x)$ and $\alpha(\AA_y)$ for $x\neq y$ introduces further conditions on the phase functions $u$. But rather than analyzing these in detail, we use the Lemma to conclude directly from Eq.~(\ref{localphase}) that ${\mathop{\rm ind}\nolimits}\,\alpha=1$. To this end, note that by applying the homomorphism $\alpha$ to (\ref{localphase}) and using $\alpha(P(c))=P(c)$, we get a corresponding formula for the iterate of $\alpha$: \begin{equation}\label{localphasen} \alpha^n\bigl((\ketbra ab)_x\bigr) =\sum_c\left(\frac{u(b,c)}{u(a,c)}\right)^n\ (\ketbra ab)_x\otimes P(c), \end{equation} for any $n\in{\mathbb Z}}\def\Nl{{\mathbb N}$. Clearly, the localization region of this operator does not increase with $n$, so by the first part of the Lemma we get ${\mathop{\rm ind}\nolimits}\,\alpha=1$. Alternatively, we can apply $\Theta$ to the equation, using $\Theta(P(c)=P(c)$. This reverses each of the ketbra operators, so $\Theta\alpha\Theta=\alpha^{-1}$. Hence ${\mathop{\rm ind}\nolimits}\,\alpha=1$ also follows with the second part of the Lemma. \qed An index for classical reversible cellular automata has been defined albeit only in the translationally invariant case. According to G. A. Hedlund (\cite{Hedlund69}, section~14), the definition is due to L.~R.~Welch, so we will call it the Welch index $i_W$ here. For the definition itself we will follow Kari \cite{Kari_index}, where it is introduced in section~3. We will show that this coincides with the quantum index. Hence the quantum index is a possible extension to non-translationally invariant systems. It is very likely that the theory in \cite{Kari_index} can also be extended directly, but we have not gone to the trouble of checking all the details. In the translation invariant case, all cell alphabets ${\mathbb A}_x\equiv{\mathbb A}$ are the same, and a cellular automaton is a map $\phi: {\mathbb A}^{\mathbb Z}}\def\Nl{{\mathbb N}\to{\mathbb A}^{\mathbb Z}}\def\Nl{{\mathbb N}$. Let $r$ be a ``large enough'' integer, and $R_\phi^r$ the set of $4r$-tuples of the form $$\Bigl(c(0),\cdots,c(2r-1),(\phi c)(-r),\cdots,(\phi c)(r-1)\Bigr),$$ where $c$ runs over all infinite configurations. Then the Welch index of $\phi$ is defined as \begin{equation}\label{iWelsh} i_W(\phi)=\frac{\|R_\phi^r\|}{{\|{\mathbb A}\|}^{3r}}\ . \end{equation} Clearly, for the identity only $\|{\mathbb A}\|^3$ different letters occur here, so $i_W({\rm id})=1$. Similarly, for a shift we get $i_W(S)=\|{\mathbb A}\|$, and parallel application of $\phi$ and $\phi'$ to parallel chains yields $i_W(\phi\times\phi')=i_W(\phi)i_W(\phi')$. The non-trivial results about the index, and the structure theory of reversible, translationally invariant classical cellular automata is developed in \cite{Kari_index}, with key results analogous to our paper: the expression (\ref{iWelsh}) does not depend on $r$ (provided it is large enough). The product formula holds, and an automaton $\phi$ is locally implementable iff $i_W(\phi)=1$. Moreover, every such automaton can be decomposed into shifts and locally implementable ones. Since a classical ``local implementation'' implies a partitioned representation of the quantum automaton, we can put these facts together to conclude that \begin{equation}\label{iW=ind} i_W(\phi)={\mathop{\rm ind}\nolimits}\,\alpha, \end{equation} for any quantum cellular automaton which restricts on the diagonal subalgebra to a classical CA given by $\phi$. In this sense our theory is a direct generalization of Kari's work, extended by the aspects of deformation classes (which make no sense in the classical discrete setting) and local computability (which makes no sense in the translation invariant setting). \subsection{Interlude: More Analogies between Walks and Cellular Automata} The two definitions of the index, (\ref{defIndW}) for walks and (\ref{defIndA}) for cellular automata are not directly analogous. Here we would like to point out the differences, and discuss how to make the analogy between these two cases even tighter by supplying the missing analogous definitions. The definition (\ref{defIndA}) considers a part of the system split into three parts L-M-R. Based on suitable inclusions, it gives a formula for the index, which immediately makes obvious that it is always a positive rational. In contrast, the walk expression Eq.~(\ref{defIndW}) is a difference of numbers which can take arbitrary real positive values, and only one cut of the system is considered. Moreover, (\ref{defIndW}) made it very easy to prove the continuity of the index under deformations, whereas neither (\ref{defIndA}) nor the abstract considerations of Sects.~\ref{sec:Gimp} and \ref{sec:Glci} clarify continuity for the index of cellular automata. Since continuity is an important feature of our index theory, we will need an appropriate expression also for the automaton case, and the analogies laid out in this subsection are intended to motivate the form of this formula. \sbsection{Dimension based formula for walks} Let us first set up an index formula for walks in analogy with (\ref{defIndA}). The analog of the support algebra is the ``support subspace of $\KK_{12}$ in $\KK_2$'', denoted $\Spp(\KK_{12},\KK_2)$, which is defined for any subspace $\KK_{12}\subset\KK_1\oplus\KK_2$ of the orthogonal direct sum of Hilbert spaces. Namely, it is the smallest subspace ${\mathcal L}\subset\KK_2$ such that $\KK_{12}\subset\KK_1\oplus{\mathcal L}$. Then the analog of Lemma~\ref{sppcomm} holds in the sense that subspaces $\KK_{12}\subset\KK_1\oplus\KK_2$ and $\KK_{23}\subset\KK_2\oplus\KK_3$ are orthogonal iff $\Spp(\KK_{12},\KK_2)\perp\Spp(\KK_{23},\KK_2)$ are orthogonal. Now consider subspaces $\HH_L\oplus\HH_M\oplus\HH_R\subset\HH$ chosen with the localization constraints as in Sect.~\ref{sec:Defindalpha}. In particular, we require $U\HH_L\perp\HH_R$, and $U\HH_R\perp\HH_L$. Then the direct analog of (\ref{defIndA}) reads \begin{eqnarray}\label{defIndWW} {\mathop{\rm ind}\nolimits}\, U&=&\dim\Spp(U(\HH_L\oplus\HH_M),\HH_M\oplus\HH_R)-\dim\HH_M \nonumber\\ &=&{\mathop{\rm rank}\nolimits}\,(P_{MR}UP_{LM})-\dim\HH_M. \end{eqnarray} Here the second equality, in which $P_{LM}$ is the projection onto $\HH_L\oplus\HH_M$ etc., follows with $\Spp(U(\HH_L\oplus\HH_M),\HH_M\oplus\HH_R)=P_{LM}UP_{MR}\HH$. \proof[of Eq.~(\ref{defIndWW})] Consider the block matrix for $U$ with respect to the decomposition $$\HH=\HH_{-\infty}\oplus\HH_L\oplus\HH_M\oplus\HH_R\oplus\HH_{+\infty},$$ where the pieces at the ends contain the appropriate infinite half chains. Using the causality assumptions, we find that \begin{equation}\label{U-LMR} U=\left(\begin{array}{ccc\|cc} \ast&\ast&0&0&0\\ \ast&\ast&\ast&0&0\\\hline 0&\lower 4pt\hbox {\Large\bf\char42}&\lower 4pt\hbox {\Large\bf\char42}&\ast&0\\ 0&\hbox{\large\bf0}&\lower 4pt\hbox {\Large\bf\char42}&\ast&\ast\\ 0&0&0&\ast&\ast \end{array}\right)\ , \end{equation} where the asterisks stand for any possibly non-zero block. We have highlighted in boldface the block $P_{MR}UP_{LM}$ appearing in (\ref{defIndWW}), and introduced two separating lines, namely the separation $-\infty,L,M\|R,+\infty$ on the domain side (i.e., a vertical line) and the horizontal separation $-\infty,L\|M,R,+\infty$ on the range side of $U$. These separators do {\em not} cross on the diagonal, which is why we cannot simply compute the index from the highlighted block via Eq.~(\ref{defIndW}). However, this is easily amended by multiplying with a suitable shift: we can introduce a basis in each $\HH_x$, and hence in $\HH$, effectively making all underlying cell dimensions one-dimensional. In this representation we can introduce a shift operation $S$, and clearly $U'=S^{\|M\|}U$ will be a unitary with the same matrix elements as $U$ shifted vertically by $\|M\|=\dim\HH_M$. Obviously, ${\mathop{\rm ind}\nolimits}\, U'={\mathop{\rm ind}\nolimits}\, U+\|M\|$, which explains the second term in (\ref{defIndWW}), and leaves us with proving that ${\mathop{\rm ind}\nolimits}\, U'={\mathop{\rm rank}\nolimits}\,(P_{MR}UP_{LM})$. Clearly, for this task the further subdivision of the blocks is irrelevant, and we can consider a general block decomposed unitary operator $$ U=\left(\begin{array}{c\|c}U_{11}&0\\\hline U_{21}&U_{22}\end{array}\right)$$ with a finite rank upper right corner. We have to show that ${\mathop{\rm rank}\nolimits}\, U_{21}=\mathop{\rm Tr}\nolimits(U_{21}^U_{21})$. But from the unitarity equation it follows that $U_{21}$ is a partial isometry, so $U_{21}^U_{21}$ is its domain projection, whose dimension is indeed the rank of $U_{21}$. \qed \sbsection{Half neighborhoods and one-cut dimension formulas} The proof of formula (\ref{defIndWW}) was essentially by reduction to the case of ``half neighborhoods'', i.e., the case that $[x_-,x_+]=[x,x+1]$, in which no influence ever spreads to the left. Then one of the off-diagonal blocks of the unitary entering (\ref{defIndW}) vanishes, and we saw directly that the other block gives an integer contribution, which can be interpreted as a dimension. Similarly, for a half-neighborhood cellular automaton we demand $\alpha(\AA_x)\subset\AA_{x-1}\otimes\AA_{x}$, where once again we have chosen the convention to match information traveling to the right, observing the Heisenberg picture. In particular, this condition is satisfied by the shift. For such automata with we can simplify the index formula in a way quite analogous to the case of half-neighborhood walks. Indeed, setting \begin{equation}\label{halfstepAlgs} {\mathcal T}_x=\Spp(\alpha(\AA_x),\AA_x) \quad\mbox{and } {\mathcal N}}\def\KK{{\mathcal K}_x=\Spp(\alpha(\AA_x),\AA_{x-1}), \end{equation} we can employ the same arguments as in Sect.~\ref{sec:Iauto} to conclude that these commute, and must be full matrix algebras ${\mathcal T}_x\cong{\mathcal M}_{t(x)}$ and ${\mathcal N}}\def\KK{{\mathcal K}_x\cong{\mathcal M}_{n(x)}$. Then, further following the previous reasoning, $\alpha(\AA_x)={\mathcal N}}\def\KK{{\mathcal K}_{x}\otimes{\mathcal T}_x$ and $\AA_x={\mathcal T}_x{\mathcal N}}\def\KK{{\mathcal K}_{x+1}$. This yields the dimension equation \begin{equation}\label{halfstepDims} d(x)=n(x)t(x)=t(x)n(x-1). \end{equation} Hence the integers $n(x)$ do not depend on $x$. In fact, ${\mathop{\rm ind}\nolimits}\,\alpha=n(x)$. This follows readily from the observation that $$ {\mathcal R}}\def\HH{{\mathcal H}_{2x+1}= \Spp\Bigl(\alpha\bigl(\AA_{2x}\otimes\AA_{2x+1}\bigr),\ \bigl(\AA_{2x+1}\otimes\AA_{2x+2}\bigr)\Bigr) ={\mathcal T}_{2x+1}\otimes{\openone}_{2x+2}. $$ Therefore, from Eq.~(\ref{dimtransfer}) we get $${\mathop{\rm ind}\nolimits}\,\alpha=d(2x+1)/r(2x+1)=d(2x+1)/t(2x+1)=n(2x+1).$$ In fact, for any cell structure on which a shift is available, we could have used this slightly simplified setup to define the index of any $\alpha$ by first shifting and regrouping to a half-neighborhood automaton, and correcting by a factor depending on the size of the necessary shift. However, since such a shift is not available in general, there was no gain in this approach. For nearest neighbor automata the structure of support algebras using just a single cut, i.e., algebras of the form $\Spp(\alpha(\AA_L),\AA_R)$ are not sufficient to define the index. As a counterexample, consider a unitary evolution $A\mapsto U^AU$ for $U\in\AA_L\otimes\AA_R$ with $\AA_L=\AA_R={\mathcal M}_d$. Clearly, as a locally implementable operation, this has always trivial index. But the support algebra written above can be just about anything. For example, taking a ``controlled unitary'' $U=\sum_i \kettbra i\otimes U_i$, we have $\Spp(\alpha(\AA_R),\AA_L)$ as the algebra of diagonal matrices, and $\Spp(\alpha(\AA_L),\AA_R)$ generated by the $U_i^U_j$, which for $\AA_R\cong {\mathcal M}_r$ can easily be $\AA_R$. On the other hand, one can easily construct an automorphism with the same support algebras, but index $d$. The algebraic structure of support algebras across a single cut is also insufficient for us in another way: it is a discrete structure, hence does not go to any trivial value as we deform an $\alpha$ to the identity. Therefore, if only to get the continuity of the index we need to look at some continuously varying quantities. We found a formula with just these properties by looking at cellular automaton analogs of the simple walk formula (\ref{defIndW}). The following section is devoted to the proof of this formula. \subsection{One-cut quotient formula} \sbsection{Notation for normalized traces} A continuously varying quantity measuring the difference between subalgebras and going to a trivial value as they come to coincide may be some kind of angle, or overlap, between the linear subspaces. It is natural to measure such angles with respect to the only scalar product between algebra elements, which is canonically defined in our context. Indeed, let $\tau$ denote the {\em normalized trace} on the algebra $\AA$ of the entire chain. That is, on any matrix subalgebra ${\mathcal B}\subset\AA$, ${\mathcal B}\cong{\mathcal M}_d$, we define $\tau(A)=\frac1d\mathop{\rm Tr}\nolimits(A)$, where $\mathop{\rm Tr}\nolimits$ is the usual matrix trace on ${\mathcal M}_d$, which is $1$ on minimal projections. The reason for this normalization is that in contrast to the matrix trace, the value of $\tau$ does not change if we consider $A$ to be embedded as $A\otimes{\openone}$ in some larger subalgebra ${\mathcal B}\otimes{\mathcal B}_1$, and is hence a well defined state on chain algebra $\AA$. In fact, it is the unique state (normalized positive functional) on $\AA$ with the property that $\tau(AB)=\tau(BA)$. This characterization is purely algebraic, which implies that, for every automorphism $\alpha$ of $\AA$ and any $A\in\AA$, we have $\tau(\alpha(A))=\tau(A)$. We now define the scalar product between algebra elements by \begin{equation}\label{HSproduct} \braket xy=\tau(x^y). \end{equation} The completion of the algebra $\AA$ as a Hilbert space with this scalar product is called the GNS-Hilbert space $\HH_\tau$ of the tracial state $\tau$. We write $\ket x\in\HH_\tau$ for the vector obtained by embedding $x\in\AA$ in the completion. The trace of operators on $\HH_\tau$ will be denoted by $\ttr$, to avoid confusion with the matrix trace $\mathop{\rm Tr}\nolimits$ of some elements of $\AA$, which is also used later. Since $\tau$ is preserved by any automorphism $\alpha$, we can define a unitary operator $V_\alpha$ on $\HH_\tau$ with \begin{equation}\label{Valpha} V_\alpha\ket x=\ket{\alpha(x)}. \end{equation} Consider now a finite or infinite dimensional subalgebra ${\mathcal B}\subset\AA$. By $P$ we denote the orthogonal projection onto the closure of ${\mathcal B}$ in $\HH_\tau$. For finite matrix algebras ${\mathcal B}\cong{\mathcal M}_d$ the matrix units $e_{ij}\cong\ketbra ij$ clearly form a basis ${\mathcal B}$, and one readily verifies that $\{\sqrt d\,\ket{e_{ij}}\}_{i,j=1}^d$ is an orthonormal basis of this $d^2$-dimensional subspace. It is sometimes also helpful to represent the projection $P$ as an integral over unitaries. That is, for a finite dimensional subalgebra ${\mathcal B}\subset\AA$ we have \begin{equation}\label{twirl} P=d^2 \int\!\!dU\ \kettbra U, \end{equation} where the integral is over the unitary group of ${\mathcal B}$, and $dU$ denotes the normalized Haar measure. For infinite dimensional subalgebras such formulas are not available. We will only need infinite dimensional projections of this type for half chain algebras, which are the closure of an increasing net of finite dimensional subalgebras ${\mathcal B}_n$. In this case the family of projections $P_n$ associated with the approximating algebras is also increasing, and converges strongly to $P$. When ${\mathcal B}_1\subset\AA$ and ${\mathcal B}_2\subset\AA$ are commuting matrix subalgebras, the corresponding matrix units, say $e_{ij}^{(1)}$ and $e_{ab}^{(2)}$, can be taken together as a set of matrix units for ${\mathcal B}_1\otimes{\mathcal B}_2$, and we get $$ \braket{e_{ij}^{(1)}}{e_{ab}^{(2)}}=\tau({e_{ji}^{(1)}}{e_{ab}^{(2)}}) =\frac1{d_1d_2}\delta_{ij}\delta_{ab}.$$ Therefore we get \begin{equation}\label{overlap1} P_1P_2=\kettbra{\openone}. \end{equation} This equation also holds for infinite pieces of the chain, e.g., a right and a left half chain localized on disjoint subsets of ${\mathbb Z}}\def\Nl{{\mathbb N}$. This readily seen by approximating each half chain by finite matrix algebras and using the strong convergence of projections. Note that (\ref{overlap1}) also implies that $P_1$ and $P_2$ commute, and the projections $P_i-\kettbra{\openone}$ with the intersection removed are orthogonal. \sbsection{Overlap of algebras} Of course, if two algebras do not commute, which requires that the localization regions of ${\mathcal B}_1$ and ${\mathcal B}_2$ overlap, the geometric position of the subspaces $P_i\HH_\tau$ is not so simple. Even if the algebras have trivial intersection ${\mathcal B}_1\cap{\mathcal B}_2=\Cx{\openone}$, so that $(P_1\HH_\tau)\cap(P_2\HH_\tau)=\Cx\ket{\openone}$ the vectors in the remainder can now have angles different from $\pi/2$, and may even approximate each other. This leads to the following definition of a quantitative notion of the overlap of two algebras, which will be the basis of the index formula we develop in this section. We state it together with a few of its basic properties. A matrix algebra here always means a subalgebra, which is isomorphic to ${\mathcal M}_d$ for some $d<\infty$ and contains the identity of $\AA$. \begin{lem}\label{overlemma} For any to subalgebras ${\mathcal B}_1,{\mathcal B}_2\subset\AA$, with corresponding orthogonal projections $P_1,P_2$ on $\HH_\tau$, we define their {\bf overlap} as \begin{equation}\label{overlap} \eta({\mathcal B}_1,{\mathcal B}_2)=\sqrt{\ttr(P_1P_2)}\ \in[0,\infty]. \end{equation} Then \begin{enumerate} \item $\eta({\mathcal B}_1,{\mathcal B}_2)=1$, for commuting matrix algebras \item $\eta({\mathcal B}_1,{\mathcal B}_2)\geq1$, for any two subalgebras (with unit). \item Let ${\mathcal B}_1,{\mathcal B}_2\subset{\mathcal B}_{12}$ and ${\mathcal B}_3,{\mathcal B}_4\subset{\mathcal B}_{34}$ are matrix subalgebras such that ${\mathcal B}_{12}$ and ${\mathcal B}_{34}$ commute. Then \begin{equation}\label{overlaptensor} \eta({\mathcal B}_1{\mathcal B}_3,{\mathcal B}_2{\mathcal B}_4)=\eta({\mathcal B}_1,{\mathcal B}_2)\eta({\mathcal B}_3,{\mathcal B}_4). \end{equation} \item Let ${\mathcal B}_1,{\mathcal B}_2,{\mathcal B}_3,{\mathcal B}_4$ be a chain of matrix algebras such that $[{\mathcal B}_i,{\mathcal B}_j]=\{0\}$, except for $i,j=2,3$. Then $\eta({{\mathcal B}_1{\mathcal B}_2,{\mathcal B}_3{\mathcal B}_4})=\eta({{\mathcal B}_2,{\mathcal B}_3})$. \item Let ${\mathcal B}_1,{\mathcal B}_2,{\mathcal B}_3$ be commuting matrix algebras with ${\mathcal B}_2\cong{\mathcal M}_d$. Then $\eta({\mathcal B}_1{\mathcal B}_2,{\mathcal B}_2{\mathcal B}_3)=d$. \item Let ${\mathcal B}_1\cong{\mathcal M}_d$ and ${\mathcal B}_2$ be finite dimensional matrix algebras, and $\alpha$ an automorphism of the ambient algebra such that $\norm{\alpha(x)-x}\leq\varepsilon\norm x$ for $x\in{\mathcal B}_1$. Then $$ \abs{\eta(\alpha({\mathcal B}_1),{\mathcal B}_2)-\eta({\mathcal B}_1,{\mathcal B}_2)}\leq \varepsilon d^2.$$ \end{enumerate} \end{lem} \proof Item 1 follows directly from Eq.~(\ref{overlap1}). For item 2, note that $P_i\geq\kettbra{\openone}$. Since we are only considering subalgebras containing the identity of the ambient algebra, the parenthetical remark is only added for emphasis. Item 3 follows by observing that the normalized trace on ${\mathcal B}_{12}{\mathcal B}_{34}\cong{\mathcal B}_{12}\otimes{\mathcal B}_{34}$ is fixed to be the product of normalized traces on the subalgebras. In this tensor product representation one readily verifies that the projection belonging to ${\mathcal B}_1{\mathcal B}_3$ is the tensor product $P_1\otimes P_3$, and similarly for $P_2,P_4$. Then the formula follows because the trace $\ttr$ also factorizes. \\ Finally item 4 follows by taking ${\mathcal B}_1{\mathcal B}_4$ and ${\mathcal B}_2{\mathcal B}_3$ as the pairing of item 2, and using item 1 to conclude that $\eta({\mathcal B}_1,{\mathcal B}_3)=1$. To prove the continuity estimate in item 6, note that overlaps are $\geq1$, so that by a gradient estimate on the square root function $$ \abs{\eta(\alpha({\mathcal B}_1),{\mathcal B}_2)-\eta({\mathcal B}_1,{\mathcal B}_2)} \leq\frac12\left\|\ttr((\widetilde P_1-P_1)P_2)\right\| \leq\frac12\norm{\widetilde P_1-P_1}_1,$$ where $\widetilde P_1,P_1,P_2$ are the projections belonging to $\alpha({\mathcal B}_1),{\mathcal B}_1,{\mathcal B}_2$, and $\norm X_1$ denotes the trace norm of $X$. We use the representation of $P_1$ in the form (\ref{twirl}), so that $$ \widetilde P_1-P_1=d^2\int\!\!dU\ \Bigl(\kettbra{\alpha(U)}-\kettbra U\Bigr).$$ We will estimate the trace norm of this expression by estimating the integrand, and using that, for any unit vectors $\phi,\psi$ in a Hilbert space, $\norm{\,\kettbra\phi-\kettbra\psi\,}_1\leq2\norm{\phi-\psi}$. Indeed, for unitaries like $U$ and $\alpha(U)$ the vectors $\ket U$ and $\ket{\alpha(U)}$ have norm 1 in $\HH_\tau$. Moreover, $\norm{\ket{\alpha(U)-U}}^2=\tau\Bigl((\alpha(U)-U)^(\alpha(U)-U)\Bigr)\leq \varepsilon^2\norm U\tau({\openone})=\varepsilon^2$. Hence $$\frac12\norm{\widetilde P_1-P_1}_1\leq \frac{2d^2}2\varepsilon\int\!\!dU=d^2\varepsilon.$$ \qed \sbsection{Index formula} With these preparations we can state the main result of this section: \begin{prop}\label{davidsformula} Let $\AA_<=\AA_{(-\infty,0]}$ and $\AA_>=\AA_{[1,\infty)}$, and $\AA_L,\AA_R$ the algebras of any two neighboring cell algebras for a nearest neighbor grouping of the chain. Then \begin{equation}\label{indDavid} {\mathop{\rm ind}\nolimits}\,(\alpha)=\frac{\eta\Bigl({\alpha(\AA_<),\AA_>}\Bigr)}{\eta\Bigl({\alpha(\AA_>),\AA_<}\Bigr)} =\frac{\eta\Bigl({\alpha(\AA_L),\AA_R}\Bigr)}{\eta\Bigl({\alpha(\AA_R),\AA_L}\Bigr)}. \end{equation} Moreover, if $t\mapsto\alpha_t$ is a strongly continuous family of cellular automata with the same cell structure and neighborhood scheme, then ${\mathop{\rm ind}\nolimits}\,(\alpha_t)$ is constant. \end{prop} \proof The square of the numerator of the second index expression is $\ttr V_\alpha P_LV_\alpha^P_R$, and we first verify that this expression is unchanged if we choose a larger $L$ and $R$, say $L'=L_1\cup L$ and $R'=R\cup R_1$. Indeed, the algebras $\alpha(\AA_{L_1}), \alpha(\AA_L),\AA_R,\AA_{R_1}$ satisfy the conditions of Lemma~\ref{overlemma}, item 4. Moreover, arguing as for formula (\ref{overlap1}) we see that not only the trace, but even the operator is independent of an enlargement. Hence taking a strong limit we obtain the corresponding expression for the infinite half-chains. From Lemma~\ref{overlemma}, item 3, it is clear that the expression thus defined satisfies the tensor product property in fact, numerator and denominator do so independently. Moreover, the formula is valid for shift automorphisms by virtue of item 5 of the Lemma. Now let $\sigma$ be a tensor product of shifts with ${\mathop{\rm ind}\nolimits}\,\sigma={\mathop{\rm ind}\nolimits}\,\alpha$, and let ${\mathop{\rm ind}\nolimits}\,'\alpha$ be the value the formula in the proposition gives for any automorphism $\alpha$. Then we have ${\mathop{\rm ind}\nolimits}\,'(\alpha\otimes\sigma^{-1})={\mathop{\rm ind}\nolimits}\,'(\alpha)({\mathop{\rm ind}\nolimits}\,\sigma)^{-1}={\mathop{\rm ind}\nolimits}\,'\alpha/({\mathop{\rm ind}\nolimits}\,\alpha)$. So it remains to prove that ${\mathop{\rm ind}\nolimits}\,'\alpha=1$ for every $\alpha$ with ${\mathop{\rm ind}\nolimits}\,\alpha=1$, which by Thm.~\ref{thmIndA} means that $\alpha$ is implemented by two layers of block unitaries. Moreover, we can forget all unitaries acting only on one side of the separation, since they do not change the algebras. Only one unitary $U_{LR}\in\AA_L\otimes\AA_R$ connecting the cells immediately adjacent to the cut remains. Hence it only remains to prove the Lemma below. For the continuity statement observe that we can make a nearest neighbor grouping jointly for all $\alpha_t$, so we can apply Lemma~\ref{overlemma}, item 6, to see that both denominator and numerator of the second fraction in (\ref{indDavid}) are continuous. Moreover, the denominator is $\geq1$, so ${\mathop{\rm ind}\nolimits}\,(\alpha_t)$ is a continuous function of $t$. On the other hand, numerator and denominator of ${\mathop{\rm ind}\nolimits}\,\alpha$ have to divide every cell dimension, so there is only a finite choice of possible values, given the neighborhood structure. Hence ${\mathop{\rm ind}\nolimits}\,(\alpha_t)$ is constant. \qed In order to state the remaining Lemma, let us consider any automorphism $\alpha$ of a tensor product $\AA_L\otimes\AA_R$ of two finite dimensional matrix algebras. We can take $\AA_x = {\mathcal B}(\HH_x)$, for some $d_x$-dimensional Hilbert spaces $\HH_x$). In that case, the automorphism $\alpha$ is implemented by conjugation with a unitary: $\alpha(x) = U x U^$, for some $U\in U(\HH_L\otimes \HH_R)$. We will express the fraction appearing in (\ref{indDavid}) in terms of $U$. In the following calculation, it turns out to be convenient to introduce orthonormal bases in the Hilbert spaces involved. Denote these bases by $\{\ket i\}\subset \HH_L$ and $\{\ket a\}\subset \HH_R$ respectively. These bases allow us to define the notion of a \emph{partial transpose} $U^\Gamma$ of $U$. We set $$ \bra{ia}(U^\Gamma)\ket{jb} = \bra{ja}U\ket{ib}. $$ While the partial transpose depends on the basis used to define it, one may easily convince oneself that the expression appearing in next lemma is independent of that choice. \begin{lem}\label{lem:contraction} When $\alpha(x)=UxU^$ is an automorphism of the tensor product $\AA_L\otimes\AA_R$ of finite dimensional matrix algebras, we have \begin{equation}\label{eqn:partialTranspose} \eta(\alpha(\AA_L),\AA_R)^2= \frac1{d_Ad_B}\mathop{\rm Tr}\nolimits\left(\bigl(U^\Gamma U^{\Gamma}\bigr)^2\right) \end{equation} Moreover, this expression is invariant under the substitution $\AA_L \leftrightarrow \AA_R$. \end{lem} \proof We introduce matrix units $e_{ij}=\ketbra ij$ as above and use that the $\sqrt d\,{e_{ij}}$ form an orthonormal basis of $\AA_L$. Thus the projection $P_L$ on $\HH_\tau$ corresponding to this algebra is $P_L=d_L\sum_{ij}\kettbra{e_{ij}}$. Of course, the transformed projection $\widetilde P_L$ for $\alpha(\AA_L)$ is obtained by substituting $\ket{\alpha(e_{ij})}$ for $\ket{e_{ij}}$. Similarly, we set $f_{ab}=\ketbra ab$ and, accordingly, $P_R=d_R\sum_{ab}\kettbra{f_{ab}}$. Then the left hand side of (\ref{eqn:partialTranspose}) becomes $$ \eta(\alpha(\AA_L),\AA_R)^2=\ttr(\widetilde P_LP_R) = d_Ld_R\sum_{ijab}\left\|\braket{f_{ab}}{\alpha(e_{ij})}\right\|^2, $$ with the scalar products \begin{eqnarray} \braket{f_{ab}}{\alpha(e_{ij})} &=& \sum_{kc}\tau(e_{kk}f_{ba} Ue_{ij}f_{cc}U^) \nonumber\\ &=& \frac1{d_Ld_R}\sum_{kc}\bra{ka}U\ketbra{ic}{jc}U^\ket{kb} \nonumber\\ &=& \frac1{d_Ld_R}\sum_{kc}\bra{ia}U^\Gamma\ketbra{kc}{kc}U^{\Gamma}\ket{jb} \nonumber\\ &=& \frac1{d_Ld_R}\bra{ia} U^\Gamma U^{\Gamma}\ket{jb}\nonumber\\ \end{eqnarray} Altogether we get Eq.~(\ref{eqn:partialTranspose}). The second claim becomes a simple corollary: we must verify that the right hand side is unchanged by the substitution $U\mapsto U^$. Since the adjoint operation commutes with the partial transpose, this amounts to a cyclic rearrangement under the trace. \qed \section{Outlook} \label{sec:out} Two directions of generalization of the theory presented here are especially suggestive and are, in fact, the subject of ongoing work in our group. We briefly comment on the prospects. \subsection{Approximate causality} In many situations in physics causality is only approximately satisfied, e.g., as a bound $\norm{U_{xy}}\leq f(\|x-y\|)$ for some function $f$ going to zero at infinity. For example, the unitary groups generated by finite range Hamiltonians would satisfy this, but are never strictly causal in the sense required here. For the key Lemma.~\ref{finrank} powerful generalizations exist \cite{Seiler}. From these it is clear that the index of approximately causal unitaries is definable, integer valued, satisfies a product formula, and is zero for the unitaries arising from Hamiltonian subgroups. The part of the theory which is less clear is related to the converses, namely the construction of strictly causal unitary walks with the same index, approximating a given approximately causal unitary. In the case of cellular automata the right notions of approximate causality are not clear. Ideally, one would only demand that $\alpha$ be an automorphism of the quasi-local algebra \cite{BraRo}. By definition, this means that the image of any localized element can be approximated in norm by localized ones. The idea of support algebras (which largely relies in its present form on picking a finite basis) is certainly too simplistic, and in any case it is unlikely that such algebras will always turn out to be finite dimensional matrix algebras. One may speculate, whether the index should take on also irrational values, but this seems unlikely, because of its dependence on the cell structure: for chains of homogeneous cell dimension $2$, the index is always a power of $2$, and not a dense set of rationals. \subsection{Higher lattice dimension} As we have shown, in lattice dimension 1 three possible classifications of walks and automata coincide: (1) the classification by locally computable invariants, (2) the classification modulo locally implementable, unitaries, and (3) the classification up to homotopy. It is very unlikely that these three coincide in higher dimension as well. In the one-dimensional theory we could allow the local systems to grow, but also the localization regions. In the higher dimensional case we will use a translation invariant metric to bound the neighborhood sizes of a ``local'' system. Generalizations can be built on coarse geometry \cite{coarse}. Locally computable invariants are probably trivial. For example, an arbitrarily large patch of the shift automorphism can be connected to the identity outside a finite enlargement of the patch. In this sense the shifts have the same invariants as the identity. To get a more interesting theory, one should take other regions for the definition of ``locally'' computable, e.g., computability on cones \cite{Buchholz}, or computability {\em outside} of any arbitrarily large region. The classification modulo local implementability is especially interesting from the physical point of view, but it might turn out to be rather wild. For example, consider some self-intersection free path in the lattice, which comes from infinity and goes to infinity. Fix walks/cellular automata, which are equal to the identity off this path and allow any of the one-dimensional systems along this path. As long as we fix the path, we can apply the one dimensional theory. For two paths, which keep a finite distance from each other, it is easy to envisage local swap-type unitaries taking one path to the other, which would bring the corresponding path-related indices under the same roof. However, if the paths move away from each other, there will be no such local operation connecting them, so systems with non-trivial indices along these paths fall into different equivalence classes modulo local implementability. However, the equivalence classes of paths modulo ``keeping a finite distance'' are a rather unmanageably large set. A useful classification cannot be expected. Incidentally, the same class of examples shows that the ``invariants computable outside any finite region'' will give a wild set. For the homotopy classification of walks there is already a theory, based on the K-theory of C-algebras and its connection with coarse geometry. Indeed, the $K_1$ group of a C-algebra just classifies the connected components of its automorphism group. This theory will most naturally apply to approximately causal walks, since strict causality cannot even be stated simply in terms of the C-algebra of the whole system. The connection with coarse geometry is being explored, for example, by Ralf Meyer and his group in G\"ottingen. Surprisingly (to us) it turns out that using Bott periodicity one can see that the $K_1$ group of approximately causal walks alternates between ${\mathbb Z}}\def\Nl{{\mathbb N}$ in odd dimension and $0$ in even dimension. Unfortunately, this theory does not apply readily to the case of cellular automata. \subsection{Higher dimensional translation invariant systems} In order to tame the wildness indicated in the previous subsection, one can restrict attention to translationally invariant systems. Immediately, the index of walks gets an obvious definition. The Fourier transform $\widehat U$ of the walk is now a Laurent polynomial in the variables $\exp(ip_k)$, where $(p_1,\ldots,p_s)$ is the momentum vector. Then $\det\widehat U$ is an invertible polynomial and we again conclude $\det\widehat U(p)=\exp(i\sum_kn_kp_k)$ for some integers $n_k$. The lattice vector $(n_1,\ldots,n_s)$ can be called the index, in direct generalization of the one-dimensional case. For cellular automata, which are products of partial shifts and local block unitaries, we can just define the index via the shift content contained in such a representation, obtaining some vector with rational components. Since it is not known, whether any QCA is of this form, this is very unsatisfactory. As a step in the right direction, one can define an index by reduction to the 1D case, without using any special decomposition: Suppose we choose vectors $a_1,\ldots,a_{n-1}$ in an $n$-dimensional lattice, and we identify sites differing by integer multiples of these vectors. Then if the $a_k$ are large enough with respect to the interaction length of the automaton, this gives a well-defined cellular automaton evolution $\alpha[a_1,\ldots,a_{n-1}]$ on the quotient lattice, which now has only one unbounded direction, so we can assign an index to it. Then we call a vector $q\in{\mathbb R}}\def\Cx{{\mathbb C}^n$ the index of $\alpha$, if \begin{equation}\label{indQuotienTI} {\mathop{\rm ind}\nolimits}\, \alpha[a_1,\ldots,a_{n-1}]=\det[q,a_1,\ldots,a_{n-1}], \end{equation} where on the right hand side the square bracket denotes the matrix with the specified column vectors. It can be verified easily that this gives the result indicated before, for any cellular automaton, which has a decomposition into partial shifts and partitioned unitaries. But in general it is not even clear that the left hand side must depend linearly on each $a_k$. \section{Acknowledgments} We gratefully acknowledge the support of the DFG (Forschergruppe 635) and the EU (projects CORNER and QUICS), as well as the Erwin Schr\"odinger Institute.	{ "redpajama_set_name": "RedPajamaArXiv" }	7,912
Former Guantánamo Detainees protest in front of US Embassy Prison watchtower facilitates monitoring inmates Four ex-prisoners from Guantánamo Bay protest outside of the US Embassy in Montevideo, Uruguay. by Zahrah Latif 4 May 2015 at 08:00 4 May 2015 at 08:00 On the 7th December last year, Uruguay welcomed six former detainees from Guantánamo Bay's prison. Four out of six of these men, who arrived under the presidency of José Mujica, camped outside of the US Embassy in Montevideo on the 24th April, in order to protest against the situation they find themselves in today. These men came to Uruguay as asylum seekers and explain that their current situation is not sustainable, therefore they are asking the US for financial help. Furthermore, they spoke of how their fellow inmates now in Germany, also find themselves in a similar situation. That is why, last Saturday, they published a statement on their website explaining that they protest in order to make their "voices heard" by the US and the rest of the world. "We do not want to be in this situation, nor is it something we have chosen, but rather we have been forced into it," they express in the statement signed by ex-inmates Abdul Din Mohammed Tawes, Abed al-Hadi Omar Farage and Ali Al Shabaan, whilst also recalling the fact that they were imprisoned at Guantánamo Bay for 13 years "without charge" until the US government "decided" to release them "and reached an agreement with Uruguay's government" to give them shelter five months ago. "They should give us the necessary means in order for us to lead a normal, dignified life as human beings", they claim in this statement, as well as explaining that it is the US who should be liable for them financially and not the South American country, due to the economic differences in both countries, but also because it was the US who locked them up all this time. "They cannot make others pay for their mistakes, they should help us and provide us with housing and financial aid", they added in another statement in which they further explain that Uruguay is the country where they would like to live and work, but in order to do this, they need their basic needs to be met. Therefore, they declare that the first thing they need and want is that they are allowed to learn Spanish. None of them can speak Spanish very well, and although two of them communicate in English and Italian, the other two can only speak Arabic. Adel Ben Mohamed explains that they will stay put in front of the embassy until they receive help. Alí Al Shabaan stresses that if it was the US who sent them to Uruguay, then they should be held accountable: "The US brought us here and they should take responsibility for us", he stated clearly in an interview. "My fellow inmates and I were imprisoned for 13 years without charge and we feel that it is their place to help us", adds another ex-prisoner. The young men relate how the SEDHU body helped them at first, but then things turned around when they did not want to sign some papers, which they felt diverged from what had been agreed with the Foreign Ministry. "Right now, we do not receive any kind of aid", they stressed, underlining the fact that they do not want to "appear ungrateful to the Uruguayan people and government". Originally published on Blasting News Spain by Patricia Gardeu. Zahrah Latif Read more on the same topic from Zahrah Latif: All set for Uruguay's municipal elections and 50 years since the Armenian genocide Blasting News recommends Nepal Earthquake- Relief operations are being hurdled Nepal Earthquake – A geological review	{ "redpajama_set_name": "RedPajamaCommonCrawl" }	333
{"url":"https:\/\/www.physicskey.com\/simple-harmonic-motion","text":"# Simple Harmonic Motion\n\nHere we discuss a simple kind of oscillatory motion also called periodic motion. One familiar example is a simple pendulum bob which undergoes periodic motion if displaced from its equilibrium position.\n\nWe will discuss a motion called simple harmonic motion abbreviated as SHM and you can see in Simple and Physical Pendulums that the oscillation of a pendulum is approximately simple harmonic for small angular displacements.\n\nAnother familiar example of the periodic motion is the oscillation of a body of a particular mass attached to one end of a spring whose other end is fixed about its equilibrium position.\n\n## Simple Harmonic Motion (SHM)\n\nA frictionless spring-mass system is shown in Figure 1 in which one end of a massless spring is fixed while the other end is attached to a box of mass $m$ and the box can oscillate about the equilibrium position when displaced.\n\nThe massless spring is an ideal spring; you'll never get a real massless spring. We neglect any non-conservative or dissipative forces which may act during the oscillation such as friction.\n\nWhen you displace the box from its equilibrium position, a restoring force is exerted on the box by the spring which tends to keep the box in its equilibrium position. Let $x$ be the displacement of the box from its equilibrium position, then the restoring force $F$ exerted by the spring on the box is\n\n$F = - kx \\tag{1} \\label{1}$\n\nwhere $k$ is the proportionality constant called force constant. The negative sign indicates that the force exerted by the spring on the box is in opposite direction of the displacement. The Eq. \\eqref{1} shows that the restoring force (the force exerted by the spring) is directly proportional to the displacement from the equilibrium position.\n\nThe oscillation in which the restoring force is directly proportional to the displacement from the equilibrium position is called simple harmonic motion (SHM). The motion of the box is horizontal and we have chosen our x-coordinate along this motion. And $a_x$ is the acceleration of the box at any instant during its motion. We can express Eq. \\eqref{1} as,\n\n${a_x} = \\frac{{{d^2}x}}{{d{t^2}}} = - \\frac{k}{m}x \\tag{2} \\label{2}$\n\nIt means the acceleration $a_x$ of the box is also directly proportional to the displacement from the equilibrium position. In Figure 1 the absolute value of the maximum displacement of the box from the equilibrium position is called amplitude $A$ of the oscillation which is always positive.\n\nConsider that a particle is moving in uniform circular motion. Now we check and see whether the simple harmonic motion is the same as the motion of the projection of the particle on a diameter of the circle or not. In Figure 2 a particle at point $p$ moves in a circle of radius $R$ whose one diameter is along the x-axis of our coordinate system.\n\nThe arrow which joins the origin and the particle on the circle pointing the particle is called phasor. The phasor shows that the angular displacement of the particle at the point $p$ is $\\theta$. If you draw a line $pp'$ perpendicular to the diameter of the circle, you'll find that the point ${p'}$ is the projection of the point $p$ on the diameter. As the particle moves in uniform circular motion its projection also moves (oscillates) along the diameter.\n\nWhen the point $p$ moves in uniform circular motion, its projection ${p'}$ moves along the diameter of the circle (the particle moves in the circle but we can say the point moves for our convenience).\n\nThe maximum displacement of $p'$ from the origin (equilibrium position) is equal to the radius of the circle and therefore the amplitude of oscillation of the point $p'$ is $A = R$. At initial time $t = 0$ the angular displacement of the particle at the point $p$ is $\\theta$ so the initial position of its projection at the point ${p'}$ is $x_i = R\\cos \\theta = A\\cos \\theta$.\n\nThe particle in the circle moves with angular velocity $\\omega$ and at any later time $t$ the angular displacement of the particle is $\\theta + \\omega t$. Note that the initial angular displacement $\\theta$ at time $t = 0$ is called the phase angle of the particle. So, the position of $p'$ on the diameter at time $t$ is,\n\n$x = A\\cos (\\theta + \\omega t) \\tag{3} \\label{3}$\n\nThe Eq. \\eqref{3} gives the position of the point $p'$ at any instant of time $t$. Notice that the value $\\theta + \\omega t$ is an angle and $\\theta$ is the phase angle. The velocity $v_x$ and the acceleration $a_x$ of the point $p'$ (which is the projection of the particle at the point $p$) at time $t$ are\n\n${v_x} = \\frac{{dx}}{{dt}} = - A\\omega \\sin (\\theta + \\omega t) \\tag{4} \\label{4}$\n\n${a_x} = \\frac{{{d^2}x}}{{d{t^2}}} - A{\\omega ^2}\\cos (\\theta + \\omega t) \\tag{5} \\label{5}$\n\nYou know from Eq. \\eqref{3} that $x = A\\cos (\\theta + \\omega t)$ and so we can write Eq. \\eqref{5} as,\n\n${a_x} = - {\\omega ^2}x \\tag{6} \\label{6}$\n\nThe Eq. \\eqref{6} shows that the acceleration of the point $p'$ is directly proportional to the displacement from its equilibrium position. Hence, the motion of the projection of the particle moving in uniform circular motion on the diameter of the circle is a simple harmonic motion. Therefore, you can compare Eq. \\eqref{2} and Eq. \\eqref{6} and obtain\n\n$\\omega = \\sqrt {\\frac{k}{m}} \\tag{7} \\label{7}$\n\nThe total time taken to complete one rotation or oscillation is called time period of the rotation or oscillation denoted by $T$ and it i always a positive quantity. In one complete rotation the particle in the circle undergoes an angular displacement of $2\\pi$ and if $T$ is the time period, the angular velocity is $\\omega = \\frac{{2\\pi }}{T}$.\n\nThe frequency of rotation or oscillation is the number of rotations or cycles or oscillations completed per unit time. In one complete rotation of a particle in a circle, the angular displacement of the particle in time period $T$ is $2\\pi$.\n\nSo the angular frequency of the rotation is $\\frac{{2\\pi }}{T}$ which is the same as the angular speed $\\omega$. Therefore, the angular frequency of oscillation of the point $p'$ is the same as the angular speed of the point $p$ and we denote both with the same letter $\\omega$. Substituting the value of $\\omega = \\frac{{2\\pi }}{T}$ in \\eqref{7} and we get\n\n$T = \\frac{{2\\pi }}{\\omega } = 2\\pi \\sqrt {\\frac{m}{k}} \\tag{8} \\label{8}$\n\nSince, one rotation or one oscillation occurs in time $T$, the frequency of oscillation is,\n\n$f = \\frac{1}{T} = \\frac{1}{{2\\pi }}\\sqrt {\\frac{k}{m}} \\tag{9} \\label{9}$\n\nThe frequency is always positive and its SI unit is hertz denoted by Hz that is, $1{\\rm{Hz}} = 1{\\rm{cycle\/s}}$. One interesting thing in Eq. \\eqref{8} is that the time period $T$ is independent of the amplitude $A$. A body which undergoes simple harmonic motion is called harmonic oscillator. For a given harmonic oscillator, the time period of oscillation is independent of the amplitude of the oscillation.\n\nAgain consider the spring-mass system as in Figure 1 where a box oscillates about its equilibrium position. If no dissipative forces act on the system, the total mechanical energy is conserved. The potential energy of the spring force at elongation $x$ from the equilibrium position is $\\frac{1}{2}k{x^2}$. And the kinetic energy at that instant is $\\frac{1}{2}mv_x^2$. So the total mechanical energy of the system is\n\n$E = \\frac{1}{2}k{x^2} + \\frac{1}{2}mv_x^2 \\tag{10} \\label{10}$\n\nNow substituting the values of $x$ from Eq. \\eqref{3} and $v_x$ from Eq. \\eqref{4} in Eq. \\eqref{10}, and solving you'll get:\n\n\\begin{align} E &= \\frac{1}{2}k{[A\\cos (\\theta + \\omega t)]^2} + \\frac{1}{2}m{[ - A\\omega \\sin (\\theta + \\omega t)]^2}\\\\ &= \\frac{1}{2}k{A^2} \\tag{11} \\label{11} \\end{align}\n\n## Vertical Simple Harmonic Motion\n\nThe harmonic oscillator in Figure 1 oscillates horizontally along x-axis of the coordinate system shown. Now we discuss about what happens when the box is hanged by the spring vertically. Again we neglect any other non-conservative forces that may act during the oscillation and suppose the mass of the spring is zero. You should know that the zero mass of the spring is an idealized concept.\n\nBut we can neglect the mass of the spring if the spring force is large enough in comparison to the mass of the spring. In Figure 3 the box is attached to the free end of the vertically hanged spring.\n\nThe weight of the box $\\vec w = m\\vec g$ stretches the spring by a distance of $l$. In Figure 3 we have chosen the positive y-axis to be vertically downwards in our coordinate system. The weight of the box is exactly balanced by the spring force at elongation $l$ that is, $w = mg = kl$. And, therefore, the equilibrium position of the box is the position at which the weight of the box is balanced by the spring force.\n\nAt an instant, suppose the box is at a distance $y$ below the equilibrium position and the total upward force exerted by the spring on the box is $- k(l + y)$. Note that the negative y-axis is in upward direction and the upward force is negative. If $a_y$ is the vertical acceleration of the box, the total force acting on the box below the equilibrium position is:\n\n\\begin{align} - k(l + y) + mg &= m{a_y}\\\\ {\\rm{or,}}\\quad m{a_y} &= - ky \\tag{12} \\label{12} \\end{align}\n\nIt means the force exerted by the spring on the harmonic oscillator is $F = m{a_y} = - ky$. If you make the positive x-axis vertically downwards and replace $y$ by $x$ in equation Eq. \\eqref{12}, you'll get $F = - kx$ which is the same as Eq. \\eqref{1}. So the box oscillating vertically in Figure 3 is a simple harmonic motion.\n\n## Angular Simple Harmonic Motion\n\nWe have a disk suspended at the centre by a string as shown in Figure 4. When the disk is slightly rotated by applying a tangential force at the rim, the disk oscillates about its equilibrium position. The rotating effect is caused by the torque $\\tau = I\\alpha$ where $I$ is the moment of inertia of the disk about the rotation axis.\n\nWhen the disk is displaced from its equilibrium position, a restoring torque is developed and it tends to restore the disk into the equilibrium position. And it is found that the restoring torque $\\tau$ is directly proportional to the angular displacement $\\theta$. Hence, we can write\n\n$\\tau = - \\kappa \\theta \\tag{13} \\label{13}$\n\nWhere $\\kappa$ is called the torsion constant. The negative sign indicates that the restoring torque acts in opposite direction of the angular displacement. The Eq. \\eqref{13} shows the angular form of simple harmonic motion called angular simple harmonic motion. Again we have;\n\n\\begin{align} I\\alpha &= - \\kappa \\theta \\\\ {\\rm{or,}}{\\kern 1pt} \\quad \\alpha &= \\frac{{{d^2}\\theta }}{{d{t^2}}} = - \\frac{k}{I}\\theta \\quad \\tag{14} \\label{14} \\end{align}\n\nComparing Eq. \\eqref{14} with Eq. \\eqref{2}, the role of $k\/m$ in Eq. \\eqref{2} is played by $\\kappa\/I$ in Eq. \\eqref{14}. The moment of inertia $I$ is the rotational analogue of mass $m$. And, therefore, you can immediately find the equation of angular frequency $\\omega$ by replacing $k\/m$ in Eq. \\eqref{7} by $\\kappa\/I$:\n\n$\\omega = \\sqrt {\\frac{\\kappa }{I}} \\tag{15} \\label{15}$\n\nNow you can easily find the time period and frequency of angular simple harmonic motion after knowing the angular frequency in Eq. \\eqref{15}.","date":"2020-08-07 04:31:15","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 2, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9570217728614807, \"perplexity\": 138.57034681796338}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-34\/segments\/1596439737152.0\/warc\/CC-MAIN-20200807025719-20200807055719-00496.warc.gz\"}"}	null	null
Фантазия и фуга до минор Op. 86 — оркестровая редакция Фантазии и фуги до минор (BWV 537) Иоганна Себастьяна Баха, созданная в 1921—1922 гг. Эдвардом Элгаром. История создания После смерти жены в 1920 году психологическое состояние и творческая активность Элгара тяжело пострадали: он практически исключил себя из музыкальной жизни и почти полностью отказался от работы над новыми произведениями — однако иногда возвращался к давним наброскам и занимался оркестровкой музыки других композиторов. Непосредственным толчком для работы над этим сочинением Баха стала встреча с Рихардом Штраусом, с которым Элгара связывали давние дружеские отношения: два композитора договорились разделить эту работу с тем, чтобы Элгар оркестровал фугу, а Штраус — фантазию. Свою часть работы Элгар завершил 25 апреля 1921 года и отправил сочинение в музыкальное издательство Novello. 27 октября в лондонском Queen's Hall Фуга до минор Баха-Элгара была впервые исполнена, дирижировал Юджин Гуссенс. В следующем году к Элгару обратился другой дирижёр, Херберт Брюэр, руководитель музыкального , с просьбой написать что-нибудь для исполнения на фестивале. Поскольку от Штрауса не было никаких вестей относительно его работы над оркестровкой фантазии, Элгар решил вернуться к этой работе сам, завершив её в июне 1922 года. Полностью Фантазия и фуга до минор в оркестровке Элгара была впервые исполнена на Фестивале трёх хоров в Глостере 7 сентября 1922 года. Как отмечал Элгар в письме органисту Айвору Аткинсу (5 июня 1921 года), он «оркестровал фугу Баха на современный лад — для довольно большого оркестра… Было много обработок Баха в изящной манере, и я хотел показать, какого величественного, великолепного и блистательного звучания он мог быть достигнуть, будь в его распоряжении наши выразительные средства» Примечания Музыкальные произведения 1922 года Произведения Эдварда Элгара Произведения для оркестра Фуги Оркестровки и инструментовки	{ "redpajama_set_name": "RedPajamaWikipedia" }	8,482
{"url":"https:\/\/brickisland.net\/DDGSpring2020\/2020\/02\/27\/assignment-2-coding-investigating-curvature-due-3-19\/","text":"# Assignment 2 (Coding): Investigating Curvature (Due 3\/22)\n\nFor the coding portion of this assignment, you will implement various expressions for discrete curvatures and surfaces normals that you will derive in the written assignment. (However, the final expressions are given below in case you want to do the coding first.) Once implemented, you will be able to visualize these geometric quantities on a mesh. For simplicity, you may assume that the mesh has no boundary.\n\nGetting Started\nPlease implement the following routines in core\/geometry.js:\n\n1. angle\n2. dihedralAngle\n3. vertexNormalAngleWeighted\n4. vertexNormalSphereInscribed\n5. vertexNormalAreaWeighted\n6. vertexNormalGaussianCurvature\n7. vertexNormalMeanCurvature\n8. angleDefect\n9. totalAngleDefect\n10. scalarMeanCurvature\n11. circumcentricDualArea\n12. principalCurvatures\n\nNotes\n\n1. The dihedral angle between the normals $N_{ijk}$ and $N_{ijl}$ of two adjacent faces $ijk$ and $ijl$ (respectively) is given by\n$$\\theta_{ij} := \\text{atan2}\\left(\\frac{e_{ij}}{\\\|e_{ij}\\\|} \\cdot \\left(N_{ijk} \\times N_{jil}\\right), N_{ijk} \\cdot N_{jil}\\right)$$\n\nwhere $e_{ij}$ is the vector from vertex $i$ to vertex $j$.\n\n2. The formulas for the angle weighted normal, sphere inscribed normal, area weighted normal, discrete Gaussian curvature normal and discrete mean curvature normal\u00a0at vertex $i$ are\n\\begin{aligned} N_i^\\phi &:= \\sum_{ijk \\in F} \\phi_i^{jk}N_{ijk}\\\\ N_i^S &:= \\sum_{ijk \\in F} \\frac{e_{ij} \\times e_{ik}} {\\\|e_{ij}\\\|^2\\\|e_{ik}\\\|^2}\\\\ N_i^A &:= \\sum_{ijk \\in F} A_{ijk}N_{ijk}\\\\ KN_i &= \\frac 12 \\sum_{ij \\in E} \\frac{\\theta_{ij}}{\\\|e_{ij}\\\|}e_{ij}\\\\ HN_i &= \\frac 12 \\sum_{ij \\in E}\\left(\\cot\\left(\\alpha_k^{ij}\\right) + \\cot\\left(\\beta_l^{ij}\\right)\\right)e_{ij} \\end{aligned}\n\nwhere $\\phi_i^{jk}$ is the interior angle between edges $e_{ij}$ and $e_{ik}$, and $A_{ijk}$ is the area of face $ijk$. Note that sums are taken only over elements (edges or faces) containing vertex $i$. Normalize the final value of all your normal vectors before returning them.\n\n3. The circumcentric dual area at vertex $i$ is given by\n$A_i := \\frac 18 \\sum_{ijk \\in F} \\\|e_{ik}\\\|^2\\cot\\left(\\alpha_j^{ki}\\right) + \\\|e_{ij}\\\|^2\\cot\\left(\\beta_k^{ij}\\right)$\n\n4. The discrete scalar Gaussian curvature (also known as angle defect) and discrete scalar mean curvature\u00a0at vertex $i$ are given by\n\\begin{aligned} K_i &:= 2\\pi \u2013 \\sum_{ijk \\in F} \\phi_i^{jk}\\\\ H_i &:= \\frac 12 \\sum_{ij \\in E} \\theta_{ij}\\\|e_{ij}\\\| \\end{aligned}\n\nNote that these quantities are discrete 2-forms, i.e., they represent the total Gaussian and mean curvature integrated over a neighborhood of a vertex. They can be converted to pointwise quantities (i.e., discrete 0-forms at vertices) by dividing them by the \u00a0circumcentric dual area of the vertex (i.e., by applying the discrete Hodge star).\n\n5. You are required to derive expressions for the principal curvatures $\\kappa_1$ and $\\kappa_2$ in exercise 4 of the written assignment.\u00a0Your implementation of principalCurvatures should return the\u00a0(pointwise) minimum and maximum principal curvature values at a vertex (in that order).\n\nSubmission Instructions\n\nPlease rename your geometry.js file to geometry.txt and put it in a single zip file called solution.zip. This file and your solution to the written exercises should be submitted together in a single email to Geometry.Collective@gmail.com with the subject line DDG20A2.\n\n## 16 thoughts on \u201cAssignment 2 (Coding): Investigating Curvature (Due 3\/22)\u201d\n\n1. kshitijgoel says:\n\nSorry, a very minor (and possibly nit-picky) request. The assignment 2 posts are uncategorized, can we put it under the assignments category?\n\n2. Liu Qiangdong says:\n\nRegarding principal curvature, it seems I can only pass the test if I trivially return [NaN, NaN]. If I used the formula derived in exercise 4 I would always fail the test. (I checked min and max before returning btw). What could be the issue here?\n\n1. Zhang Zetian says:\n\nSame here. I found that the test cases actually run the function for thousands of times and definitely the correct answers cannot all be NaN. I think there are some problems with the test cases.\n\n1. Alex says:\n\nThe test file is checking to see if your curvatures are within 10e-5 of the correct answer. But the check always evaluates to false because it seems NaN when compared to any other real number evaluates to false(instead of throwing an error). We will update the tests to account for this.\n\nIf you implement principalCurvatures correctly using the formula this should pass all the test cases. When you fail a test case your result and the correct result are printed in the developer\u2019s console. Are either of you very close(off by less than 10e-2) when not returning NaN?\n\n1. Lqq88888 says:\n\nSame problem, I added following code to test files :\n\nlet kk1 = minPrincipalCurvatures_sol[v.index];\nlet kk2 = maxPrincipalCurvatures_sol[v.index];\nlet H = scalarMeanCurvatures_sol[v.index];\nlet K = scalarGaussCurvatures_sol[v.index];\nconsole.log(kk1 * kk2 \u2013 K);\nconsole.log(kk1 + kk2 \u2013 2 * H);\n\nAnd here is the output after two loops:\n\n628.0986399694585\n101.71179525902217\n-47.06615205836211\n54.75796170084138\n\nI think there might be something wrong since all values are extracted from the solution file and K = k1k2 and H = (k1 + k2)\/2 failed.\n\n1. Lqq88888 says:\n\nGot it, I should divid them by area:)\n\n2. manugopa says:\n\nCould you explain why the area division works?\n\n3. Lqq88888 says:\n\nSure, because discrete scalar Gaussian\/Mean curvature are discrete 2-forms, you have to convert them into 0-forms by dividing the area.\n\n4. Daniel Li says:\n\nI\u2019ll clarify a bit more here. Our standard definitions of discrete Gaussian\/Mean curvature have them as discrete 2-forms. These are integrated quantities. As an example, angle defect doesn\u2019t describe the discrete Gaussian curvature technically. It describes the discrete Gaussian curvature integrated over the dual cell. Thus, we actually need to divide by the area of the dual cell to recover the discrete Gaussian curvature. If we carry this factor of area in our calculations for principal curvature, if you work through the math again, you will see that our answers get messed up because of the square root terms. Hope this helps!\n\n3. Wei Dong says:\n\nShould Corner.vertex() in corner.js be this.halfedge.next.vertex instead of this.halfedge.prev.vertex?\nSuppose we have a triangle ijk, if I understand correctly:\n\u2013 halfedge ij (opposite to k) corresponds to the corner k,\n\u2013 ij.prev.vertex is i; ij.next.vertex is k.\n\n1. Alex says:\n\nWe identify a halfedge h with the vertex at its base(ie. the one \u201cpointed to\u201d h.prev) so I think this.halfedge.prev.vertex does correctly return the corner vertex opposite halfedge h.\n\n4. hawner says:\n\nShould we be avoiding trigonometric functions like atan?\n\n1. Daniel Li says:\n\nThe notes to this assignment recommend using atan2 to compute dihedral angle. atan2 calculates one unique arctangent value as opposed to just atan. I don\u2019t really see where else you may need trig in this assignment.\n\n5. hawner says:\n\nDo the Gauss curvature normal and mean curvature normal need to be divided by K and H, respectively? I\u2019ve tried just using the summation, dividing by K or H, and dividing K or H by the circumcentric dual area before dividing, and I still can\u2019t pass the tests.\n\n1. Keenan says:\n\nI\u2019m not sure how the TAs have the test setup, but at most it would make sense to divide the mean\/Gauss curvature normals by the dual area of the vertex. For instance, the mean curvature normal is (assuming I\u2019m remembering the constant correctly\u2026)\n\n$(HN)_i := \\tfrac{1}{4} \\sum_{ij} (\\cot\\alpha_{ij} + \\cot\\beta_{ij})(f_j \u2013 f_i).$\n\nThis quantity is a dual discrete differential 2-form, i.e., it corresponds to an integral over a dual 2-cell. If $A_i$ is the dual area associated with vertex $i$, then $(HN)_i\/A_i$ is the corresponding primal 0-form, i.e., a value at a primal vertex. Dividing the mean curvature normal by the scalar mean curvature does not have (to me) any clear meaning; likewise for Gaussian curvature.","date":"2022-08-17 08:08:21","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 3, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9377018213272095, \"perplexity\": 1899.7794010992056}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-33\/segments\/1659882572870.85\/warc\/CC-MAIN-20220817062258-20220817092258-00022.warc.gz\"}"}	null	null
DELETE FROM krim_perm_attr_data_t WHERE attr_val = 'KRMS_TEST' AND perm_id = ( SELECT perm_id FROM krim_perm_t WHERE nm = 'Maintain KRMS Agenda' AND nmspc_cd = 'KR-RULE-TEST' ) ;	{ "redpajama_set_name": "RedPajamaGithub" }	4,767
Q: How does peer classloading work in Apache Ignite? I'm currently researching the following issue, which occurs in our project under high load: class org.apache.ignite.IgniteDeploymentException: Failed to deploy user message: java.nio.HeapByteBuffer[pos=0 lim=180 cap=180] at org.apache.ignite.internal.util.IgniteUtils$8.apply(IgniteUtils.java:825) at org.apache.ignite.internal.util.IgniteUtils$8.apply(IgniteUtils.java:823) at org.apache.ignite.internal.util.IgniteUtils.convertException(IgniteUtils.java:944) at org.apache.ignite.internal.IgniteMessagingImpl.send0(IgniteMessagingImpl.java:106) at org.apache.ignite.internal.IgniteMessagingImpl.send(IgniteMessagingImpl.java:82) ... Caused by: class org.apache.ignite.internal.IgniteDeploymentCheckedException: Failed to deploy user message: java.nio.HeapByteBuffer[pos=0 lim=180 cap=180] at org.apache.ignite.internal.managers.communication.GridIoManager.sendUserMessage(GridIoManager.java:1571) at org.apache.ignite.internal.IgniteMessagingImpl.send0(IgniteMessagingImpl.java:103) ... 25 more In short, the case is as follows: * Distributed cache on three nodes, all nodes run on a single workstation (in this test); Workers on each node; Messaging between workers is done using IgniteMessaging (topic has the type of String and I've tried both byte[] and ByteBuffer as a message class); Client connects to the cluster and triggers some business logic, that causes cross-node messaging and scan queries. Queries and messaging are being performed concurrently. We use peer classloading with continuous deployment mode (the problem is the same with shared mode). According to the Ignite documentation, the classes should be redeployed only if the version is changed, but it does not seem to work. I've noticed lots of similar messages in the logs: 2017-05-05 13:31:28 INFO org.apache.ignite.logger.java.JavaLogger info Removed undeployed class: GridDeployment [ts=1493980288578, depMode=CONTINUOUS, clsLdr=WebAppClassLoader=MyApp@38815daa, clsLdrId=36c3828db51-0d65e7d5-77bf-444d-9b8b-d18bde94ad13, userVer=0, loc=true, sampleClsName=java.lang.String, pendingUndeploy=false, undeployed=true, usage=0] ... 2017-05-05 13:31:29 INFO org.apache.ignite.logger.java.JavaLogger info Removed undeployed class: GridDeployment [ts=1493980289125, depMode=CONTINUOUS, clsLdr=WebAppClassLoader=MyApp@355f6680, clsLdrId=1dd3828db51-1b20df7a-a98d-45a3-8ab6-e5d229945830, userVer=0, loc=true, sampleClsName=java.lang.String, pendingUndeploy=false, undeployed=true, usage=0] ... This is when I use ByteBuffer as message type. In case of byte[], class B[ is being constantly re-deployed. I've analyzed the Ignite kernel a bit, and got a suspicion that undeploy is being triggered for all classes in a classloader, when at least one class that resides in that classloader was re-deployed in some other loader. It happens inside org.apache.ignite.spi.deployment.local.LocalDeploymentSpi#register * At first, we get a "Map of new resources added for registered class loader" using LocalDeploymentSpi#addResource. Then we "Remove resources for all class loaders except {@code ignoreClsLdr}." using LocalDeploymentSpi#removeResources. Inside this method, it looks like we add all loaders that contain the old version of the new resource to a "doomed" collection. *Finally, we iterate this collection and call onClassLoaderReleased for each element. The latter action actually causes all the classes to be undeployed (finally causing the "Removed undeployed class" messages). I don't understand this concept. Why are there multiple classloaders? Why do we undeploy the whole classloader in such cases? I'd be grateful, if someone could explain, how does peer classloading work in Ignite "under the hood". P.S. I'm looking at the sources of a fresh snapshot of Ignite 2.1.0, but the behavior is the same with the standard Ignite 1.9.0. A: This is discussed on Apache Ignite users mailing list: http://apache-ignite-users.70518.x6.nabble.com/Understanding-the-mechanics-of-peer-class-loading-td12661.html	{ "redpajama_set_name": "RedPajamaStackExchange" }	9,517
{"url":"http:\/\/physics.stackexchange.com\/tags\/stress-strain\/new","text":"# Tag Info\n\n2\n\nThe shear modulus is a property of the material not of the shape the material is cut into. You normally see shear modulus explained using a cuboidal shape something like this: But this is just because it's simpler to explain. If a non-cuboidal shape is deformed the shear stress won't be constant but will depend on the shape of the object and the way the ...\n\n1\n\nYes, we can calculate the stress in the case you have given, and that stress is still given by F\/A. Why is the stress for the case in which the wire is attached to ceiling at one end and pulled with a force F at the other also F\/A? In the ceiling case, the net force is zero just as in your case. So the force exerted by the ceiling on the wire to pull it ...\n\n2\n\nHope this helps! The force of tension actually acts throughout the length of the wire from left to right keeping it together. It 'effectively' acts however, at the center of mass\n\n1\n\nIf the wire is ideal, the only force that can cause elongation is the net external force on the wire. i.e: mv^2\/r + mg. Also however, the magnitude of net external force mv^2\/r + mg is co-incidentally equal to net tension T just to keep the net force equal to zero. You say that the centrifugal force is the only force that causes elongation. But that would ...\n\n1\n\nObviously, the Tension is what always causes the elongation.Here at the lowest point, forces (under vertical equilibrium),(from wire frame of reference which is non inertial) net upward force equals net downward force T=mg + mrw^2 . Now if we look from outside the wire(inertial frame) then there is no centrifugal force .Here for the wire to rotate, the net ...\n\n0\n\nI think you're talking about the shear modulus. (picture from the Wikipedia link above) If you take a block of some material and apply a sideways force $F$ the shear strain is defined as: $$\\gamma = \\frac{x}{l}$$ The shear stress is the applied force divided by the area over which it's applied: $$\\sigma = \\frac{F}{A}$$ And the shear modulus is ...\n\nTop 50 recent answers are included","date":"2014-10-23 01:53:34","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.5770225524902344, \"perplexity\": 346.2848128691204}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2014-42\/segments\/1413507448896.34\/warc\/CC-MAIN-20141017005728-00108-ip-10-16-133-185.ec2.internal.warc.gz\"}"}	null	null
Linkedon Autopilot will get results? Ascertain if this ebook is what you're looking for. Here we shall uncover the truth about Linkedon Autopilot. You're about to find out what could very well be the most effective ebook ever authored. You may invest from a dollar to fifty dollars when choosing these guides. Some of the fine things is that if you prefer to seek out new guides it's possible to discover some quite fine offers when you do your research to determine whether the course would be worth it and not a rip-off. The good outweighs the bad. If you know what traps in order to avoid linkedIn could possibly be the great advertising resource for Moderate and Small business specialists –. You'll be able to avoid what most of the people do- wasting time-on LinkedIn with arbitrary checking, probably sending out one or two link needs. OR you certainly can do a lot more! LinkedOn Autopilot will reveal how to supercharge every part of your LinkedIn knowledge. Possibly you've heard that LinkedIn is marketing that was only about. It's not. It has over 300 thousand people, as well as in the program you will learn how to employ techniques and instruments to discover your target customers. LinkedOn Autopilot will reveal how to push traffic that is targeted to your business. But don't be confused: this is simply not just traffic, but large- currently changing prospects. Because when you can target effectively on LinkedIn, you are able to truly increase your ROI with remarkable outcomes.	{ "redpajama_set_name": "RedPajamaC4" }	5,715
{"url":"https:\/\/science.sciencemag.org\/content\/368\/6491\/553","text":"EDITORIAL\n\n# Beat COVID-19 through innovation\n\nSee allHide authors and affiliations\n\nScience\u00a0 08 May 2020:\nVol. 368, Issue 6491, pp. 553\nDOI: 10.1126\/science.abc5792\n\nAs coronavirus disease 2019 (COVID-19) has spread, public health and economic well-being are increasingly in conflict. Governments are prioritizing public health, but the current solution\u2014social isolation\u2014is costly as commerce remains shut down. Restarting economies could rekindle the pandemic and cause even worse human suffering. Innovation can help societies escape the untenable choice between public and economic health. The world needs effective vaccines, therapies, or other solutions. But how do we achieve these solutions, and achieve them quickly?\n\nInnovation policy can accelerate advances, with high returns. In the United States, COVID-19 has reduced gross domestic product (GDP) by \u223c30%. What if additional investment in research and development (R&D) could bring forward an effective vaccine by just 1 day? If this investment costs less than the daily loss in GDP ($18 billion in the United States alone), it would pay for itself. Even large incremental funding to support R&D will be miniscule in scale compared to the$2.8 trillion the U.S. government is spending to compensate for the economic shutdown.\n\nWhat principles should guide government innovation policy to battle COVID-19? It is critical to support many independent avenues of research. Outcomes from R&D investments are uncertain. Many avenues will be dead ends, so many different paths\u2014each corresponding to an independent effort\u2014should be pursued. Consider funding 10,000 such efforts. Even if each had only a 0.1% chance of producing an advance in prevention, treatment, or infection control, the probability of at least five such advances would be 97%. By contrast, if efforts crowd into only a few prospects, the odds of collective failure can become overwhelming.\n\nThis innovative push must draw widely on talent. Research talent is plentiful, but many laboratories and teams are now shuttered and dispersed by the pandemic. Private investment gravitates toward marketable solutions, but key insights are likely to come from asking \u201cwhy\u201d questions (for example, basic research into the pathophysiology of the disease) and not simply from \u201cshovel ready\u201d drug development projects. Moreover, good ideas often come from unexpected corners. Useful solutions may be discovered outside biomedicine, including through engineering disciplines and information technology.\n\nWhat would a bold innovation policy agenda look like? In the United States, funding for R&D must be fortified, as recently called for by the Task Force on American Innovation and 17 other organizations. Also, a principal investigator already receiving public funding should be able to receive immediate support to work on COVID-19 with minimal application burden and decisions within 1 week. The National Institutes of Health (NIH) has taken some first steps with emergency procedures to supplement existing grants, but these efforts need to draw on additional labs and talent, and to accelerate review. The marginal investment through the NIH, at \\$3 billion, appears modest in size, equating to the U.S. GDP loss in just 4 hours. Globally, researchers with relevant expertise are essential workers; they should have access to their labs and additional resources to engage in the COVID-19 battle.\n\nGovernment support for private sector R&D should be delivered at great speed. A \u201cPandemic R&D Program\u201d could deploy loans that are forgivable later, based on actual investment in COVID-19\u2013related innovations, thus ensuring that financial constraints do not slow down solutions. More support could come through supplementing the R&D tax credit system, which already exists in the United States and other countries.\n\nIn June 1940, the U.S. government created the National Defense Research Committee (NDRC), composed of eminent scientists and innovators in the public and private sectors, with the mandate to achieve innovations related to the war effort. This leadership structure drove the rapid development of numerous technologies, including weapons systems but also antimalarial drugs and penicillin manufacturing. A COVID-19 Defense Research Committee could similarly be empowered to coordinate and fund solutions to the pandemic. This group would track R&D efforts, create a public clearinghouse documenting the avenues pursued, fund innovations and the scaling of successful advances, and streamline bureaucracy. The new vaccine effort, Operation Warp Speed, moves in this direction. But we also need efforts beyond vaccines.\n\nCOVID-19 presents the world with a brutal choice between economic and public health. Innovation investments are essential to avoiding that choice\u2014yet tiny in cost compared to current economic losses and other emergency programs. Even the slight acceleration of advances will bring massive benefits.\n\nView Abstract","date":"2020-06-03 20:28:02","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.17797857522964478, \"perplexity\": 5133.921439999926}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-24\/segments\/1590347435987.85\/warc\/CC-MAIN-20200603175139-20200603205139-00418.warc.gz\"}"}	null	null
Federația Algeriană de Fotbal (, )este forul ce guvernează fotbalul în Algeria. Deși exista o echipă națională neoficială încă din 1958, primul meci recunoscut de către FIFA a avut loc în ianuarie 1963, la șase luni de la obținerea independenței. Legături externe Official website Algeria - FIFA website. Algeria - CAFOnline Algeria Fotbal în Algeria	{ "redpajama_set_name": "RedPajamaWikipedia" }	1,886
gTorah \| The Dvar Torah Service > New > Sources > Rabbeinu Bachaye What Does it Mean to be the "Chosen" People? By Neli On September 6, 2012 · Add Comment The concept of chosenness is widely known, yet widely misunderstood. It has been held up by some people as a sign of superiority, and by some of our enemies as a superiority complex. As Rabbi Sacks put it, Judaism embodies a unique paradox in that it honors both the universality of the human condition and the particularity of Jewish faith. We believe that God is a universal creator who creates humanity in the image of God; yet also has a covenant with a particular chosen people. This tension between universal and particular has caused issues between the Jewish People and others, and within Judaism itself: הַיּוֹם הַזֶּה, ה אֱלֹהֶיךָ מְצַוְּךָ לַעֲשׂוֹת אֶת-הַחֻקִּים הָאֵלֶּה–וְאֶת-הַמִּשְׁפָּטִים; וְשָׁמַרְתָּ וְעָשִׂיתָ אוֹתָם, בְּכָל-לְבָבְךָ וּבְכָל-נַפְשֶׁךָ. אֶת-ה הֶאֱמַרְתָּ, הַיּוֹם: לִהְיוֹת לְךָ לֵאלֹהִים וְלָלֶכֶת בִּדְרָכָיו, וְלִשְׁמֹר חֻקָּיו וּמִצְו‍ֹתָיו וּמִשְׁפָּטָיו–וְלִשְׁמֹעַ בְּקֹלוֹ. וַה הֶאֱמִירְךָ הַיּוֹם, לִהְיוֹת לוֹ לְעַם סְגֻלָּה, כַּאֲשֶׁר, דִּבֶּר-לָךְ; וְלִשְׁמֹר, כָּל-מִצְו‍ֹתָיו. וּלְתִתְּךָ עֶלְיוֹן, עַל כָּל-הַגּוֹיִם אֲשֶׁר עָשָׂה, לִתְהִלָּה, וּלְשֵׁם וּלְתִפְאָרֶת; וְלִהְיֹתְךָ עַם-קָדֹשׁ לה אֱלֹהֶיךָ, כַּאֲשֶׁר דִּבֵּר – Today, Hashem your God commands you to perform these laws and statutes; to guard and keep them – with all your heart and soul. Regarding Hashem you have said today, that He will be a God to you; that you will walk in his ways, to keep his laws and statutes; and listen to His voice. Hashem has said of you this day, for you to be a Chosen People for Him, as He has said to you; and you will keep His mitzvos. And He will place you supreme, above all the nations He made; for praise, honor, and glory, that you would be a holy nation dedicated to Him, as was said. (26:16-19) What does it mean to be "chosen"? Rabbeinu Bachye teaches that being "chosen" is not a genetic status; it is an achievement that we each must earn. R' Shamshon Raphael Hirsch sharply notes that what the Torah literally says is that we become chosen on the day we observe the Torah and uphold its laws and ideals – הַיּוֹם: לִהְיוֹת לְךָ לֵאלֹהִים וְלָלֶכֶת בִּדְרָכָיו, וְלִשְׁמֹר חֻקָּיו וּמִצְו‍ֹתָיו וּמִשְׁפָּטָיו–וְלִשְׁמֹעַ בְּקֹלוֹ. וַה הֶאֱמִירְךָ הַיּוֹם, לִהְיוֹת לוֹ לְעַם סְגֻלָּה. Being chosen does not mean an intrinsic superiority, because there can be no intrinsic superiority when everyone is created in God's image. The only difference there can be between one human and another is the choices we make. When our actions embody ethics and morality, we become a moral beacon for others to aspire to emulate, or put differently, "a light unto the nations" – עֶלְיוֹן, עַל כָּל-הַגּוֹיִם. Improving ourselves, (and thereby, the world,) through our actions – is a consistent undercurrent of many fundamental concepts in the Torah. When a theme is recursive, it's hard to deny. Being chosen does not mean special privileges and free license; it means extra scrutiny on our obligations and responsibilities towards God and each other. The Torah assures us that perfection of the world comes through the perfection of ourselves. With a little more humility, kindness and gratitude; and a little less materialism, your world will change. We become chosen when we choose to live good lives. United We Stand, Divided We Fall By Neli On May 11, 2010 · Add Comment וַיְדַבֵּר ה' אֶל מֹשֶׁה בְּמִדְבַּר סִינַי בְּאֹהֶל מוֹעֵד בְּאֶחָד לַחֹדֶשׁ הַשֵּׁנִי בַּשָּׁנָה הַשֵּׁנִית לְצֵאתָם מֵאֶרֶץ מִצְרַיִם לֵאמֹר- Hashem spoke to Moshe in the Sinai Desert, in the Tent of Meeting on the first day of the second month, in the second year after the exodus from the land of Egypt, saying. (1:1) באחד בניסן הוקם המשכן, ובאחד באייר מנאם- Rashi explains, When He came to cause His Divine Presence to rest among them, He counted them. On the first of Nissan, the Mishkan was erected, and on the first of Iyar, He counted them. A question arises. Why weren't they counted already by the first of Nissan? Rashi mentions it had something to do with the shechina coming down to Bnei Yisroel and that had already occurred on the first of Nissan. דַּבֵּר אֶל בְּנֵי יִשְׂרָאֵל וְיִקְחוּ לִי תְּרוּמָה מֵאֵת כָּל אִישׁ אֲשֶׁר יִדְּבֶנּוּ לִבּוֹ תִּקְחוּ אֶת תְּרוּמָתִי- Speak to Bnei Yisroel, and have them take for Me an offering; from every person whose heart inspires him to generosity, you shall take My offering. (Exodus 25:2) אמרו רבותינו שלש תרומות אמורות כאן, אחת תרומת בקע לגלגלת, שנעשו מהם הא-דנים ואחת תרומת המשכן נדבת כל אחד ואחד- Rashi mentions the three times Bnei Yisroel were counted during their first year after leaving Egypt. One of them is when each member of klal Yisroel gave half a shekel for the sockets of the mishkan. This was, of course, before the first of Nissan, before the mishkan was set up. There is a deeper meaning to the counting of Am Yisroel, as explained by the Rabbeinu Bechaya and other Rishonim. The two sets of counting are to show how we are all united; we are all one unit. (In gemara, we constantly find the connection and importance of the number 600,000.) Therefore, there was great importance to each of the two sets of counting. The first one, which took place when Bnei Yisroel donated for the sockets of the mishkan, was to gather all the single members of Bnei Yisroel and weld them (no pun intended) into one unit. After it had already been established that we are all one unit, and the shechina had already come to rest on Am Yisroel, the time came to show how each person in klal Yisroel is an individual, even whilst they are part of the single unit; they still have their own unique way to express themselves! The Apter Rov, the Oihev Yisroel was once asked how it is possible to love every Jew. It is written in Masechet Gittin, 6a, that the Torah has 600,000 letters to represent Bnei Yisroel. If even one letter of the Torah is missing, it is incomplete and therefore, considered pasul (unfit for use). So too, each Jew is part of a collective whole; a part that we can not exist without. Love every Jew; all of them together complete the whole unit, while still retaining their individuality and their own purpose in this world.	{ "redpajama_set_name": "RedPajamaCommonCrawl" }	965
{"url":"https:\/\/physics.stackexchange.com\/questions\/63070\/are-gravitational-time-dilation-and-the-time-dilation-in-special-relativity-inde","text":"# Are gravitational time dilation and the time dilation in special relativity independent?\n\nThere are two kinds of time dilation:\n\n\u2022 One because the other clock moves fast relative to me (special relativity).\n\n\u2022 Another one because the other clock is in a stronger gravitational field (general relativity), or accelerating rapidly (equivalence principle).\n\nSo are these two effects are totally independent? Is it possible to derive the general relativity case from the special relativity case?\n\nLet me try and expand a bit on Ben's answer.\n\nStarting with special relativity, the key thing to understand is that all the weird stuff, and indeed the Lorentz transformations, is derived from a property called the metric. If you have two points in spacetime separated by ($\\mathrm dt,~\\mathrm dx,~\\mathrm dy,~\\mathrm dz$) then the metric tells us how to calculate the interval between them. For SR this is:\n\n$$\\mathrm ds^2 = -\\mathrm dt^2 + \\mathrm dx^2 +\\mathrm dy^2 +\\mathrm dz^2$$\n\nThe interval $\\mathrm ds$ is referred to as the line element and is an invariant, i.e., every observer no matter how fast they are moving, will calculate the same value for $\\mathrm ds$.\n\nThe equation for the line element should remind you of Pythagoras' theorem, and indeed the only difference is that the sign of $\\mathrm dt^2$ is negative not positive. It's this difference in the sign that is responsible for effects like time dilation. This is the important point to take home: this metric is all you need to calculate time dilation.\n\nNow consider general relativity, and the effect of gravity. But first let me rewrite the special relativity equation for the line element in polar co-ordinates:\n\n$$\\mathrm ds^2 = -\\mathrm dt^2 +\\mathrm dr^2 + r^2 (\\mathrm d\\theta^2 + \\sin^2\\theta~\\mathrm d\\phi^2)$$\n\nand now I'll write the equation for the line element near a black hole, i.e. the Schwarzschild metric:\n\n$$\\mathrm ds^2 = -\\left(1-\\frac{2M}{r}\\right)\\mathrm dt^2 + \\frac{\\mathrm dr^2}{\\left(1-\\frac{2M}{r}\\right)} + r^2 (\\mathrm d\\theta^2 + \\sin^2\\theta~\\mathrm d\\phi^2)$$\n\nIf you compare these two equations it should be immediately obvious that they are very similar, and indeed if you let the mass of the black hole, $M$, go to zero or if you go a long way away, so $r \\rightarrow \\infty$, then the two equations are the same.\n\nThis means the GR metric includes everything that the SR metric predicts, but it adds to it. So there isn't a distinction between the time dilation due to just velocity and the time dilation due to gravity. The GR metric is an extension of the SR metric and includes both. However let me reinforce Ben's cautions: it generally isn't useful to try and separate the time dilation due to velocity and the time dilation due to gravity.\n\nIt's not true that gravitational time dilation is based on the strength of the gravitational field. By the equivalence principle, the gravitational field equals zero for any inertial observer, and can have any other value you like for some other appropriately chosen observer. Gravitational time dilation is based on the gravitational potential.\n\nNeither kinematic nor gravitational time dilation requires general relativity. You can have a gravitational field and a gravitational potential in flat spacetime, e.g., for an observer inside an accelerating elevator. There are straightforward special-relativistic arguments that derive the gravitational time dilation from thought experiments involving accelerating elevators.\n\nNeither kinematic nor gravitational time dilation is fundamental. What's fundamental is the metric. Either effect can be calculated from the metric.\n\nGravitational time dilation can't be fundamental because the gravitational potential isn't even well defined unless the spacetime is static. For example, cosmological spacetimes aren't static.\n\nA good popular-level book that explains the fundamental status of the metric very clearly is Geroch, General Relativity from A to B.\n\nYes, you can solve with a very simple formula the equivalent speed you would need to go to have the same time dilation as caused by a gravitational field.\n\nAll you need is how many Schwarzschild radii you are from the mass (this essentially gives you how deep you are in a gravitational field). Once you have that get the square root of how ever many Schwarzschild radii and you get a number that is equivalent to how much faster light is going than object moving for time dilation.\n\nFor instance:\n\nIf an object is 9 Schwarzschild radii away from Mass it will experience the same time dilation as an object going 3 times less the speed of light.\n\nSame for 4 Schwarzschild radii and the speed of light going 2 times faster.\n\nit boils down to $$x=y^2$$\n\nTo get to this formula, first you start with the gravitational time dilation formula where:\n\n$$T_1=T\\sqrt{1-\\frac{2GM}{rc^2}}$$\n\nand rather than entering $r$ for the radius we replace $r$ with the Schwarzschild radius formula $(2GM\/c^2)x$ with an $x$ at the end representing how many Schwarzschild radii you are away from the center. This brings the formula to look like:\n\n$$T_1=T\\sqrt{1-\\frac{2GM}{\\frac{2GM}{c^2}xc^2)}}$$\n\nWhich when simplified breaks down to:\n\n$$T_1=T\\sqrt{1-\\frac{1}{x}}$$\n\nand if you make $T=1$ then you just get\n\n$$T_1=\\sqrt{1-\\frac{1}{x}}$$\n\nThis is very similar to the one in many physics books $=\\sqrt{1-r_0\/r}$, where $r_0$ is equal to the Schwarzschild radius and then $r$ equals the radius from the center. The formula above it just makes it slightly simpler due to making $r_0$ equal to 1 and $x$ equal to how many radii a point you are observing is from the center of the mass.\n\nThat is the gravitational time dilation side portion of this relationship. Now for the velocity time dilation side we use a similar methodology and start with:\n\n$$T_0=T\\sqrt{1-\\frac{v^2}{c^2}}$$\n\nNow we make $T$ equal to 1, $v$ equal to one, and $c$ to $y$ because now we are going to make $c$ a variable.\n\n$$T_0=\\sqrt{1-\\frac{1}{y^2}}$$\n\nWhat you see now \"$1\/y^2$\" is showing the velocity as a constant 1 and $y$ represents how much faster light is going than the velocity constant of 1. If the above were to show the fraction as $1\/5^2$ then this would be the same as saying an object is going at a velocity 1\/5th the velocity of light. So now if we solve the velocity and gravitational time dilation formulas so that we can see how they dilate time to come up with the same result:\n\n$$\\sqrt{1-\\frac{1}{x}}=\\sqrt{1-\\frac{1}{y^2}}$$\n\nWe can simplify this to\n\n$$x=y^2$$\n\n\u2022 More details about how you arrive at this result would be nice. \u2013\u00a0Brandon Enright Jan 4 '15 at 22:34\n\u2022 I just edited my answer to include how you get to the simple x=y^2 \u2013\u00a0Joe Jan 4 '15 at 23:21\n\nFrom an engineer: I interpreted the answer from the practical point of view of how to combine effects from velocity-related time dilation and gravity-related time dilation. They can be treated independently, and then either multiple the factors together or, since the factors are usually very close to 1, you can add (1-factors). For example, for GPS satellites, the velocity is high so the clock runs a little slower via the equation $t\/t_0 = 1\/\\sqrt{1-v^2\\over c^2}$ (about 7 microseconds per day). But the gravity is lower so the clock runs about 45 microsecs\/day faster: You need to solve $t\/t_0=1\/\\sqrt{1-2GM\\over rc^2}$ for the surface and the orbit and subtract the difference. The net result is we build clocks that would run 45 - 7 = 38 microseconds a day slow here on earth, but they work perfectly in the GPS orbit.\n\nAs to how the two factors are related, I think of it conceptually as the gravity on a planet's surface is the energy equivalent of the kinetic energy to escape earth. Kinetic energy is $1\/2 mv^2$ and gravitational potential energy of an object far from Earth is $GMm\\over r$. Set them equal and you get the escape velocity, or the value of $v^2 = {2GM\\over r}$. That is, instead of the kinetic energy causing the object's internal clock to slow down, the gravitational potential energy is causing the clock to slow down. When the energies are equal, the impact on the internal clock is the same.","date":"2020-04-08 13:34:47","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8598562479019165, \"perplexity\": 227.31103863003287}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-16\/segments\/1585371813538.73\/warc\/CC-MAIN-20200408104113-20200408134613-00192.warc.gz\"}"}	null	null
\section{Introduction} A massive three loop Feynman diagram $I(N)$ with a local operator insertion can be written in terms of multiple integrals or multiple sums, which depend on a discrete variable $N \in \mathbb{N}$ and the dimensional parameter $\varepsilon = D - 4$, where $D \in \mathbb{R}$ denotes the space-time dimension, see e.g. see~\cite{Blumlein:2010zv,Weinzierl:13}. Then one is interested in the first coefficients of its formal Laurent series w.r.t.\ $\varepsilon$ (in short $\varepsilon$-expansion) \begin{equation}\label{Equ:IExpansion} I(N)=\varepsilon^{o}I_{o}(N)+\varepsilon^{o+1}I_{o+1}(N)+\varepsilon^{o+2}I_{o+2}(N)+\dots \end{equation} with order $o\in\mathbb{Z}$. In this article we present tools to decide algorithmically if the coefficients $I_i(N)$ up to a certain order can be written in terms of indefinite nested hypergeometric sums (in short, nested hypergeometric sums) which can be defined as follows. Let $f(N)$ be an expression that evaluates at non-negative integers (from a certain point on) to elements of a field $\set K$ containing the rational numbers $\set Q$. Then $f(N)$ is called a nested hypergeometric sum expression w.r.t.\ $N$ if it is composed by elements from the rational function field $\set K(N)$, the three operations ($+,-,\cdot$), hypergeometric expressions of the form $\prod_{k=l}^Nh(k)$ with $l\in\set N$ and $h(k)$ being a rational function in $k$ and being free of $N$, and sums of the form $\sum_{k=l}^Nh(k)$ with $l\in\set N$ and with $h(k)$ being a nested hypergeometric sum expression w.r.t.\ $k$ and being free of $N$. This class of special functions covers as special cases harmonic sums~\cite{BlumVerm}, \begin{eqnarray}\label{Equ:HarmonicSumsIntro} S_{a_1,\ldots ,a_k}(N)= \sum_{N\geq i_1 \geq i_2 \geq \cdots \geq i_k \geq 1} \frac{\sign{a_1}^{i_1}}{i_1^{\abs {a_1}}}\cdots \frac{\sign{a_k}^{i_k}}{i_k^{\abs {a_k}}} \end{eqnarray} for non-negative integers $N$ and nonzero integers $a_i$ $(1 \leq i \leq k)$ and more generally, generalized harmonic sums~\cite{Moch:2001zr,Ablinger:2013cf}, cyclotomic harmonic sums~\cite{Ablinger:2011te} or nested binomial sums~\cite{BinSums,Ablinger:2014bra}.\footnote{For surveys on these quantities see e.g. \cite{REF1}.} In order to calculate the coefficients in~\eqref{Equ:IExpansion}, the summation package \texttt{Sigma} enhanced by the package \texttt{EvaluateMultiSums}~\cite{Summation,CASummation}, the integration package \texttt{MultiIntegrate}~\cite{Integration}, and the package \texttt{HarmonicSums}~\cite{HarmonicSums} have been applied successfully in many applications. However, in the course of recent calculations, these tools turned out to be not sufficient and we extended them significantly by using the integration by parts (IBP) identities~\cite{IBP}. Namely, encoding $I(N)$ by a generating function (formal power series) $$\hat{I}(x)=\sum_{N=0}^{\infty}I(N)\,x^N,$$ we can activate the powerful {\tt C++} program {\tt Reduze~2}~\cite{Reduze2} based on Laporta's algorithm \cite{Laporta:2001dd} to reduce $\hat{I}(x)$ to a linear combination of master integrals. In many calculations, see~e.g.,~\cite{Ablinger:2014uka,DiffCalculations,VLadders} these remaining integrals are now suitable for symbolic summation and integration. However, some of the master integrals are rather hard too handle or are not in the proper form for symbolic summation and integration. Here we utilize the fact that {\tt Reduze~2} can produce recursively defined coupled systems of linear differential equations in terms of these master integrals. Following the tactics in~\cite{DEQ} the main task is to extract the required information from these coupled systems and to reassemble information of the coefficients $I_i(N)$ in~\eqref{Equ:IExpansion} for further processing. In this article we are interested in computing the $I_i(N)$ in closed form. If a first-order coupled system has a specific form, one could use, e.g., the methodology described in \cite{Henn:2013pwa}. In the following we introduce a very general and efficient approach relying on decoupling algorithms~\cite{UNCOUPL,Zuercher:94,OreSys}, recurrence solvers~\cite{dAlembert,ParticularSol} and difference ring algorithms~\cite{DRTheory,Schneider:10b,DRTheoryMain}: we obtain a complete algorithm that extracts the first coefficients of the Laurent series and computes simultaneously the representation of the coefficients in terms of nested hypergeometric sum expressions, whenever this is possible. The first ideas of this new algorithm have been introduced in~\cite{NewUncouplingMethod} and the main features are worked out in~\cite{VLadders} by concrete examples coming from massive $3$-loop ladder and $V$-diagrams. In the following we will complement these achievements by precise input-output specifications and further details of the algorithms. Moreover, we will illustrate how the differential equation algorithm can be executed within the new package \texttt{SolveCoupledSystem} that relies on the packages \text{Sigma} and \texttt{OreSys}. In addition, the package \texttt{HarmonicSums} is used to gain significant speed-ups. \medskip We will use the following notations. Let $\set K$ be a computable field containing the rational numbers as sub-field (e.g., $\set K=\set Q$). In the following $\mathbb{K}[N]$ (or $\mathbb{K}[\varepsilon,N]$) denotes the ring of polynomials in the variable $N$ (or in the variables $\varepsilon$ and $N$). Moreover, $\set K(N)$ (or~$\set K(\varepsilon,N)$) denotes the field of rational functions in the variable $N$ (or in the variables $\varepsilon$ and $N$). We denote by $\mathbb{K}((\varepsilon))$ the field of formal Laurent series, i.e., elements are of the form $\sum_{k=o}^{\infty} f_k\varepsilon^k$ with $f_k\in\mathbb{K}$ and $o\in\mathbb{Z}$. Furthermore, we denote by $\mathbb{K}((\varepsilon))[[x]]$ the ring of power series whose elements are of the form $\sum_{i=0}^{\infty}f_i\,x^i$ with $f_i\in\mathbb{K}((\varepsilon))$. Furthermore, $\mathbb{K}^{\mathbb{N}}$ (or $\mathbb{K}((\varepsilon))^{\mathbb{N}}$) denotes the ring of sequences with entries form $\mathbb{K}$ (or from $\mathbb{K}((\varepsilon))$). \section{The algorithmic machinery} First, we will address the problem how one can decide algorithmically, if a sequence can be calculated by a nested hypergeometric sum expression provided that the sequence is described by a linear recurrence (linear difference equation) in terms of nested hypergeometric sum expressions (see Theorem~1). Given this technology, we can extract the first coefficients of a Laurent series expansion in terms of nested hypergeometric sum expressions provided that the Laurent series is a solution of a recurrence of certain kind (see Theorem~2). Using uncoupling algorithms, this result can be generalized further to coupled systems (see Theorem~3). Finally, we can carry over this result to coupled systems of linear differential equations (see Theorem~4). \subsection{Finding nested hypergeometric solutions of linear recurrences}\label{Subsec:RecSolver} The main engine relies on the following algorithmic result~\cite{CASummation,DRTheoryMain,dAlembert,ParticularSol}. \medskip \noindent\textbf{Theorem 1.} Suppose that a sequence $\langle I(N)\rangle_{N\geq0}\in\mathbb{K}^{\mathbb{N}}$ is a solution of the difference equation \begin{equation}\label{Equ:SimpleRec} a_0(N)I(N)+a_1(N)I(N+1)+\dots+a_d(N)I(N+d)=r(N) \end{equation} with $N\geq0$ for given rational functions $a_0(N),\dots,a_d(N)\in\mathbb{K}(N)$, not all zero, and a nested hypergeometric sum expression $r(N)$. Then one can determine an $m\in\mathbb{N}$ with the following property.\\ If one is given the values $I(N)$ for all $0\leq N\leq m$, then one can decide algorithmically if there exists a nested hypergeometric sum expression that calculates the values $I(N)$ for all $N\geq0$ (or at least from a certain point on). \smallskip \noindent\textit{Proof.} For this result we refer to Section~4.3 in~\cite{CASummation} and Section~2.4~\cite{DRTheoryMain}. It has been implemented within \texttt{Sigma} as follows. The recurrence operator is factorized as much as possible into linear factors. Then each linear factor leads to one additional linearly independent solution of the homogeneous version of the recurrence by introducing one extra indefinite summation quantifier and introducing one hypergeometric expression~\cite{dAlembert}. In this way one finds a basis of all solutions of the homogeneous recurrence that can be expressed in terms of nested hypergeometric sum expressions. If the recurrence factorizes completely, the particular solution can be obtained straightforwardly. However, if the recurrence does not fully factorize, one has to activate algorithms from~\cite{ParticularSol} in order to calculate a particular solution in terms of nested hypergeometric sum expressions or to prove that such a representation is not possible. If there is not such a solution, $I(N)$ cannot be represented by a nested hypergeometric sum expression.\\ In the process of this calculation one can determine a $\mu\in\mathbb{N}$ such that the solutions in terms of nested hypergeometric sum expressions can be evaluated and are a solution of the recurrence. Now compute the finite set $R$ of all non-negative integer roots of $a_d(N)\in\mathbb{K}[N]$. If $R=\{\}$, set $\mu'=\mu$, else set $\mu':=\max(1+\max(R),\mu)$. Thus for all $\lambda\in\mathbb{N}$ with $\lambda\geq\mu'$ we have that $a_d(\lambda)\neq0$. Then using $d$ initial values, namely $I(\mu'),\dots,I(\mu'+d-1)$, one can check if the found solutions can be combined to an expression which produces the same initial values. If this is possible, this expression agrees with $I(N)$ for all $N\geq \mu'$: since the leading coefficient of~\eqref{Equ:SimpleRec} does not evaluate to zero, there is exactly one sequence which has these $d$ initial values and which is a solution of the recurrence. Note that this construction is always successful if one computes $d$ linearly independent solutions of the input recurrence (the particular solution is then just a by-product). Otherwise, if this construction fails, it follows that $I(N)$ cannot be expressed by a nested hypergeometric sum expression (i.e., that at least one solution of the homogeneous recurrence is of different nature). Summarizing, if we can compute the first $m:=\mu'+d-1$ initial values of $I(N)$, we can execute the decision procedure described above. \smallskip \noindent\textit{Example.} Consider the sequence $I(N)$ that is determined by the linear recurrence \begin{mma}\MLabel{MMA:SimpleRec} \In rec=-2 (N+1) (N+2)^2 I[N] -(N+2) \big( -6 N^2-28 N-32\big) I[N+1]\newline \hspace{2cm}+\big(-6 N^3-50 N^2-136 N-120\big) I[N+2] -(-N-2) (N+4) (2 N+8) I[N+3] ==-\frac{4 (N+2)}{3 (N+3)};\\ \end{mma} \noindent (loaded into Mathematica) and the initial values $I(1)=5$, $I(2)=\frac{130}{27}$, $I(3)=\frac{169}{36}$. Loading in the summation package \text{Sigma} into Mathematica, one can solve the recurrence in terms of nested hypergeometric sum expressions as follows. \begin{mma} \In << Sigma.m \\ \Print \LoadP{Sigma - A summation package by Carsten Schneider \copyright\ RISC-Linz}\\ \notag \MLabel{MMA:SolveRec} \In recSol=SolveRecurrence[rec,I_{1,-3}[N],IndefiniteSummation\to False]\\ \vspace{-0.2cm} \Out \{\{0 , \frac{1}{-N-1}\}, \{0 , -\frac{\sum_{i=1}^N 1}{N+1}\}, \{0 , -\frac{\displaystyle \sum_{i=1}^N \sum_{j=1}^{i} \frac{1}{j \big( 1+j\big)}}{N+1}\}, \{1 , -\frac{\displaystyle \sum_{i=1}^N \sum_{j=1}^{i} \frac{\displaystyle \sum_{k=1}^{j} \frac{2}{3}}{j \big( 1+j\big)}\big)}{N+1}\}\}\\ \end{mma} \noindent Here the first three entries are linearly independent solutions of the homogeneous version of the recurrence and the last entry is a particular solution of the recurrence itself.\\ Within \texttt{Sigma} a strong toolbox has been developed to simplify these solutions by flattening the sums optimally and by finding denominators with minimal degrees within the setting of difference rings~\cite{Summation,CASummation}. In particular, the simplified expressions are built by sums that are algebraically independent~\cite{Schneider:10b}. These features can be activated by dropping \texttt{IndefiniteSummation$\to$False} in~\myIn{\ref{MMA:SolveRec}}. For the class of harmonic sums, generalized harmonic sums, cyclotomic harmonic sums and binomial nested sums these features are also available within the package \begin{mma} \In << HarmonicSums.m \\ \Print \LoadP{HarmonicSums by Jakob Ablinger \copyright\ RISC-Linz}\\ \notag \end{mma} \noindent For such sums the rather involved difference ring theory can be avoided, and one can calculate very efficiently the simplified representation as follows: \begin{mma}\MLabel{MMA:ReduceToBasis} \In recSol=ReduceToBasic[TransformToSSums[recSol],Dynamic\to Automatic]\\ \Out \{\{0 , \frac{1}{-N-1}\}, \{0 , -\frac{N}{N+1}\}, \{0 , \frac{1}{(N+1)^2} +\frac{\displaystyle S_1(N)}{N+1}\}, \{1 , \frac{2 \big( N^2+N-1\big)}{3 (N+1)^2} -\frac{\displaystyle 2 (N+2)}{3 (N+1)}S_1(N)\}\\ \end{mma} \smallskip \noindent\textit{Remark.} Internally, only the so-called basis-sums remain that cannot be eliminated by relations induced by the underlying quasi-shuffle algebra. For harmonic sums these ideas are worked out in~\cite{Blumlein:2003gb} and have been extended for cyclotomic sums, generalized harmonic sums and nested binomial sums~\cite{HarmonicSums,Ablinger:2013cf,Ablinger:2011te,Ablinger:2014bra}. We remark further that the basis sums produce sequences which are algebraically independent~\cite{AIHarmonicSums}. \smallskip Summarizing, the solution set of~\myOut{\ref{MMA:ReduceToBasis}} is given by the set $$\{c_1\,\tfrac{-1}{N+1}+c_2\tfrac{-N}{N+1}+c_3\Big(\tfrac{1}{(N+1)^2} +\tfrac{ S_1(N)}{N+1}\Big)+\tfrac{2( N^2+N-1)}{3 (N+1)^2} -\tfrac{2 (N+2)}{3 (N+1)}S_1(N)\| c_1,c_2,c_3\in\mathbb{K}\}$$ of nested hypergeometric sum expressions. The initial values $I(1),I(2),I(3)$ can be fulfilled with $c_1=-\frac{49}{9}, c_2=-\frac{41}{9}, c_3=-\frac{2}{3}$ which yields \begin{equation}\label{Equ:RecSolverSol} I(N)=\frac{59 N^2+120 N+49}{9 (N+1)^2} -\frac{2 (N+3) S_1({N})}{3 (N+1)}. \end{equation} Hence we have shown that $I(N)$ can be calculated for $N\geq0$ by a nested hypergeometric expression. \subsection{Finding Laurent series solutions of linear difference equations} During the calculation of a Feynman integral $I(N)$ one often obtains linear recurrences for $I(N)$ depending on a dimensional parameter $\varepsilon$ with $D=4+\varepsilon\in\mathbb{R}$. In lucky situations one finds a nested hypergeometric sum representation of $I(N)$ using the recurrence solver of Subsection~\ref{Subsec:RecSolver} with $\varepsilon\in\mathbb{K}$. However, in most cases one fails to find any solution of the given recurrence in terms of nested hypergeometric sum expressions, but one finds an $\varepsilon$-expansion whose coefficients can be represented by nested hypergeometric expressions using the following algorithmic machinery~\cite{Blumlein:2010zv}. \medskip \noindent\textbf{Theorem~2.} Suppose that the sequence $\langle I(N)\rangle_{N\geq0}\in\mathbb{K}((\varepsilon))^{\mathbb{N}}$ with~\eqref{Equ:IExpansion} is a solution of the difference equation \begin{equation}\label{Equ:RecExpansion} a_0(\varepsilon,N)I(N)+a_1(\varepsilon,N)I(N+1)+\dots+a_d(\varepsilon,N)I(N+d)=r(N) \end{equation} for explicitly given $a_0(\varepsilon,N),\dots,a_d(\varepsilon,N)\in\mathbb{K}(\varepsilon,N)$ and for a sequence $\langle r(N)\rangle_{N\geq0}\in\mathbb{K}((\varepsilon))^{\mathbb{N}}$ with \begin{equation}\label{Equ:RecRExpansionOrg} r(x)=\varepsilon^or_{o}(N)+\varepsilon^{o+1}r_{o+1}(N)+\varepsilon^{o+2}r_{o+2}(N)+\dots \end{equation} Here we assume\footnote{\label{ftn:aiProp}This assumption can be always guaranteed by multiplying an appropriate factor $\varepsilon^{s}$ with $s\in\mathbb{Z}$ on both sides of~\eqref{Equ:IExpansion}.} that the $a_i(\varepsilon,N)\|_{\varepsilon\to0}$ do not introduce poles for $0\leq i\leq d$ and that not all $a_i(0,N)$ are zero. Then for any $u\in\mathbb{Z}$ one can determine an $m\in\mathbb{N}$ with the following property.\\ If one is given the values $I_{j}(N)$ for all $o\leq j\leq u$ and $0\leq N\leq m$ and one is given for all $o\leq j\leq u$ nested hypergeometric sum expressions that calculate the values $r_{j}(N)$ for all $N\geq0$ (or at least from a certain point on), then one can decide algorithmically if for all $o\leq j\leq u$ there exist nested hypergeometric sum expressions that calculate the values $I_{j}(N)$ for all $N\geq0$ (or at least from a certain point on). \medskip \noindent\textit{Proof.} Let $u\in\mathbb{Z}$ and suppose that the $r_{o}(N),\dots,r_{u}(N)$ can be represented in terms of nested hypergeometric sum expressions. We make the Ansatz~\eqref{Equ:IExpansion} with unknown coefficients $I_{j}(N)$ and plug them into~\eqref{Equ:RecExpansion}. Then the left and right hand sides are both Laurent series which are equal if and only if the coefficients agree. In particular, the lowest term must agree, i.e., we obtain the following constraint \begin{equation}\label{Equ:ModRec} a_0(0,N)I_{o}(N)+a_1(0,N)I_{o}(N+1)+\dots+a_d(0,N)I_{o}(N+d)=r_{o}(N) \end{equation} which is a linear recurrence of order $d'=\max\{0\leq i\leq d\| a_i(0,N)\neq0\}\geq0$. Activating Theorem~1 to this recurrence with appropriately chosen initial values (given by Theorem~1) one can decide algorithmically if $I_o(N)$ is expressible by a nested hypergeometric sum expression. If such a representation is not possible, the theorem is proven. Otherwise, we take this representation and make the Ansatz~\eqref{Equ:IExpansion} with the known coefficient $I_{o}(N)$ and the unknown coefficients $I_{j}(N)$ ($j>o$) and plug them into~\eqref{Equ:RecExpansion}. Then by construction the coefficients of $\varepsilon^{o}$ on the left and right hand sides agree and the term of $\varepsilon^o$ can be eliminated by subtracting it on both sides. Now one repeats this process for the next lowest term. In this way one can decide algorithmically if all $I_o(N),\dots,I_u(N)$ can be represented by nested hypergeometric sum expressions. In the process of this construction we choose $m\in\mathbb{Z}$ such that the used initial values are covered by $I_j(0),\dots,I_j(m)$ with $o\leq j\leq u$. \medskip \noindent\textit{Example.} Take $\langle I(N)\rangle_{N\geq0}$ with the $\varepsilon$-expansion~\eqref{Equ:IExpansion} of order $o=-3$ where the first two coefficients are determined by the initial values \begin{equation}\label{Equ:InitialI} I(1) = \tfrac{5}{\varepsilon^3} -\tfrac{163}{12 \varepsilon^2}+O(\varepsilon^{-1}),\quad I(2) = \tfrac{130}{27 \varepsilon^3} -\tfrac{695}{54 \varepsilon^2} +O(\varepsilon^{-1}),\quad I(3) = \tfrac{169}{36 \varepsilon^3} -\tfrac{395}{32 \varepsilon^2} +O(\varepsilon^{-1}) \end{equation} and the linear recurrence \begin{mma}\MLabel{MMA:epRec} \In recEp=-2 (N+1) (N+2) (2 +\varepsilon +N ) I[N]-(N+2) \big( -32 -7 \varepsilon +2 \varepsilon^2 -28 N -5 \varepsilon N -6 N^2 \big)I[N+1]-\big(120 +3 \varepsilon -14 \varepsilon^2 -\varepsilon^3 +136 N +13 \varepsilon N -4 \varepsilon^2 N +50 N^2 +4 \varepsilon N^2 +6 N^3 \big) I[N+2] +(2 -\varepsilon +N ) (4 +\varepsilon +N ) (8 +\varepsilon +2 N ) I[N+3]\newline \quad\quad== \frac{1}{\varepsilon^3}\frac{-4 (N+2)}{3 (N+3)} +\frac{1}{\varepsilon^2}\Big[-\frac{2 (2 N+7) S_1}{3 (N+3)} -\frac{2\big( 4 N^4+35 N^3+101 N^2+105 N+25\big)}{3(N+1) (N+2) (N+3)^2}\Bigr]+O(\varepsilon^{-1}).\\ \end{mma} \noindent We seek to calculate a nested hypergeometric sum representation for $I_{-3}$, and $I_{-2}$, i.e., we set $u=-2$. Note that the expansion on the right hand side of~\myIn{\ref{MMA:epRec}} is sufficiently high expanded. The recurrence~\eqref{Equ:ModRec} in our concrete instance is precisely~\myIn{\ref{MMA:SimpleRec}} with $I_{-3}(N)=I(N)$. In addition, the initial values agree with~\eqref{Equ:InitialI}. Hence the found nested hypergeometric sum expression~\eqref{Equ:RecSolverSol} represents $I_{-3}(N)$. Continuing this process we can calculate the coefficient $I_{-2}(N)$. Within \texttt{Sigma} this calculation can be carried out automatically with the function call \begin{mma}\MLabel{MMA:GenerateExpansion} \In GenerateExpansion[recEp[[1]],\{Coefficient[recEp[[2]],\varepsilon^{-3}],Coefficient[recEp[[2]],\varepsilon^{-2}]\}, I[N],\{\varepsilon,-3,-2\},\newline \hspace{6cm}\{\{ 5 , \frac{130}{27},\frac{169}{36}\}, \{-\frac{163}{12}, -\frac{695}{54},-\frac{395}{32}\}\},MinInitialValue\to1]\\ \Out \{\frac{59 N^2+120 N+49}{9 (N+1)^2} -\frac{2 (N+3) S_1({N})}{3 (N+1)},-\frac{2(20 N^3+58 N^2+57 N+22)}{3(N+1)^3} +\frac{2 (N+2) (2 N-1) S_1}{3 (N+1)^2} -\frac{S_1^2}{N+1} -\frac{S_2}{N+1}\}\\ \end{mma} \smallskip \noindent\textit{Remark.} For further details and speed-ups we refer to~\cite{Blumlein:2010zv}. \subsection{Finding Laurent series solutions of coupled systems of linear difference equations}\label{SubSec:CoupledRec} We generalize Theorem~2 to solve coupled systems as follows~\cite{VLadders}. \medskip \noindent\textbf{Theorem~3.} Suppose that the sequences $\langle I_1(N)\rangle_{N\geq0}\rangle,\dots,\langle I_n(N)\rangle_{N\geq0}\rangle\in(\mathbb{K}((\varepsilon)))^{\mathbb{N}}$ with $$I_i(N)=\varepsilon^{o}I_{i,o}(N)+\varepsilon^{o+1}I_{i,o+1}(N)+\varepsilon^{o+2}I_{i,o+2}(N)+\dots$$ are solutions of the coupled system of difference equations \begin{equation}\label{Equ:GenericCRS} A_0 \left(\begin{matrix}I_1(N)\\ \vdots\\ I_n(N)\end{matrix}\right) +A_1 \left(\begin{matrix}I_1(N+1)\\ \vdots\\ I_n(N+1)\end{matrix}\right) \dots+A_d \left(\begin{matrix}I_1(N+d)\\ \vdots\\ I_n(N+d)\end{matrix}\right)= \left(\begin{matrix}r_1(N)\\ \vdots\\ r_n(N)\end{matrix}\right) \end{equation} for explicitly given $n\times n$ matrices $A_0,\dots,A_d$ with entries from $\mathbb{K}(\varepsilon,N)$ and for some sequences $\langle r_1(N)\rangle_{N\geq0},\dots,\langle r_n(N)\rangle_{N\geq0}\in\mathbb{K}((\varepsilon))^{\mathbb{N}}$ with \begin{equation}\label{Equ:RiExpr} r_i(N)=\varepsilon^or_{o,i}(N)+\varepsilon^{o+1}r_{o+1,i}(N)+\varepsilon^{o+2}r_{o+2,i}(N)+\dots \end{equation} Then for any $u_1,\dots,u_n\in\mathbb{Z}$ one can determine $m_1,\dots,m_n\in\mathbb{N}$ $v_1,\dots,v_n\in\mathbb{Z}$ and $w_1,\dots,w_n\in\mathbb{Z}$ with the following property.\\ If one is given the values $I_{i,j}(N)$ for all $1\leq i\leq n$, $o\leq j\leq v_i$ and $0\leq N\leq m_i$ and one is given for all $1\leq i\leq n$ and $o\leq j\leq w_i$ nested hypergeometric sum expressions that calculate the values $r_{i,j}(N)$ for all $N\geq0$ (or at least from a certain point on), then one can decide algorithmically if for all $1\leq i\leq n$ and $o\leq j\leq u_i$ there are nested hypergeometric sum expressions that calculate the values $I_{i,j}(N)$ for all $N\geq0$ (or at least from a certain point on). \medskip \noindent\textit{Proof.} The algorithmic steps can be summarized as follows. First, we transform the coupled system~\eqref{Equ:GenericCRS} to a first order system as explained in~\cite{VLadders}. Then we can apply any decoupling algorithm from~\cite{UNCOUPL} to uncouple the system, e.g., w.r.t.\ $I_1(N)$. In our implementation we chose Z\"urcher's algorithm~\cite{Zuercher:94} implemented in the package~\texttt{OreSys}~\cite{OreSys}. In the generic case one obtains one linear recurrence in $I_1(N)$ which is of the form~\eqref{Equ:RecRExpansionOrg}. We can assume that the evaluations $a_i(0,N)$ are possible and that not all $a_i(0,N)$ are zero (see Footnote~\ref{ftn:aiProp}). In addition, the decoupling algorithm expresses the remaining sequences $I_2(N),\dots,I_{n}(N)$ by a linear combination of the shifted versions of $I_{1}(N)$ and shifted versions of the~\eqref{Equ:RiExpr}.\\ A subtle point is to which order $\varepsilon^{w_i}$ the expressions in~\eqref{Equ:RiExpr} should be expanded. To extract this knowledge, we decouple the system by considering $r_1(N),\dots,r_n(N)$ first as unspecified sequences. Then analysing the corresponding output gives an upper bound for the $w_i$; details on these aspects can be found in~\cite{VLadders}. Since the description of the $I_2(N),\dots,I_n(N)$ is given in terms of a linear combination of the shifted versions of $I_1(N)$, it might be necessary to expand $I_1(N)$ higher than $u_1$. E.g., if $\varepsilon^l I_1(N+i)$ with $l<0$ is one of the components. Analysing these combinations yields the required order $\nu_1$. Now we are ready to apply Theorem~2 to calculate the values $I_{1,i}(N)$ with $o\leq i\leq\nu_1$ by means of a linear recurrence. In this process we determine that the first $m_1$ initial values are needed\footnote{In all our examples $m_1$ agreed with the recurrence order plus some extra points induced by the physical problem.}. If one fails to get the representation of $I_1(N)$ in terms of nested hypergeometric sum expressions, the theorem is proven. Otherwise, by the properly chosen $\nu_1$, the $w_1,\dots,w_n$ and $m_1$, this yields also a nested hypergeometric sum representation of the $I_2(N),\dots,I_{n}(N)$.\\ In the degenerated case, the decoupling algorithm provides several scalar linear recurrences, say in the $I_1(N),\dots,I_l(N)$, and the remaining $I_{l+1}(N),\dots,I_n(N)$ are expressed by a linear combination of the shifted versions of the $I_1(N),\dots,I_l(N)$ and the $r_i(N)$. Applying Theorem~2 with the corresponding $w_i,\nu_i,m_i$ (as described for the generic case) $l$~times leads to the desired result. \smallskip \noindent\textit{Example.} Consider the sequences $I_1(N),I_2(N),I_3(N)$ which are solutions of the coupled system~\eqref{Equ:GenericCRS} with $d=1$ and $n=3$ where \begin{align} A_0=\left(\begin{smallmatrix} N+1 & 0 & 0 \\ \varepsilon (3 \varepsilon+2) & -2 (3 \varepsilon+1) & -2 (-1 +\varepsilon -2 N ) \\ -\varepsilon (3 \varepsilon+2) & 2 (3 +3 \varepsilon +2 N ) & 2 (\varepsilon+1) \\ \end{smallmatrix}\right),&& A_1=\left(\begin{smallmatrix} -2 -\varepsilon -N & 2 & 0 \\ -2 \varepsilon (3 \varepsilon+2) & 2 (5 \varepsilon+2) & 4 (-1 +\varepsilon -N ) \\ 0 & -2 (4 +\varepsilon +2 N ) & 0 \\ \end{smallmatrix}\right) \end{align} and \begin{equation}\label{Equ:riConcrete} \begin{split} r_1(N)&=(-\tfrac{4 (N+3)}{3 (N+2)}\varepsilon^{-3}+\big(\tfrac{2}{3}\tfrac{6 N^3+29 N^2+45 N+21}{(N+1) (N+2)^2} -\tfrac{2 (2 N+3) S_ 1({N})}{3 (N+2)}\Big)\varepsilon^{-2}+O(\varepsilon^{-1}),\\ r_2(N)&=-\tfrac{8}{3}\varepsilon^{-3} +\Big(\tfrac{4 (3 N+1)}{3 (N+1)} -\tfrac{8S_ 1({N})}{3}\Big)\varepsilon^{-2}+O(\varepsilon^{-1}),\\ r_3(N)&= \tfrac{8}{3}\varepsilon^{-3} + \Big(\tfrac{-4 (3 N+1)}{3 (N+1)} +\tfrac{8S_ 1({N})}{3}\Big)\varepsilon^{-2}+O(\varepsilon^{-1})). \end{split} \end{equation} In particular, we are given the initial values~\eqref{Equ:InitialI} for $I_1(N):=I(N)$ We want to derive the $\varepsilon$-expansions for the $I_i(N)$ up to the order $u_i=-2$ for $1\leq i\leq 3$. Uncoupling the system (first with generic right hand sides) shows that $w_1=w_2=w_3=-2$, i.e., the $\varepsilon$-expansions in~\eqref{Equ:riConcrete} are sufficiently high expanded. In particular, we obtain the linear recurrence~\myIn{\ref{MMA:epRec}} with $I(N)=I_1(N)$ and can express $I_2(N)$ and $I_3(N)$ by the shifted versions of $I_1(N)$ and $r_1(N),r_2(N),r_3(N)$. Summarizing, the coefficients $I_{1,-3}(N)$ and $I_{1,-2}$ are computed in \myOut{\ref{MMA:GenerateExpansion}}. This yields the needed information to calculate the $\varepsilon$-expansions of $I_2(N)$ and $I_3(N)$ up to $\varepsilon^{-2}$. The full machinery can be summarized after loading in the packages \begin{mma} \In << OreSys.m \\ \Print\LoadP{OreSys by Stefan Gerhold (optimized by C. Schneider) \copyright\ RISC-Linz}\\ \In << SolveCoupledSystem.m \\ \Print\LoadP{SolveCoupledSystem by Carsten Schneider \copyright\ RISC-Linz}\\ \end{mma} \noindent First, we execute the following command from the package \texttt{SolveCoupledSystem}: \begin{mma}\MLabel{MMA:AnalyzeCoupledRecSystem} \In AnalyzeCoupledRecSystem[\{(A_0.\{I_1[N],I_2[N],I_3[N]\}+A_1.\{I_1[N],I_2[N],I_3[N]\},\{I_1[N],I_2[N],I_3[N]\}, \varepsilon,{-2,-2,-2}]\\ \Out \{\{\{I_1[N],3,-2\}\},\{-2,-2,-2\},\{\}\}\\ \end{mma} \noindent This means that one can solve the system by providing the three consecutive initial values of $I_1(N)$ up to order $\nu_1=-2$ (the starting point depends usually on the physical problem) and that one needs the $\varepsilon$-expansions of $r_1(N),r_2(N),r_3(N)$ up to the orders $m_1=m_2=m_3=-2$. Providing the required information, we execute \begin{mma} \In coupledSys=A_0.\{I_1[N],I_2[N],I_3[N]\}+A_1.\{I_1[N],I_2[N],I_3[N]\}-\{r_1[n],r_2[n],r_3[N]\};\\ \In\label{MMA:SolveCoupledRecSystem} SolveCoupledRecSystem[coupledSys,\newline \{I_1[N],I_2[N],I_3[N]\}, \varepsilon,-3,\{-2,-2,-2\},\{I_1[N],1,\{\tfrac{5}{\varepsilon^3} -\tfrac{163}{12 \varepsilon^2},\tfrac{130}{27 \varepsilon^3} -\tfrac{695}{54 \varepsilon^2},\tfrac{169}{36 \varepsilon^3} -\tfrac{395}{32 \varepsilon^2}\}\}]\\ \Out \Big\{ \frac{1}{\varepsilon^3}\Big(\frac{4 \big( 3 N^2+6 N+4\big)}{3 (N+1)^2} +\frac{4 S_1}{3 (N+1)} \Big) +\frac{1}{\varepsilon^2}\big(-\frac{2(20 N^3+58 N^2+57 N+22)}{3(N+1)^3} +\frac{2 (N+2) (2 N-1) S_1}{3 (N+1)^2} -\frac{S_1^2}{N+1} -\frac{S_2}{N+1} \big),\newline \hspace{0.4cm}\frac{4}{3 \varepsilon^3} -\frac{2}{\varepsilon^2}, \frac{8}{3 \varepsilon^3} +\frac1{\varepsilon^2}\big(-\frac{4 \big( 4 N^2+7 N+2\big)}{3 (N+1)^2} +\frac{4 (N+2) S_1}{3 (N+1)} \big)\Big\}\\ \end{mma} \noindent and obtain the $\varepsilon$-expansions of $I_1(N),I_2(N)$ and $I_3(N)$ up to the orders $-2,-2$ and $-2$, respectively. \subsection{Finding power series solutions of coupled systems of linear differential equations} Finally, we are ready to present our differential equation solver for coupled systems. \medskip \noindent\textbf{Theorem~4.} Suppose that the power series $\hat{I}_1,\dots,\hat{I}_n\in\mathbb{K}((\varepsilon))[[x]]$ with \begin{equation}\label{IHatExp} \hat{I}_i(x)=\sum_{N=0}^{\infty}\Big(I_{i,o}(N)\,\varepsilon^{o}+I_{i,o+1}(N)\,\varepsilon^{o+1}+I_{i,o+2}(N)\,\varepsilon^{o+2}+I_{i,o+3}(N)\,\varepsilon^{o+3}+\dots\Big)x^N \end{equation} for some common $o\in\mathbb{Z}$ are solutions of the coupled system of differential equations\footnote{Here $D_x$ stands for the derivative operator.} \begin{equation}\label{Equ:GenericCDS} A_0 \left(\begin{matrix}\hat{I}_1(x)\\ \vdots\\ \hat{I}_n(x)\end{matrix}\right) +A_1 D_x\left(\begin{matrix}\hat{I}_1(x)\\ \vdots\\ \hat{I}_n(x)\end{matrix}\right) \dots+A_{\delta} D_x^{\delta}\left(\begin{matrix}\hat{I}_1(x)\\ \vdots\\ \hat{I}_n(x)\end{matrix}\right)= \left(\begin{matrix}\hat{r}_1(x)\\ \vdots\\ \hat{r}_n(x)\end{matrix}\right) \end{equation} for explicitly given $n\times n$ matrices $A_0,\dots,A_{\delta}$ with entries from $\mathbb{K}(x)$ and for some $\hat{r}_1(x),\dots,\hat{r}_u(x)\in\mathbb{K}((\varepsilon))[[x]]$ with \begin{equation}\label{Equ:RxDef} \hat{r}_i(x)=\sum_{N=0}^{\infty}\Big(r_{i,o}(N)\,\varepsilon^{o}+r_{i,o+1}(N)\,\varepsilon^{o+1}+r_{i,o+2}(N)\,\varepsilon^{o+2}+r_{i,o+3}(N)\,\varepsilon^{o+3}+\dots\Big)x^N. \end{equation} Then for any $u_1,\dots,u_n\in\mathbb{Z}$ one can determine $m_1,\dots,m_n\in\mathbb{N}$ and $w_1,\dots,w_n\in\mathbb{Z}$ with the property as stated in Theorem 3. \medskip \noindent\textit{Proof.} This result follows straightforwardly by holonomic closure properties. Namely, take the $n$ partial linear differential equations in the $\hat{I}(x)$ and clear denominators by multiplying them with an appropriate polynomial from $\mathbb{K}[\varepsilon,x]$. Take one of the terms of the $n$ equations, say $a(\varepsilon,x)\,D^k \hat{I}_i(x)$ with $0\leq k\leq\delta$, $1\leq i\leq n$ and $a(\varepsilon,x)\in\mathbb{K}[\varepsilon,x]$. With the Ansatz~\eqref{IHatExp} we get \begin{align} a(\varepsilon,x)\,D^k \hat{I}_i(x)=&a(\varepsilon,x) D^k\sum_{N=0}^{\infty}\Big(I_{i,o}(N)\,\varepsilon^{o}+I_{i,o+1}(N)\,\varepsilon^{o+1}+I_{i,o+2}(N)\,\varepsilon^{o+2}+\dots\Big)x^N\\ =&a(\varepsilon,x) \sum_{N=0}^{\infty}\Big(I_{i,o}(N)\,\varepsilon^{o}+I_{i,o+1}(N)\,\varepsilon^{o+1}+I_{i,o+2}(N)\,\varepsilon^{o+2}+\dots\Big)\prod_{j=0}^{k-1}(N-j)x^{N-k}. \end{align} Now we plug all these terms and~\eqref{Equ:RxDef} into the $n$ equations. Doing coefficient comparison w.r.t.\ $x^N$ leads to a coupled system of linear difference equations in the $I_1(N),\dots,I_n(N)$ and the $r_1(N),\dots,r_n(N)$. Performing an appropriate shift in $N$ yields a coupled system of the form~\eqref{Equ:GenericCRS} with the right hand sides $r'_i(N)$ which depend linearly on the $r_i(N)$ and their shifted versions from~\eqref{Equ:RxDef}. Note that the coefficients in $r'_i(N)$ can be expressed in terms of nested hypergeometric sum expressions since the coefficients in $r_i(N)$ can be expressed in terms of nested hypergeometric sum expressions. Thus we can apply Theorem~3 and obtain the claimed result. \medskip \noindent\textit{Example.} Consider the integrals $\hat{I}_1(x),\hat{I}_2(x),\hat{I}_3(x)$ given by $\hat{I}_1(x) = J_6(1,1;x)$, $\hat{I}_2(x) = J_6(2,1;x)$ and $\hat{I}_3(x) = J_6(1,2;x)$ where \begin{equation}\label{Equ:J6} J_6(\nu_2,\nu_4;x) = \int \frac{d^Dk_1}{(2 \pi)^D} \frac{d^Dk_2}{(2 \pi)^D} \frac{d^Dk_3}{(2 \pi)^D} \,\, \frac{1}{P_2^{\nu_2} P_4^{\nu_4} P_5 P_7 P_8 P_{10}} \end{equation} with the propagators $P_2=(k_1-p)^2-m^2$, $P_4=(k_2-p)^2-m^2$, $P_5=k_3^2-m^2$, $P_7=(k_3-k_2)^2$, $P_8=(k_1-k_2)^2$ and $P_{10}=1-x \Delta.k_1$. Note that $\hat{I}_i(x)$ can be given in the power series representation~\eqref{IHatExp} and the main task is to determine the coefficients $I_{i,j}(N)$. The IBP algorithm of \texttt{Reduze~2}~\cite{Reduze2} delivers e.g. the coupled system~\eqref{Equ:GenericCDS} with $n=3$ and $\delta=1$ where $A_1$ is the $3\times3$ identity matrix and $$A_0=-\left( \begin{matrix} \frac{\displaystyle 1 +\varepsilon -x }{\displaystyle (x-1) x} & \frac{\displaystyle -2}{\displaystyle (x-1) x} & 0\\ \frac{\displaystyle -\varepsilon (3 \varepsilon+2) (x-2)}{\ds4 (x-1) x} & \frac{\displaystyle -2 -5 \varepsilon +x +3 \varepsilon x }{\displaystyle 2(x-1) x}& \frac{\displaystyle (-2 \varepsilon -x +\varepsilon x )}{\displaystyle 2(x-1) x} \\ \frac{\displaystyle \varepsilon (3 \varepsilon+2)}{\displaystyle 4 (x-1)} & \frac{\displaystyle 2 +\varepsilon -3 x -3 \varepsilon x }{\displaystyle 2(x-1) x} & -\frac{\displaystyle \varepsilon+1}{\displaystyle 2 (x-1)} \end{matrix}\right).$$ Furthermore, the $r_i(x)$ are given by a linear combination of master integrals where each one has a power series representation of the form~\eqref{IHatExp}. In particular, one can use symbolic summation tools~\cite{Summation,CASummation} to calculate the coefficients of the coefficients (up to a certain modest order in $\varepsilon$) in terms of nested hypergeometric sum expressions. For other situations multiple integration methods \cite{Integration} are the appropriate tool. Thus the $\hat{r}_i(x)$ have a power series representation of the form~\eqref{Equ:RxDef} where the $r_{i,j}(N)$ can be given (up to a certain modest $\varepsilon$-order) explicitly in terms of nested hypergeometric sum expressions.\\ Now we activate our machinery. By holonomic closure properties we obtain precisely the coupled difference system from Example~\ref{SubSec:CoupledRec}. Taking the data from~\myOut{\ref{MMA:AnalyzeCoupledRecSystem}} we calculate the required $r_{i,j}(N)$ by means of symbolic summation. Furthermore, we calculate the initial values~\eqref{Equ:InitialI} by exploiting the $\alpha$-parametrization of the integrals; for further details on this method we refer to~\cite{Ablinger:2014uka}. Note that in other situations we also used our summation tools, provided a reasonable sum representation has been derived. Finally, we activate the function call~\myIn{\ref{MMA:SolveCoupledRecSystem}} to get the final result. \smallskip \noindent\textit{Remark.} The integrals $\hat{I}_1(x) = J_6(1,1;x)$, $\hat{I}_2(x) = J_6(2,1;x)$ and $\hat{I}_3(x) = J_6(1,2;x)$ with~\eqref{Equ:J6} themselves are master integrals produced by \texttt{Reduze 2}~\cite{Reduze2} in order to calculate the diagram\footnote{The graph has been produced by {\tt Axodraw}~\cite{Vermaseren:1994je}.} \begin{equation}\label{Equ:D12} \vcenter{\hbox{\includegraphics[width=4cm]{axo5_12.pdf}}} \end{equation} in~\cite{VLadders}. There we calculated the $\varepsilon$-expansion up to order $3$ (and not just to order $-2$) in terms of 40 harmonic sums up to weight 7. The total calculation time was 229 seconds. The most complicated coupled system for diagram~\eqref{Equ:D12} had dimension $n=4$. Interestingly enough, the right hand sides of~\eqref{Equ:GenericCRS} can be given in terms of generalized harmonic sums only, but the solution is given in terms of nested binomial sums. This strongly indicates that straightforward tactics, like transforming the system to a particular shape and reading off the solutions, are not sufficient for such systems.\\ Note that the obtained results in $N$-space presented in~\cite{VLadders} and also in~\cite{DiffCalculations,Ablinger:2014uka} can be transformed to $x$-space by using iterated integral representations over general alphabets, generalizing in parts Poincar\'{e} iterated integrals~\cite{Ablinger:2014bra}. \section{Conclusion} We worked out a solver for coupled systems of linear differential equations where in one stroke \begin{enumerate} \item the coefficients of the formal power series solution are expanded in its $\varepsilon$-expansion; \item the coefficients of the $\varepsilon$-expansion are given up to the desired order in terms nested hypergeometric expressions. \end{enumerate} More precisely, we presented a complete algorithm which either provides such a solution or proves that such a representation is not possible. These algorithms have been implemented in the new Mathematica package \texttt{SolveCoupledSystem} which is based on the packages \texttt{Sigma} and \texttt{HarmonicSums}. In concrete calculations IBP-techniques provide a recursively defined system of coupled equations. In~\cite{VLadders} a new method has been worked out in order to treat these recursive systems fully automatically by using the algorithms presented in this article. \vspace*{3mm}\noindent {\bf Acknowledgement.} We would like to thank A.~Behring and A.~von Manteuffel for discussions.	{ "redpajama_set_name": "RedPajamaArXiv" }	8,955
{"url":"https:\/\/rna-tools.readthedocs.io\/en\/latest\/_modules\/rna_tools\/tools\/clanstix\/rna_clanstix.html","text":"# Source code for rna_tools.tools.clanstix.rna_clanstix\n\n#!\/usr\/bin\/python\n# -- coding: utf-8 --\n\"\"\"rna_clanstix - a tool for visualizing RNA 3D structures based on pairwise structural similarity with Clans.\n\nWe hacked Clans thus instead of BLAST-based distances between sequences, you can analyze distances between structures described as p-values of rmsd (based on the method from the Dokholyan lab.)\n\nQuickref::\n\nrna_clanstix.py --groups-auto 10 --color-by-homolog --shape-by-source thf_ref_mapping_pk_refX.txt input2.clans\n\nRunning Clans:\nTo run CLANS you need to have Java 1.4 or better installed (java can be downloaded HERE). For full functionality you will also need the NCBI BLAST,PSI-BLAST and formatdb executables (NCBI). For command line parameters and basic help please refer to the README file.\n(source: http:\/\/www.eb.tuebingen.mpg.de\/research\/departments\/protein-evolution\/software\/clans.html)\n\n.. image:: ..\/..\/rna_tools\/tools\/clanstix\/doc\/yndSrLTb7l.gif\n\nThe RMSDs between structures are converted into p-values based on the method from the Dokholyan lab or some hacky way developed by mmagnus .\n\nColor groups\n---------------------------------------\n\n.. image:: ..\/..\/rna_tools\/tools\/clanstix\/doc\/rna_clanstix.png\n\nTo get colors, run a cmd like this::\n\nrna_clastix.py rnapz17_matrix_farfar_HelSeedCst.txt --groups 20:seq1+20+20+20+20+20+20:seq10\n\nwhere with the + sign you separate groups. Each group has to have a number of structures. Optionally it can have a name, e.g., 20:seq1, use : as a separator. If a provided name is native then this group will be shown as starts.\n\nGet inspiration for more colors (http:\/\/www.rapidtables.com\/web\/color\/RGB_Color.htm)\n\nHow to use ClanstixRNA?\n----------------------------------------\n\n1. Get a matrix of distances, save it as e.g. matrix.txt (see Comment below)\n2. run ClanstixRNA on this matrix to get an input file to Clans (e.g. clans_rna.txt)::\n\nrna_clanstix.py test_data\/matrix.txt # clans.input will be created by default\n\n3. open CLANS and click File -> Load run and load clans_run.txt\n4. You're done! :-)\n\nComment: To get this matrix you can use for example another tool from the rna-pdb-tools packages::\n\nrna_calc_rmsd_all_vs_all.py -i rp18 -o rp18_rmsd.csv\nrna_clastix.py --groups 1:native+5:3dRNA+\n5:Chen+3:Dokh+5:Feng+5:LeeASModel+\n5:Lee+5:RNAComposer+10:RW3D+5:Rhiju+\n1:YagoubAli+3:SimRNA rp18_rmsd.csv clans.in\n\nrna_clastix.py --groups 100+100+100+100+100+100+100+100+100+100+1:native rp18_rmsd.csv\n\nwhere rp18 is a folder with structure and rp18_rmsd.csv is a matrix of all-vs-all rmsds.\n\n.. image:: ..\/..\/rna_tools\/tools\/clanstix\/doc\/rp18_clanstix.png\n\nHajdin, C. E., Ding, F., Dokholyan, N. V, & Weeks, K. M. (2010). On the significance of an RNA tertiary structure prediction. RNA (New York, N.Y.), 16(7), 1340\u20139. doi:10.1261\/rna.1837410\n\nAn output of this tool can be viewed using CLANS.\n\nFrickey, T., & Lupas, A. (2004). CLANS: a Java application for visualizing protein families based on pairwise similarity. Bioinformatics (Oxford, England), 20(18), 3702\u20134. doi:10.1093\/bioinformatics\/bth444\n\"\"\"\nfrom __future__ import print_function\nimport argparse\nimport rna_tools.tools.rna_prediction_significance.rna_prediction_significance as pv\nimport numpy as np\nimport math\nimport logging\nimport time\n\nlogging.basicConfig(level=logging.INFO,\nformat='%(message)s',\ndatefmt='%m-%d %H:%M',\nfilename='rna_clanstix.log',\nfilemode='w')\n\nconsole = logging.StreamHandler()\nconsole.setLevel(logging.INFO)\nformatter = logging.Formatter('%(message)s')\nconsole.setFormatter(formatter)","date":"2020-12-03 16:05:31","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.30950847268104553, \"perplexity\": 13038.184718324852}, \"config\": {\"markdown_headings\": true, \"markdown_code\": false, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-50\/segments\/1606141729522.82\/warc\/CC-MAIN-20201203155433-20201203185433-00577.warc.gz\"}"}	null	null
LIMA, PA – December 5, 2017 – Pilot Freight Services (Pilot), a worldwide provider of transportation and logistics services, announces the opening of a new 70,000 sq. ft. warehouse at 7015 Corporate Plaza Drive in Las Vegas, NV. Conveniently located near McCarran International Airport and the Las Vegas Strip, Pilot's new warehouse is ideal for not only the ever-increasing demand for long and short-term storage solutions for trade show, gaming and concert related freight ranging from elaborate booths to the massive stage and lighting systems to video display equipment. The warehouse is set to open on January 20, 2018 and will add five new employees. The new facility boasts 32 ft. ceilings, 20 dock doors and sophisticated climate control. A combination of brand-new construction and a roof made of Polar-Ply Radiant Barriers offer a unique pure aluminum foil sheet which prevents 97 percent of summer radiant heat from entering the building, reducing temperatures by up to 50 degrees. This climate technology will sustain the entire warehouse at a constant temperature regardless of exterior temperatures. These features are beneficial for storing products and technology that are sensitive to extreme temperatures including medical devices like imaging machines as well as consumer electronics and gaming industry merchandise. State-of-the-art security with round-the-clock motion, audio and camera sensors offer complete interior and exterior monitoring with live personnel. The inventory in the facility will be managed by Pilot's eWMS, which allows maximum flexibility and system interaction in the warehouse. The system is completely customizable and able to integrate with customers' systems. Through this, Pilot is able to better manage the supply chain processes and significantly improve employees' workflows, equating to large increases in productivity, efficiency and increased quality. The Las Vegas facility is a strategic addition to Pilot's strong domestic and global network of stations that move freight throughout the world and provide custom shipping and logistics services through the entire supply chain. High level customer service is from live, local personnel 24-hours a day, 365-days a year.	{ "redpajama_set_name": "RedPajamaC4" }	7,250
Motoring Tesla founder left his 25.6 million Twitter follows with no doubt. Motoring Concerns about data being stored in Tesla electric cars. Motoring Ford is preparing a Mustang-inspired EV. Motoring Fisker has given a glimpse of its new compact electric SUV. Motoring Latest Tesla expected to be the best seller yet. Motoring Elon Musk undertakes a U-turn. Motoring Long-promised "Standard" Model 3 is finally entering production. Motoring Musk: "Self-driving" cars will hit the road this year. Motoring Tesla has put criminals on notice. Motoring Here's what's coming in luxury cars during 2019. Motoring Musk's answer to "soul-destroying traffic". Motoring Some are questioning Elon Musk's stability.	{ "redpajama_set_name": "RedPajamaC4" }	7,204
Imena baranjskih naselja Ovo je popis svih naselja u Baranji koja imaju status samostalnog naselja. Uz službena imena dana su njihova narodna ili stara imena, mađarska imena te etnici koji im odgovaraju. Narodna i stara imena Pod narodnim imenima podrazumijevaju se imena koja danas izgovaraju Baranjci kad govore hrvatski (književnim jezikom ili šokački) ili srpski (književnim jezikom ili lokalnim dijalektom), a razlikuju se od službenih imena. Takvo je npr. ime Suljoš ili skraćena imena Beli odn. Bezdan. Stara su ona narodna imena koja se više ne čuju ili se čuju rijetko (npr. Tarda) ili ih uglavnom upotrebljavaju stariji stanovnici (npr. Monoštor). Mađarska imena Mađarska su imena zapisana mađarskim pravopisom i ona su mnogo starija od slavenskih ili poslavenjenih imena, koja su nastala poslije Poslije prvog svjetskog rata. Etnici Etnici su zabilježeni onako kako se čuju u govoru Baranjaca ili kako se mogu pročitati u lokalnim novinama. U govoru nebaranjaca mogu se čuti i drugačiji oblici (npr. Bolmančanin, što se u Baranji rijetko čuje), a u medijima se ponekad mogu pročitati i neobični etnici (npr. Batinarac), koji su očito neosnovane novinarske konstrukcije. U nekim leksikografskim djelima, npr. u Hrvatskom enciklopedijskom rječniku, navode se etnici koji se u skladu s pravilima tvorbe etnika, ali se na terenu ne upotrebljavaju (npr. Branjinčanin, Kneževljanin). Vidi i: Baranjska naselja, Baranjske općine, Baranjske katastarske općine Izvori: Mađarska imena Martin Jakšić: Divanimo po slavonski, Zagreb, 2003. (str. 335-336) Baranjski leksikon Imena baranjskih naselja	{ "redpajama_set_name": "RedPajamaWikipedia" }	5,180
Q: List of currently displayed rows in DataGridView I have a List(Of String) which I want to contain a list of primary keys based on if the associated row in dgv is displayed. I need to both add and remove values from the list as they are displayed/hidden. Currently I am doing this: Private Sub dgv_RowStateChanged(sender As Object, e As DataGridViewRowStateChangedEventArgs) Handles dgv.RowStateChanged If e.StateChanged = DataGridViewElementStates.Displayed Then If Not VisibleRows.Contains(e.Row.Cells("SQ").Value.ToString) Then VisibleRows.Add(e.Row.Cells("SQ").Value.ToString) End If End If End Sub However this will just add an item to my list when a new row is displayed without removing the hidden row's primary keys. I can remove a value from the list using VisibleRows.Remove(e.Row.Cells("SQ").Value.ToString) however I don't know how to identify that a row is no longer displayed. What is the result of e.StateChanged when a row is no longer displayed? A: Hmmm. DataGridViewElementStates is an enum containing flags. You might want to check for it like this: If e.StateChanged And DataGridViewElementStates.Displayed = DataGridViewElementStates.Displayed Then ... End If I don't know if the event gets triggered for rows that become invisible. But then again, I would not want to keep track of such a list of strings. Smells not so well. Personally (if I really need a list of strings containing the visible items), I would do the following: * fill the list only when I need it (for example by using a readonly property that refreshes the list if it is invalid). invalidate (or simply dispose of) the list in the dgv_RowStateChanged event handler (or perhaps in a more appropriate event handler; I would need to check) Something like this: Private _visibleRows As List(Of String) 'Only use this inside the VisibleRows property and the dgv_RowStateChanged event handler. For all other usage of the list, use the VisibleRows property! Private ReadOnly Property VisibleRows As List(Of String) Get If _visibleRows Is Nothing Then _visibleRows = New List(Of String) For Each row As DataGridViewRow In dgv.Rows If row.Displayed Then _visibleRows.Add(row.Cells("SQ").Value.ToString) End If Next End If Return _visibleRows End Get End Property Private Sub dgv_RowStateChanged(sender As Object, e As DataGridViewRowStateChangedEventArgs) Handles dgv.RowStateChanged _visibleRows = Nothing End Sub But it still does not smell right. Depending on the rest of your code, this might also have a dramatically bad performance. Edit: You might replace the For-loop in the VisibleRows property with the following code: Dim index As Integer = dgv.FirstDisplayedScrollingRowIndex Dim row = dgv.Rows(index) While (row.Displayed) _visibleRows.Add(row.Cells("SQ").Value.ToString) index += 1 row = dgv.Rows(index) End While This might be faster... Edit 2: The code in my first edit has a bug: you might get an index-out-of-range-exception when you scroll down to the bottom of the datagrid. So you also need to check inside the While-loop if the increased index value is valid before you try to fetch that next row or exit the loop otherwise. But I'm not going to correct this. I don't like this entire "solution" at all. ;)	{ "redpajama_set_name": "RedPajamaStackExchange" }	8,191
Luggage packed and ready, capes and turbans, trunks full of spell books. By train, by boat, by balloon. We are in January 1952, and the Annual Bruges Convention is about to be held in some secret location on the border in Bratislava, where the Alps intersect with the Carpathians. They come from Mexico, Shanghai, Paris, Tokyo, Edinburgh, Bucharest, Lyon, Prague. They wear turbans, kimonos, capes, slippers. They speak different languages, they are of different ages, they have led different lives, but they understand each other. We turn away from the witch as a symbol of the unknown, the evil, the hidden, the irrational. The woman suspected of being free, the woman defamed, the woman pointed at. We want to strip the witch of her dark, supernatural, political, religious, archetypal burden. She inspires us, instead, as a synthesis of an independent woman, who follows her instinct, who believes in a shared ancestral feminine wisdom. The witch who laughs at herself: the witch who loves to be called a witch. The witch has a power, which is her infinite freedom, her inner strength. Fashion -like work, like love, like friendship- is a spell that makes us powerful. When we wear our favourite clothes, magic begins: we attract luck, we are more lucid, we look at the world more kindly. A dress can be a lucky charm, a magic wand, a broom on which to fly away from the ignorant looks that judge, that whisper and distrust. Witches? Yes, and very honourable. The Bruges Convention only happens once a year, and asks for the best clothes. Each witch represents her country, and -whether veteran or novice- wants to be worthy of such a great event. This spell-making syndicate wears plumetti, organza, velvet, leopard, raffia on tulle, tartan, mink. Nature accompanies them: stars, mountain ranges, owls, lemurs, beetles. The result is an exotic, opulent, dreamy and festive collection.	{ "redpajama_set_name": "RedPajamaC4" }	2,147
Children's experiences of fun and enjoyment during a season of sport education Trish Gorely Department of Nursing and Midwifery Research Quarterly for Exercise and Sport Gorely, T. (2008). Children's experiences of fun and enjoyment during a season of sport education. Research Quarterly for Exercise and Sport, 79(3), 344-355. Gorely, Trish. / Children's experiences of fun and enjoyment during a season of sport education. In: Research Quarterly for Exercise and Sport. 2008 ; Vol. 79, No. 3. pp. 344-355. @article{28cbce212dc344a78e10ee45b02b1319, title = "Children's experiences of fun and enjoyment during a season of sport education", author = "Trish Gorely", journal = "Research Quarterly for Exercise and Sport", publisher = "American Alliance for Health, Physical Education, Recreation, and Dance", Gorely, T 2008, 'Children's experiences of fun and enjoyment during a season of sport education', Research Quarterly for Exercise and Sport, vol. 79, no. 3, pp. 344-355. Children's experiences of fun and enjoyment during a season of sport education. / Gorely, Trish. In: Research Quarterly for Exercise and Sport, Vol. 79, No. 3, 2008, p. 344-355. T1 - Children's experiences of fun and enjoyment during a season of sport education AU - Gorely, Trish JO - Research Quarterly for Exercise and Sport JF - Research Quarterly for Exercise and Sport Gorely T. Children's experiences of fun and enjoyment during a season of sport education. Research Quarterly for Exercise and Sport. 2008;79(3):344-355.	{ "redpajama_set_name": "RedPajamaCommonCrawl" }	683
January 18, 2019 5:22pm Comment Adam Conway A Google WiFi successor may be coming with a new Qualcomm chip The Google WiFi router is a must have router in any technology enthusiast's household. Its easy configuration plays a large part in its excellence—you place them in key areas of your home, scan a QR code, and you're set. It supports all major features you'd expect a premium router to have, most notable is an easy-to-use app and QoS support. Now, according to several commits we found on the Chromium Gerrit, it seems that Google is working on a successor. That successor goes by the code-name of "Mistral," and it runs on a currently unreleased Qualcomm chipset. The code-name "Mistral" fits Google's naming conventions for their previous WiFi products, all relating to wind. The Google WiFi's code-name is "Gale" while the Google OnHub is code-name "Whirlwind." It is also important to note that "Mistral"s kernel is using "Gale" as a base. The currently unreleased Qualcomm chipset is the QCS405, a chipset made for Internet of Things devices. It stands to reason that it would go into a Google WiFi successor given that it too was powered by a Qualcomm chipset. If we are following Qualcomm's typical naming conventions (4xx, 6xx, 7xx, 8xx), then it's safe to assume that the QCS405 is lower-end when compared to the QCS605 released last year. We don't have any information about it just yet, other than it's already being used in a device that Google is making. Google releasing a successor to the Google WiFi suggests that it will be an improved device. With a newer Qualcomm chipset to power it, it's possible that we get new features over its predecessor. Information is scarce about what the QCS405 actually is other than that it follows the IoT SoC naming convention that Qualcomm has used in the past. The code-name mistral device first appeared publicly in November of 2018, which apparently was powered by the QCS404. It was soon upgraded to use the QCS405, and since then has received updates that have slowly improved upon its functionality. For example, it has confirmed Bluetooth support and even SD card support. On top of that, it appears it may also have USB ports. The Google WiFi was a very basic device, but it worked well. With upgrades in the right places and support for SD cards and the like, Mistral could well be a worthy successor and can rightfully be described as the right direction for Google to go in. Modern routers typically have mass storage support so that you can stream content over your network, so it only makes sense for a more complete device that support would be implemented. We'll be keeping a close eye on Mistral, and we'll be sure to let you know of any further updates. One thing is for certain, this particular device is in the very early stages of development, and a lot could change before its release. Tags Googlegoogle wifiinternet of thingsQualcomm XDA » Full XDA » A Google WiFi successor may be coming with a new Qualcomm chip POCO explains its new market strategy ahead of its next phone launch Gboard prepares to let you paste images you copy into multiple social and messaging apps Realme will launch its 5G phone globally at MWC 2020	{ "redpajama_set_name": "RedPajamaCommonCrawl" }	4,065
Why the Success of the Pfizer Vaccine Trial Is Personal for Me By Molly Jong-Fast When Pfizer announced on November 9 that an early analysis of its coronavirus vaccine trial suggested that the vaccine was more than 90% effective in preventing COVID-19, the world reacted with surprise, relief, and nearly unbridled optimism. Scientists and health experts hailed the announcement by Pfizer and its trial partner, the German drugmaker BioNTech, as the breakthrough they had been waiting for; the stock market soared to new heights; and Joe Biden, who two days earlier had been declared the new president-elect, greeted the news as a sign that the global pandemic might be on the verge of being controlled. "I congratulate the brilliant women and men who helped produce this breakthrough and to give us such cause for hope," Biden said. Even Dr. Anthony Fauci, perhaps the nation's most respected authority on the coronavirus and someone who has been careful to mute overly optimistic predictions of a quick vaccine, signaled that this was a momentous achievement. "I'm going to look at the data, but I trust Pfizer," Fauci said in an interview on MSNBC. "I trust the FDA. These are colleagues of mine for decades, the career scientists. If they look at this data, and they say this data is solid, let's go ahead and approve it, I promise you, I will take the vaccine, and I will recommend that my family take the vaccine." I too felt enormous excitement when I heard that news. But for me the success of the Pfizer vaccine is a personal one. While I'm not one of the doctors or one of the many scientists who spent months working around the clock, I played my own role in the development of the Pfizer vaccine. For the past three months, I have been a volunteer participant in the Pfizer vaccine trial study. Like the many other participants in medical trials, it's my blood and my body that helped Pfizer test the safety and efficacy of the coronavirus vaccine. You see, I am patient number 1133. I joined the Pfizer trial in August at the Yale New Haven Hospital study site. A lot of people in my position, as the mother of three, might not jump to join a medical trial. But I was convinced that I had to do it. I heard on television that they were running large-scale coronavirus trials and needed volunteers. I immediately signed up on every site I could find. As someone who has struggled with health anxiety, being a medical-trial participant wasn't an obvious life choice. But I felt I had to. After living in New York during those horrific months of March and April, when the virus was first raging through the city, the collective loss of so many human souls was indelible, impossible to shake. I had a front-row seat for the carnage that the virus had wrought, and while my kids were watching reruns of The Office, I was absorbing the tragedy unfolding around me. The sounds and the smells of that particular period still haunt me, from the refrigerated trucks to the incredible, inescapable, crushing silence punctuated by the occasional screaming ambulance. Every day contained a lifetime of tragedy. A friend of a friend had a heart attack in his car in a hospital parking lot; four friends buried their fathers. The collective loss was crushing. I'm only 42, but it's hard for me to imagine a time when those particular months won't haunt me. My DNA has been irrevocably changed by the experience. During those dark months in American life, the president of the United States used his televised daily coronavirus briefings to spread misinformation. He pumped up miracle cures while playing down the science of basic handwashing and mask wearing. There was something so very bleak about living through a pandemic with a federal government that had completely, utterly, and totally rejected science. There was something so incredibly grim about watching the federal government fail its people on a scale that seemed unimaginable. I was living under an administration that was taking radical anti-science measures. Participating in this trial was one tangible way I could reject Trumpism and embrace science. I also knew I could write about the experience, and perhaps that would make others feel more comfortable about taking the vaccine themselves. The actual experience was surprisingly mundane. A nurse drew blood. I self-administered a coronavirus test. Two nurses came into the room and gave me a shot. Then, after waiting for about 30 minutes to make sure I didn't have any kind of allergic reaction, I went home. But I have to say that I am not totally surprised by the positive results. I had sort of suspected that the Pfizer vaccine's efficacy number would be high because of the many casual conversations I've had with study doctors and other trial patients over the last three months, all of whom seemed optimistic about how the trials were going. One of the doctors even told me that "people had so few symptoms that they thought they were in the placebo arm of the study." (I experienced no side effects except for a little fatigue—but who isn't feeling tired these days?) It's important to note that this is a double-blind study, which means one half of the study gets the vaccine and the other gets the placebo, so I won't know which I got—the actual vaccine or the placebo—until the study gets unblinded. Also, the news that the vaccine is coming doesn't mean the pandemic is behind us. While this trial is a very exciting, tangible step, this is not the end of the pandemic. We still have months to go, and even when the vaccine is widely available, probably sometime between spring and summer of 2021, there will still be hurdles, including capacity and delivery. (The Pfizer vaccine, like the Moderna one, requires two shots, approximately 21 days apart.) Then there's the question of vaccine hesitancy. Four years of Trumpism has been very bad for scientists and for Americans' belief in science. You'll remember that in 2007, a pre-presidency Donald Trump postulated that vaccines might be responsible for the uptick in autism (they're not), an irresponsible statement he has never retracted. And according to a CNN poll conducted by SSRS, only about half of Americans say they would take the COVID-19 vaccine, perhaps fearing it will be rushed to market before its safety has been proven. The good news about this coronavirus vaccine is that the efficacy is so high that it will take less time to get to herd immunity. And a new Biden administration, one that actually believes in science, may be able to convince more people that this vaccine will be safe. This week, when my podcast colleague Rick Wilson and I interviewed Dr. Eric Topol, a noted medical researcher and author, he called the new vaccine a "super-human vaccine," the kind that, like the measles vaccine in the 1960s, could eradicate an illness with its efficacy. Pfizer and Moderna aren't the only players in this game, of course. There are still a lot of vaccine trials going on around the world, and volunteers are needed. (My husband recently enrolled in a different vaccine trial.) At the White House briefing on Friday, at which Trump tried to claim credit for the Pfizer vaccine and also refused to answer questions about when he would concede the election to Joe Biden, Moncef Slaoui, the person in charge of Operation Warp Speed, reiterated there is still much work to do. "I would like to take this opportunity to invite as many Americans as possible who would like to volunteer to participate in these clinical trials," Slaoui said, "as that's the only way we are able to achieve a demonstration of the safety and the efficacy of these vaccines." We have an opportunity to do good here. I am not a particularly brave person, but in a country with uncontrolled virus spread, I'd much rather take my chances with the vaccine than with the virus. As I write this column, tens of thousands of Americans are getting infected with the coronavirus. You have a chance to save others and change the course of history. Will you do it? I did.	{ "redpajama_set_name": "RedPajamaCommonCrawl" }	958
© 2007 by Tom Rogers Cover and internal design © 2007 by Sourcebooks, Inc. Cover photo © Getty Sourcebooks and the colophon are registered trademarks of Sourcebooks, Inc. All rights reserved. No part of this book may be reproduced in any form or by any electronic or mechanical means including information storage and retrieval systems—except in the case of brief quotations embodied in critical articles or reviews—without permission in writing from its publisher, Sourcebooks, Inc. All brand names and product names used in this book are trademarks, registered trademarks, or trade names of their respective holders. Sourcebooks, Inc., is not associated with any product or vendor in this book. Published by Sourcebooks Hysteria, an imprint of Sourcebooks, Inc. P.O. Box 4410, Naperville, Illinois 60567-4410 (630) 961-3900 Fax: (630) 961-2168 www.sourcebooks.com Rogers, Tom Insultingly stupid movie physics : Hollywood's best mistakes, goofs, and flat-out destructions of the basic laws of the universe / by Tom Rogers. p. cm. ISBN 978-1-4022-1033-4 (trade pbk.) 1. Motion pictures--Miscellanea. 2. Physics--Miscellanea. I. Title. PN1998.R569 2007 791.43--dc22 2007033901 Printed and bound in the United States of America. VP 10 9 8 7 6 5 4 3 2 1 To the world's physics and engineering teachers, who on a regular basis stand before an often difficult crowd and share their passion for the subject. To Dr. Thomas Thorpe, whose high school lecture opened my eyes when he demonstrated momentum by knocking the podium on the floor. And to the best teacher I ever had, Professor P. K. Stein. ## CONTENTS Acknowledgments Introduction Chapter 1: The Noble Cause: _Striking a Blow for Decency in Movie Physics_ Chapter 2: Moviemaker Mathematics: _How Hollywood Shoots from the Hip_ Chapter 3: Conservation of Mass and Energy: _Is Anything Sacred?_ Chapter 4: Scaling Problems: _Big Bugs and Little People_ Chapter 5: Inertia and Newton's First Law: _Why Blowing Up Spacecraft is a Bad Idea_ Chapter 6: Newton's Third Law: _That Special Hollywood Touch_ Chapter 7: Creative Kinematics: _Explosive Entertainment_ Chapter 8: Hollywood Bombs: _How Filmmaker Physics Misses the Boat_ Chapter 9: Leaping Logic: _Why Moviemakers Say "How High"When the Director Says Jump_ Chapter 10: Acceleration and Newton's Second Law: _How to Get Started, Use Brakes, or Change Direction, Hollywood Style_ Chapter 11: High-Energy Films: _Nuclear Firecrackers, Falling People, and Cars as Weapons_ Chapter 12: Movie Momentum: _The Attractive Force of Glass, Rail-Gun Recoil, and Cosmic Toyotas_ Chapter 13: JFK and Momentum: _Hollywood's Conspiracy to Assassinate History_ Chapter 14: Scenes with Real Gravity: _Celebrating Disasters with Happy Hollywood Endings_ Chapter 15: Scenes with Artificial Gravity: _The Good, Bad, and Ugly Space Stations_ Chapter 16: The Movie Merry-Go-Round: _How Filmmakers Create Ridiculous Spin_ Chapter 17: Hollywood Disasters: _Global Warming, Tsunamis,Tornadoes, and Other Big Winds_ Chapter 18: The Moviemaker's Cookbook: _Cigarettes as Lighters, Exploding Cars, Burning Bugs, and Other Recipes for Foolishness_ Chapter 19: Wars versus Trek: _Forgiving versus Forgetting_ Chapter 20: All-Time Stupid Movie Physics Classics: _"They Said the Physics Were Impossible..."_ Notes Index About the Author ## Acknowledgments Few large projects get done without the support of others and this book is no exception. My son Scott was invaluable for his many insightful suggestions in the preparation of the book. He patiently read and edited my drafts repeatedly. Likewise, without the tireless support of my wife and soul mate Sandy, I could not have succeeded. Not only did she repeatedly proofread the developing manuscript, she was also a constant source of positive support. My son Mark and daughter Kelly also provided numerous suggestions, as did Bill Burns. ## Introduction Contrary to the notion that art should resist the intrusion of science, this book steadfastly maintains that the art of moviemaking should embrace the science of physics, because at a gut level people understand physics better than is commonly believed. (Does any living soul not have first hand experience with force, acceleration, velocity, gravity, etc.?) What's more, with a little study and reference materials like this one, it's really not all that hard to understand basic physics at an intellectual level. In spite of its esoteric reputation, physics books are actually fairly popular—the science sections of bookstores are full of them. People are fascinated by cutting-edge topics such as string theory, black holes, dark matter, and the weirdness of quantum physics. Oddly, it's the more straightforward classical physics that often gets ignored, even though it's extremely useful and the foundation of almost everything in modern science and technology. Once again, this book breaks with the norm by concentrating almost exclusively on the commonplace physics principles taught in just about any good high school physics course. Even though many of these physics principles date back hundreds of years to the time of Newton (his major work, _Philosophiae Naturalis Principia Mathematica_ , was published in 1687), they are still incredibly relevant and fascinating in their own right. Yes, there are equations and calculations inside for the mathematically inclined, and as a tool of understanding for physics students taking introductory courses. Hopefully, the book will give them a deeper appreciation of the subject. For the budding filmmaker or science fiction writer, the book is filled with all kinds of useful details. However, most of the calculations and heavier technical detail are enclosed in boxes so that the casual reader can skip over them. Extra detail that does not require a mathematical background is enclosed in shaded boxes, again for easy scanning. Those who spend some time with the book will learn to see movies more clearly, understand the world around them better, and hopefully have a lot of fun in the process. ## CHAPTER 1 ## THE NOBLE CAUSE: ### Striking a Blow for Decency in Movie Physics ### IT'S ONLY A MOVIE "It's only a movie," is often spoken by fans in defense of flicks with flaky physics, as though reviewing movies for physics content is an insult. But isn't the fact that Hollywood thinks they can feed us stupid physics the real insult? Let me explain why reviewing movies for something they need is not insulting, or unnecessary—starting with a hypothetical. Imagine a football movie: a group of plucky individualists have been forged into a team by the tough yet big-hearted coach. No one gave them a chance; yet, here they are in the big game playing their hearts out as Murphy, their beloved teammate, lies in the hospital with bandaged eyes, listening to the contest via radio. The team is behind and desperate. It's the seventh down in the eleventh quarter, so they punt a touchdown pass from the 127th yard line. But wait, this isn't football. It's nonsense. Anyone with football knowledge would think it was ridiculous; some would be offended. The scene would never appear in a movie— not because it's unlikely or hackneyed, but because it's unthinkable to take artistic license with the rules of football. (For those who don't favor American-style football, substitute basketball, soccer, hockey, or just about any other team sport. With a few modifications, the plot will still work.) Artistic license isn't a driver's license; it's an ambulance license. It grants the right to break rules without suffering petty penalties like traffic tickets. But rule breaking can cause errors, leading to serious penalties: wrecks. Rule breaking requires care; it's not a good idea unless there's a good reason. Hollywood would never take such a gamble with the manmade rules of football. So, when it comes to something profound like the guiding rules of the universe, why, of course, break the rules at will—no risk here. Okay, I realize that Hollywood isn't likely to reform, but at least by discussing bad movie physics it's possible to repair some of the damage done to our clear thinking by constant exposure to foolishness. Sadly, Hollywood has a rational reason for affording more respect to the rules of football than the laws of physics: audiences are more likely to know them. Ironically, movies may be part of the cure for this ailment: Hollywood's bad physics examples are good physics teaching tools. Besides, movies are almost as entertaining as physics, so what could be more fun than combining the two? In 1997, after years of watching one Hollywood physics wreck after another, I took a stand for decency in movie physics by founding what has become the premier movie physics site on the Internet. Since American moviegoers are used to rating systems warning of possible affronts to their sensibilities from strong language, violence, and sexuality, and since warning systems are, of course, highly effective deterrents, how could I resist? I created a similar system to warn about affronts from bad physics. Well, maybe ratings aren't so effective but at least they're fun. #### Movie Physics Rating System GP = Good physics in general PGP = Pretty good physics (just enough flaws to be fun) PGP-13 = Children under 13 might be tricked into thinking the physics were pretty good; parental guidance is suggested RP = Retch XP = Obviously physics from an unknown universe NR = Unrated. When a movie is obviously a parody, fantasy, cartoon, or is clearly based on a comic book, it can't be rated but may still have some interesting physics worth discussing. ### THE IMPACT ON ARTISTIC QUALITY To understand when the rules (the laws of physics) should not be broken, it's best to start with the situations where they can or should be. These include cartoons, parodies, and fantasies. Even top-notch science fiction routinely stretches the boundaries of physics for the sake of story. Time-travel is a good example of acceptable physics-bending for the sake of story. Ask ten physicists about time travel and you'll get eleven different answers, and that's with two abstaining. The truth is nobody really knows for sure if it's possible, let alone how to do it. Without it, however, there would be no Terminator movies, a definite loss of some great cinematic moments (not to mention catchy gubernatorial campaign slogans). In _The Terminator_ [PGP] (1984), computers/machines have developed consciousness and a need for entertainment along with it. What to do: work a few math problems—for a computer, how mundane—or kill off humanity? It's a no-brainer: kill people. Unfortunately, those irascible humans are unenthusiastic about extinction. A human leader steps forward and pulls together an effective resistance movement.To remedy this affront, the machines send a terminator—a metal robot covered with living tissue (Arnold Schwarzenegger)—back in time to assassinate the resistance leader's mother and snuff the movement before it starts.The humans, somehow, get wind of the plot and send back one of their own to protect the mother. Both protector and terminator arrive naked since, according to the movie, anything nonliving has to be surrounded by living tissue in order to be transported backwards through time. (Evidently hair, dead skin, and fingernails are the exception.) Okay, the business about having to surround metal with living tissue and only send naked people back in time has no scientific basis, but it's necessary for the film's central conflict. If the human could carry a futuristic weapon, he could easily blow away the terminator and spoil the fun. Instead, he's a rabbit desperately trying to avoid the jaws of a bloodthirsty wolf in possibly the highest intensity chase ever filmed. The nakedness also taps into the deepest levels of the human psyche. Imagine arriving naked, not just at work or school but in an entirely different era. The moviemakers do the arrival scene right: they depict a gray area of physics, time travel, with a minimum of scientific mumbo-jumbo and considerable artistic purpose. It's another matter to defy well-established physics principles for no good reason. Any bright high school physics student (probably not a target audience) can easily spot such foolishness. Many people feel it—like an annoying itch—even when they have no physics background whatsoever. They may not be able to verbalize reasons but have experienced gravity, velocity, acceleration, force, and energy firsthand their entire lives. Individuals with military experience—shooting guns, setting off explosives, flying helicopters—are especially cranky about the itch. Here's a scary thought: in spite of physics' reputation for difficulty, it's really not all that hard to learn; verbalizing soon follows. #### Guidelines for Safe Movie Physics 1) Never break laws or principles taught in high school or first year college classes unless the movie is obviously a: Parody Fantasy—including cartoons Comic book adaptation Keep in mind that most of these physics principles have been around for decades—some for centuries. Lots of people know about them. 2) It's okay to occasionally stretch physics knowledge beyond its current boundaries when all of the following four conditions are met: The stretched area of physics is not fully understood and is at least remotely possible. The story cannot be done without the stretch and the stretch creates unique entertainment or artistic opportunities. The stretch is explained with a minimum of scientific mumbo jumbo. The stretch does not obviously contradict the first law of thermodynamics (see Chapter 3). People do at times watch movies for mindless entertainment, but they also watch to vicariously expand their experience. It's like gaining an additional lifespan. For about two hours they can be a criminal, a saint, a drugged-out loser, or a charismatic genius without all the messy consequences. Movies provide emotional release. Vicariously blowing up an evil emperor's death star helps release the pent-up emotions from not blowing up a discourteous driver's SUV. Oddly, even a total fantasy must seem real. Moviemakers know this and go to great lengths in such areas as set and costume design to give the illusion of reality. The _Passion of The Christ_ [NR] (2004), depicting the crucifixion of Jesus, was a box office hit at least partly for this reason. For example: fake beards were applied meticulously one hair at a time. Had moviemakers applied beards the way they apply physics, the hair would have been drawn with magic markers— phosphorescent orange ones just to make sure the whiskers were exciting. Its not that filmmakers are neglectful or unappreciative of movie physics—never. They love it, to the point of creating movie physics' very own body of clichés: exploding cars, flashing bullets, visible red laserbeams, gasoline lit with cigarettes, and so forth. These serve the cause of movies almost as well as verbal clichés serve the cause of literature. While they last, clichés are a filmmaker's joy but eventually get moldy and have to be tossed. _Tora! Tora! Tora!_ [PGP] (1970) carefully depicted the bombing of Pearl Harbor and was awarded an Oscar® for best visual effects, along with four other nominations including one for sound. The sound track used copious quantities of canned ricochet noises—which sound fake to anyone who has heard real bullets ricochet—but then the fake sounds were a standard movie physics cliché.Today, these sounds have been updated. Movies like _Saving Private Ryan_ [GP] (1998), which depicted the D-Day battle with realistic bullet-sounds, have ruined this cliché's chance for a comeback. Since successful movies require the feeling of reality, why would any moviemaker allow indecent physics into his or her film? The tools to do it right—such as computer generated imaging (CGI) software with realistic physics algorithms—exist. But generating excitement in action scenes with realistic physics takes more time and thought because it imposes more constraints.With less freedom in special effects, moviemakers might be forced to— gasp—work harder on acting, plot, and dialogue. ### THE DANGER TO CLEAR THINKING Artistic perfection is a worthy goal, but the real reason for improving movie physics is the fact that many people actually believe it, even as they say, "It's only a movie." The foolishness works its way into our collective knowledge as fact, reinforcing major misconceptions of physics along the way. These have to be unlearned before the subject can be mastered. Okay, learning physics may not be at the top of everyone's to-do list, but it is rather helpful for designing cars, computers, refrigerators, television sets, and all the bazillions of other items modern society is based on. Hollywood moviemakers are masters of making audiences see only what they're supposed to believe. Take the case of the reader who wrote to set me straight about, arguably, the most famous vehicle "jump" ever, in _Speed_ [PGP-13] (1994). A madman has placed a bomb aboard a city bus filled with unsuspecting riders. The bomb will demolish the bus if it slows below 50 mph (80.5 km/hr). Just when disaster seems certain, a heroic cop perilously jumps aboard and bravely takes charge. After numerous near disasters on congested streets, his superiors—typical bosses who, of course, always know best—unwittingly direct him onto an uncongested route containing an unfinished overpass bridge with a 50-foot gap. Naturally, to keep from exploding, the heroic cop orders the bus's driver to speed up and jump the gap— doing the impossible to compensate for his bosses' directive. I had written that the jump couldn't have been made on the bridge as shown in the movie. My reader wrote that if I watched in slow motion I'd see that the jump was actually done. Sure enough, when viewed this way, there are images of a bus flying through the air—exactly what the moviemakers wanted viewers to see. But look closer: the incline or ramp required for jumping is nonexistent. At the gap, the bridge is flat. Even traveling at 70 mph (113 km/hr), when the bus reached the far side of the gap, the bus would have been about 3.8 ft (1.16 m) below the roadway, slammed into the edge, and been blown apart by the bomb. (See Chapter 8 for more detail on speed.) As for the missing section of bridge, look even more closely: it's possible to see its shadow on the ground below. There was no gap. It was created on film with thousands of dollars worth of special effects. Even thousands of dollars worth of special effects couldn't gloss over flaws in _The Core_ [XP] (2003). The entire movie was based on an absurd premise: a sinister earthquake weapon, developed by an unscrupulous scientist working for misguided military men, had stopped the rotation of the Earth's core thereby disrupting Earth's magnetic field. A group of stereotypical movie heroes, inside a magical ship, must bore down to the core and restart it. In the process, they risk their lives braving the horrifying dangers of various petty human conflicts, not to mention other inconveniences like pressures and temperatures exceeding those directly beneath the Hiroshima atomic bomb blast. It seemed obvious _The Core_ did not contain rigorous science. Yet, in response to my review, a self-proclaimed scriptwriter indignantly wrote that "the science in _The Core_ was mostly accurate." His key argument: the moviemakers had retained a PhD scientist as a consultant. In reality, the moviemakers retained not one but three respected planetary scientists (all with PhDs). They were used for the momentous task of providing background information like: ". . . . the scale and size of things, how hot it gets in the core and what kind of material could conceivably withstand such a temperature." (Hint: There isn't one.) Who cares that the science consultants didn't sit in the director's chair and didn't have real authority over the movie's content. Just being there said . . . well, that they were there. The man who did sit in the director's chair (Jon Amiel) and did have authority over movie content described it as: "...a little bit of science, a certain amount of fact and a lot of fiction." Strangely, the movie's science accuracy didn't seem to top his list of concerns. He is, after all, a boss and may have bungled the description, but then the PhD science consultants were mysteriously silent about correcting him. California Institute of Technology physicist Dr. David Stevenson was not so silent. At about the time the movie came out, he had actually published a paper in the prestigious scientific journal _Nature_ –— to the glee of _The Core_ ' _s_ producers who smelled publicity—outlining a way to send an unmanned probe into the core. Although some of his colleagues scoffed at it, the proposal had a serious purpose: to generate discussion. However, even Dr. Stevenson admits it was close to science fiction: The Earth's crust would be split with a nuclear bomb and the crack filled with a million tons or so of molten steel topped with a small probe.The molten steel would sink towards the core, carrying the probe with it. In theory, the probe would last just long enough to send back some information before being destroyed by the extreme conditions. The joyful producers contacted Dr. Stevenson, offering payment for public endorsements—a golden opportunity for both the movie's backers and the good doctor. He declined. It wasn't the "fantastic/ridiculous stuff about sending a manned probe to the core"; he felt this could never be mistaken for serious science because it was obvious fantasy. (Wow, if only he knew.) Instead, he primarily objected to the movie's premise that the core had stopped rotating, thereby disrupting the Earth's magnetic field— a notion he describes as "just silly." Furthermore, he had issues with the movie's simplistic explanation for how the magnetic field is generated. Certainly, Dr. Stevenson qualified as an open minded and imaginative scientist and had a reputation as such, so his less-thancomplimentary public comments about _The Core_ must have really hurt.The movie's producer contacted Dr. Stevenson, yet again, and chewed him out as though he had actually taken their money. Dr. Stevenson doubts he will ever be asked to consult on another movie. _The Core_ 's trailers alone boosted it to classic status. I was inundated with requests to review it even before it hit theaters. Rarely have I seen such excitement. _The Core_ became a major contender for the distinction of "worst physics movie ever." (See Chapter 20: All-Time Stupid Movie Physics Classics) It's so bad it's good. However, asserting that _The Core_ 's science is "mostly accurate" is like insisting the Earth is mostly flat. At first glance it does look that way but even a little research shows it isn't. While not so noteworthy as _The Core_ , _Pearl Harbor_ [PGP-13] (2001) achieved status with its make-believe history as well as its make-believe physics (see Chapter 8). It tells the story of a young band of WWII fighter pilots stationed in Pearl Harbor just in time to survive various romantic entanglements as well as distractions, such as being strafed and bombed by Japanese planes. Of course, the devastating U.S. defeat at Pearl Harbor isn't the stuff for a traditional Hollywood happy ending. No problem—the moviemakers merely modified history: Pearl Harbor recruits were trained to fly fighters by, no less than, the famous Jimmy Doolittle and later assigned to fly bombers in his famous raid on Japan. The actual raid did little damage in Japan but was a public relations triumph in America and a useful high note for the movie's ending. When WWII started, Doolittle was actually in Detroit helping the auto industry prepare for wartime production. He had nothing to do with training Pearl Harbor-based fighter pilots and not a single one of them participated in his famous raid. In my movie review, I briefly commented about the moviemakers' manipulation of history. (I have had at least one veteran write me that the movie made him sick to his stomach but, as mentioned earlier, military guys tend to be cranky. Geez, I wonder why.) The physics of dropping bombs in level flight is totally different from the physics of dogfighting. So, of course, training fighter pilots for a critical bomber mission when experienced bomber crews were available made perfect sense—in dreamland. The real Doolittle raiders were all from experienced B-25 bomber crews as would be expected. Several readers wrote, with great authority, that the movie was right. One even recommended a book on the Doolittle Raid from a reputable author who backed the movie's account. This seemed incredible and when I contacted the book's author it turned out it was. He told me his book said nothing about fighter pilots from Pearl Harbor flying in the Doolittle Raid and that the idea was preposterous.Yet, I know of at least one otherwise intelligent individual who could pass a lie detector test while describing nonexistent passages supporting the movie's false account. Why would so many believe the movie's bogus account? It had a persuasive pseudo-explanation: Pearl Harbor pilots were the only ones with combat experience. Combine this with compelling images and dramatic dialogue overlaid with rousing music and it went straight to the subconscious as fact. Of course, such misconceptions can be jolly fun, but internalizing them doesn't exactly lead to clear thinking—but then, maybe one shouldn't set such high expectations. Lets be honest—extensive knowledge squeezes the very joy out of misconceptions and heartlessly ruins their chances of being internalized. I have friends who can't watch a movie version of a coma patient without commenting. Their son was in a coma following a serious traffic accident and they know all too well what real comas are like. Why of course, the patient suddenly wakes up fully alert years later and within hours proceeds to use undiminished martial arts skill for revenge against bad guys just like in _Kill Bill_ [NR] (2003). Yeah, right. Real comas are heartwrenching. Their victims almost always require lengthy physical therapy and rarely completely recover. Any form of knowledge makes it harder to digest nonsense, and physics knowledge is no exception. Blatant disregard by moviemakers for well-established physics often gives people with physics knowledge mental indigestion. But, here's a shock: physics knowledge isn't the problem—ability to discern truth doesn't lead to a life of boredom and suffering. It leads to a pleasant sensation: understanding. Internalizing cleverly packaged nonsense is the real problem; it leads to muddled thinking. Still, some may find this type of thinking, if not desirable, at least entertaining. For those who do then, please, read no further. It will spoil your fun. #### Summary of Movie Physics Rating Rubrics The following is a summary of the key points discussed in this chapter that affect a movie's physics quality. These are ranked according to the seriousness of the problem. Minuses [-] rank from 1 to 3, 3 being the worst. However, when a movie gets something right that sets it apart, it gets the equivalent of a get-out-of-jail-free card. These are ranked with pluses [+] from 1 to 3, 3 being the best. [-] [-] [-] A major plot pretext which defies the well established physics principles commonly taught in high school. In the best case, this brands a movie as a cinematic comic book or a fantasy. [-] [-] Scenes which defy the well-established physics principles commonly taught in high school, and are not essential to the plot. [-] Using an obvious stupid movie physics cliché. [+] Avoiding lengthy mumbo-jumbo explanations when stretching physics in a gray area and using this technique only when it's required for telling the story. ## CHAPTER 2 ## MOVIEMAKER MATHEMATICS: ### How Hollywood Shoots from the Hip ### COUNTING SHOTS The action hero kicks open the door and steps through with akimbo (one in each fist) .45 caliber Mac 10 submachine guns. At first the villains are dumbfounded, even though there's a dozen of them and only one action hero. In predictable ignorance they reach for their weapons. The double Macs blaze out a high calorie response at a combined rate of 2,000 rounds per minute. Bottles and mirrors explode as bullets chew up everything in sight.The action hero sweeps the room with gunfire continuously for three minutes. Eventually, when the double Macs fall silent, the bad guys look like ground beef patties. So, where are the sidekicks with wheelbarrows? Only 1.8 seconds of continuous fire empties the thirty-round magazine of a fully loaded Mac 10. Push a button, drop an empty magazine, snap in a fresh one, and it's ready to zip off another thirty shots. Even if the action hero spends half his time reloading (of course, done off camera), in three minutes the two Mac 10s will blast out 3,000 chunks of lead weighing 15 grams each, for a total of 99 pounds (45 kg)—not including the weight of 3,000 empty cartridge cases and one hundred empty magazines now scattered on the floor. The action hero would need a sidekick with a wheelbarrow just to supply the ammo. Besides, how's the hero going to reload when he has a weapon in each hand? The hero could reduce weight problems by using a submachine gun with a slower firing rate and smaller bullets—at a cost of appearing less macho. But then the benefits would be mostly academic.When fired, gunpowder inside a cartridge burns, producing extremely hot, high-pressure gasses, which not only propel the bullet, but also momentarily torch gun barrel internals with a white hot flame. If not allowed to cool, the moving parts in any submachine gun, Mac 10 or otherwise, will seize, similar to the way a car's engine eventually seizes when driven with an empty radiator. The short cooling time available during reloading would not prevent the disastrous temperature increase caused by three minutes of maximum rate firing. Submachine guns are lightweight devices designed for firing in a few, short, intermittent bursts. Characters in _The Matrix Revolutions_ [NR] (2003) actually did supply ammunition with wheelbarrows during the loading dock battle. Alas, the wheelbarrows weren't for realism; they were a plot device used for placing a young hero in imminent danger. The scene depicts a group of humans who have escaped from slime-filled bathtubs controlled by machines, who now live joyfully in a bleak, underground city. They are forced to make an Alamo-like stand when the machines decide to tunnel down and wipe them out. Their Alamo is a large concrete-domed room called the loading dock, which is defended, at least partly, by enormous, humanoid robotic devices called APUs, each of which is controlled by a person strapped to its front. Two gorilla arms extend from each APU torso, with heavy-duty, automatic 30-millimeter cannons attached in place of hands. These fire pretty much continuously at an invading horde of octopus-like machines called sentinels, which conveniently stream by the thousands directly toward the cannons. The scene's young hero—apparently underage for driving an APU—is relegated to the unglamorous task of wheelbarrowing ammunition. He waits nervously in a tunnel until the APU he is supplying runs out of ammunition.The situation is desperate. He scrambles to resupply the APU just as its driver is mortally wounded. The lad not only ends up driving the APU, but also using it to heroically save the day, at least temporarily. It's all very thrilling, except that using wheelbarrows to supply two cannons is as effective as powering a bus with a hamster wheel. Let's assume a firing rate of six hundred rounds per minute for each APU cannon, and a cartridge similar to the 30 × 113-millimeter round used by the U.S. military in Apache helicopter gunships. Each cartridge has a mass of 447 grams. The total mass of ammunition required for one minute of sustained fire by an APU with both cannons blazing is a whopping 1,180 pounds (536.4 kg). A box containing one hundred rounds would weigh over 98 pounds (44.7 kg). With both cannons firing, this box would last a mere five seconds. Keeping the APUs supplied with ammunition would not have required wheelbarrows; it would have required a fleet of Mack trucks! Hollywood moviemakers, traditionally, have never felt a need to count gunshots and keep them to a plausible level. In the heyday of cowboy movies during the 1950s, all handguns were six-shot revolvers, yet bursts of gunfire so regularly exceeded six shots that it became a hackneyed joke among moviegoers. Counting shots was actually a plot gimmick in Clint Eastwood's famous portrayal of a 44-magnum toting, rulebreaking detective in _Dirty Harry_ [PGP] (1971). After shooting it out with bank robbers, Eastwood approaches one lying wounded in the street. As the robber is about to reach for a nearby shotgun, Eastwood levels his hefty revolver and goes into a lengthy dissertation about whether he has fired five or six shots. He had fired six but manages to bluff the bad guy into surrendering. In a later scene, Eastwood repeats the lines while leveling his revolver at a clever psychopath who is also about to reach for a gun. Unlike the bank robber the psychopath goes for the gun, but this time Eastwood isn't bluffing. While bank robbers might be stupid, at least they're not crazy. Today, action movies are filled with semiautomatic handguns, which can blast from half a dozen up to twenty shots before reloading, not to mention the ubiquitous, rapid-firing submachine guns. Audiences simply can't count shots like they used to. Nevertheless, filmmakers have actually begun responding to the jokes about firearms never running out of ammo. Movies now show guns being reloaded, at least occasionally. Eventually, Hollywood will also have to face the fact that submachine guns can't be used in sustained fire for more than a few seconds. In the meantime, there are always wheelbarrows. ### THE GEOMETRY OF SHOOTING FROM THE HIP Hollywood is as creative about the geometry of aiming shots as it is about counting them. In movies, shooters—if they're good guys—routinely hit tiny targets when firing handguns from the hip without using gun sights, while bad guys routinely miss, at least, when shooting at the hero. In reality even well-trained police officers can easily miss a human-sized target when shooting a handgun from the hip at distances over 10 feet (3 meters)—which just might explain why they're trained to use a two-handed hold along with the gun sights. A little geometry combined with some physics illustrates why. For simplicity let's mathematically model hip-shooting as though the handgun has no recoil, the shooter's elbow is fixed in space, and his wrist has no flexibility. Bullets tend to drop due to the downward force of gravity, but at close range the drop in a handgun bullet is so small that we'll overlook it. The point of impact for the bullet, then, will be determined only by the alignment of the end of the handgun's barrel, with a line drawn between the shooter's elbow and the target. Let's call this the aiming line. This model of shooting from the hip focuses on horizontal misses, because the critical area—the torso and head—of humansized targets is roughly twice as tall as it is wide, so it's easier to miss in the horizontal than vertical dimension. (These assumptions may seem too simplistic, but if a simple analysis indicates that a miss is likely, then a detailed one accounting for complexities like recoil, bullet drop, hand tremors, and misalignment of the body's many joints will make missing even more likely.) Figure 2 shows a top view of the aiming line and the hypothetical line the bullet takes. Note the triangle formed by connecting the dots at A. elbow, B. muzzle, and E. a point directly across from the muzzle on the aiming line. Connecting the dots at A. elbow, C. bullet's point of impact, and D. target forms a similar triangle. Anyone who has taken geometry will recognize that the properties of similar triangles can be used to calculate how far the bullet misses the target, given the distance to the target, the misalignment, and the elbow-to-muzzle distance as shown in the diagram. This is calculated as follows: If the muzzle is misaligned by only 2 inches (5 cm), the bullet will miss the target by a foot at a distance of 10 feet (3 m) from the shooter's elbow. When aimed at its center, that's enough to just graze the edge of a human-sized target. At a distance of 50 feet (15.2 m), the bullet will miss by 5 feet (1.52 m). To understand how easy it is to be misaligned by two or more inches, try a simple experiment with a laser pointer. Hold it as though shooting from the hip, aim at a target 50 feet away, and turn it on briefly to simulate a shot. Do not move the red dot while it's turned on and note how far it misses the target. Try this multiple times from the same position on the same target. Invariably, the first shot will completely miss. Subsequent shots will get closer until by the third or fourth, the dot may be fractions of an inch from the target. Repeated shots provide the feedback required to hit the target and may seem like a substitute for gun sights. Unfortunately, this type of feedback doesn't work as well with a handgun. First, recoil tends to misalign it, so you have to align from scratch after each shot. Second, it's often hard to see where bullets are landing. And finally, in real situations, the target is probably going to be moving or even shooting back. Shooting from the hip or without using gun sights is woefully inaccurate for most shooters, especially if the target is more than 10 feet away. In _Pulp Fiction_ [PGP] (1994) the moviemakers got just the right mix of physics precision and artistic ambiguity. During the movie two chatty hit men make a house call to remedy a misunderstanding. It seems that a misguided group has failed to uphold an agreement with the hit men's employer. After the hit men collect the overdue account, they "enlighten" the hapless souls to ensure—in the most reliable way—that there are no future misunderstandings. Suddenly, a nervous shooter bursts from hiding across the room and empties his revolver at the startled hit men. He misses with all six shots and subsequently gets himself "enlightened," courtesy of the hit men, who do not miss when they fire back. The scene is a classic movie moment embodying the enigmatic quality of great artwork. One hit man interprets the missed shots as a message from God wrapped in a miracle, the other as mere random chance. Had the shooter fired from the hip, random chance would have been the best explanation. But, the shooter fired in a police-style stance using both hands, making the chances of completely missing much lower. What's more, we're given a fleeting glimpse of the bullet-hole pattern in the wall behind the hit men. It looks like the bullets should have passed through the hit men, yet we can't be sure. We're left with an enigma that stirs thought long after the movie has ended. By contrast, the two-handed submachine gun shooting, discussed earlier, is neither artful nor realistic. While extremely dangerous to innocent bystanders, it would be marginal for stopping multiple bad guys. The combination of hip shooting and jarring Mac 10 recoil would all but guarantee that the bad guys would only be hit by random chance.When the firing begins, they would scatter and dive for cover. Less than two seconds later, when the good guy held empty Macs, the surviving bad guys would pop up and serve him the ketchup. Innocent bystanders would probably be oblivious to the danger until it was too late. A Mac 10's bullets can injure at distances up to a mile. With the exception of heavy stone, brick, and concrete construction, the bullets can penetrate walls and injure or kill people on the other side. In a big city there would be many more innocent people within the deadly range of a Mac 10 than villains. The two-handed Mac 10–wielding action hero is the worstcase scenario for quickly running out of ammo when continuously firing a submachine gun. The best case is probably a Thompson submachine (or Tommy) gun equipped with a fifty-round drum magazine.These show up in 1930s-style gangster movies and could be fired continuously for a whopping five seconds, with an accuracy not much better than firing double Mac 10s. It's hard to believe that anyone who's serious about surviving a gun fight would shoot this way. ### THE GEOMETRY OF AIMING SNIPER RIFLES Shooting from the hip with a rifle is about as accurate as shooting from the hip with a handgun, but raise it to the shoulder, use the gun sights, squeeze the trigger—and a rifle becomes deadly accurate at much longer ranges. Carefully rest the rifle (a wellmade bolt-action one with a telescopic sight) against a stable object, and it can become a sniper weapon capable of taking out targets at distances on the order of 1,000 yards (914 m). Mathematically model rifle aiming like handgun hipshooting, and the distance AB (see Figure 1) becomes the distance from the shoulder to the muzzle of the rifle or about 1 yard (.914 m). Misalignments with a rifle fired from a steady position and using the gun sights are likely to be less than 1/16 inch (1.6 mm) compared to the 2-inch (5 cm) misalignment likely with a handgun fired from the hip. At 100 yards (91 meters) a 1/16-inch (1.6 mm) misalignment will cause the bullet to miss the point of aim by 6.25 inches (0.16 m). The shooter is not going to win any contests, but the bullet can still hit a human-sized target in a vital area. At 1,000 yards the same misalignment will cause the bullet to miss the point of aim by 62.5 inches (1.6 mm) or, in other words, completely miss a human-sized target. While hitting a human-sized target at distances less than 100 yards is no big deal when firing a rifle from a steady rest position, shooting at ranges near 1,000 yards is a Zen-like mix of physical awareness, physical control, and physics designed to release incredible violence from utter stillness. Simply jerking the trigger in an amateurish way, rather than squeezing it—a skill that takes both coolness and practice—can cause misalignment on the order of 1/16 inch and a complete miss of a human-sized target. Highly skilled shooters will time the trigger pull with their muscle tremors and heart beats. Breathing while aiming is out of the question. All thoughts of the rifle butt painfully recoiling into one's shoulder, or other useless emotions, must be cast into the void. The rifle and shooter must become as one, with the singleminded purpose of sending the bullet to its target. Sniper rifles are the Stradivarius of firearms: finely tuned, precision instruments which exactly reproduce the right vibration pattern when "played." Pull the trigger and the bullet exploding down the rifle barrel will vibrate it in a way analogous to drawing a bow across a violin string.Touch the barrel, tighten or loosen the screws holding it to the rifle's stock, and the effect is like touching, tightening, or loosening a violin string. The change in vibration can change the impact point of the bullet in unpredictable ways. To hit the target at great distances, rifles have to be carefully sighted in and then left undisturbed until fired. So, how does the typical Hollywood sniper practice his coldblooded trade? He sits in front of a window, snaps open his custom brief case filled with rifle parts (each with a fitted slot in the case's foam lining), twists together the parts of his weapon with that oh-sohigh-tech click, adjusts the scope, aims, and fires. However, by disassembling and reassembling his instrument, he runs the risk of detuning it to a different vibration pattern, which will give the bullet a different point of impact relative to the point of aim. If he's shooting at a target less than 100 yards away (91 meters), no problem. At 1,000 yards (914 m) he'd have to spend roughly the price of a used compact car to get the engineering and craftsmanship required to create a breakdown rifle with the needed accuracy. Even then it would be questionable whether he could get it—but hey, a typical long-range assassin–(if such people exist) would probably consider it just another business expense. Besides, he'd probably do most of his work at less than 500 yards (457 m). Even with a precision rifle and a Zen master pulling the trigger, the rifle barrel has to be elevated above the horizontal, much like the cannon on a battleship, in order to hit a target at 1,000 yards. Figure 3 shows bullet trajectories for a 7.62-millimeter NATO rifle, which is considered the world's most common sniper cartridge. When sighted in at 600 yards, but fired at a target only 300 yards away, the bullet strikes 36 inches (0.91 m) higher than the point of aim. When fired at a target 1,000 yards away, the bullet strikes 230 inches (5.8 m) low. At these distances even a gentle 10-miles-per-hour (16 kph) wind makes the bullet drift horizontally by a whopping 108 inches (2.74 m). If the target itself is moving sideways, the sniper must lead or aim ahead of it so that the bullet arrives at the same time as the target—the longer the distance to the target, the longer the lead. If the target is moving straight away or straight toward the shooter, the task is much easier, but still not as easy as shooting a stationary target. The long-range sniper must account for all these variables, which is a daunting task. On the other hand, neither bullet trajectory, wind, nor motion of the target are big problems when shooting a high powered rifle like the 7.62-millimeter NATO at ranges under 100 yards. At worst, the shot will go high by about 2 inches (assuming it's sighted in at 200 yards), or drift from the point of aim by an inch (2.5 cm) in a 10-mile-per-hour (16 kph) wind. If the target moves it will have only about a tenth of a second to get out of the bullet's path. At 100 yards the bullet has over four times as much kinetic energy as at 1,000 yards. At the closer range it is capable of blasting unimaginably gruesome wounds in whomever it strikes. A hit in the head, neck, or chest cavity will likely be fatal, even if the bullet smashes into its victim several inches from the most lethal point of impact. According to Oliver Stone's controversial 1991 move _JFK_ [RP], the Kennedy assassination was a conspiracy and could not have been carried out by an ex-marine using a scoped, highpowered, bolt-action rifle fired from a steady position, at a distance of 88 yards. Who knows? Maybe it was a conspiracy. Certainly, the CIA, mafia, communists, Cubans, police, and Girl Scouts could all be responsible. Yes, as bolt-action rifles go, Oswald's Italian-made 6.5-millimeter Mannlicher Carcano was no Stradivarius and Oswald was no sniping maestro. But while not as powerful as a 7.62 NATO rifle, the Carcano could easily have inflicted a wound gruesome enough to be fatal, nearly anywhere on a person's head. A couple inches of inaccuracy one way or the other would have been insignificant. Oswald was no rank amateur; he was trained to shoot by the U.S. Marines. And he was shooting at a distance well under 100 yards. At that time there were thousands of hunters, shooters, and ex-military people in the U.S. who had more than enough shooting skill to carry out the heinous act. What made Oswald uniquely capable was not his shooting skill, but his pathologically coolheaded and remorseless ability to squeeze the trigger with the president's head in his gun sight. ### GETTING GUNFIGHTS RIGHT Some moviemakers do get gunfight scenes right, as in, for example, _Black Hawk Down_ [GP] (2001). The movie depicts 123 elite U.S. soldiers fighting a desperate battle in Mogadishu, Somalia on Oct. 3, 1993, on a mission to capture a renegade warlord's key associates. In realistic manner the characters rarely fire anything from the hip, even when firing fully automatic weapons. Large machine guns are actually reloaded and tend to be fired in short bursts lasting no more than a few seconds at most. One scene lends an unusual touch of realism when the hot, empty cartridge cases ejected from a rapid-firing minigun in an overhead helicopter shower down on a hapless soldier, giving him minor burns.These weapons look like old-fashioned, hand-cranked multibarreled Gatling guns, but that's as far as the comparison goes. Unlike Gatling guns, miniguns are rotated at high speed by an electric motor, which gives them an incredible firing rate. Their multiple barrels are needed to keep them from melting. Even at that, empty cartridge cases ejected from them are too hot to touch. Moviemakers are intelligent, talented, and well funded. They can hire a busload of top experts for the price of a single supporting actor, but it does little good unless the experts are granted some power. In _Black Hawk Down_ the moviemakers didn't just pay experts, they paid attention to them. ### THE GEOMETRY OF DRIVING In _The Italian Job_ [PGP-13] (2003), moviemakers once again shot from the hip with respect to geometry, but in a different manner. The movie is about a happy-go-lucky group of professional criminals who steal millions of dollars worth of gold, only to be double-crossed by one of their own, who kills their leader and swipes their haul. The survivors spend the rest of the movie trying to remedy the affront. Much of the movie's plot centered on the Mini Cooper car. Supposedly, it's so small that it could be driven down the 6-footwide hall of the villain's house to the room where his safe was located.When the safe was opened, the Mini would be loaded with gold and driven away. This was all well and good, except that such a maneuver required 90-degree turns in the hallway and the Mini has a 17.5-foot turning radius. While it would be jolly fun to write a mathematical proof demonstrating that the turn cannot be made, the same thing can be done with a simple scaled drawing. Figure 2 shows clearly that the turn cannot be made; there just isn't enough room. _The Italian Job_ actually contained a sophisticated wire-framestyle 3-D animation of the car driving through the hallway. The term wire-frame means that the visual images of the car and hallway looked like see-through objects constructed with wire-framelike line drawings. The animation appeared to be drawn to scale and would have taken many hours to create. It could have been rotated on a computer's screen and looked at from any conceivable angle, making it easy to spot clearance problems. There's almost no way animators could have made such a model and not known the car couldn't make the turns. At first glance it seems they would have made use of their own animation and avoided the problem by adjusting the dimensions of the hallway or eliminating the turns. Only they know why it was portrayed incorrectly. However, it's safe to say that, as is the case with many examples of bad movie physics, it was probably based on a conscious decision, rather than an accident. Considering that physics is the most mathematical of all the sciences, it's no wonder moviemakers routinely distort it. They can't resist the urge to distort even simple mathematics. #### Summary of Movie Physics Rating Rubrics The following is a summary of the key points discussed in this chapter that affect a movie's physics quality. These are ranked according to the seriousness of the problem. Minuses [-] rank from 1 to 3, 3 being the worst. However, when a movie gets something right that sets it apart, it gets the equivalent of a get-out-of-jail-free card. These are ranked with pluses [+] from 1 to 3, 3 being the best. [–] [–] Shooting ridiculous amounts of ammo without reloading or the barrel overheating. When really overdone, a movie starts looking like a comic book. [–] Continuous bursts of fully automatic submachine gun fire lasting more than a few seconds. [–] Shooting from the hip and hitting anything smaller than a man-sized target at a distance of under 10 feet (3 m). [–] Shooting from the hip and hitting anything at a distance of over 10 feet (3 m). [–] Sniper rifles in brief cases. [–] Ignoring limitations imposed by simple geometry, such as maneuvering vehicles in impossibly small areas. [+] Depicting the fact that guns get really hot from rapid fire. ## CHAPTER 3 ## CONSERVATION OF MASS AND ENERGY: ### Is Anything Sacred? ### LAWS VERSUS MODELS A few hundred years ago, the science of physics was started by an enlightened few who viewed the world as divinely created by a law-giving entity. These laws—the Ten Commandments—were provided to humanity, along with free will. Inanimate objects weren't so lucky; they just got laws. The enlightened few began to realize they could attain magic-like power by taking advantage of the inanimate world's order and lack of free will. Categorizing the universe's order into the principles and laws of physics essentially gave the enlightened few an operating manual for the universe. In reality, the laws of physics are more like Barbie dolls than immutable laws of creation. Barbie is a model that avoids unneeded complexity and only deals with a few aspects of reality, but deals with them effectively. She is useful for modeling hair and clothing styles, in order to inexpensively predict what will look good on real people—at least on magnificently proportioned ones. Barbie lacks many real-world features such as fully workable joints, a pancreas, and a large intestine. Using her for surgery practice would be a poor application. Internal organs, however, aren't needed for understanding clothing styles. Likewise, the laws or models of physics aren't useful for modeling everything, but are remarkably helpful in the areas where they can be applied. For example, they allow engineers to predict that an aircraft will actually fly long before it's completely built. Most modern innovations, including movie cameras, sound systems, and air-conditioned theaters, owe their existence at least in part to our understanding of the models of physics. Devices such as these have granted Hollywood the power to create entire celluloid worlds. Not every model in physics has achieved the status of being called a law. This term is usually applied only to the most tested and reliable of models. Due to their reliability, physics' laws are never repealed, but they are sometimes refined. Often the refinement involves a better definition of the law's limitations. For example, Newton's second law does not work well when an object's speed approaches the speed of light. For that situation, Einstein's theory of relativity is needed. Yet for slower speeds, both Newton and Einstein gave the same answers. ### THE FIRST LAW OF THERMODYNAMICS—A SYNOPSIS Unlike Hollywood where nothing seems sacred, physics has a law that is as close to absolute truth as anything known to humanity. It's called the conservation of energy, and is sometimes referred to as the first law of thermodynamics. The first law says that matter is essentially a form of energy, and that while energy can change its form, it cannot be destroyed or created. This law started out as two laws: the law of conservation of energy and the law of conservation of mass, but, when Einstein showed that mass could be converted into energy and vice versa, the two laws were combined into one. In this case, refining a law consisted of simplifying it. According to Nobel Prize–winning physicist Richard Feynman, "There is no known exception to this law—it is exact so far as we know." If someone ever finds an exception it will shake science to its foundations. #### EINSTEIN SIMPLIFIES THE FIRST LAW At one time conservation of mass was considered separate from conservation of energy. Then Einstein demonstrated that mass could be converted to energy and vice versa, according to his famous equation: E = mc 2 Where: E = energy released when converting mass to energy, or energy required when converting in the opposite direction m = amount of mass converted to energy or amount of mass produced if converting in the opposite direction c = velocity of light in a vacuum Assume m = 1.0 kg E = 1.0 kg (3 × 108 m/s)2 [] = 9.0 1016 J or 21.5 megatons of TNT Fortunately, it's incredibly difficult to convert mass into energy, or even an innocuous object such as the phonebook could become a nuclear bomb. The conversion of energy into mass is likewise incredibly difficult. Movie violations of the first law should be unforgivable, and yet they're common. In _The Hulk_ [NR] (2003), a nerdy looking scientist transforms into a massive brute over two times taller, with no apparent intake of matter. The Hulk appears to grow larger as he absorbs the energy of various attempts to kill him. True, energy can be converted into matter, but the conversion is incredibly difficult and requires a massive amount of energy to produce a miniscule amount of mass. The energy output of roughly a 100-megaton nuclear bomb—the largest ever built—would create just 10 pounds (4.6 kg) of matter, assuming the conversion is 100 percent efficient. By contrast, any energy absorbed by the Hulk would be minor. Even if he could use it to increase his mass, the result would be imperceptible. For the Hulk, the only real possibility is to find a source of matter that can be easily scooped up, and air is about the only choice. Inconveniently, its density is at least a thousand times lower than the Hulk's. Absorbing enough mass to make the hulk huge and maintain his density would create a whirlwind around him, not to mention inconvenient problems with chemistry. How are a few thousand pounds of oxygen and nitrogen atoms going to be transformed into Hulk-type material? In _Spider-Man_ [NR] (2002), Peter Parker is bitten by a genetically modified spider, which imparts spider-like qualities to him. He finds he can shoot strands of spider web from his wrists. These web strands adhere instantly to objects like tall buildings, and enable Spider-Man to swing Tarzan-like while traveling great distances at fairly high speeds. Unfortunately, the web strands would also require a great deal of matter that seems to come from nowhere. A web strand would probably need to be at least 0.5 centimeters in diameter to support Spider-Man's web-swinging antics. If such a strand were 100 meters long, it would have a volume of 0.002 cubic meters, compared to Spider-Man's estimated volume of 0.07 cubic meters. Spider-Man would lose 2.9 percent of his volume every time he shoots a 100-meter-long web. Web swinging a mere mile (1.61 km) of horizontal distance would use up about 33 percent of his body volume (assuming his web makes a 45-degree angle with the vertical at the beginning and end of each swing, and each web is 100 m long). He would be skeletal by the time he arrived and would have to eat huge volumes of food to compensate.Yet, none of this happens in the movie. This analysis assumes that the volume of web-producing chemicals stored in Spidey equals the volume of web produced. However, even if the chemical volume were half the web volume, Spidey's volume is still going to fluctuate wildly if he does much web swinging. Yes, he could grow a spider fluid tank that could fill and drain as needed. But, assuming he continues to require human internal organs to live, where is he going to inconspicuously put the tank? On the other hand, _Spider-Man_ and _The Hulk_ are obviously based on comic books, so . . . okay . . . they have to be begrudgingly forgiven. ### THE SECOND LAW OF THERMODYNAMICS—YET ANOTHER SYNOPSIS The second law of thermodynamics is much more difficult to state, not to mention grasp, but is considered about as immutable as the first law. It would be easy to write a book about the second law and still not totally explain it or explore all its aspects. Frank L. Lambert, Professor Emeritus, Occidental College summarizes the second law as follows: Energy spontaneously tends to flow only from being concentrated in one place to becoming diffused or dispersed and spread out. Mechanical energy and electrical energy can be considered concentrated forms, while heat or thermal energy would be considered dispersed. A concentrated form of energy is like water in a container on top of a hill. Tip the container over and the water flows downward, spreading out as it goes to a lower level. For all practical purposes it would never be possible to get all of the water back in the container. Likewise, concentrated forms of energy can easily be transformed into dispersed forms, but it's difficult to do the reverse. Heat can, figuratively speaking, be pumped uphill from its dispersed state into a concentrated form, but it can't be done with 100 percent efficiency. For example, less than 40 percent of the heat used to generate electricity in a typical coal-fired power plant actually ends up as electrical energy. The other 60 percent remains as heat and is dumped out of the power plant into the environment. In essence this is the cost for producing the electrical energy. #### CARNOT EFFICIENCY—THE ULTIMATE LIMIT Heat engines are the devices used to convert thermal energy (heat) into useful power. These include steam engines, gas turbines, and the various forms of internal combustion engines used in cars. The second law places strict limits on the maximum possible efficiency of heat engines. This maximum efficiency is called Carnot (pronounced car-no) efficiency and is calculated as follows: e = (1 – T C/TH) • 100. Where: e = efficiency in % T C = cold temperature at which heat is expelled into the surrounding environment T H = hot or elevated temperature produced within the heat engine by combustion, solar energy, geothermal energy, nuclear energy, or some other source Actual efficiencies are a fraction of the Carnot efficiencies. The Carnot calculation does not account for real-world losses due to problems such as heat loss out the walls of the engine or any form of friction. In the case of automobiles, heat has to be removed from the walls of the engine's cylinders to keep them from welding themselves to the moving pistons inside. Yet even in a perfect world with no friction, the Carnot efficiency says that 100 percent of the energy contained in gasoline or any other fuel could never be converted into useful work by a car's engine. Generally, lowering the temperature of the heat source rapidly lowers the efficiency of converting it to electrical energy. Current power plants, even nuclear ones, typically get efficiencies less than 40 percent.The 60 percent or more of unusable heat dumped into the environment after exiting the power plant is now at a much lower temperature. It seems that this exiting heat could be run through yet another power plant to convert more of it to electrical energy, but the temperature is now too low. The heat ends up being wasted because the efficiency would be too low to reasonably attempt converting it to electrical energy. When energy from a concentrated form, such as mechanical energy, is converted by friction to a dispersed form such as heat, it essentially can never be converted back. Hence, the second law says that there can never be a perpetual motion machine, except possibly in a frictionless environment. Unfortunately, friction is ubiquitous. The first law says that if a perpetual motion machine did exist, it could do no useful work on outside objects because that would drain energy out of it and eventually cause it to stop. ### BATHTUBS AND BATTERIES _The Matrix_ [RP] (1999) was rising as a cinematic masterwork until about midway through, when it plummeted into the pit of first law violations. During the masterful first part, its main character, Neo (Keanu Reeves)—unknowingly trapped inside a vast computer simulation—begins to question his existence. He is approached by Trinity (Carrie-Anne Moss) and later Morpheus (Laurence Fishburne) who offer him the chance to find answers. When Neo accepts, he discovers that he, along with most of humanity, actually exists in clear slime-filled bathtubs with all sorts of tubes and cables connecting him to a gigantic computerized machine system. The tubs are housed in a cavernous room tended by gargantuan mechanical tarantulas and are illuminated in part by frequent lightning-like, high-voltage discharges. After freeing Neo and giving him lengthy rehabilitation treatments, Morpheus reveals the truth. The machines were given artificial intelligence (AI), which apparently turned them into control freaks. One might think that possessing intelligence—artificial or otherwise—would have led to understanding, but no, it led to war. The machines were running on solar energy, so humans attempted to pull the plug by blotting out the Sun. This was very clever since humans are powered by food, which also depends on an abundant supply of solar energy. Evidently, humans stocked up on canned goods before blotting out the Sun. The machines turned the tables by enslaving humans and plugging into them as a power source. Morpheus tells us that a human has the bioelectrical energy of a 120-volt battery; but is it a camera battery, a car battery, or something else? Volts are a measure of electrical potential energy per unit of charge, not just a measure of energy. A small 120-volt battery could provide a tiny flow of charge and, hence, a tiny amount of energy; a large 120-volt battery, a huge amount. Besides, 120-volt batteries are hard to find. Certainly, Wal-Mart doesn't carry them, so what Morpheus means when he refers to one is hard to discern. We're also told that humans put out 25,000 British thermal units of body heat. If this happens continuously each second, it's an impressive rate of 26.4 megawatts. If the heat could magically be converted to electricity, it could power a small city. If the body heat were given off over a year, it would be a paltry rate of 0.84 watts. Even if it were magically converted to electricity, 0.84 watts would not be enough to power most light bulbs. Unfortunately, the second law casts doubt on whether any significant part of body heat could be converted to electrical energy. Body heat is a very dispersed form of energy, while electrical energy is a very concentrated form. Body temperature is so low that converting the body's heat to electrical energy would have a miniscule efficiency. How human body heat would be useful to a vast electronic computer system is a mystery. Generally, electronics have to be cooled. Morpheus concludes his energy discussion by lofting a copper-topped D-cell flashlight battery (ironically rated at 1.5 volts), implying that this represents the puny power output of a human. It's meant as a highly dramatic gesture, but the numbers make it look like a parody. A bed-ridden, six-foot-tall, 160-pound, twenty-five-yearold male requires about 2,000 kilocalories worth of food energy per day just to stay alive. Note, that one food calorie equals 1,000 calories. In other words the calories reported for foods are really kilocalories. (Why they're not called kilocalories instead of capitalizing the "c" is anyone's guess.) This works out to a power rate of 96.6 watts, or about as much as a typical incandescent light bulb. In a day's time a tub-bound human uses 2.3 kilowatt-hours of energy to stay alive. A copper-topped D-cell flashlight battery holds about 0.023 kilowatt-hours of energy. In other words, it would take about one hundred D-cells worth of food energy every day to keep a human going. The first law clearly says that humans cannot produce more energy than they consume. Hence, humans cannot be considered an energy source. At best, they are devices that can convert food energy (a type of chemical energy) into electrical energy. If they produce the output of a D-cell, they have a best-case food conversion efficiency of less than 1 percent. However, the energy required to collect and distribute the food as well as maintain the slime tubs would be more than the human electrical output. Why would the machines bother to keep them? Feeding liquefied dead humans (as done in the movie) back to the living ones doesn't help. Meeting human energy needs with this system would make it a giant perpetual motion machine—clearly impossible according to the second law of thermodynamics. A 160-pound human probably contains about as many food calories as (please forgive the comparison) 160 pounds of hamburger meat. At about 1,200 kilocalories per pound this works out to 19,200 kilocalories of possible food energy. Just to stay alive for fifty years this human would have to consume over 36 million kilocalories—equivalent to ingesting 190 recycled humans, or about 3.8 dead humans a year. Where are all these people supposed to come from? _Matrix_ apologists have proposed that humans are not a primary power source but a backup source like the battery in a car. Here's a thought: why don't the machines just use car batteries? Had the machines been thinking, they would have raided their local Wal-Mart for automotive batteries before starting the war. Surely the machines have some nonhuman form of energy storage in their hordes of sentinels—the octopus-like robots that float around in subterranean tunnels seeking to kill humans who've escaped their bathtubs. Sentinels would have to carry a large amount of stored energy to keep going. To cover itself, the movie throws in a quick mention that the human energy source powering the machines is combined with a source of fusion. This is like getting on a jet airliner and having the captain explain in great detail that the plane is rubber band powered, then adding that it also has four jet engines. Guess which power source gets it off the ground? Duh. ### MYTHICAL ROBOTS _A.I.: Artificial Intelligence_ [XP] (2001) couldn't even make it past the opening without slamming into the first and second laws. The movie opens with a scene of churning surf. The narrator proclaims that greenhouse gasses have warmed Earth, causing the ice caps to melt and flood major cities in coastal areas. As a result, populations have been displaced and "hundreds of millions" in poor nations have starved. So far it's science fiction, but not for long. The narrator continues by announcing that prosperous nations have sustained their prosperity to a large extent by creating the perfect low-cost labor force: robots. According to the narrator, these robots require no resources beyond those used to create them. In other words, we're asked to believe that the robots never need to be recharged, refueled, or rebuilt. They are essentially perpetual motion machines, which break the first and second laws. As mentioned in the first chapter, sometimes there are good artistic reasons to defy a law of physics. Great artists have often been defiant. Edouard Manet and René Magritte are both famous for creating paintings that look realistic but use impossible physics. Manet defied physics to provoke the French Academy. His painting _Le Bar aux Folies-Bergère_ ( _The Bar at the Folies-Bergère_ ) deliberately shows an impossible reflection of a young woman in a mirror. The viewer is standing directly in front of the young lady. Her reflection in the mirror on the wall behind her should be directly behind her and almost impossible to see. Instead, Manet painted it to the far right side (see Figure 6). This no doubt horrified official art critics of the time, much to the delight of Manet. Magritte broke the laws of physics as a type of visual joke or riddle. His painting _L'Empire des Lumieres_ ( _The Domain of Lights_ ) shows a night scene occurring during the day. The sky is noticeably in daylight while the house below is obviously illuminated as it would be at night. There's a big difference between insightful or clever rule breaking and the clumsiness of an amateur who can't get perspective, proportions, and the overall physics of vision right. Unfortunately, the statements concerning robots in _A.I_. don't seem to be particularly clever or insightful. The tendency to view machines as superior to their biological counterparts has been widespread. Biomedical engineering literature of the early 1970s proclaimed that science would produce a viable mechanical heart replacement for humans in about twenty years. By now, individuals with artificial tickers should be commonplace—a heart was, after all, merely a pump. How hard could it be to replace it? But even today, replacing a human heart with a mechanical device is still in the experimental phase. Yes, considerable progress has been made, but the truth is, biologically produced hearts are still vastly superior to mechanical ones. Apologists for _A.I_. often say that the narrator in the opening scenes is not to be taken literally. What he really means is that the robots can go for extremely long periods of time without being recharged, refueled, or rebuilt. These lengthy time spans make it seem as though robots need no resources beyond those used to create them. Ten years between refueling is about the shortest time that would give the illusion of robots needing no outside resources. So let's see how much energy storage would be needed. Gasoline is used for energy storage in automobiles not just because it's available but because it has one of the best energy to mass ratios of any energy storage medium currently available. It seems like a good starting point. As mentioned earlier, a typical male human requires about 2,000 kilocalories of food energy per day just to stay alive; if he performs manual labor, he needs about 2,500 kilocalories. Assume the human is replaced with a 100 percent efficient gasoline-powered robot. A ten-year fuel supply would require 1,900 pounds (864 kg) of gasoline. Obviously, no humansized robot is going to be walking around with that much fuel aboard, let alone be 100 percent efficient. To be viable as a tenyear energy supply, a storage medium would have to contain about one hundred times more energy per pound than gasoline— fat chance. The only solution would be to use some type of nuclear fuel. Needless to say, this has all kinds of problems: radioactivity, for one. Certainly, the movie's scene in which obsolete robots are destroyed in sick ways to entertain a cheering circus-like throng could never be done.The crowd would be irradiated from leftover fuel and nuclear waste inside the robots. Nuclear fuel produces heat, which then has to be converted to electrical energy in order to be useful inside a robot. There's no known mechanism for producing electricity directly from nuclear fuel.The second law says that only a fraction of the heat produced by the nuclear fuel will actually end up as electrical energy. The rest has to be dumped into the environment as waste heat. To get any appreciable amount of efficiency, the heat converted to energy has to be produced at an elevated temperature, probably at least 932 degrees Fahrenheit (500°C). Aside from being radiation hazards, the robots would likely be fire hazards. The movie's main character—a robot that looks like a little boy— becomes depressed because his adopted human mother doesn't love him. At the end of his emotional rope, he jumps into salt water in a suicide attempt. He's rescued, but before he can dry off he ends up piloting a helicopter-turned-submarine to the bottom of the ocean where he accidentally becomes trapped. When rescued—a mere 2,000 years later—he functions like he'd been on the bottom a few minutes. Not even his t-shirt has deteriorated. Park a car for two years, turn the ignition key, and you'll be lucky if it sputters. Obviously, the moviemakers took the opening narrator pretty seriously. A 2,000-year supply of nuclear fuel for the hypothetical 160-pound bedridden human described earlier would add up to the energy equivalent of 1.4 kilotons of TNT. This is like a lowyield tactical nuclear device that could take out a neighborhood. Even if the child robot had half as much, combine his stored energy with 2,000 years of neglect and he'd be a walking Chernobyl waiting for meltdown. _A.I_. seems to be a movie that wants to make serious statements about the nature of love and the mother-child relationship, yet, from a physics standpoint, achieves pure silliness. Its violations of the first and second laws are not consistent with its serious tone and are unforgivable. It's easy to obey the first and second laws, especially in movies with serious science fiction themes. If it's not done, the movie becomes, at best, a science fantasy or cinematic comic book. At worst, the movie turns into pure nonsense. #### Summary of Movie Physics Rating Rubrics The following is a summary of the key points discussed in this chapter that affect a movie's physics quality rating. These are ranked according to the seriousness of the problem. Minuses [–] rank from 1 to 3, 3 being the worst. However, when a movie gets something right that sets it apart, it gets the equivalent of a get-out-of-jail-free card. These are ranked with pluses [+] from 1 to 3, 3 being the best. [–] [–] [–] Serious violations of the first law. Includes the metamorphosis of creatures into a very large size with no apparent source of matter or reduction in density. [–] [–] [–] Depictions of perpetual motion machines. [–] [–] [–] Depictions of superhuman robots that never need recharging, refueling, or rebuilding. At best this categorizes a film as a cinematic comic book. [–] [–] Minor violations of the first or second laws that are not significant parts of the story line or plot. [+] [+] Depicting robots that break down and regularly need to be refueled or recharged. ## CHAPTER 4 ## SCALING PROBLEMS: ### Big Bugs and Little People It's an old movie gimmick: radioactive contamination, toxic waste, genetic engineering, or some other out-of-control technology abnormally shrinks or expands someone or some creature. While the gimmick is certainly entertaining, the physics are flaky. ### SCALING DOWN HUMANS In _Honey I Shrunk the Kids_ [NR] (1989), Rick Moranis plays a whacky inventor named Wayne Szalinski who works at home and successfully builds a device for miniaturizing objects. Naturally, his son, daughter, and two neighbor kids end up accidentally (surprise, surprise) getting shrunk. After Szalinski unknowingly sweeps them up and throws them out, they must journey across the foreboding backyard to get back to the house. Who would have guessed that hanging around the backyard could be such an adventure? Ordinary matter is almost entirely filled with empty space. The vast majority of mass in an atom is contained in its nucleus. The mass of its electrons is inconsequential by comparison. On an atomic level, there are huge distances between the nucleus of an atom and the nuclei of its nearest neighbors, even in a solid. Other than containing a few small specks, namely electrons, the space between nuclei is filled with essentially nothing. It is not filled with air, it's filled with void. It's conceivable that people could be shrunk by somehow removing some of the empty space inside them. This happens in a black hole, although to a much more dramatic extent. Of course, there are many problems associated with squeezing empty space out of matter. For example, the repulsion forces between nearby atoms would increase to levels much higher than normal, making it extremely hard to keep the atoms from moving apart— explosively. However, let's ignore the problems and assume the space can be magically removed. Using this system, a 100-pound teenager reduced to the size of an ant would still have exactly the same number of atoms in her body. This means she would have exactly the same amount of mass and weight. When something is scaled up, all its dimensions are multiplied by the scaling factor. When scaled down, all its dimensions are divided by the scaling factor. Note that any area on any object will scale up and down with the square of the scaling factor. For example, scale a human up by a factor of 10, and the area under her feet will increase by a factor of 102, or 100. Scale her down by a factor of 10, and the area under her feet will scale down by a factor of 100 or become 1/100 its original size. Let's assume Szalinski's teenage daughter's foot is about 10 inches (25.4 cm) long by 4 inches (10.2) wide, giving an area of 40 square inches. When walking or running, her weight would momentarily be applied to the area of a single foot. This yields a pressure as follows: Pressure = weight/area = 100 lbs/40 sq inches = 2.5 psi or 0.18 atm If the teenager is scaled down by a factor of 100, her foot will now be 0.1 inches long by 0.04 inches wide for an area of 0.004 square inches. This increases the pressure beneath her feet by a factor of 10,000. If she places her weight on one foot, the pressure would equal 25,000 pounds per square inch. Standing on both feet, the pressure would be 12,500 pounds per square inch. Either of these pressures would easily exceed the compressive strength of concrete (typically 3,000 to 4,000 psi). But walking on a concrete surface might break her feet before it broke the concrete. The miniature teenager will have feet with areas similar to the ends of small screwdriver blades. Place two of these vertically with the tips touching the soft soil of a typical back yard and try standing on them. They will immediately sink into the ground. Without doing any further analysis, it's possible to say that Szalinski's two kids and their two friends are never going to make it across the yard. There's only one other conceivable way to shrink children: remove some of their molecules. Removing electrons isn't helpful because they don't have enough mass—not to mention that it would create ions and alter chemical bonds. Removing protons alters atoms into completely new materials. Pull a proton out of an oxygen atom and it becomes nitrogen. Doing this to the oxygen atoms in a room would suffocate its occupants. Removing neutrons eventually results in unstable radioactive isotopes. Take a neutron out of normal oxygen and it becomes a radioactive isotope that decays rapidly into an isotope of nitrogen. This process has a half-life of only 122.2 seconds. In other words, half of the radioactive oxygen is gone in a little over two minutes. Removing an atom from a molecule creates a totally different compound. Taking an oxygen atom from a water molecule converts it to hydrogen gas. So removing atoms also can't be done. The only possibility left is removing whole molecules. The question becomes, how many molecules can be removed before problems arise? Sweating, for example, removes molecules, but at some point it results in dehydration. To analyze this possibility, let's assume that the miniature person has to end up with the same density as he started with. We have to first do a little magic (called algebra) to understand this: ### STARTING WITH THE DEFINITION OF DENSITY Density = mass/volume We can derive the following: Mass = (volume) × (density) This equation says that mass will be directly proportional to volume since density will be constant. For example, if volume is decreased by a factor of 10, mass will decrease by a factor of 10. Obviously, we need to know how volume scales up and down to find out how much the mass has to decrease when shrinking a teenager. To understand this, imagine a sphere. Its volume is equal to 4/3 pi times the quantity of the radius cubed. In this case, if we scale the radius up by a factor of 10, the volume increases by 103, or 1000. Likewise, if we scale down by a factor of 10, the volume decreases by a factor of 103, or 1000. In other words it will be 1/1000 of its original size. It turns out that regardless of an object's shape, its volume will scale up and down with the cube of the scaling factor, in other words with (scaling factor)3. If a teenager is shrunk by a factor of 100, her volume will decrease by a factor of 1003, or 1,000,000. This means for every molecule left in the tiny version of the teenager, 999,999 molecules will have to be removed. We could, perhaps, remove cells instead of molecules, but imagine what would happen to a person if 99.9999 percent of his or her brain cells were removed. According to the first law of thermodynamics (see Chapter 3), all the removed molecules can't simply disappear. They have to go someplace, for example, into a barrel of goo. The barrel of goo is certainly a problem, but it's only the beginning. It's going to be a nightmare figuring out which molecules in what ratios have to stay in order to end up with a working human after miniaturization. The situation gets worse when considering that humans are warm-blooded. Like all warm-blooded creatures, humans have to eat a great deal of food just to maintain their body temperature. This food intake is proportional to surface area and scales down by the square of the scaling factor. Hence, the tiny teen's food requirement will be 1/10,000 times what it was in her full-sized form. So, what's the big deal? Assume the normal teen eats 1 percent of her body weight in a day to maintain her temperature. Her food intake has certainly decreased, but her volume has decreased even faster since it scales down by the cube of the scaling factor. Because density was held constant, her mass and weight have decreased by the same factor as her volume. So, she will now have to eat 100 percent of her body weight every day just to maintain her temperature. Even if the ambient temperature is 70 degrees Fahrenheit (21°C), she would have to eat constantly to avoid hypothermia. This is why small critters such as ants are typically cold-blooded. It is also why tiny warm-blooded animals such as shrews have to eat constantly. Even allowing for some magic, physics says that scaling a human down by large factors simply can't be done if it's desirable to keep her alive. Obviously, scaling problems are major flaws in movie physics and should immediately kill the chances of getting anything better than an RP rating. So why is _Honey I Shrunk the Kids_ not even rated? Simple, it's a Disney family movie. There is not a speck of serious science fiction in it. It's supposed to be silly, and it is. ### SCALING UP HUMANS In a sequel called _Honey I Blew up the Kid_ [NR] (1992), Rick Moranis is again creating accidental science experiments. This time, his two-year-old son Adam gets blown up to gargantuan size.The youngster is no Godzilla, but he does treat his neighborhood like a giant toy box. Once again, there are only two conceivable ways to expand a kid. The first is to increase the space between and inside of molecules. This would likely change him into a random cloud of gas or ions that would disperse at the first sign of wind. However, let's assume that by magic his molecules stay together but with more space between them. #### By How Much Could a Human Be Scaled? To fully answer this question we'd have to define what it is to be human. A very large or very small human would likely not have the same thinking ability (it could be better or worse), lifespan, movement, or biological design as a human on the opposite end of the spectrum. The shortest recorded man was Gul Mohammed at 1.88 feet (0.572 m) and the tallest Robert Wadlow at 8.93 feet (2.72 m), for roughly a scaling factor of 4.8 between the two. Allowing a little extra room, it seems likely that the largest humans could be about five times bigger than the smallest ones and still live. In other words, adult human heights could range from about 1.8 feet (0.549 m) to about 9 feet (2.74 m). The large humans would have 1.5 times the difference in blood pressure between their feet and head and likely have more health problems, including early heart failure, than those who are a more normal size of 6 feet (1.8 m) tall. (Wadlow died of an infected foot blister at age 22.) The pressure load on their joints would be 1.5 times higher than the 6-foot person, possibly leading to early arthritis. While their food intake would be less per unit of body weight, such large people would have to eat about 2.3 times as much food and spend more time finding and consuming it than the 6-foot person. Their brains would be larger than normal, but with longer nerves, bigger organs to control, more challenges to their immune systems, higher food requirements, and so forth, they'd likely not be any better at reasoning and problem solving than their normal-sized counterpart. As for the miniature humans, while they might have some arthritis advantages, their blood vessels would be far smaller than normal and, hence, more prone to clogging. They would have to eat a greater proportion of their body weight in food to maintain their temperature and so would have to spend more time eating. With their much smaller brains they'd certainly have no advantage in thinking ability. Normal-sized humans really are near the optimum size. In the movie, the youngster is scaled up by roughly a factor of 50. His volume increases by a factor of 125,000. Since his mass remains constant, his density will also decrease by a factor of 125,000. In other words, he will be 1/125,000 times as dense. Humans have a density similar to water (1.0 g/cc) because they are mostly water. Hence, the expanded youngster will end up with a density of 8 × 10-6 grams per cubic centimeter. This is less than 1/10 the density of hydrogen gas, which is about 9 × 10–5 grams per cubic centimeter. In other words, the title of the movie should be _Honey I Blew up the Kid and He Blew Away_. The other alternative is the constant density approach. Add 124,999 molecules to the kid for every one he now contains. He'd have to be pumped up with an Olympic-sized swimming pool full of goo, all the while hoping the molecules would all somehow find their proper place. If we assume the additional molecules wouldn't kill him, there would be other serious problems. We can model the youngster's leg bones as though they are vertical cylinders similar to the columns that held up ancient Greek temples. Of course, this assumes he is standing. In this position, the leg bones or columns' ability to hold up weight will be proportional to their cross-sectional area—in other words, the area of the circle that would just fit around the outside of the column. Note that the load on a leg of a standing child, or adult for that matter, is caused by gravity.This acts in the vertical direction and is called a compression load since it tends to compress the leg. The cross-sectional area is in a horizontal plane. In other words, the cross-sectional area that determines the strength of the leg is perpendicular to the compression load's direction. Since cross-sectional area is indeed an area, it will scale up and down with the square of the scaling factor. Hence, if the bone's diameter is doubled, its cross-sectional area and subsequent ability to support weight will increase by a factor of 22,or 4 (assuming no change in material properties). Obviously, its strength will increase or decrease very rapidly when scaled up or down. When two-year-old Adam is scaled up by a factor of 50, the weight his leg bones can support will increase by a factor of 502,or 2,500. Unfortunately, his weight will also increase by a factor of 503 or 125,000. So his leg bones would have to be fifty times stronger. His neck and spine support compression loads and would also need to be fifty times stronger. But they contain numerous joints, which tend to be weaker than bones. Most likely, joints and bones all over his body would fail, and he would collapse into a very un-Disney-like mess. #### King Kong _King Kong_ [PGP-13] (2005) features a giant gorilla that ends up rampaging around New York City. It's one of the most enduring Hollywood movie images, but how realistic is its physics? The question can be answered in part by calculating the scaling factor. A real gorilla is, at most, about 5 feet 7 inches high (1.75 m) and 396 pounds (180 kg) in weight. Increase its height to a King Kong–sized 25 feet (7.6 m) and the scaling factor is 4.5—a value within the design range of many types of animals, such as dogs (a Great Dane, for example, is at least four times taller than a Chihuahua), or for that matter humans. Carbon-based biological creatures in the size range of King Kong—namely dinosaurs—have existed. The great ape would have a weight of 18 tons (16,000 km) compared to a brachiosaurus weight of 84.8 tons (77,100 kg) or a tyrannosaurus weight of 7 tons (6,400 kg), again within the values for real (albeit extinct) animals. Such an enormous gorilla is conceivable, but could it behave as depicted in the movie? The muscle strength to weight ratio would be less than onefourth its original value (assuming muscle strength scaled up with cross-sectional area.) Hence, the great beast would not have the leaping and climbing ability depicted in the movie. Many of the beast's features, such as eye and nose size, would be way over designed, representing a poor level of optimization. A giant squid is about the only animal with such large eyes, and these are designed to be able to gather enough light for vision even in the near-lightless depths of the ocean. When standing, Kong would have about 410 times more gravitational potential energy stored in his body than a gorilla. However, his bones would only be about 20 times stronger (in tension or compression). If King Kong fell during a fight, he would be prone to injuries like broken bones. Could he successfully hold an uninjured blonde in one hand while fighting three tyrannosauruses simultaneously? Yeah right. These "terrible lizards" with massive jaws full of 12-inch- (30-cm-) long serrated teeth designed to tear flesh and penetrate bone, would be fully optimized oversized meat grinders. King Kong would end up looking like ground round and probably bleed to death even if he won. As for the blonde, she'd probably be shaken and bounced to death. ### ANTS, ELEPHANTS, AND ELASTIC STABILITY The analysis of scaling humans up and down has ignored something called elastic stability. A typical column fails in compression when the weight it supports is too high. Its maximum weight is directly proportional to its cross-sectional area but is not at all influenced by column length. However, make a column too long, and length becomes an issue. The longer the column, the more likely it is to fail because it lacks elastic stability. When it fails, it will suddenly buckle and collapse with much smaller loads than those needed to cause a compression failure in a shorter column. The bones in a person's legs aren't long enough to make elastic stability an issue, but obviously it imposes a limit on how long a creature's legs can ultimately be. Ants are famous for their ability to carry fifty times their weight. If scaled up from 3 millimeters to 3 meters Hollywood-style (a scaling factor of 1,000), they would indeed be formidable and terrifying. Of course, scaling up Hollywood-style means they could still carry fifty times their weight. To understand why this is nonsense, let's make the same analysis as was just done for the two-year-old. The ant's leg strength in compression would increase by a factor of 1,0002, or 1 million. However, the ant's weight would increase by a factor of 1,0003, or 1 billion. The ratio of weight to leg strength in compression would increase by a factor of 1,000. Each leg in the ant's large-size version would have to be 1,000 times stronger than needed in the ant's original size. Most likely, the ant would collapse under its own weight. However, the scenario gets even worse. Ant legs are very long and thin. If scaled up, they would have elastic stability problems as described earlier. The effects of elastic stability can be demonstrated with a soda straw. Cut a 2-centimeter-long piece. Compress it like a leg bone by squeezing it between your thumb and index finger. It takes a lot of force to make it fail. Conduct the same experiment with a 12-centimeter-long straw and you'll find that the longer straw buckles immediately with the slightest side force or misalignment. The longer straw has elastic instability. The long, thin legs of ants, spiders, and other crawly little critters would be a complete disaster in an oversized version. The simple truth is that the design of creatures is dictated in large part by the physics of their size. They just can't be scaled up or down by much without a design change.That's why elephants have proportionally larger legs than goats. Most of the incredible strength of critters such as ants and spiders is related to their small size. These amazing abilities simply do not scale up. If a magical spider bit a human and turned him into a man-sized spider-person with properly scaled-up spider strength, he would be lucky if he could get out of bed. ### SCALING MACHINERY In general, things get proportionately weaker from a mechanical standpoint and considerably heavier when scaled up. A multipleengine bomber will have proportionately larger wings than a fighter plane in order to provide the additional lift required to counteract the bomber's much higher weight. Due to its smaller size, the fighter will be able to make maneuvers that would tear the wings off a bomber. This table shows a comparison of a P-51 single-seat fighter aircraft to a fourengine B-17 bomber, both WWII aircraft. Actual scaleup factors are the bomber's values—wing span, length, height—divided by the fighter's values. In a Hollywood-style scale-up, every dimension on the aircraft would be multiplied by a constant scale-up factor. Figure 8: fighter to bomber comparison ratio As a result, parameters such as weight would scale up by the cube of the scale-up factor. Scaling up motor horsepower is more complex. If it scaled up with the engines displacement volume, motor horsepower would be increased by a factor of 22,952. Generally, Hollywood assumes that performance factors such as speed would also increase by the scale-up factor, following the principle that bigger has to be better. In this case, such an assumption would be especially silly since it would make the bomber supersonic, and supersonic aerodynamics are completely different from subsonic. Note that actual scale-up factors are inconsistent with the Hollywood factors. In other words, a WWII bomber is not simply a scaled-up fighter. It has to be redesigned specifically for its mission. Some aspects of performance, such as maneuverability and air speed, have to be sacrificed to gain others, such as payload. Likewise, the pilot of a bomber is not going to be interchangeable with the pilot of a fighter, and vice versa. While both men may be capable of flying the other's craft, it's going to take a lot of hours of flying to master it. The business of using fighter pilots to fly a bomber mission as depicted in _Pearl Harbor_ (see Chapter 1) is a Hollywood fantasy. This chapter has dealt with only a handful of scale-up issues. The problems extend into all areas of science and engineering. For example, physicists currently use quantum mechanics on the atomic level and general relativity on an astronomical level; the two are not interchangeable. Efforts have been repeatedly made to combine them into a set of universal principles. Eventually, this may be done. Meanwhile, even the principles of physics are subject to scaling issues. #### Summary of Movie Physics Rating Rubrics The following is a summary of the key points discussed in this chapter that affect a movie's physics quality rating. These are ranked according to the seriousness of the problem. Minuses [–] rank from 1 to 3, 3 being the worst. However, when a movie gets something right that sets it apart, it gets the equivalent of a get-out-of-jail-free card. These are ranked with pluses [+] from 1 to 3, 3 being the best. [–] [–] [–] Scaling a living creature up or down by incredible amounts without killing it. This almost always tags a movie as comic-book-like when done as a major plot device. [–] [–] Claiming that the incredible strength of small critters, such as spiders, can be passed on to a much larger critter, such as a human. Again, this tends to tag a movie as comic-book-like. Of course, if it is based on a comic book, then it's not necessarily a problem. [–] Portraying significantly larger or smaller inanimate objects as though they will behave similarly to their regular size. ## CHAPTER 5 ## INERTIA AND NEWTON'S FIRST LAW: ### Why Blowing Up Spacecraft Is a Bad Idea ### NEWTON'S FIRST LAW—A BRIEF HISTORY Newton's first law could be called the bunny principle—it states that objects keep going and going, just like the Energizer bunny, until a net force changes their motion. The change could be speeding up, slowing down, or a change in direction. Newton's first law is more typically called the law of inertia, since inertia is the property of mass that resists a change in motion. The higher the amount of mass, the more difficult it is to get an object moving. Once moving, the higher the mass, the harder it is to stop or change the object's direction. It took geniuses to figure out this simple principle; Leonardo da Vinci was one of the first to do so. Human experience tells us that a force is required to keep an object moving. When the ox quits pulling, the cart stops; so it seems obvious that a force is needed for motion. But, what if there were always a force present that took over and caused stopping as soon as the pulling force ended? In our world, it's essentially impossible to be totally free of friction or some other resistance force, such as air resistance. So, objects do tend to stop if nothing is pushing or pulling them in the direction of motion, but it's because there's virtually always a resistance force pushing in the opposite direction of the motion. The difference between the resistance force and pushing force is called the net force. If the pushing force is larger than the resistance force, the object speeds up. If it's the opposite, the object slows down. If the two forces are exactly the same size, the object stays at constant velocity. If it's moving, it continues to move. If it's stationary, it remains stationary. Da Vinci most likely understood the ubiquitous nature of resistance forces like friction. He couldn't create a frictionless environment, but could imagine one. He might have visualized a friction-free world with only a single moving object in it. In other words, there would be no other objects for it to collide with and no resistance forces to alter its motion. He would then have asked a key question: what happens to the object's motion over time? The answer: nothing. The object would move in a straight line at the same speed forever. This profound principle was called Leonardo's law. Then along came Newton. He embellished Leonardo's law with two additional related laws, invented calculus, and managed to get Leonardo's law named after himself. It's now known as Newton's first law. ### WWII NAVAL BATTLES AND THE PROTECTIVE NEWTONIAN SHIELDS Both the concept that it takes a net force to change an object's motion and the idea that there's almost always some sort of resistance force opposing motion are profound. Let's take a look at an example to see why. Imagine a WWII battle, and a massive convoy is moving slowly through enemy waters with gun crews on alert. There are destroyers, cruisers, battleships, and aircraft carriers seemingly in every direction. Suddenly a lone aircraft swoops from the sky, diving straight for the deck of an aircraft carrier. Every gun crew on every ship that sees the aircraft opens fire. At the last moment the aircraft comes apart in a ball of fire and falls harmlessly into the sea. The aircraft carrier is safe. Careful observation would show that the aircraft continued its forward motion even as it broke into pieces.The forces exerted by the bullets, even cannon shells, are not high enough to stop the aircraft's forward motion. They do, however, punch it full of large holes that damage the airframe, disable the control systems, wipe out the engine, and rupture the gas tanks. With the engine disabled and the aircraft falling apart, air resistance slows the pieces and gravity pulls them downward as though the ship were protected by a giant Newtonian shield. As long as the aircraft comes apart well before it reaches the aircraft carrier, the shield works and the pieces fall harmlessly into the ocean. But the shield has a weakness—if the aircraft gets too close before coming apart, it hits the ship and does a lot of damage. Holding together just long enough to hit a ship was the principle behind kamikaze suicide attacks. Even if the airplanes were shot up, if they got close enough, they could still do damage. In WWII, antiaircraft guns often could not shoot a plane down at a safe distance, and so kamikaze attacks did indeed inflict lots of damage. Of course, the damage was not just caused by the hurtling aircraft's mass but also by the explosives it carried. If a kamikaze plane, or for that matter a bomb or torpedo, hit a ship and blew it up, the explosion usually did little damage, if any, to nearby ships. These explosions would typically send both large and small chunks of metal hurling through the air, but nearby ships would once again be protected by their Newtonian shields. The combined forces of air resistance and gravity forming the shields would cause the chucks to harmlessly fall into the ocean long before they could strike a nearby vessel. Without air resistance, even the act of shooting at attacking aircraft would have been highly dangerous to other ships in a convoy. The 20-millimeter, 40-millimeter, and 5-inch (126 mm) cannon rounds fired by the thousands at approaching enemy aircraft were easily capable of inflicting serious damage to a navy ship if they struck it at full velocity. However, air resistance usually did a good enough job of slowing them down to prevent serious damage. Typically, larger cannon rounds containing high explosives were fused to explode long before falling back to Earth.The shell would burst into hundreds of smaller misshapen pieces. Although still moving forward, they would be less aerodynamic. With higher air resistance, the pieces would quickly slow down. The lower velocity in combination with a smaller size would greatly decrease the damage if they rained down on nearby ships. WWII antiaircraft gun crews wore helmets to protect themselves from such falling debris. While a helmet offered no protection from a cannon round at full velocity, it would protect against small pieces of falling shrapnel. ### WWII-STYLE SPACE BATTLES WWII naval battles have been the model for numerous movie space battles, such as those in _Star Wars_. Unfortunately, a good resistance force is hard to find in outer space, so fighting a space battle WWII-style would be highly dangerous to all participants. Blowing up an enemy spacecraft, regardless of size, could damage other vessels, even at great distances. If the fighter craft were small and attacking at high speed on a collision course with a much larger battle cruiser, there would be no safe way to "shoot down" the smaller craft. Such a craft could easily be closing in at several thousand miles per hour— many times the velocity of a speeding bullet. If the fighter craft were blown up, its pieces would still continue forward with many, if not all, pieces smashing into the battle cruiser. These pieces would not be like shrapnel falling from the sky. There would be no air resistance to slow them or gravity to pull them "downward." They would impact at high velocity and include not just large pieces of shrapnel but also gasses or plasma liberated by the explosion. These fluids could easily strike with velocities several times higher than the atomic blast wave at ground zero in Hiroshima (estimated at a mere 980 mph). Blowing up such a craft would be worse than turning a rifle shot into a shotgun blast. Okay, armor plating would work better against numerous small high-velocity particles than against a single large particle, but many of the smaller particles would gain kinetic energy from the explosion when the ship blew up. Even small high-energy particles would be capable of knocking out sensors and weakening armor plating, not to mention sending shock waves into a battle cruiser's interior. If two large battle cruisers were flying side by side and a small spacecraft flew between them, the larger ships would face an added dilemma. If they shot at the small enemy ship and missed, they'd hit each other. Any projectiles they fired would go in a straight line. There would be no gravity to pull the projectiles downward into the water between them. (There would be no water either.) A gunner could fuse his projectiles so they blew up in the space between the cruisers, but then he'd shower the opposite cruiser with high-velocity shrapnel.The fact that the shrapnel was misshapen and had poor aerodynamics would be no help.There's no air to provide air resistance in outer space. Lasers and high-energy particle beams would have similar problems. There would be no way to limit a laser's range, and if one cruiser fired a beam and it missed the intended target, the beam would damage any other cruiser in the beam's path. But then such a beam should never miss. Even so, the problems of nearby exploding craft would persist. Compared to space gunners, WWII antiaircraft gunners had far less danger of injury from blowing up nearby enemy craft, but they also had far more difficulty doing so. WWII projectiles had a downward curving trajectory and would have been moving slowly enough that a fast-moving aircraft could get out of their way. The WWII gunner couldn't aim directly at the aircraft. He would have had to estimate where the aircraft would be when the bullet arrived and how much the bullet would drop during its flight to the target—and then aim accordingly. Generally, thousands of rounds of ammunition were fired for every WWII aircraft shot down. On the other hand, laser or high-energy particle beams travel in straight lines so fast that they arrive almost instantaneously. Even ordinary projectiles travel in straight lines and reach much higher average speeds in outer space, due to zero air resistance. It would be much easier for a space gunner to hit a target. The ratio of hits to beams fired would be vastly better than for WWII antiaircraft guns. The difficulty of hitting aircraft with antiaircraft gun fire made bombers and torpedo planes formidable and generally reusable antiship weapons in WWII. If enough aircraft attacked from different directions, they could get through antiaircraft fire and sink a ship with bombs or torpedoes. If the pilots were willing to commit suicide, the chances were even better. In outer space, with the higher accuracy of laser or ultra-high-velocity particle beams, attacks of a smaller spacecraft against a larger one would invariably be suicide missions. If the smaller craft survived the antispacecraft fire and used a torpedo, missile, or some other weapon to blow up a larger battle cruiser, the exploding cruiser would probably take its attacker with it. In fact, it would pepper all nearby spacecraft with highvelocity chunks of shrapnel. Blowing up a battle cruiser as depicted in movies would be a very dangerous thing to do. While the WWII naval battle model used for Hollywood space battles is exciting, it's not realistic. So, how can Hollywood possibly justify its use? Filmmakers invented a convenient device called shields, which are supposedly force fields that surround space craft and protect them from harm. As long as the shields hold, one spacecraft can blow up another nearby and not have to worry about high-velocity shrapnel or blast waves. It's arguable whether this is or isn't a legitimate use of artistic license. On the one hand, shields are an important plot device and are usually not overexplained with scientific mumbo-jumbo. In fact, they're rarely explained at all. On the other hand, there's no known mechanism to show how they could work, not even a reasonable theory. The exception is a magnetic field used to shield against high-velocity charged-particle beams. A magnetic field will cause a force on a moving charged particle. Since the force will be perpendicular to the direction of motion, the particle will be deflected. This is how Earth's magnetic field helps protect us from the charged particles emitted by the Sun. ### REALISTIC SPACE BATTLES? In a "real" space battle—possibly an oxymoron—the craft would fight at great distance. If the ships were inhabited by biological beings similar to humans, these beings would have to breathe. At first glance, it seems that the object of battle would be to punching large holes in the hull to depressurize the opposing ship. Aside from killing the inhabitants, the depressurization could disrupt weapon systems. The Joule-Thompson effect predicts that dropping the air pressure inside the ship would also lower its temperature. Certainly, if the temperature dropped to cryogenic levels (cold enough to liquefy or freeze most gases), the equipment would most likely cease to function. However, Joule-Thompson cooling alone would not be sufficient to do this. Although we're used to thinking of space as a very cold place, there is no super-cold air in outer space to rush in when the ship depressurizes. It could take some time for the interior of the ship to reach cryogenic temperatures. After losing its atmosphere, further cooling would depend on radiant heat transfer. Radiant heat transfer tends to be slow unless an object is extremely hot, such as the surface of a star. Since it would take a while to freeze the ship, a ship with robust automatic systems could continue fighting even after it was depressurized and all its biological inhabitants were dead. An enemy ship would have to be severely damaged or blown up to keep it from continuing the fight. That could be a challenge. There are several ways an enemy ship could protect itself from attack. Beams of charged particles could be deflected with magnetic fields. Reflective coatings on the ship's hull or a cloud of reflective dust-sized particles surrounding the ship could help protect against lasers. Ordinary aluminized party balloons could be used to confuse incoming guided missiles. Since there's no air resistance, the balloons could be launched at high velocity. Put small thrust nozzles on the balloons along with some appropriate microcircuits and the gas pressure inside them could provide the thrust required for steering the balloons. The balloons could be programmed to behave like a flock of birds that would look like a spacecraft to distant attackers. Such a deception could draw fire away from the real ship. Cloaking and stealth devices would be easy to implement in outer space. Paint the ship black, and at a distance it would be impossible to distinguish it from the blackness of outer space. Put a TV camera on one side and a TV screen the size of the ship on the other, and even the motion of the ship could be disguised. As the ship moved, the stars it blocked would be displayed on the big screen. Radar stealth could be achieved with the same technology currently used on Earth. An entire book could be written on possible space battle weapons, decoys, defenses, and tactics. So why has Hollywood continued to use the WWII model instead of something more creative? The answer lies in what could be considered the first law of Hollywood inertia: once a movie proves profitable, any scene in it shall remain the standard of profitability until a movie with an alternative scene becomes even more profitable. ### INDOOR GUN BATTLES Blowing up spaceships in outer space is safe compared to the way the humans defend themselves in _The Matrix Revolutions_ [NR] (2003) loading dock battle. (See Chapter 2 for a description.) Here, octopus-like sentinels stream toward defenders who are strapped to the front of robotic devices called APUs. With fully automatic 30-millimeter cannons attached to each APU arm, they blast away continuously at the sentinels streaming into the large concrete dome. Unlike outer space, the room in the movie has two very dependable forces that can alter the forward motion of projectiles.The first is provided by the concrete dome, which, in the best case, stops cannon projectiles. If a collision with the dome doesn't stop a cannon projectile, it makes it change direction or ricochet.The second force, provided by gravity, then sends spent cannon shells back, along with concrete chunks, raining down on APU operators' heads. Since distances inside the room are relatively short, air resistance has little effect because it doesn't have enough time to significantly slow down the ricocheting projectiles. Ultimately, the particles have to be slowed to a stop either by striking something they penetrate or by losing some velocity on each ricochet. Every time they exploded, cannon projectiles containing high explosives would send high-velocity shrapnel and possibly concrete chips flying and ricocheting all over the room, increasing the probability of hitting people. Those unprotected by armor or helmets would be injured or killed. Ironically, APU stands for armored personnel unit. Yet the personnel strapped to their fronts have no protective armor. They do not even wear helmets. This is one of the silliest battle scenes ever created. In reality, the APU operators would have killed or disabled each other in minutes from the combination of ricochets and falling debris. The sentinels are equally suicidal (assuming the term can apply to machines). They form into streams and attack the APUs head-on. The APU operators merely have to stand their ground, point their cannons in one direction, and keep firing. However, the depiction once again ignores Newton's first law. Even a cannon shell will exert only a momentary resistance force as it tears through a sentinel. Like a kamikaze plane, the sentinel will continue forward and likely plow into the unprotected APU operator. Blow up a sentinel, and the pieces will pepper the APU with shrapnel. It's not just the physics that make the scene ridiculous; it's the tactics. Why form a stream with hundreds of sentinels and flow straight toward the blazing barrel of a fully automatic cannon? Yes, that would overwhelm the APU operator thanks to Newton's first law, but it would also turn hundreds of sentinels into junk. If the sentinels had scattered and approached simultaneously from multiple directions, an APU operator couldn't possibly have swung and aimed his cannons fast enough to shoot down more than a few. A more thoughtful group of sentinels would have bored a hole in the ceiling and dropped piñatas through it. When the APUs opened up, as mentioned before, they would have killed or disabled each other with ricocheting cannon rounds and falling bits of concrete. Imagine the scene: as the room falls silent, a bleeding APU operator reaches over and grasps the head of a broken piñata. Taking his last breath, he grimaces in the horrifying knowledge that he dies defending humanity from papier-mâché animals filled with toys and goodies—how poignant. ### BULLET PENETRATION Sometimes movies pretend there is a stopping force for projectiles when there isn't. In _Young Guns II_ [PGP] (1990), Billy the Kid (Emilio Estevez) comes to the governor's house to bargain for a pardon. Always the shrewd negotiator, young Billy entertains the governor and his cronies with a little gunplay. The Kid blows the tips off several candles with rapid fire from his sixshooter, much to the delight of the group. Of course, this would have also blown holes through the window behind the candelabra and possibly killed hapless souls and livestock on the other side. As Newton's first law tells us, a bullet needs a force to stop its motion, and neither candles nor windows are up to the task. Interior walls aren't much better than candles and windows for stopping bullets. In fact, with the exception of log cabins, even the exterior walls of wooden houses are usually inadequate. The common movie practice of hiding behind wooden walls while shooting at bad guys through the window would likely prove fatal. The bad guys' bullets would typically go right through the wall. _The Road to Perdition_ [GP] (2002) gets bullet penetration right. In the movie,Tom Hanks plays a 1930s salesman. He's a regular guy except for the .45 automatic he carries and the Thompson submachine gun he keeps in the garage with an extra fifty-round magazine of "sales literature" for those special occasions demanding rapid-fire "closings." Unfortunately, his son accidentally witnesses just such a closing, and Hanks is compelled to flee with his son in order to keep him alive. It seems that a sinister business associate doesn't trust the son to keep quiet. After the associate hires a hit-man to kill the fugitives, Hanks fights back by stealing the organization's books from its accountant. With a shotgun under his coat, the hit-man sneaks up during the theft, and a gunfight ensues. The hit-man opens fire and blasts the wall behind Hanks, but Hanks prevails. He manages to wound the hit-man and escape. The buckshot goes through the wall and deposits itself in the accountant on the wall's other side. It seems like a trip to the hospital for a buckshot withdrawal would be in order, but alas, the hapless accountant has expired. As simple as it is, one would think that Hollywood could get Newton's first law right; but they don't. In space battles, moviemakers neglect the dangers of having no resistance forces to slow down high-velocity projectiles. In _The Matrix Revolutions_ loading dock battle, they ignore the peril of having forces that change the direction of high-velocity projectiles. In shootouts, they pretend that high-velocity projectiles can be stopped with inadequate forces. When they do get the forces right, it's worth noting. _The Road to Perdition_ was not just paved with good intentions but with at least one good movie physics portrayal. By contrast, it seems that Hollywood's road to good physics isn't paved at all. #### Summary of Movie Physics Rating Rubrics The following is a summary of the key points discussed in this chapter that affect a movie's physics quality rating. These are ranked according to the seriousness of the problem. Minuses [–] rank from 1 to 3, 3 being the worst. However, when a movie gets something right that sets it apart, it gets the equivalent of a get-out-of-jail-free card. These are ranked with pluses [+] from 1 to 3, 3 being the best. [–] [–] [–] Using the WWII naval battle model in space battles without thought about armor plating or shielding to protect spacecraft from other exploding vessels. [–] [–] Using the WWII naval battle model in space battles and providing armor plating or shielding to protect spacecraft from other exploding vessels. [–] Failing to account for the dangers of ricocheting bullets or bullet penetration. [+] Depicting realistic bullet penetration. [+] [+] Actually treating space battles in creative ways as though they are not simply extensions of WWII. ## CHAPTER 6 ## NEWTON'S THIRD LAW: ### That Special Hollywood Touch ### NEWTON'S THIRD LAW—A SYNOPSIS It's the yin and yang of physics, or as Paul Hewitt puts it, Newton's third law says that a person can't touch without being touched. Touch something forcefully, and it touches back with equal force. Imagine a courtroom drama: the defendant stands accused of punching his victim in the nose. When asked for his plea, the defendant confidently replies, "Innocent." Why? When he punched the victim, the victim's nose punched back simultaneously with an equal but opposite force—not much of a defense, but true according to Newton's third law. Boxers wear gloves as much to protect their hands from being broken as to protect the faces of their opponents from being cut. It's easy to break a knuckle when punching another person's head. The force on the knuckle is equal to the force on the head, and heads are often stronger. Movies have actually begun to recognize this fact. These days when a movie character throws a knockout punch, it's as likely as not that he'll grasp or shake his hand in an expression of pain. Newton's third law tells us that forces always occur in pairs. Each force is exactly the same size or magnitude and occurs simultaneously but acts in the opposite direction of its twin. Force pairs always involve a pair of objects. One object creates a force on the other, and vice versa. If a moth smacks into the windshield of a bus, the force exerted on the moth by the bus's windshield is exactly the same magnitude as the force the bus exerts on the moth. Of course, the moth gets squished while the bus doesn't, but that's because it takes a lot less force to squish a moth than a bus. #### HOW TO PREDICT MOTION—THE FREE-BODY DIAGRAM If forces always come in pairs and are equal and opposite in direction, then how can physics predict motion? The easy answer: the two forces act on two different bodies. Action-reaction force pairs can never cancel each other because they never act on the same object. The fun answer: free-body diagrams (FBD). These show all the forces acting on an object from the outside world. By looking at a free-body diagram, it's clear whether the forces on an object cancel each other or not. If they don't, the object's motion is going to change. If the object is stationary, it's going to move. The rules for FBDs: 1. Forces the outside world creates on the object are always shown. 2. Forces the object creates on the outside world are never shown. 3. Internal forces within the object are never shown. 4. Forces are always drawn touching the object. 5. Forces are always represented as arrows pointing in the correct orientation. 6. Other quantities such as velocity and acceleration are also represented as arrows and are sometimes drawn near FBDs but never drawn touching the object. A picture of the object is usually simplified to a box or even at times a single point representing the object's center of mass. The example below represents a tennis ball struck by a tennis racket. Where: Fr = the force coming from the racket Fw = the weight or gravity force acting on the racket. Note that even a round tennis ball can legitimately be represented as a square. The forces clearly show that the ball will be accelerated down and to the right. The example below represents a stationary tennis ball sitting on the ground. Where: Fn = the normal force of the ground acting upward on the ball. Note that all the forces cancel or counteract each other, indicating that the ball will remain stationary. Note also that, for convenience, the normal force (Fn) has been moved from the bottom to the top of the box. The normal force is the force the floor exerts on the ball, and although it acts on the lower surface, it's okay if the force is draw on the upper surface as long as the force's orientation with the vertical and horizontal dimensions is maintained. ### SURVIVING WINDOWS Billy Bob finds himself in possession of an old plate glass storm door and decides to demonstrate his manliness (based on a true story, well sort of). He sets it up in his back yard and, wearing the latest fashion in sleeveless t-shirts, rushes the window like it was the opposing team's quarterback, oblivious to the fact that plate glass doesn't like being "touched," let alone rushed. True to Newton's third law, the glass expresses its disdain by producing an equal and opposite "touching force" on Billy Bob, as it turns into hundreds of pointed, extremely sharp shards of glass. As Billy charges forward he pushes the shards horizontally out of the way—that is, except for the pointed ones that get stuck in his bare shoulder. The other shards slice as they are pushed aside. Many of them, pulled vertically downward by the force of gravity, slice and dice as they rain on Billy Bob, who is now a redneck with a blood-red neck. Fortunately for Billy Bob, all the shards miss major arteries. While washing off the blood with his "hose pipe," he flashes a big bubba grin for his buddy's video camera. Yup, it does take the rest of the evening to pick out the glass imbedded in him, but hey, Billy Bob wasn't feeling any pain even before he charged the glass. Very little force is needed for razor sharp glass to seriously cut a human. Jumping or walking through a plate glass window usually results in an injury—often a serious one. That's why safety glass was created. It's designed to shatter into small pieces with very few sharp edges. The smaller pieces reduce the amount of force an individual piece of glass can exert on the human it falls on and, in combination with the reduced sharpness, decreases the tendency for cutting. Laminated safety glass adds a thin layer of plastic sandwiched between layers of safety glass for reinforcement. When the window is broken, the pieces tend to stick to the laminate rather than becoming deadly projectiles. Car windshields are generally made of laminated safety glass. Nevertheless, when craniums impact car windows at high speed, the result is often a head injury, including lacerations and broken bones. Safety glass in general is four to ten times stronger (depending on whether or not it's laminated) than an equal thickness of ordinary glass. A large piece of it in a store window is a very hard surface and takes a fair amount of force to break. It also has a lot of inertia, so even when it does break, a lot of force is needed to move it out of the way. Naturally, the sheet of glass will create an equal and opposite force on the person who does the breaking and moving. While slamming into a large sheet of safety glass is far less likely to cause serious injuries than slamming into plate glass, it can still cause cuts, bruises, and broken bones, especially if done at high speed. So, how does Hollywood send humans crashing through windows without so much as a scratch? The simple answer: they cheat. At times, moviemakers have used panes made of sugar in glass-breaking scenes. That's right, candy windows! They look like glass and break like glass but have no sharp edges. More recently the candy has been replaced by a commercially available product called SMASH! plastic, which simulates glass without the safety problems. The product's manufacturer recommends that panes of the material be no more than 1/8 inch (3.2 mm) thick to avoid impact injury.The thin sheet reduces both the force required for breaking and the inertia of the fake glass. Bottles used as clubs in fight scenes are generally made of fake glass, yet when a stunt man jumps through a window, it's often made of real glass. But fear not, there are still tricks involved. First, the glass will be safety glass. Second, when the stunt man runs toward the window, a helper blows the window out with small explosive charges an instant before the stunt man hits the window. If the helper screws up and doesn't blow the window, the stunt man gets the vinegar knocked out of him when he hits the glass—not a good time to be the helper. Even when all goes well, stunt men sometimes still get cut. However, with safety glass and a correctly timed explosion, the cuts are usually minor. In _True Lies_ [PGP-13] (1994) Arnold Schwarzenegger is a secret agent who neglects to mention this fact to his wife. In one scene, Arnie has a fight and shootout with terrorists who attack him in the men's room. When one of the terrorists escapes, Arnie chases him through a shopping mall. The terrorist runs into a store and jumps through the display window onto the sidewalk beyond.When this scene is run in slow motion, it's easy to see the small explosive charges go off just before the stunt man hits the window. (Score one for the helper.) ### NEWTON'S SCHOOL OF ACTING Discharge a firearm, and a bullet is pushed forward.The gun recoils and is pushed backward exactly as predicted by Newton's third law (see Chapter 12 for calculations). However, fire a blank and very little force is needed to push the burning gunpowder out the end of the barrel because the powder has far less mass than a bullet, not to mention far less friction. Hence, blanks cause very little recoil. At first glance, it looks like the way to make realistic movies would be to use real ammunition. However, as mentioned in the last chapter, bullets have a nasty habit of going great distances, penetrating walls, and causing embarrassments like killing innocent bystanders. About the only solution to this is something called acting. Actors need to understand some physics, especially if they play the roles of characters shooting firearms. Even though firing a blank produces little recoil, actors can make it look realistic. They need to spend a day being videotaped at a shooting range alternately firing real ammunition and blanks, and then adjust their fake recoil to match the real thing. They also need to try shooting from the hip in order to understand how ridiculous it is to do so (see Chapter 2). The movie _Pearl Harbor_ [PGP-13] (2001) (see Chapter 1) has one of the more egregious examples of absent recoil. During the Japanese attack, the dashing young fighter pilots Rafe (Ben Affleck) and Danny (Josh Hartnett) take to the air to fight back.With Zeros (Japanese warplanes) bearing down on their tails, they radio their ground crews and instruct them to "get some guns in the control tower." The ever-obedient ground crew all but fly up the stairs to the tower's top while carrying an assortment of weapons, including a .50 caliber machine gun weighing 84 pounds (38 kg). They set the machine gun on a window sill and fire it, along with the other weapons, at a passing Zero. Of course they save the day and down the Zero with their very Hollywood-style mix of last-minute cleverness, enthusiasm, and teamwork. Keep in mind that a single .50-caliber machine gun bullet is so powerful it can cut a moderate-sized tree in half with a single bullet. The recoil from a single shot would be nearly intolerable to a person firing it. Yet it spits out 550 rounds per minute. The weapon simply cannot be fired unless it's mounted on a specially designed tripod or a vehicle. When mounted in a vehicle like a fighter aircraft, heavy machine guns will act like thrusters when they're fired. Although the recoil thrust is not enough to stop the aircraft, it will certainly jostle it about. The 20-millimeter cannons mounted in the wings of the Japanese Zeros would have produced an even greater recoil force per round fired than a .50-caliber machine gun. When firing these cannons, the aircraft would have vibrated significantly, causing small changes in the aim point. Add to this the normal bumpiness of flight, and the cannon shells would have scattered in a random manner around the point of aim. So how do the moviemakers in _Pearl Harbor_ portray strafing runs by cannon-firing Zeros? They have the cannon shells strike the water in evenly spaced rows lining up perfectly with the cannon barrels in the wings. ### NEWTON'S THIRD, AT A DISTANCE Newton's third law works at a distance as well as up close. When someone jumps out of an airplane (hopefully with a parachute) Earth exerts a downward gravitational force on the person, and the person exerts an upward gravitational force on Earth. The two forces are equal in magnitude but opposite in direction. Of course, the skydiver does almost all of the moving. She has a much lower mass and hence a much lower inertia than Earth. Inertia, as mentioned earlier, is resistance to motion. In the famous fight between Yoda and Count Dooku (Christopher Lee) in _Star Wars Episode II_ [NR] (2002), Dooku uses the Force and causes large chunks of the ceiling to fall. About to be crushed, Yoda raises his palm and projects a force that stops the heavy pieces in mid air. To do so, Yoda must maintain an upward force on the rocks equal to their weight. Newton's third law says that the rock will simultaneously exert an equal but opposite force on Yoda, not a healthy situation for the little guy.Yet,Yoda is uninjured. Yoda had intervened to prevent Dooku from killing both Anakin Skywalker (Hayden Christensen) and Obi-Wan Kenobi (Ewan McGregor). Dooku had first disabled Obi-Wan, who was left lying helpless on the floor. When Anakin came to the rescue, Dooku lopped off his arm. Raising his palm, Dooku projected a force and sent Anakin flying. Of course, Newton's third law says that Anakin would have created an equal but opposite force on Dooku.Yet Dooku shows no sign of being pushed backwards. Even his raised palm and arm show no signs of recoil. Evidently, the force he projected was not just from a galaxy far, far away but from a different universe—one that doesn't follow Newton's third law. ### NEWTONIAN MARTIAL ARTS By using the right technique, it is possible to remain stationary while pushing a person backwards. If the push is applied with a slightly upward motion near the center of the pushed person's mass, it tends to lift him slightly off his feet and move him backward. A forceful push in this manner can so seriously disrupt a person's balance that he is sent running backward across an entire room. It looks incredibly fake, but it's not! The initial push sets the person in motion, causing him to take a step backward to keep from falling. Unfortunately, the step reinforces the backward movement, which requires yet another step and another and another in rapid succession to keep from falling down. Often the person has to run into something, such as a wall, in order to stop. An equal but opposite force acts on the person doing the pushing. However, this force acts slightly downward as well as backward. If the person doing the pushing is relaxed and standing in a stable martial arts stance, she will not lose her balance and be thrown backward. The slightly downward direction of the reaction force acting on her tends to push her feet more firmly against the ground, which helps hold her in place. The pushing action described above is commonly done during pushing hands practice in the martial art of Taijiquan. Pushing hands is a type of sparring in which the participants stand in fixed positions and try to unbalance each other. Participants are expected to remain relaxed and generally use very little physical force. It's definitely not a Western-style wrestling match. Taijiquan is often practiced for its stress-relieving effect and is notable for its slowly flowing individual forms. It's also an effective martial art. In some ways it's similar to Yoda's use of "the Force." Taijiquan practitioners visualize chi or life force circulating through their bodies that can then be used for performing what seem like superhuman martial arts feats. In reality, they are merely remarkable applications of simple physics. Taiwanese moviemaker Ang Lee got the physics right in his gemstone, _Pushing Hands_ [GP] (1992). In the movie Mr. Chu (Sihung Lung) is a Taijiquan master who has not only lost his wife but been forced to move to America and live with his son. His daughter-in-law has typical yuppie values that clash with the traditional ways of Mr. Chu. Admirably, Mr. Chu spends a significant part of his day watching and criticizing the ridiculous martial arts depictions in Hong Kong kung fu movies. Thanks to his martial arts expertise, he is unable to suspend his disbelief while watching such nonsense. In one scene Mr. Chu is teaching pushing hands to a group of students in a large room. At the other end of the room, the widow Mrs. Chen (Jean Kou Chang) is teaching a cooking class. Mr. Chu wants to get to know her but is not one for the usual shallow pickup lines. Instead, he begins practicing pushing hands with a rotund student and carefully lines him up with Mrs. Chen's table. At just the right moment, Chu pushes his hapless student and sends him running backwards across the entire room while trying to regain his balance. The student crashes into Mrs. Chen's table, bringing about the meeting. In the _Star Wars_ movie, Dooku's push is far more forceful than Mr. Chu's and looks like it is directed slightly downward rather than upward, judging by the position of his palm. Anakin flies completely off his feet, so his backward motion has nothing to do with losing his balance. Dooku should have recoiled backward and upward, but as mentioned before shows no sign of it. If a Taijiquan master applies a larger force with a more upwardly directed angle than used in pushing hands, he can also send a person flying, but it's just a few feet off the ground and a few feet backward. It's nothing like the exaggerated backward flight of Dooku's victims. Pushing people off their feet is typically not done in pushing hands practice, for the obvious reason that it can cause injuries. A push with even greater force will act like a palm strike rather than a push. Here the result is more likely to be broken bones or internal injuries than a dramatic backward motion. The human body simply cannot hold up to the force required to send it flying across the room with a quick push. So how do special effects experts send actors flying across the room in movies without injuring them? First, they fit the actor with a specially designed vest to distribute the force over as much area as possible. A rope or wire is attached to the vest on the person's back, and at the right moment the person is pulled slightly upward and backward, making him or her fly across the room. It takes a much lower force to do so since it is applied for a longer time. ### NEWTON IN SPACE The movie _2001: A Space Odyssey_ [GP] (1968) is often cited as one of the best examples of movie physics, yet it too contains some questionable Newton's third law scenes. In the movie an out-of-control computer named HAL controls every aspect of a spacecraft on a mission to Jupiter. When a pair of humans questions his decisions, HAL decides to deactivate them. He waits until one is attempting a repair during an extravehicular activity (EVA), then attacks using the mechanical claw on a nearby space pod, leaving the hapless human adrift in space, with a broken air hose, struggling for his last breath.The other human, Dave, immediately attempts a rescue using the remaining pod. This proves futile, and Dave ends up begging HAL to open the mother ship's airlock door so he can come back inside. Surprise, surprise—HAL refuses. Naturally, there's an emergency airlock that can be opened from outside, but there's also a small problem: in his haste, Dave forgot his pressurized helmet, and he cannot dock the pod with the airlock door. To use the airlock he must first exit the pod into the vacuum of outer space. His exposed head will be subjected to the vacuum of outer space before he can enter, close the door, and pressurize the airlock. He uses the pod's claw and opens the emergency airlock anyway. He then lines up the pod's door with the airlock, holds his breath, and blows the door's bolts. Conveniently, these have been designed with explosive devices built into them. We know this because it's written on the outside of the pod. Escape hatches with explosive bolts were standard equipment on capsules used in early NASA manned space flights. The capsules returned to Earth by parachuting into the ocean. If one started sinking, it was handy to have a quick way out. Why a fast exit is needed in outer space is a mystery. After blowing off the door, Dave shoots into the airlock, presumably propelled by air pressure escaping from the pod. He bounces around and almost immediately closes the airlock door. He survives, and HAL is now at his mercy. When the door, Dave, and the air were expelled out the back of the pod, the pod should have gone flying the other direction into space but did not. Dave may have set the pod's thruster controls so that it would push the pod against the mother ship; however, it's unlikely that the thrusters would have been strong enough to completely counteract the reaction force created on the pod when the door blew. It's a flaw but is perhaps forgivable in light of the many things the movie _2001_ did right. Even a prestigious scientific organization like NASA has had problems with Newton's third law. Before attempting to send people to the Moon, NASA thought it wise to work out a few details such as space-walking or EVA. Astronauts might need to go outside their spacecraft and make repairs on long journeys to the Moon, just as depicted in _2001_. Unfortunately, when they tried EVAs during the Gemini program, they received some nasty surprises due to Newton's third law. The first EVA went flawlessly, but the astronaut involved, Ed White, did not attempt to do any work. The second EVA was a near disaster: Gene Cernan was supposed to venture out of the spacecraft and put on a flying backpack while on the dark side of Earth, where he had very little light. Every time he attempted to turn a valve, his entire body turned. Anything he touched touched back and repelled him. He had neither gravity nor friction to hold him in place. After just a few minutes, Cernan began to overheat and sweat from exertion. His space suit became like a steam bath. His heart raced at 170 beats per minute. Inside the Gemini capsule, fellow astronaut Tom Stafford became increasingly concerned. He knew that if Cernan lost consciousness, there would be no way to get him back in the capsule for reentry. Stafford would have no choice except to cut Cernan free and leave him floating in orbit. In consideration of the desperate situation, the EVA was aborted. Both men returned safely to Earth, but when NASA workers examined Cernan's space suit, they poured over a pound and a half of sweat out of each boot. The next two EVAs went almost as badly as Cernan's. Finally, after three bungled tries, NASA started thinking about how Newton's third law worked. Subsequently, they completely reworked their EVA training, procedures, and equipment. After these changes, EVAs became routine. When NASA has a flaw in its understanding of a situation's physics, it gets fixed fast. By contrast, Hollywood serves up the same physics mistakes over and over again. It could do better if revenues were any indication of its ability to do so. Hollywood gleans about nine billion dollars a year from newly released films alone, not including rentals, DVDs, videos, and spin-off product royalties. By comparison, NASA's Gemini program cost only 1.28 billion dollars over three years, with only a small fraction used for fixing the EVA flaws related to Newton's third law. However, a flaw has to be defined as a problem before it can be fixed, and here the difference between NASA and Hollywood is striking. For NASA problems are defined in life-and-death terms. Since even minor flaws in understanding a situation's physics can be deadly, they are, by definition, problems. For Hollywood problems are defined in terms of profit. When a movie with egregious physics flaws turns a profit, by definition it has no problems. #### Summary of Movie Physics Rating Rubrics The following is a summary of the key points discussed in this chapter that affect a movie's physics quality rating. These are ranked according to the seriousness of the problem. Minuses [–] rank from 1 to 3, 3 being the worst. However, when a movie gets something right that sets it apart, it gets the equivalent of a get-out-of-jail-free card. These are ranked with pluses [+] from 1 to 3, 3 being the best [–] [–] Actors slamming their fists through car windows with no discernible injury. [–] [–] Actors jumping through plate glass windows with no discernible injuries. (Note: plate glass would be found in older buildings or in ordinary residential windows. Sliding glass doors are an exception. They usually are made of safety glass.) [–] Actors effortlessly jumping through large safety-glass display windows. [–] Actors shooting highpowered firearms without any discernible recoil. [–] The bullets from a strafing aircraft striking in nice neat evenly spaced rows. ## CHAPTER 7 ## CREATIVE KINEMATICS: ### Explosive Entertainment ### WORLDWIDE EXPLOSIONS An ancient asteroid impact triggers a sea of flame spreading about 6,000 miles (9,700 km) around the globe in seconds. It brings fiery death to everything in its path: trees, ferns, insects, and dinosaurs (opening scene _Armageddon_ [RP]). Modern evidence indicates an ancient impact did indeed touch off a major firestorm and doomed the dinosaurs, but probably didn't look like the movie version. First, there's the flame-front speed depicted in the movie, calculated as follows: SPEED = DISTANCE/TIME (EQUATION 7.1) = 6,000 mi / (30 sec 1/3600 hr/sec) = 720,000 mph or 1,160,000 kph This speed is about 29 times faster than the minimum speed needed for an object to escape Earth's gravity (escape velocity of Earth) and 950 times faster than the speed of sound: fast enough to blow away Earth's atmosphere—impossibly fast. A global-sized flame front spreading at a speed greater than the speed of sound is by definition a detonation. To maintain such velocities, the Earth would just about have to be covered in a thin sheet of explosive material like TNT. A rapidly expanding fire ball is like a jet airplane: even when it runs out of fuel, it will move forward, but not for hundreds and hundreds of miles. To keep moving it must have a source of fuel and the ability to consume it fast enough to maintain its speed, hence the need for the TNT. Even a flame front traveling at the edge of subsonic speed (just below 760 mph or 1200 km/hr) would have to consume combustibles in its path at an explosive rate to fuel its high velocity. Such high velocities could not be maintained without continual energy input. This near-sonic-speed wall of fire would take about eight hours to spread 6,000 miles around the world. While such a front might be hundreds of miles wide, it would burn so fast that it would leave a large burned-out area behind it as it spread. From space, the flames would look more like a wide slow-moving ribbon than an all encompassing sea of fire—that is, if the flames were not completely obscured by smoke. At the other extreme, forest fires release the energy stored in brush and trees much more slowly and generally travel at less than 4 mph (6.4 km/hr)—a speed that would take more than two months to spread 6,ooo miles around the world. By either estimate—high or low—an entire hemisphere is unlikely to be engulfed in flame all at the same time. Still _Armageddon_ 's opening depiction of an asteroid strike earns reasonably good marks. Its extraordinarily high flame velocity can be forgiven as a time-lapse effect, its sea of flame as over exuberance. The depiction could have benefited from scientific studies done with computer simulations but the overall visual effect was scary enough to make even a politician think about preventative action—a much needed activity. Unfortunately, the rest of the movie had a solution about as reliable as a campaign promise. A realistic defense for preventing an asteroid strike could take decades and billions of dollars to develop. Sadly, it will probably also take a disaster—hopefully one in a lightly populated area— before humanity is willing to spend the money. Splitting a major sized asteroid in half with a nuclear bomb from our cold war arsenal will not be part of the plan. Such bombs simply do not have the required energy output (see Chapter 11). #### How Explosions Propagate An explosion's effects are related to the ways its energy propagates, or spreads. As a rule of thumb these are: 1. Blast front: a wind-like movement of expelled materials including gasses, plasma, or debris such as shrapnel. Expelled materials can travel at very high, even supersonic, initial velocities. This material usually includes any fireball from fuel or explosive not consumed in the initial blast. Expelled material is often superheated and can cause secondary fires and burns. On Earth, if expelled gasses travel at supersonic speeds they can compress air ahead of them enough to cause superheating and result in secondary fires. Expelled materials lose kinetic energy rapidly due to air resistance or, in the case of solid debris such as shrapnel, due to being pulled to the ground by gravity. In outer space expelled materials generally lose kinetic energy only when they impact another object. 2. Shock wave: a high pressure pulse traveling as a wave through air and caused by the blast front moving at or above the speed of sound. The shock wave can continue traveling considerable distances at the speed of sound long after the blast front has slowed down. On Earth shock waves can do considerable damage. In outer space there are no shock waves because there is no matter to act as a medium for propagating the wave. 3. Electromagnetic (EM) pulse: a broad spectrum pulse of electromagnetic energy that can include everything from radio waves to gamma rays (for nuclear blasts). The pulse travels at the speed of light and can interfere with electronic equipment. It often includes a large amount of infrared radiation, enhanced by fireballs, burning objects, or superheated materials emitting infrared or thermal radiation for as long as they remain at elevated temperatures. This radiation can set secondary fires and cause burns. In outer space, the blast front and EM pulse expand like two giant bubbles—surface area increasing with the square of distance from the blast—albeit the EM "bubble" expands much faster than the blast front. Since both kinetic and EM energies remain constant the intensity of the explosion (the total energy absorbed per unit of area for structures in the path of the blast) will decrease with the square of the distance from the blast. Doubling distance reduces intensity to one-fourth its original strength. The exceptions are chunks of solid debris or shrapnel which can be just as damaging at a distance as up close. On Earth, an explosion's intensity will decline even faster due to air resistance. In general, an explosion in space can damage at much greater distances than its equivalent on Earth. _Armageddon_ concluded when the Texas-sized asteroid, on a collision course with Earth, was split in half by—you guessed it— a nuclear bomb, just in the nick of time to save humanity. The plume from the blast radiated outward in the shape of a disk about three times the diameter of the asteroid (a total comparable to the distance across the United States) in about two seconds (a speed of about 4,000,000 mph or 6,400,000 kph)—quite a blast for a device that normally produces a fireball a few miles in diameter and a shock wave traveling no more than a few times the speed of sound (760 mph or 1200 kph). ### EXPLODING WORLDS Hollywood recipes for planetary disasters are not just served with baloney, they're made of it. When the Empire's Death Star blows up Alderon (an Earth-sized planet) the pieces fly outward, amid a swirling orange-white fireball, a distance of about twice the diameter of the planet in about two seconds—a speed of 28,800,000 mph (46,400,000 km/hr), all the more remarkable because the exploding particles have to overcome the gravitational forces pulling the parts back into the form of a planet. Keep in mind that a typical detonation travels no more than a few times faster than the speed of sound (760 mph or 1200 km/hr). While there is no law of physics that says a planet can't be blown apart at such high velocities, certainly the numbers cast doubt on the notion that a death star could do it. Okay, blowing up an entire planet is unlikely but if it did happen, would it look like the _Star Wars_ depiction? Certainly the explosion would be like a gigantic nuclear blast and as a rule of thumb, about half of the energy in such a blast goes into heat and the rest into kinetic energy. The kinetic energy of a single 1 kg blob moving at the speed depicted in the movie would be about the equivalent of 20 kilotons of TNT, not quite twice the energy released by the 12.5 kiloton bomb dropped on Hiroshima. An equivalent amount of heat would be enough to vaporize a city, let alone a 1 kg blob—duh. Multiply the amount of energy for a single blob by the 6 × 1024 (more than a trillion times a trillion) similar blobs contained in an Earth-sized planet and the amount of energy released in the blast would be the equivalent of the Sun's total energy output for about 800 centuries—released in a couple of seconds. Would the blast look like the movie depiction? Not likely. The planet would vaporize in a huge flash of blinding light. When the flash began fading, the vapor would start condensing into a gigantic slowly expanding dust cloud. A less extreme exploding Earth-like planet would probably look like a balloon filling with liquid to its limits then popping, all in slow motion. The liquid in this case would be the glowing molten material of the inner planet. To fly apart the pieces would have to travel at least at terminal velocity (25,000 mph or 40,300 kph for Earth). Assuming a speed twice as high as terminal velocity, the debris from the planet's surface would expand outward a distance of twice the planet's diameter in about 19 minutes. On the other hand, if the pieces didn't reach terminal velocity, they would fly outward and then collapse backwards into a turbulently swirling molten planetary blob. Since the mass contained in the planet's solid crust would be small compared to the planet's molten interior (assuming it's Earth-like), the crust would essentially be swallowed up in a sea of brightly glowing lava. While not as dramatic as a sudden explosion, a more realistic explosion would have its own type of horror: the type that comes from the slow realization that a catastrophe is occurring and there's nothing that can be done to stop it. Filmmakers are well aware that blowing up a small scale model does not look the same as blowing up the real thing. Small explosions have similar velocities to large ones, but the flying pieces travel much shorter distances making the small explosions appear to happen much faster than the large ones being simulated. Cameramen compensate with slow motion photography. They film small explosions at higher than normal frame rates so that when the film is projected at its normal rate, the explosions are slowed down and look like they're full sized. Filmmakers should use the same principles in reverse to deduce that a planetary explosion—occurring on a gigantic scale—would look like it was happening in slow motion. Movies with exploding planets are rare, but it's safe to say that the next one will probably look like the last one. It's the law of Hollywood inertia: never alter the formula used in a successful movie. ### THE SUPER SPEED OF SPACE TRAVEL Space travel poses a different speed problem: it takes an incredibly high speed to get anywhere.The Apollo 10 mission holds the speed record for manned spacecraft at roughly 25,000 mph (40,300 km/hr). Double it and it would still take about 13 years to travel across the solar system (assuming that it is roughly circular with a diameter equal to the average distance from the Sun to Pluto of 2.8 billion miles). Travel to the nearest star outside our solar system, Proxima Centauri at a distance of 4.3 light-years or 2.5 × 1013 miles (4.1 × 1013 km) would take about 58,000 years—a little long to keep the kids in the back seat alive let alone entertained. Decide to travel around our galaxy (the Milky Way) and the need for speed gets even more extreme. Traveling at the speed of light—about 1,300 times faster than the 50,000 mph used in the previous examples—it takes about 100,000 years to travel across the galaxy. To go much of anywhere, a spacecraft would need to travel about 1,000 times the speed of light, assuming that human lifetimes can be expanded to at least 200 years and suspended animation technology is available to facilitate return trips. But above all else, society would need the willpower to devote the major resources required for such journeys. Currently, we can't even cough up the funds for a mere moon base. Of course, intergalactic travel could be done more cheaply with machines than humans, but there's no movie in that. Unfortunately, the speed limit for spacecraft is set below the speed of light, at least according to the famous galactic traffic cop, Albert Einstein. On a practical basis, it's set far lower. Einstein taught us that the mass of an object approaches infinity as the object approaches the speed of light—a puzzling statement that makes a lot more sense if the word inertia is substituted for mass. Recall: inertia is resistance to change in motion. Einstein is saying that it gets more and more difficult to change an object's motion once it reaches speeds near the speed of light—making it infinitely difficult to actually reach such a speed. And infinitely difficult problems are rather hard to solve. To put the problem in perspective: at 25 percent of the speed of light (c) the inertia is 3 percent higher; at 50 percent c, the inertia is 15 percent higher; at 99 percent c, the inertia is 709 percent higher than at rest. Obviously, there's no way to carry enough fuel to reach the speed of light. The problem is further complicated by something called time dilation—exemplified by the twin paradox. Find a set of twentyyear-old twins, leave one on Earth, and send the other into space on a lengthy trip at a speed of 99 percent c. On returning, if she has aged by ten years, her twin sister—who stayed on Earth—will have aged by seventy one years. Start sending star ships on long missions at similar speeds all over the galaxy and no one will be able to keep their clocks synchronized. The result: a major breakdown in organized exploration. _Star Trek_ solved the problem for its spacecraft by warping space. Take a sheet of paper and ask a friendly ant to walk across it as you time the journey. It will take a while. Fold the paper so that it hangs in a loop with the ends touching each other at the top of the loop; the ant will need much less time to traverse from one end to the other. You have just warped space—as far as the ant is concerned. No one knows how to do it for a spacecraft but at least it's conceivable. _Star Trek_ 's space ships can travel the galaxy at sublight speeds, keep their clocks synchronized, yet warp space for quick long distance journeys. According to Lawrence M. Krauss in _The Physics of Star Trek_ there is even some theoretical support for it. Space could conceivably be warped by a super strong gravitational field. But don't hold your breath waiting for the day. There are monumental problems in the way. As for more conventional thruster type technology, even short hops around a solar system will continue to be expensive, lengthy, and difficult. ### OUTRUNNING EXPLOSIONS Not all speed problems are galactic: take the problem of outrunning fiery explosions—a useful skill on the human scale. Sometimes the explosion occurs in the open and the object is to run and jump into the nearest body of water before the fireball hits the would-be escapist. Once underwater, the camera generally shows the deadly fireball sweeping overhead. If the explosion were far enough away—say, 1000 meters away—such an escape might actually be possible. #### THE PHYSICS OF OUTRUNNING WHATEVER When someone tries to outrun something like a car or an explosion he or she has to have a head start or it's hopeless. To model the situation we'll assume that the subject or person running away, as well as the object pursuing, both move at constant velocity. We'll also assume that the object being outrun moves faster than the person. Otherwise, the subject is in no danger of being overtaken, and what drama is there in that? We'll represent the head start as a distance dh. Distances can be calculated from the following kinematic equation: d = v • t (EQUATION 7.2) Where: d = distance (note this is actually displacement or distance in a straight line) v = velocity t = time We'll use o and p subscripts to denote the object doing the chasing and the person chased respectively. The distance traveled by the object doing the chasing looks like this: Substituting the two above equations into equation 7.3 yields: Equation 7.4, as mentioned above, will work for any type of chase situation including either an expanding fireball or car chasing a person attempting to run away. For example, assume an explosion is 50 meters away traveling at the speed of sound and the person running from it can run 100 meters in 10 seconds (9.1 m/s, fast by any standard). The time such a person has to escape before being engulfed by the fireball is calculated as follows: The distance the person could run is calculated as follows: If the person were standing on the edge of a dock and dove off a dock exactly 0.15 seconds before the fireball arrived, the distance he or she would fall toward the water would be calculated as follows (assuming that the person could not push off the dock in a way which gave an initial velocity in the downward direction): Where: d y = the vertical distance fallen g = the acceleration due to gravity. (On Earth g = 9.8 m/s2) Obviously, the person is going to get flamed before he or she hits the water. But, not all fireballs travel at the same velocity. If the fireball traveled at a much more sedate speed of say half the speed of sound, the person attempting escape would have a whopping 0.3 seconds to escape and could fall 17.2 in (44 cm) toward the water—a short enough distance to still get torched. Within 50 m of the explosion, victims are pretty much doomed to be engulfed by the fireball (assuming it's big enough) and slammed by the shock wave. Even in the best case scenario, with a "slow" moving fireball, victims will have at most a few tenths of a second to run and jump in the nearest body of water. If they are neither knocked unconscious nor killed outright by the shock wave, flying debris, or shrapnel; and they hit the water soon enough to avoid severe burns, they might even survive. The probability of survival without horrible injuries increases rapidly with increasing distance from the blast. But the benefits of running and jumping in water remain limited. Fireballs with enough energy to travel great distances usually do so at high velocities. Such enormous high-temperature fireballs also emit large amounts of infrared radiation (IR) that can burn victims at a distance even when the fireball does not contact them. The IR radiation travels at the speed of light—a little hard to outrun. If a person is close enough to the blast to be in grave danger, chances are he or she will not have the time to run and jump in the water. On the other hand, if a person has the time to run and jump in the water, chances are he or she is too far away from the blast to be in any real danger. So how do movies do it? The actor stands in front of the fuel dump, building, or whatever is to be blown up and is filmed using a telephoto lens.This makes the actor appear to be standing close to the object to be blown up when in reality he or she is at a safe distance. The camera is turned off, a stunt person is substituted for the actor, the camera is turned back on, and ka-boom. The explosion is started with a black powder blast demolishing a container of fuel, the fuel mixes with air, and a second black powder explosion is used to ignite the vapor into a fireball. The fireball's image fills the entire screen making it look enormous. Black powder in combination with a fuel is ideal because its explosion produces lots of highly visible smoke and flame with relatively little damaging blast power (compared to more powerful explosives like dynamite, TNT, or C-4, which give off very little smoke and flame with powerful blasts). Energy used to produce smoke and flame is essentially wasted because it's unavailable for producing the high-pressure blasts that pulverize materials. The more powerful explosives are less visible and less spectacular precisely because they are more efficient and effective for just about every purpose but movies. _Saving Private Ryan_ and the miniseries _Band of Brothers_ did an excellent job of depicting explosions. Neither artillery shells nor hand grenades produce large fireballs in these movies. In real life, even grenades such as those containing white phosphorus or thermite designed for marking targets or starting fires do not produce the typical fireballs of burning gasoline seen in movies. An exploding white phosphorus grenade looks very similar to a white fireworks shell bursting on the ground and sending glowing streamers flying outward in every direction. Although white phosphorous burns at about 5000°F (2760°C), a white phosphorus grenade does not produce a large-sized yellow-orange fireball. Thermite grenades typically are not even designed to burst. They burn vigorously in a local area at temperatures of around 4000°F (2200°C) and produce a by-product of molten iron. These grenades work extremely well for destroying enemy equipment such as artillery pieces. By contrast, the commonly used general purpose fragmentation grenade produces even less fire and smoke. It's designed to convert the grenade's explosive energy into the kinetic energy of hundreds of pieces of high velocity shrapnel. For such a grenade, fire and smoke are a waste of energy. ### EXPLOSIONS IN SHAFTS AND TUNNELS There are many variations of the running from explosions theme, such as the fiery elevator shaft. The heroes are climbing out of the elevator shaft as a fireball races up from below. They pull themselves out just as the flames sweep past—not a problem, they're heroes. Long tubes such as elevator shafts confine fiery blasts and increase their pressure thereby increasing their velocity.Yet, heroes—in moments of great stress—have that unique ability to tap into their simian ancestry of millions of years past and conjure up long dormant genetic abilities to climb out of elevator shafts hundreds of times faster than competitive runners can run. There are also the escapes in which a hero on a motorcycle blast velocity skillfully outruns a gigantic blast-wave/fireball. If he's 100 m from the blast and going 100 mph (161 kph), he's got 0.33 seconds to escape. This is naturally enough time for him to glance backwards repeatedly at the impending doom and lay down the motor cycle just in time so he ends up in a convenient ditch as the blast passes overhead—all with no injuries. _Collateral Damage_ [PGP-13] combined the fiery explosion in a tunnel and the motorcycle escape into a single scene when a pair of villains on a motorcycle set off a natural gas explosion, racing down a tunnel while firing a handgun at the movie's hero, Arnold Schwarzenegger. Arnie, naturally, not only dodges the bullets but also outruns the blast and ducks behind a door just before the explosion hits. The less fortunate villains are knocked off their motorcycle by the blast (they are, after all, villains and aren't expected to outrun it). While bruised and battered, they, nevertheless, are able to engage in lengthy hand-to-hand combat with Arnie who eventually proves to be far more deadly than the explosion. This illustrates yet another law of Hollywood: really evil villains can never die from the first few fatal causes. This chapter has been able to debunk numerous typical Hollywood movie scenes with a single basic kinematic equation: the equation for constant velocity, which is often taught in one class period at the beginning of high school physical science—not exactly rocket science. So why do moviemakers assume that their audiences won't notice? As described in Chapter 1, they're counting on the power of the movies: combine rousing music with dramatic images in adrenaline-pumping scenes, and even silliness can go straight into the brain unopposed by logic. #### Summary of Movie Physics Rating Rubrics The following is a summary of the key points discussed in this chapter that affect a movie's physics quality. These are ranked according to the seriousness of the problem. Minuses [-] rank from 1 to 3 with 3 the worst. However, when a movie gets something right that sets it apart, it gets the equivalent of a get-out-of-jail-free card. These are ranked with pluses [+] from 1 to 3 with 3 being the best. [-] [-] Planets that explode in a few seconds. [-] [-] Heroes outrunning or outclimbing nearby fiery explosions, especially those in elevator shafts or tunnels. [-] [-] Traveling the galaxy or even around a large-sized solar system with spacecraft powered by conventional thrusters. [-] [-] Fragmentation hand grenades or high explosives such as TNT, C4, or dynamite detonating with large fireballs. [0] Terrestrial fireballs traveling great distances at hypersonic speeds (incorrect but forgivable). [+] [+] Fragmentation hand grenades or high explosives such as TNT, C4, or dynamite detonating without large fireballs. ## CHAPTER 8 ## HOLLYWOOD BOMBS: ### How Filmmaker Physics Misses the Boat ### THE PHYSICS OF BOMBING Sailors sleep as the aircraft approaches, its bombardier squinting through his bombsight at the toy-like image 9,840 feet (3000 m) below. When the aircraft is directly over the target below, the bombardier releases his deadly payload. It falls straight down, penetrating deep into the USS Arizona and blasting it into history as the emblem for the United States' worst military defeat. No, it's not the day of infamy. It's the movie _Pearl Harbor_ [PGP-13] (2001) perpetuating the infamous physics misconception that bombs dropped from moving aircraft fall straight down. If all the Japanese bomber crews had shown such ignorance of physics, none of their bombs would have hit their targets and the USS Arizona might today be a floating museum rather than a sunken tomb. At best—or worst, depending on whose flag one saluted—only Japanese torpedo planes would have damaged ships during the first-wave attack. Had the attack been planned by physics fools, even the torpedoes would have gone awry. Pearl Harbor was notoriously shallow, so torpedoes dropped from aircraft had to be modified with wooden fins and dropped from a carefully determined height to keep them from going too deep and slamming into the muddy bottom. Errors in understanding the physics would have rendered the torpedoes useless. Dive bombers might have remained effective even in a time of physics foolishness, but then they didn't attack ships—at least, not in the first wave. Dive bombers used what could be called bombing physics for dummies or, more correctly, bombing physics for maniacs. Start from the same altitude as highlevel bombers, dive straight at the target, release the bomb at maniacally close range, then pull up sharply to avoid becoming as one with the target—hopefully without blacking out from multiple gs. Unlike a bomb dropped from a high level that depended only on gravity for downward velocity, a dive bomber's load would already have a high downward velocity when released and would travel a much shorter distance to the target, making it easier to predict the bomb's path. American dive bomber pilot Harold Buell described the process as "shooting" a bomb at the target. By contrast, the erudite practice of high-level bombing required accurate knowledge of a bomb's physics if its path were to be predicted reliably enough for proper arrival at its destination. Although bomber crews were denied the joy of making the calculations, a bomb's physics had to be precisely designed into the bombsight and the altitude and speed of the aircraft carefully controlled for the bombsight to work. A bomb dropped from 9,840 feet (3000 m) takes about 25 seconds to reach the ground whether dropped from a moving airplane or a stationary blimp (see Pearl Harbor Bomb Drop Calculations). Combining the bomb's constant horizontal velocity with the ever-increasing downward velocity caused by gravity would make the bomb fall in a downward sloping parabolic path. The situation is similar to drawing with the popular toy called Etch a Sketch®. Turn one knob and a horizontal line appears on the screen. Turn the other knob and a vertical line appears. Obviously, the two knobs are independent. But turn both knobs simultaneously and it's possible to obtain a curved line. Remarkably, a bomb's motion in the horizontal dimension has no influence over its motion in the vertical dimension. They are like two entirely separate worlds. Speeding up the horizontal velocity will not make the object fall more slowly or more quickly. Likewise, making an object fall in the vertical dimension will not influence velocity in the horizontal dimension. Ironically, films of real WWII bombing runs, shot through cameras mounted in bomb bays, are often misinterpreted as proof that bombs fall straight down. In the films, the bombs look like they're falling straight down and exploding directly below. But the camera isn't stationary. It's moving forward with the airplane. To give the appearance of falling directly below the camera, the bomb has to be moving forward at roughly the same speed as the camera. The films also confirm that the air resistance slowing the bomb's forward motion is negligible. If air resistance acting on the bomb were significant, the bomb would appear to fall behind the aircraft. #### PEARL HARBOR BOMB DROP CALCULATIONS To calculate the time for a Japanese bomb to fall and strike the USS Arizona, we can use the simple mathematical model, or kinematic equation, shown below. Since this equation will be used in both the vertical (or y-dimension) and the horizontal (or x-dimension), we will use x and y subscripts to denote the respective dimensions. Where: d = displacement a = acceleration vo = starting velocity t = time Assumptions: 1. The acceleration is constant. 2. There is no air resistance. In a bomb drop, the starting downward y-dimension velocity is zero. This simplifies the model as follows: To solve for the time the bomb falls before hitting its target, we rearrange the equation and substitute the acceleration due to gravity for ay and the altitude of the bomber for dy as shown: Now that we know the time, we can switch to the x-dimension and solve for the horizontal distance the bomb travels before hitting its target. In this dimension the bomb starts out moving at 225 miles per hour (101 m/s). Because we ignore air resistance, there is no horizontal force, hence, no horizontal acceleration. (Gravity acts only in the y-dimension.) The equation simplifies to: In the 24.7 seconds it takes the bomb to fall, the bomb travels 2,490 meters, or 1.55 miles. In other words, the bomb has to be dropped 1.55 miles before the aircraft reaches the target in order to hit it. The logic of using high-level horizontal bombers against ships in the first wave rather than the more accurate dive bombers was simple: the physics were favorable. Having ships tied up at dock simplified the bombing physics, while the physics required to defend the ships was horrific. For starters, shipboard antiaircraft guns were only marginally effective at the distance bombs were dropped. WWII warship antiaircraft guns ranged from rapidfiring .50 caliber machine guns to slow-firing five-inch cannons. At the moment a bomb was released from a high-level bomber, the aircraft would be 1.55 miles (2,490 m) away, measured horizontally. Antiaircraft guns would have to start shooting long before the airplane reached this point to have any hope of downing the attacker. At such distances only cannons would have had the required range. Actually hitting a small fast-moving target such as an aircraft at long range is a major physics problem beyond the capabilities of human intuition. An antiaircraft cannon's projectile fired upward would have a noticeable arc caused by the downward force of gravity. The projectile would be less massive and travel much faster than a bomb, making the effects of air resistance significant. To down an aircraft, the projectile and aircraft would have to arrive at exactly the same location at the same time or, at least, come close enough for the projectile to explode near the aircraft. To make the required calculations, a gunner needed to measure the range, height, and velocity of the aircraft, not to mention have detailed information about the cannon shell's curved path. To make the projectile explode near the aircraft, he had to calculate exactly how long it would take for the projectile to arrive and set the fuse accordingly. He could never aim directly at the target. Instead, he would have to calculate an aiming point that accounted for all the variables. Making physics calculations using pencil and paper in the heat of battle would, no doubt, have been jolly fun and stress relieving were it not for the time constraints. A Japanese horizontal bomber would have been closing at a speed of 3.75 miles (6.04 km) each minute. If the gunner spotted an incoming bomber at 5 miles (8.05 km) away, he and his crew would have had less than a minute to make the required measurements and calculations, set the fuse, and load and aim the cannon in order to fire before the aircraft dropped its bomb. The results of failing this physics test would be far worse than a failing grade. Calculating devices, ironically called "directors," were available during WWII. Directors were mechanical computers that used gears and levers to make physics calculations. Several individuals had to keep the crosshairs of velocity-, altitude-, and range-finding devices aligned with incoming aircraft. These devices fed data to the director, which processed it and provided gun crews much needed information about where to aim and how to set their cannon shell fuses. Unfortunately, the antiaircraft directors weren't much better than Hollywood directors at making accurate physics calculations. A standard U.S. Navy five-inch cannon shell fired at an enemy aircraft had no better than a 0.1 percent chance of downing it during WWII. On the other hand, catching a large stationary battleship by surprise on a clear day was a horizontal bomber's dream. Under normal battle conditions in open water, these ships would be zigzagging while laying down smoke screens to obscure their position and, of course, shooting back in a most uncooperative manner, not to mention having extremely annoying fighter aircraft cover. In sufficient numbers, American fighter planes could have swept Japanese bombers from the sky, so the first wave of dive bombers focused on destroying the planes before they could take off. The higher accuracy of dive bombers was needed to hit the small targets of airplanes sitting on runways. Because they attack at fairly close range, dive bombers were more susceptible to antiaircraft fire than high-level horizontal bombers. However, with the element of surprise, a dive bomber could blow up parked aircraft with relative impunity. Compared to ships, air fields were not well guarded by antiaircraft guns. They depended primarily on getting their fighters in the air for protection. For Americans, December 7, 1941, is an "if-only" kind of date. If only the American aircraft hadn't been parked in easily bombed clusters and had gotten in the air. If only the American military had heeded the signs of an impending attack and stood ready at their guns. If only the DVD had existed, Americans could have corrupted the physics knowledge of the Japanese with Hollywood movies, thereby ruining the aim of their high-level bombers and causing their torpedoes to be harmlessly dropped in the mud. Such are the thoughts of Monday-morning generals and armchair admirals. Unfortunately, using Hollywood fantasy to counteract physics knowledge is worse than using a knife in a gun fight; it's like using a water balloon in a gun fight.When it comes to real-world tasks, even a small amount of physics knowledge held by a few individuals can overpower a flood of filmmaker foolishness. ### BOMB-LIKE JUMPS Bogus bombing physics isn't limited to just WWII aircraft depictions. From the standpoint of physics, the terrorist who motorcycles off the top of a skyscraper in _True Lies_ [PGP-13] (1994) is a falling bomb. In the movie, the motorcycle-riding terrorist (the same bad guy who jumped through the window described in Chapter 5) roars through the lobby of a classy hotel to escape the relentless pursuit of Arnold Schwarzenegger. Admittedly, it's a fantasy far better than running with scissors. Roaring around indoors on a motorcycle vicariously slams all the indoor rules set forth by mommies and grade school teachers everywhere. What satisfaction! Then Hollywood logic takes over. To escape a pursuer, what should one do? Naturally, go to the highest point in any nearby structure, preferably a perilous place where there is no chance of hiding or escaping. Dutifully, the terrorist rides his cycle into an elevator and pushes the top floor's button. At the top, he suddenly realizes there's no place to hide or reasonable means of escape. What a surprise. In desperation, he revs up his machine and races over the side. At this point he has a horizontal velocity and a downward acceleration just like the previously described bomb. Like a bomb, his horizontal velocity has no influence over his downward acceleration caused by gravity. By the same token, the downward force of gravity has no influence on his horizontal velocity. Only air resistance can exert a horizontal force. Put the horizontal velocity and ever-increasing downward velocity together and, just like a bomb, the cyclist will travel in a downward-sloping parabolic path. After going over the side, the bad guy remains airborne for roughly 7.5 seconds. He lands with a slightly downward angle in a swimming pool on top of a shorter building, a considerable distance from where he jumped.The impact does nothing more than get him soaking wet. He walks away without so much as a limp. A falling motorcyclist is definitely not as aerodynamic as a bomb, but then he is not going as fast. Considering that the terrorist only had about a 66-foot (20 m) runway, his horizontal speed could have been no more than twenty-five miles per hour (40 kph) before his take off, as compared to 225 miles per hour (362 kph) for the previously discussed WWII bomb when first dropped. Poor aerodynamics makes air resistance higher, but lower velocity makes air resistance lower. As a rule of thumb, air resistance goes up by a factor of 4 when velocity is doubled. Low speed would tend to compensate for poor aerodynamics, so it's still possible to evaluate the jump using a simple calculation and ignoring air resistance altogether. #### _TRUE LIES_ MOTORCYCLE JUMP CALCULATIONS We can estimate the height (dy) of the fall by using the same bomb drop equation derived in the _Pearl Harbor_ example: In other words, the bad guy fell a distance of 904 feet, or roughly 74 stories. His final vertical velocity would have been: The terrorist's horizontal velocity can be estimated using the distance equation again to estimate his acceleration as follows: Rearranging yields: As depicted in the movie, the motorcycle's acceleration on the roof took 4 seconds and occurred in a distance estimated to be 20 meters. The velocity is found as follows: Allowing for some possible inaccuracy in the distance estimate, his horizontal velocity would have been, at most, 25 miles per hour (40 kph or 11.2 m/s). The vertical and horizontal velocities can be combined as follows: Terminal velocity is the highest velocity a falling object reaches and occurs when an object's downward weight force is exactly equal to its upward air-resistance force. Increasing an object's weight or making it more aerodynamic gives an object a higher terminal velocity. Terminal velocity for a human falling with outstretched arms and legs is around 124 miles per hour (200 kph). If the person folds into a ball, the terminal velocity increases to 200 miles per hour (322 kph). Adding the motorcycle's weight to the terrorist would increase the terminal velocity above 124 miles per hour, and so the 166 miles per hour final speed of the cyclist looks reasonable. Using the slowest conceivable velocity of 124 miles per hour, the height would have been overestimated by only 34 percent. In other words, the motorcyclist would still have fallen about forty-nine stories. The horizontal distance the motorcycle would have traveled, assuming it had an initial horizontal velocity of 25 miles per hour, would be calculated as follows: Based on the analysis and calculations, the terrorist would have fallen seventy-four stories and landed in the swimming pool at about 166 miles per hour (267 kph). When it hit the water, the motorcycle would have slowed abruptly, causing the bad guy's torso to pivot at the waist and violently slam his head forward. He would have ended up wearing a shiny new handlebar mustache in the middle of his face, courtesy of the motorcycle. It's easy to see that this was not a jump he was likely to walk away from. Furthermore, he would have experienced all the problems a bombardier faces when trying to accurately place a bomb. Even a small error in speed, or aim, could easily have caused him to completely miss the rather small target of a distant swimming pool. To make matters worse, the terrorist had no bombsight. In fact, he would not have even been able to see the pool until he was close to the edge of the building and it was too late to correct his aim. Aiming issues aside, the motorcycle would probably have fallen far short of the swimming pool. In the 7.5-second jump it would have traveled only 92 yards (84 meters) in the horizontal direction. Judging from the tiny appearance of the people around the pool, the horizontal distance was farther than the 100-yard length of a football field. If the terrorist actually did fall seventy-four stories, the Marriott Hotel he jumped off would have had to be eighty or more stories high for him to land on top of another building. Keep in mind that the observation deck of the Empire State Building is only eighty-six stories high.Yet, even this height would have been inadequate to give the jumper enough time in the air to travel the horizontal distance needed for reaching the pool. While _True Lies_ does serve up some motorcycle-jumping silliness, at least it does so with a sense of humor. Not to be outdone by a motorcycle-riding terrorist, Arnie, who's riding a horse, attempts the same jump. Unlike the terrorist, the animal has horse sense and stops short, sending Arnie over the side. He's left dangling on the end of the reins. In a parody of old cowboy flicks from the fifties, Arnie finally convinces his not-so-trusty steed to back up and rescue him from certain destruction. ### THE POWER OF DIRECTORS So, why does Hollywood give us these bogus bomb scenes? The answer is a combination of box office savvy and physics ignorance. The director of _Speed_ (see Chapter 1) was driving down the highway and saw an overpass bridge with a missing section. Being an imaginative guy in the process of making a movie, he immediately visualized a scene in which his movie's bus would be compelled to jump such a gap. He had no idea if the jump could actually be done, nor did he care. He wanted to do something big for boosting box-office appeal, and his intuition told him this was it. The writers were less than enthusiastic, but that mattered little. On the set the director speaks with the voice of a god. There were, naturally, problems. As described in Chapter 1, the bridge was flat in the area where the jump was to take place, not to mention that the gap was created on film by carefully erasing the bridge's image. Had there been a real gap, as soon as the bus went off the end it would have, from a physics standpoint, become a falling bomb. The fact that it was moving forward would have in no way stopped or slowed the falling action. As stated in Chapter 1, the bus's wheels would have fallen at least 3.8 feet (1.16 m) below the roadway, causing the bus's front end to slam into the edge when it reached the gap's far side (assuming the bus had reached the unlikely high velocity of 70 mph or 113 kph before arriving at the gap). In the movie, this problem was solved with the distraction of dramatic music, screaming actors, and rapid camera cuts to prevent viewers from focusing on the flatness of the bridge. Ironically, a real bus jump was also filmed and artfully edited into the movie to give the scene realism. So it's understandable that the reader described in Chapter 1 completely missed the fact that this bus could not possibly have been jumping the gap depicted in the movie. The highly modified bus used in the actual jump drove up a specially made ramp at over sixty miles per hour (97 kph) and traveled over twice as far as the length of the 50-foot gap before slamming into the ground, blowing out its front tires, and destroying its oil pan. Afterward, the bus was undrivable. To the horror of the moviemakers, the bus also traveled so far that it wiped out all but one of the cameras placed in its path. The last camera did get the shot, but it was improperly framed, although eventually used in the movie. All of this could have been prevented if the moviemakers had just made the right calculations. Even more ironically, had the moviemakers spent more time making calculations and studying the physics of the jump, they could have designed a jump in which the bus actually traveled across a 50-foot gap and remained drivable, but that's a subject for the next chapter. #### Summary of Movie Physics Rating Rubrics The following is a summary of the key points discussed in this chapter that affect a movie's physics quality rating. These are ranked according to the seriousness of the problem. Minuses [–] rank from 1 to 3, 3 being the worst. However, when a movie gets something right that sets it apart, it gets the equivalent of a get-out-of-jail-free card. These are ranked with pluses [+] from 1 to 3, 3 being the best. [–] [–] Bombs that fall straight down. [–] [–] Jumps in which a person falls like a bomb for several seconds and walks away uninjured. [–] [–] Impossible vehicle jumps. [+] Any of the above that are presented tongue-in-check or with a sense of humor. ## CHAPTER 9 ## LEAPING LOGIC: ### Why Moviemakers Say "How High" When the Director Says Jump ### JUMPING BUSES The passengers scream and the driver ducks as the bus hurls towards the edge of disaster. Suddenly, within inches of the gap in the freeway bridge, the front of the bus miraculously flips upward, having hit a short ramp just seconds from oblivion, restoring hope for survival. But when the back wheels approach, the ramp fails. It seems to have disappeared. Instead of being projected upwards like the front, the back wheels go over the edge and fall below it—ending all hope of survival. The camera angle changes rapidly as the bus drifts across the chasm. When the bus reaches the far side of the gap, are its back wheels even further below the edge? Does it smash into it and explode? Why, no! The back wheels touch down on the roadway. It's a miracle! The columns holding up the bridge have shrunk in height, dropping the roadbed to a lower level. Yes, the moviemakers did film an actual bus jump of sorts in _Speed_ that was then skillfully edited into the film. However, the jump was not made across a gap in a flat section of an overpass bridge as depicted in the movie. The bus drove at a speed of about sixty miles per hour (97 kph) up a special ramp built on a ground-level section of unused highway. A small additional ramp, called a kicker plate, was positioned at the top and did indeed flip the front of the bus sharply upward as the front wheels drove over it. The kicker then fell out of the way so that it had no effect on the back wheels. Had the bus merely gone over the ramp, the back wheels would not have immediately fallen below the edge of the ramp. The kicker plate caused the bus to rotate around its center of mass with the front moving higher and the back lower than normal. Since the top of the ramp was about 12 feet (3 m) above the level of impact on the roadbed below, the bus flew horizontally over 100 feet before its rear wheels slammed into the ground, followed by the front wheels slamming downward even more violently. Such a landing left the bus undrivable, a condition that would have doomed the passengers to die in a fiery blast (assuming they were still alive). To prevent serious injury during the landing, the stunt driver was suspended in a special shock absorbing restraint. Had the stunt driver driven the bus in the normal manner, he would have almost certainly broken his back—an occupational hazard for stunt drivers before the invention of the shock absorbing restraint. As it was, he forgot to wear his mouth guard during the jump and accidentally bit his tongue. Needless to say, the bus was not an off-the-shelf variety. It was specially modified with driving controls located halfway between the front and back of the bus—a section where normally only passengers sit. This was done to help the driver line up the bus with the ramp as well as put the driver in a less vulnerable position. If the bus went out of control, the front was the most likely part to get smashed in. Everything that could be removed from the bus was taken out to reduce the bus's weight. #### SIMPLIFIED BUS JUMP CALCULATIONS Traditional projectile-motion equations, which ignore air resistance, work well for modeling compact objects such as balls projected off ramps. While ignoring air resistance is not a big source of error for calculating the length of a bus jump, there are other possible errors. When the front wheel goes over the edge, the bus's center of mass is still well behind the edge but is no longer supported by the bus's front wheel. The center of mass essentially has to cross a larger gap than the front wheels. If the bus is not moving fast enough, the bottom of the bus can actually scrape the edge of the ramp. With the front wheels over the end of the ramp, the back wheels will still be in contact with the ramp and create an upward normal force. This force will tend to rotate the front of the bus downward. On the other hand, the torque applied to the back wheels by the engine will tend to rotate the front of the bus upward. For motorcycle-jump-length calculations, these differences are not a big problem, since the length of the cycle is fairly short. A bus, however, is a lot longer, and making a precise jump length calculation for it would require a computer simulation. Still it's possible, even with a simple equation, to make a reasonable approximation for a bus jump in order to determine if the jump is at all possible. To start, let's assume that the bus's center of mass is located about half a bus length behind the bus's front tire at the moment the wheel goes beyond the edge of the ramp. When the bus reaches a similar elevation on the other side as it lands, the bus's center of mass will be about half a bus length in front of the gap. So let's model the gap as though it were the length of the actual gap plus the length of the bus. Even when ignoring rotation caused by the normal force on the back wheels and counterrotation from engine torque, this length should yield a conservative estimate of whether or not the jump is possible. The simple projectile-motion equation for horizontal displacement or range of a jump is as follows: Where: d x = the range or length of the jump v = velocity of the bus up the ramp or takeoff velocity g = the downward acceleration due to gravity, 9.8 m/s2 ß = the ramp angle above the horizontal Note that the bus's mass does not appear anywhere in the equation. The jump depends only on ramp angle and speed. Could the jump have been achieved under more realistic conditions, and could the bus have remained drivable? The answer: yes, but with some qualifications. It would have required matching ramps on both sides of the gap and a precise bus speed. Surprisingly, the ramps' angles needed to be no more than 11 degrees and the bus's speed roughly sixty miles per hour (97 kph) in order to make it across the 50-foot gap. Having a landing ramp at the same angle as the takeoff ramp allows the bus to gently touch down, because the bus's net velocity will be nearly parallel to the ramp. This lets the bus roll down the ramp rather than collide with it. Ramps act like velocity splitters. The takeoff ramp converts part of the bus's horizontal velocity into a vertical velocity component that moves the bus upward and a horizontal component that moves the bus forward. The gravitational force acts in only the vertical dimension and slowly reduces the vertical velocity component until it is zero at the top of the trajectory. At the top, the gravitational force then increases the bus's vertical velocity component in the downward direction. The bus has to be up in the air above the takeoff ramp long enough for its horizontal velocity to carry it across the gap. When the bus lands, it has the same downward vertical velocity as it would have if it were raised using a crane and dropped from the same height as the top of the trajectory. If the bus lands on a horizontal surface, it will slam into it with a considerable force. The bus's downward velocity component will drop almost instantaneously to zero when the bus lands on such a surface, yielding extremely high accelerations and, subsequently, extremely high forces (see Chapter 10). Here's the big surprise: as long as the bus reaches the correct takeoff speed at the correct takeoff angle (assuming negligible air resistance and vehicle rotation), the bus's mass is not a factor in the length of the jump! Why? It goes back to Galileo, who was perhaps the first person to understand that all objects fall at the same rate regardless of their mass. Aside from takeoff speed and angle, the rate of falling is the primary factor determining the distance of the jump. Although a jump with a takeoff and landing ramp would have been more realistic than the one filmed for the movie, the doubleramp jump also has its hazards, not to mention problems with reality. If the bus takeoff velocity were too low, the front of the bus would smash into the landing ramp. Too fast and the bus would partially overshoot the ramp and experience a hard landing, be undrivable, and explode or merely break the bus driver's back and seriously injure most of the passengers. Realistically, the speed would have to be higher than the exact level for the crossing because it's better to risk a hard landing than a crash into the landing ramp.Throw in the need to keep the bus drivable and the margin for error is next to nothing. But all this discussion about adjusting to the precise speed needed for surviving the jump is hypothetical. Takeoff and landing ramps that are exactly the correct angle for making the jump are not likely to be found on overpass bridges. For one thing, changing from an upward to an equal but downward slope in only 50 feet of distance would cause vehicles traveling above sixty miles per hour to go airborne as they crossed the _completed_ bridge's peak—a poor design at best. So while the jump may be possible, it's pretty far-fetched. Still, the true bridge-jump believers are right, in a sense. In theory, the bus jump could have been made even without the ramps—that is, if the bus had been driven fast enough to put it in a circular orbit with a radius equal to the radius of Earth. This jump would have required a takeoff velocity of about 17,700 miles per hour (28,500 kph)—a little quick for most city busses. Air resistance would also have been a factor but might not have been all that bad for a mere 50 feet. The driver and passengers would have likely blacked out from the acceleration required for reaching 17,700 miles per hour, if they survived it. The sonic boom would have smashed windows and rattled nearby buildings but, hey, it would certainly have added excitement. So, in the next movie bus jump, maybe a nuclear rocket scientist will be aboard and just happen to have his latest miniature nuclear rocket creation in his brief case. ### JUMPING HULKS There's no question that the Incredible Hulk is one bad dude and, at first glance, the jumps attributed to him in his movie seem reasonable. But they're not. Such a jump yields projectile motion similar to a bus jump off a ramp. Once airborne the only forces acting on the projectile—in this case the Hulk—are air resistance and gravity, neither of which can help make the jump longer. Sometimes aerodynamically shaped objects such as the discus used in Olympic events can experience lift, a factor that does extend the distance traveled. But lift is unlikely with a boxy object such as the Hulk. This lack of an assisting force after takeoff means that the length of the jump will be dictated entirely by the take off velocity and angle. The movie depicts the Hulk making jumps on the order of a kilometer—an impossibility given his rather slow takeoff velocity. #### HOW JUMPING DISTANCE SCALES UP IN CRITTERS Equation 9.1 established that the length of a jump is only a function of the takeoff velocity squared and the angle. The same relationship is true for cars, critters, or people. Assume that a critter starts its jump from zero velocity and reaches takeoff velocity by the time its feet (or paws) leave the ground. From kinematics Where: v = takeoff velocity a = constant acceleration in the same dimension as v m = mass of the critter being accelerated d = distance the leg force acts on the critter before the critter's feet leave the ground combined with F = ma yields: Where: F = the constant force provided by legs but F is proportional to the cross sectional area A of the muscle producing the force. So, again, referring to equation 9.1 for calculating the range or horizontal length of a jump: The range X is proportional to V2 or (A/m)D A scales up with the square of the scaling factor (S). m scales up with cube of the scaling factor (S3) and D with S (see Chapter 4). If an animal is scaled up by the factor S, the new jumping distance will be In other words, the new jumping distance will be the same as the old, assuming that the animal was not scaled up so much that it collapsed under its own weight. So, why are tall people often able to jump higher than short ones? They are not scaled up proportionally. Generally, the big difference between short and tall people is the length of their legs. Leg length makes up a larger proportion of a tall person's height as compared to a short person. Proportionately longer legs would be an advantage for jumping because the jumping force they produce when bent and straightened rapidly during a jump would be applied over a longer distance. However, the torso moved by the legs would still weigh about the same as a short person's torso. Although the tall person's legs would weigh more, the torso still accounts for most of a person's weight. Hence a tall person could jump farther than a short one, assuming both had similar athletic conditioning and skill. So what takeoff velocity would the big guy need to travel 1 kilometer in a single leap, and what would he look like making such a leap? If we ignore air resistance and assume the takeoff angle is forty-five degrees, the Hulk would need a takeoff velocity of about 222 miles per hour (357 kph). He would appear to move away quickly then seem to be slowing down as his image got smaller with increasing distance. While the movie is not a perfect match for the calculated behavior, it's at least in the ballpark, except for one very sticky detail: air resistance cannot realistically be ignored. The Hulk is too large, too boxy, and too fast. Accounting for air resistance is tricky. First, air resistance changes with velocity—unlike a more cooperative force such as gravity, which remains constant (at least in projectile-motion problems). But it gets worse: at low speeds air resistance can be approximated as follows: (air resistance) = (coefficient of drag) × (cross-sectional area) × (velocity) At higher speeds the velocity term in the above equation changes to velocity squared. In other words, the air resistance becomes even more dependent on velocity. As for the coefficient of drag (CD), it's just a constant, or as engineers call it, a fudge factor—a factor tossed into the equation to fudge the numbers so they come out right. And where would this fancy fudge factor come from? From wind tunnel measurements on the Hulk. That poses a problem: the Hulk is not on hand and probably wouldn't cooperate if he were. To complicate matters further, the CD measurement is only good for one wind direction and one Hulk configuration. When jumping, the Hulk would have to always keep himself oriented in the direction of his velocity and hold his arms and legs in the same position as when his CD was measured. Otherwise, his CD, not to mention his cross-sectional area would change during his jump. Without turning the analysis into a career, about the best that can be done is to model the Hulk as a sphere and use a computer simulation package such as Interactive Physics to get an idea of how much air resistance affects the Hulk's jumping distance. When we do so, we get an amazing result: the Hulk's takeoff speed must be around 1,250 miles per hour (2,020 kph), faster than the speed of sound, faster even than a speeding .22-caliber long rifle (LR) bullet (873 mph or 1,410 km/hr). Okay, we made a lot of assumptions, but keep in mind that the maximum distance a .22-caliber bullet will travel is only about 1.1 miles (1.8 km). Since the bullet is far more aerodynamic than the Hulk, the Hulk would need to start at a much higher speed to reach even the shorter distance of 1 kilometer (0.62 mi). So how would the Hulk really look if he made a 1-kilometer jump? He'd look like a giant green cannon ball; he'd go so fast he'd be a blur. His landing velocity (134 mph, or 216 kph) would be far slower than his takeoff velocity due to the effects of air resistance, but when he landed the impact would be impressive. The Hulk's takeoff would also be dramatic. If he were standing still and decided to leap, he would first bend his knees then very quickly push off. As he straightened to his full height, his feet would break contact with the ground and he'd be launched into the air. The acceleration propelling him into the air would only occur during the short distance between his bent knee and fully straightened position: a distance of, at most, 30 inches (0.8 m). Once his feet broke contact with the ground, he would no longer be able to increase his takeoff velocity. His average acceleration during takeoff would exceed 30,000 gs. The force his feet exerted on the ground would be his normal weight times the acceleration in gs, or about 15,000 tons—enough to break concrete. Pound for pound, the Hulk's muscles would have to be thousands of times stronger than human muscles to make his lengthy jumps. If an animal is scaled up or down, the distance it can jump (assuming it does not collapse under its own weight) will not change. For example, if a flea can jump 20 inches (0.5 m) in its normal size it will still only be able to jump about 20 inches if scaled up to the size of a cricket. The only way it could jump further would be to get stronger muscles. The Hulk is similar in build to a Neanderthal wrestler on steroids (had there been one). Scale up such a wrestler to the Hulk's size, and he'd still only be able to jump his normal amount—a few meters—not the Hulk's incredible 1,000-meter leap. So when it comes to jumps in Hollywood movies, the important question is not what the laws of physics say; it's what the director says. When the director says jump, rather than wasting time on calculations, moviemakers simply ask how far and how high. #### Summary of Movie Physics Rating Rubrics The following is a summary of the key points discussed in this chapter that affect a movie's physics quality rating. These are ranked according to the seriousness of the problem. Minuses [–] rank from 1 to 3, 3 being the worst. However, when a movie gets something right that sets it apart, it gets the equivalent of a get-out-of-jail-free card. These are ranked with pluses [+] from 1 to 3, 3 being the best. [–][–] Creatures making incredibly long jumps at low velocities with little indication of high takeoff or landing force. [–][–] Hapless souls, heroes or otherwise, cast through windshields for no good reason. [–] Large creatures with leaping abilities far greater than the smaller versions they were scaled up from. [–] Simulated vehicle jumps that depart from reality. [+] Vehicle jumps filmed under realistic conditions. ## CHAPTER 10 ## ACCELERATION AND EWTON'S SECOND LAW: ### How to Get Started, Use the Brakes, or Change Direction, Hollywood Style ### NEWTON'S SECOND LAW—A SYNOPSIS Newton's second law rests on the definition of acceleration, which like most things in physics doesn't have the same meaning as in everyday language. Like force and velocity, acceleration is one of those strange quantities called vectors—represented by arrows. The arrow indicates the quantity's direction, and the length of the arrow indicates the quantity's magnitude or size. Acceleration is simply a measure of how fast the velocity is changing. A change in velocity can mean that an object is slowing down, speeding up, or changing direction. If the change happens quickly, we get a high acceleration; and if it happens slowly, we get a low acceleration. Newton's second law teaches that Force = (mass) (acceleration) or F = ma (EQUATION 10.1) In other words, force and acceleration are directly proportional. They go hand in hand. If one increases, the other must also increase; if one decreases, the other must also decrease. The arrow representing acceleration and the arrow representing force always point in the same direction. By contrast, the arrow representing velocity can go in an entirely different direction from the arrows representing the force or acceleration. If the arrow representing acceleration or force points in the opposite direction from the arrow representing velocity, the object is slowing down. If the two arrows point in the same direction, the object is speeding up. For physics purists, the term deceleration—gasp!—doesn't exist. Okay, some physics books regrettably use this abominable term, but to the pure of heart, it's bad form. To many, it seems like Newton's second law is just a repeat of Newton's first law in equation form. There's some truth in that, but there's an additional difference: a complete description of Newton's first law defines something called an inertial frame of reference, which must exist for Newton's second law to be true. A frame of reference is whatever is assumed to be stationary (often the floor). An inertial frame of reference is one where Newton's first law holds true. Is there a place where Newton's first law doesn't hold true? Yes, and it's found even in some fairly ordinary places. An inertial frame of reference can be moving at constant velocity but cannot be accelerating with respect to any other inertial frame of reference. An inertial frame of reference cannot, for example, be a merry-go-round because its parts are changing direction or accelerating with respect to the ground as they go around and around. If a person riding on one side of a merry-go-round tries to throw a ball straight across to a person riding on the other side, the ball will appear to go in a curved path relative to the rotating merry-go-round. Even Earth's surface cannot be considered a true inertial frame of reference because it's rotating. But don't worry; Earth is so large that it can be considered as though it were a flat immobile surface, at least for all the examples in this chapter. ### HOW TO ENJOY A CRUISE SHIP CRASH A runaway cruise ship ( _Speed II_ [PGP-13])—its engines unstoppable—is headed straight for a dock in the greatest movie ship crash scene ever filmed (not that ship crashes are common). Its passengers scream as the boat rips through the wooden dock. Conveniently, the first mate calls out the boat's speed to reassure viewers that the boat is indeed slowing down (duh). In the middle of the crash, for added excitement (as if there weren't enough), the movie's heroes are hurled through the boat's windshield onto the deck below. The ship's windshield—made of laminated glass to resist wave impact during storms—would lacerate the flesh, shatter the face bones, and knock out the teeth of any unfortunate soul who smashed through it. But miraculously the heroes are uninjured. After taking out the dock and a few condos, the giant boat comes to rest. So, why were the people aboard the craft screaming? They should have relaxed in a deck chair, sipped a cold drink, and enjoyed the spectacle. There never was any danger, at least not to them. As for the heroes crashing through the ship's windshield, consider the same situation for a car traveling forty-five miles per hour (72 kph) that hits a brick wall and stops almost instantaneously, in say 0.01 seconds. The driver (who considers seat belts unmanly) crashes through the windshield. By contrast, the boat is traveling all of seven miles per hour (11 kph) and takes thirtythree seconds to stop. Common sense alone says that the boat crash is incredibly gentle compared to the car wreck. A quick calculation shows that the stopping acceleration is over 200 gs for the car and around 0.01 gs for the ship. People will stay put in the car or boat if they have exactly the same acceleration as their respective vehicle. If not, the people will continue moving forward as the car or boat stops. We say that they are "thrown" forward, but really they're not. They passively continue moving forward until a force or combination of forces acts to stop them: in the case of the car's driver, crashing through the windshield and smashing into the wall beyond it provides the combination of restraining forces. In the more gentle case of the ship, the people will never move forward with respect to the ship as long as the friction force between the passengers and deck is high enough to restrain them. The maximum friction force acting on passengers standing on the deck would typically be at least half their weight. Such a force could keep a passenger fixed to the deck with ship stopping accelerations up to 0.5 gs, or about fifty times greater than depicted in the movie. While it might be difficult to keep one's balance under such conditions, as soon as one fell to the deck, the friction force would be restored and any forward motion with respect to the deck would cease. The windshield of a ship would be capable of providing a very high stopping force. For the windshield to break from human impact, the ship would need a stopping acceleration of at least five gs. At a speed of seven miles per hour (11 kph), the ship would have to slam into a perfectly solid barrier and come to a complete stop in a remarkably small distance of 3.8 inches (9.6 cm). This distance includes any deformation or crumpling of the ship's front. Is there any way the giant ship could have momentarily experienced a stopping acceleration high enough to send the heroes through the window? No. A high acceleration requires a high rate of change in motion, but Newton's first and second laws say the ship's huge mass will strongly resist any change in motion. If the velocities shouted by the first mate as the ship slowed down are plotted against time, remarkably, they fall in a straight line. The slope at any point along the line is equal to the ship's acceleration at that moment. But since it's a straight line, the slope is constant, and so is the acceleration. This steady acceleration is way too low to send the heroes through the windshield. The force that the windshield's glass would have needed to restrain a hero's forward motion would have been equal to his mass times his acceleration. For a 150-pound man during the _Speed II_ ship crash, this works out to a whopping 1.5 pounds. Conversely, Newton's third law says that the man exerts an equal but opposite force on the glass. Surely a windshield could resist a 1.5-pound force. Surely a ship demolishing a dock and several buildings is exciting enough even without propelling the heroes through the ship's windshield. #### USING NEWTON'S SECOND LAW As mentioned in the text, if a car traveling forty-five miles per hour (72 kph, or 20 m/s) hits a brick wall and stops almost instantaneously, in say 0.01 seconds, the acceleration is as follows (assuming acceleration is constant): The acceleration just happens to be negative in this case. A negative sign only indicates direction such as forward or backward. Since the velocity was positive, the acceleration had to be negative or point in the opposite direction for the car to slow down. Note also that gs are a unit of acceleration, not force. The force this would create on a 220-pound (100 kg) bubba is as follows: (Note: as long as the acceleration occurs on Earth, the force acting on a person can be calculated as the person's weight times the number of gs.) If the initial velocity and stopping distance are known but the time is not, the acceleration can be found as follows (assuming constant acceleration): where: x = stopping distance If a ship slammed into a perfectly solid barrier and came to a complete stop in a distance of roughly 3.8 inches (10 cm) from a speed of seven miles per hour (11 kph, or 3.06 m/s), the ship's acceleration would be as follows: ### IT'S NOT THE FALL. . . . It takes no imagination to understand that jumping from a tall building onto a sidewalk is going to do more than just hurt. It turns out that the stopping acceleration is inversely proportional to the stopping distance. When a person hits the sidewalk, it may crack but it is essentially not going to move. The stopping distance has to be entirely provided by crumpling the person. Assume the person is six feet (1.8 m) tall and lands feet first at the terminal speed of a sky diver: 120 miles per hour (193 kph). If the stopping force is provided by crumpling the person 25 percent—in other words crushing the person's legs to about half their normal length—the person will be subjected to 327 gs. At such accelerations, blood flow to the head will stop, blood vessels rupture, and internal organs crash into the bones underneath them. Such a fall is not survivable. Is any fall from a great height survivable? Based on various unplanned experiments, the answer is yes For example, Lieutenant I. M. Chisov, a Russian airman, was badly injured but survived when he fell nearly 22,000 feet without a parachute after his bomber was attacked by German fighters in 1942. He hit the edge of a snow-covered ravine and rolled to the bottom. In 1944 Nicholas Alkemade—tail gunner in a badly damaged British Lancaster bomber—discovered to his horror that his parachute was in flames after being ordered to bail out. He jumped anyway, landing in trees, brush, and drifted snow. He ended up with a twisted knee and a few cuts. The common element in survival is always an extended stopping distance provided by crumpling materials or objects other than the human who falls. Water can extend the stopping time, but is of limited benefit. To enter water, a person has to push a volume of water equal to their body's volume out of the way. Since water tends to have a lot of mass, it takes a lot of force to accelerate it out of the way, especially if done quickly. The water exerts a resistance force on whatever does the pushing. Naval academy cadets are forced to jump feet first into water from a ten-meter (32.5 ft) high platform in order to prepare them for the day they might have to abandon ship. They are taught to hop off the platform rather than leaning forward until falling off, because the leaning could misalign them from a perfect vertical position. Any head movement can result in minor injuries such as a bloody lip. Needless to say, above a height of 10 meters, water is going to be a very dangerous landing pad—it only needs to knock a person out to kill them by drowning. In the movie _XXX State of the Union_ [RP] (2005), Darious Stone (Ice Cube) jumps from a train moving at 160 miles per hour across a tall bridge over water. Assuming that the bridge was 300 feet high (91 m) and neglecting air resistance, the hero would hit the water with a vertical velocity of about 94 miles per hour (152 kph). His horizontal velocity would be reduced by air resistance but would probably still be at least as high as his vertical velocity. To have any hope of survival, the hero would have to enter the water feet first to prevent head injury. He'd also have to be facing upward and hit at exactly the same angle as his velocity vector: about forty-five degrees, in order to prevent back and neck injury. Even then, the horizontal component of his legs' velocity would slow down more quickly than the same component of his head and torso, creating a bending action on his body. If facing upward, the body would bend in a direction it's designed for (the same direction as bent in toe touching). Otherwise, the body would be bent backwards, resulting in a back or neck injury. If the hero entered in the traditional diving position—perpendicular to the water, arms then head—as soon as his arms and head hit the water, their vertical and horizontal motion would abruptly slow almost to a stop. Meanwhile, his legs and torso would continue with their same vertical and horizontal velocity. The result would be an even more extreme bending action on the body, easily enough to break a neck or even a back and slam the person's torso onto the water's surface, breaking ribs and damaging internal organs in the process. So what does the hero do? He shoots the water with some type of handgun that looks like a sawed, off grenade launcher and foams up the water below him. Although it's not likely to be effective, foaming the water with gunfire would lower its density and reduce the resistance force it would exert on the hero when he hits it—at least slightly. The hero dives into the foamy water vertically head first. Does he die? Does he suffer? Why no, it's a miracle! He not only remains conscious but survives unscathed. After all, it's not the fall; it's the stop at the end of the fall that kills and, of course, this stop was perfectly safe by Hollywood standards. ### DEATH BY RESCUE Falling off a tall building is almost certain death unless one is miraculously rescued. So, when Lois Lane falls from the fiftieth floor and is inches from impact with the sidewalk, Superman must rush—faster than a speeding bullet—to save her by whisking her off in a horizontal direction. As she falls she will roughly reach the terminal speed of a sky diver and be closing with the sidewalk at 120 miles per hour (193 kph). On the other hand, the man of steel will be closing with her at a velocity in excess of a speeding bullet say around 1,400 miles per hour (2250 kph). When he catches Lois, he must increase her velocity from zero in the horizontal direction to match his horizontal velocity and stop her downward velocity almost as fast as if she had hit the sidewalk. If it takes 0.1 seconds to do this, Lois will be subjected to over 6,000 gs of horizontal acceleration, and Superman will end up with an armful of bloody mush. It makes no difference whether high acceleration occurs in the horizontal or vertical direction. It's going to hurt. Superman could stop—he is after all superhuman—the instant before he hits Lois, catch her, and then accelerate off in a horizontal direction at a rate that would not injure her. Just before stopping, he would have 10,000 times more kinetic energy than a 7.62 NATO machine gun bullet. The law of conservation of energy demands that something be done with the energy. About the only option is converting it to heat. When he stopped, Superman would become red hot and likely set Lois on fire—not in the romantic sense. Lois would be french fried. And since she's inches from the sidewalk, Superman is still going to have to subject her to a high vertical acceleration to get her stopped—but certainly not 600 gs. There's really no way he can save her, unless he stays close at hand so that he would not have to move so fast to catch her. #### Acceleration Injuries Human tolerance for acceleration depends on many factors, including age, physical fitness, direction of acceleration, and use of safety equipment. The following data is offered only as a rough indication. Blackout from prolonged exposure \| 4–6 gs ---\|--- Chest acceleration limit during car crash at thirty miles per hour (48 kph) with airbag \| 60 gs Head acceleration experienced by Princess Diana during fatal car wreck \| 100 gs Chest acceleration experienced by Princess Diana during fatal car wreck \| 70 gs ### CORNERING CALLING FOR A CORONER The spacecraft from Earth (SFE) changes its direction to fight an enemy ship. It is traveling a mere 0.25c (25 percent of the speed of light) and makes a gentle 180-degree turn with a 1.0-mile radius (1.6 km). The enemy ship departs slowly without bothering to fire. Has it given up, surrendered, or retreated in fear? No, there is no need for any of these responses. The crew members of the SFE have turned themselves to bloody mush by making the 180-degree turn. They have subjected themselves to roughly 3.6 × 1011 gs of acceleration. Even making the turn at a mere 1,000 miles per hour (1,600 kph) would subject the crew to 12.7 gs of acceleration—enough to cause blackouts and even fatalities. The truth is that space battles would have to be fought at rather sedate speeds if the ships were supposed to make turns and keep the crew alive at the same time. If a spaceship makes a turn, it has obviously accelerated because it has changed direction. In making the turn the ship will generally follow a circular arc. Anytime an object goes around in a circle, or for that matter even a part of a circle, it will be subjected to centripetal acceleration. And acceleration is acceleration, whether it is caused by traveling in a circle or some other type of activity. High acceleration leads to high forces that cause damage. If centripetal acceleration is such a big problem for humans on spaceships, then how do air force jets flying at supersonic speeds engage in dogfights? Simple, they don't. First, if they want to down an enemy aircraft, they will typically use a small guided missile, which travels much faster than the jet, locks onto the target, and destroys it when it's several miles away. Small missiles can handle far more acceleration than humans and don't blackout. If a jet fighter does engage in a conventional dogfight with blazing cannons, it has to drop to subsonic speeds (below 760 mph, or 1,200 km/s). Centripetal acceleration has been a boogeyman for military pilots since WWII. Dive bombing took a special kind of courage. Not only did the pilot have to dive straight at a target that was likely shooting back, but once he'd released his bomb he had to pull up sharply to avoid slamming his aircraft into the target.This subjected him to multiple gs of centripetal acceleration at a most inconvenient time for a blackout. Blackouts were so common among dive bombers that the German Stuka bomber was designed with a type of autopilot that would pull the aircraft out of its dive as soon as the bomb was released. For spacecraft, even slowing down would be a major problem. If a spacecraft traveling at 0.25c (25 percent of the speed of light) decided to stop and limited its acceleration to 1.0 gs, it would take 3 months to come to a stop. Even if spacecraft could attain incredible speeds, simply stopping would make space journeys lengthy. If the spacecraft were rotating in order to create artificial gravity (see Chapter 15) and wanted to slow down, it would have to turn off the rotation and reorient all the spacecraft floors so that the downward direction in the spacecraft's rooms pointed in the same direction as the forward motion of the craft. While not impossible, it would take a sophisticated design to pull this off. Stop in thirty seconds from a speed of 0.25c, and the crew would be bloody mush (acceleration = 2.6 105 gs), that is, if the spacecraft did not incinerate itself. Its kinetic energy would have to be converted into another form—most likely heat. _Star Trek_ dealt with this annoying little problem by creating "inertial dampers." These fictitious devices operate on an unknown principle of physics and somehow dramatically reduce the effects of high acceleration. As stated earlier, Newton's second law says that F = ma, and it's actually the F (or force) that causes the damage. The m is generally referred to as the object's mass, but really is its linear inertia or resistance to change in linear motion. Einstein theorized that m could be increased dramatically without adding a single molecule to it. All the object had to do was go fast enough to approach the speed of light and— presto—the object's linear inertia would approach infinity. Surely, if inertia can be increased, then it can be decreased, hence, the creation of a fictitious inertia-decreasing device or inertial damper—a device that stretches physics like a rubber band. Decrease a person's m to nearly zero, and people can tolerate high accelerations because the high accelerations will produce low levels of force on them. Having the inertial dampers go offline due to damage by attacking enemy warships is standard practice in _Star Trek_ episodes. When this happens, the starship's interior jiggles about and crew members fall down. It's all great fun. If such an event actually happened, the crew members would be puréed the first time the spaceship made a high-speed maneuver. _Star Trek_ is not consistent in its use of inertial dampers, and there is no real scientific basis for them. But the writers have avoided trying to explain them with useless scientific babble. The mere mention of inertial dampers makes it clear that the writers know there are serious problems with high-speed maneuvering. Without the dampers, storyline fallacies would abound. Inertial dampers border on comic-book science, but at times science fiction has to resort to pure fiction in order to have a story. #### Summary of Movie Physics Rating Rubrics The following is a summary of the key points discussed in this chapter that affect a movie's physics quality rating. These are ranked according to the seriousness of the problem. Minuses [–] rank from 1 to 3, 3 being the worst. However, when a movie gets something right that sets it apart, it gets the equivalent of a get-out-of-jail-free card. These are ranked with pluses [+] from 1 to 3, 3 being the best. [–] [–] Movie characters subjected to huge accelerations with no significant injury. [–] [–] Movie characters riding in vehicles are thrown through windshields as the vehicle slows down with lowto-moderate acceleration. [–] [–] Space battles with ultra-high-speed turns and maneuvers and no physiological effects on crew members. [+] Sparing use of makebelieve devices that are not explained with a lot of scientific mumbo-jumbo but at least recognize that a scene's physics would otherwise be impossible. ## CHAPTER 11 ## HIGH-ENERGY FILMS: ### Nuclear Firecrackers, Falling People, and Cars as Weapons ### NUCLEAR FIRECRACKERS Up close a nuclear bomb blast is deadly but merciful—instantly vaporizing breathing, feeling humans into shadows on the ground. At a distance, it's pure cruelty. It can melt flesh off a face or cause prolonged torment through all kinds of trauma, not to mention radiation sickness, cancer, or genetic mutation. Few events can match its horrifying effects on people. It's our ultimate boogeyman, yet our ultimate bodyguard. We can choose where, when, and how to unleash its incredible power. And when we do, anything or anybody that threatens us had better watch out. So, of course, when giant spaceships, enormous asteroids, or huge masses of uncooperative molten iron threaten Earth's tranquility, it's time to reach for the nuclear button. The problem is that on a planetary scale, our boogeyman bodyguard is a squeaky little mouse. Oversized saucers 15 miles in diameter, sent by a mother ship, arrive from outer space in fiery clouds and park over major cities around the globe. At first, the inhabitants below the saucers respond with a mix of excitement, curiosity, and fear. But when the saucers start blowing up cities with single blasts from their death rays ( _Independence Day_ [RP]) the confusion vanishes—along with the White House. It's show time for the nuclear bomb, our boogeyman bodyguard. But wait! David Levinson (Jeff Goldblum), always the devoted environmentalist, shouts "stop." Nuking alien invaders over American cities would be an environmental disaster. How could anyone unleash such a boogeyman? On the other hand, letting alien ships incinerate entire cities complete with birds, trees, and nuclear power plants is—by golly—also an environmental disaster. Less emotional military officials (nitwits according to Hollywood) decide to nuke the aliens anyway, to no useful effect. It seems the saucers have protective force fields. As Goldblum predicted, Earth gets the boogeyman but not the bodyguard. What to do? For every Goliath there's a stone. An alien saucer must turn off the shield around its death ray just before firing it. Fly a jet aircraft up the death-ray port and voila: the alien ship explodes and falls down, all 15 miles in diameter of it. Krauss, in _Beyond Star Trek_ , estimates a saucer would weigh about 100 billion tons and that dropping it from a height of about 1 mile would release over 10,000 times as much energy as the nuclear bomb used on Hiroshima. It's hard to imagine that an object falling from a height of 1 mile would create the equivalent of a gigantic nuclear bomb blast—but then it wouldn't. The blast would be worse than an exploding bomb. A falling 15-mile-diameter disk would act like a gargantuan piston. Air underneath would be forced sideways out of the gap between the piston and the ground, forming a horizontal blast wave in the process. A nuclear bomb releases energy upward as well as horizontally, but it's the horizontal energy that destroys cities and countryside. The falling saucer would waste little of its destructive energy in the vertical direction. The drop would mostly unleash energy in a horizontal blast wave. The air velocity out the gap would be equal to the downward velocity of the saucer times the ratio of the saucer's area to the area of the gap at the saucer's perimeter (assuming that the air underneath acted as though it were incompressible). As the saucer fell, the gap would get smaller and smaller. When the saucer was 0.25 miles above the ground, the area of the saucer would be fifteen times as large as the area of the gap. If the saucer were falling at about half the terminal velocity of a sky diver, sixty miles per hour (97 kph), the horizontal wind coming out of the gap would be 900 miles per hour (1450 kph).These velocities are easily comparable to those of the Hiroshima nuclear blast. True, air is compressible and so the wind will be lower, but the gravitational potential energy of the spaceship that is not converted into wind speed will be converted into elevated pressure and temperature beneath the spaceship, both of which cause damage. Make the same calculation at a height of 100 feet, and the area of the saucer would be 198 times as large as the area of the gap. The wind velocity would be nearly 12,000 miles per hour (19,300 kph)—an impossibly high number. Obviously, instead of the extreme wind speeds, air would now be compressed to very high pressures, attaining high temperatures in the process. Combustibles under the saucer would likely ignite and blast a high-speed wall of fire out the sides of the gap. Unlike a nuclear blast radiating in all directions from a point source, the saucer blast wave would occur along its 47.1-mile perimeter and be focused in a horizontal direction. The effect would devastate a much wider area than an equivalent nuclear bomb blast. Okay, the saucer would probably tilt as it fell, but if it's only 1 mile off the ground, the tilt would be less than seven degrees. If it fell from a height of, say, 15 miles, the tilt could approach ninety degrees, but then the ship would also have fifteen times as much potential energy. Besides, if the ship tilted as it fell, the first side to touch the ground would block air flow, meaning that airflow out the elevated side would be higher than if the ship did not tilt. Tilting is going to do little or nothing to moderate the severity of the disaster. To be capable of traveling back to its mother ship, the saucer would need fuel with at least 1,000 times as much energy as the blast it set off by falling 1 mile. Imagine the environmental damage this would cause when it leaked out and/or exploded during the ship's crash. Killing these Goliaths all around the globe would be no cause for celebration. It would change weather patterns, ignite massive fires, and fill the sky with debris that would blot out the sunlight. As for the mother ship, while the Davids on Earth were readying themselves to fight the Goliath saucers, the nerdy Goldblum and ace pilot, Captain Steven Hiller (Will Smith) flew a captured alien fighter craft to the mother ship, bluffed their way inside, planted a virus in the mother ship's computer, and left a—you guessed it—nuclear boogeyman. The pair made their escape just before the entire mother ship detonated. Talk about a lucky rock to the temple. The ship is one-fourth the size of the moon with an outside surface area nearly four times the land area of Texas. Under normal circumstances, blasting such a colossus with a single nuclear warhead would be as effective as tossing a firecracker at a hornet's nest—just enough damage to make them really mad. But here the boogeyman apparently sets off the alien ship's fuel supply, destroying the entire mother ship in the process. The explosiveness of the mother ship's fuel does not bode well for resistance forces back on Earth. Assuming the saucers' fuel is the same as the mother ship's, when the saucers crashed, their fuel would most likely explode, making a bad situation worse. Humanity would be lucky to survive. But there's no such unhappy ending in the movie. The heroes return victorious, minus the usual brave but minor characters sacrificed to provide just the right touch of sadness, and humanity is saved. ### INCOMING ASTEROIDS In _Armageddon_ [RP] a Texas-sized asteroid—bigger than Ceres, the largest known asteroid in the solar system—is headed toward Earth at a speed of 22,000 miles per hour. The usual lovable assortment of misfits and neurotics in a complete spectrum of shapes and sizes is gathered, trained, strapped into space shuttles and sent to drill an 800-foot-deep hole, plant a nuclear bomb on a convenient fault line, and split the asteroid in half—the preparations having been accomplished in a mere eighteen days. Curiously, this gigantic asteroid has been able to sneak into the solar system on a collision course with Earth, travel for around two decades, and avoid detection until it's almost too late. First, imagine an 800-foot hole (hardly Texas-sized) compared to the size of the asteroid it's drilled in. Then imagine the overall damage if a nuclear bomb went off in such a hole drilled in "nowhere" Texas. The result: not much. Okay, maybe there would be some radioactive fallout and a big blast hole, but the Lone Star State is still going to be largely intact. It doesn't seem likely that the same setup in a Texas-sized asteroid is going to do much more damage. Of course, the movie's military morons—there hasn't been an intelligent movie general since _Patton_ [PGP] (1970)—fail to appreciate the importance of the last few feet of depth in the hole. In fact, they fail to appreciate the hole. When the project falls behind and the last possible moment for detonation is fast approaching, they try to explode the bomb even though it has not been properly planted. An asteroid the diameter of Texas (diameter = 1,271,900 m) with the same density as Earth would have a mass of about 6 1021 kilograms. The largest nuclear bomb ever built was a Russian device rated at 100 megatons TNT and weighed a whopping 60,000 pounds (27,000 kg), nearly the 24,400 kilogram payload of a space shuttle. If the bomb were miniaturized and used on the asteroid, and all of its energy went into pushing the halves apart with no energy wasted on the splitting, each half would end up with a velocity of 0.02 miles per hour (0.03 kph). The drillers land on the asteroid after it has traveled past the moon, giving them around ten hours before it hits Earth. Allowing eight hours for drilling leaves only two hours before the halves reach Earth after the bomb is set off. Multiplying this time by the separation velocity of the halves equals the separation distance when they reach Earth: a whopping 66 yards (60 m) apart (assuming no gravitational attraction force between them). A computer simulation is needed to account for gravitational attraction between the halves. Such a simulation calculates that the asteroid halves require a separation velocity of 4,738 miles per hour (2,119 m/s) to miss Earth by the 400 miles stated in the movie. This means that each asteroid half would have to gain 6.7 × 1027 joules of kinetic energy, requiring at least 64-billion 100-megaton nuclear bombs to do so. Earth's gravitational pull would cause the asteroid halves to slingshot around the Earth and collide back together on the other side. The kinetic energy gained to separate the asteroid halves would then be converted back into heat about 1,000 miles above the Earth's surface. The release of energy would be astonishing and likely cause fires and damage on Earth directly beneath the blast. Here's the scary part: slapping together a plan for destroying even a small incoming asteroid in a few weeks time and splitting or vaporizing it with a nuclear bomb is ridiculous. A realistic movie portrayal of Earth's current ability to deal with asteroid strikes would have been a public service and a much needed wake-up call. Such a movie could not come from Hollywood, however, because it would lack the required happy ending. _Armageddon_ makes no such errors. Its plucky drilling crew overcomes all the obstacles and blows the asteroid in half, albeit at the cost of several crew members. Nevertheless, this loss adds just the right amount of pathos to the joyous ending as humanity is saved, yet again. ### RIDICULOUS ROTATION Not to be outdone by other nuclear bomb follies, _The Core_ [XP] has the Earth's core stop rotating—caused, naturally, by military morons playing with their new earthquake weapon, which was invented by a brilliant scientist with an ego as big as a house and no head for long-term consequences. In this movie it takes a mere three months to build a magical ship called the Virgil that can carry a rescue team down to the core for restarting it with, guess what, nuclear bombs. At least this time they send five bombs. If we assume that the bombs are 100 megatons each and 100 percent of their energy goes into restarting the core, the crew is still short by at least 685 bombs. Keep in mind also that currently the biggest bomb in the U.S. arsenal is only nine megatons. There are other small details such as creating the twisting action, or torque, required to get the core spinning. Exploding nuclear bombs tend to create force in all directions, which would only produce a net force acting directly through the core's center of mass. Such a force cannot cause rotation. For rotation, the force must be applied at a ninety degree angle to the core's radius in order to produce the needed torque. As usual, nothing goes as planned and the mission reaches the brink of failure.The movie's five-star moron decides to restart the core by using the earthquake machine in reverse. This seems like a much better plan than drilling down to the core, but, alas, an enlightened _Virgil_ crew member warns that it will cause all of Earth's volcanoes to erupt. Use of the earthquake device would also doom the _Virgil_ and its remaining crew members. Fortunately, the military moron's scheme is foiled and the crew triumphs again, at a cost.The older, less good-looking crew members die, once more providing just the right mix of pathos and triumph for the joyous ending. All of this assumes that Earth's core could stop rotating while the crust and mantel continued happily spinning—an assumption that goes beyond silliness. There would have to be a zero viscosity, friction-free layer between the mantel and core for this to happen. The rotational kinetic energy of the previously rotating core would also have to go somewhere. About the only choice would be to turn it into heat. Surely an extra 69,000 megatons of TNT worth of heat appearing inside the Earth would cause earthquakes, volcanoes, tsunamis, or something. Certainly, it would take more than a military gismo to cause it and more to fix it than a device that, on a global scale, amounts to a military firecracker. ### FALLING HUMANS It's a deadly but simple principle: the gravitational potential energy stored in an object becomes kinetic energy during a fall. It's the same type of energy that makes bullets lethal. Kinetic energy is calculated as follows: (kinetic energy) = 1⁄2 (mass)(velocity)2 A .45-caliber bullet, for instance, has a mass of 0.015 kilograms and a muzzle velocity of around 254 meters per second, giving it a kinetic energy of 483 joules (Remington Express 230 MC). For comparison, let's assume an action hero with a mass of 49.3 kilograms (108 lbs) falls out of bed. The bed is an old-style, double-post model that Lincoln could have slept in—a little higher than normal—say one meter high. Her gravitational potential energy in bed can be calculated from the following: (Potential Energy) = (mass)(g)(height) The gravity constant g is 9.8 meters per second squared (using metric units) on Earth. Thus, her gravitational potential energy in bed is 483 joules. Since this energy is converted into kinetic energy during the fall, the hero hits the ground with the kinetic energy of a .45-caliber bullet! The hero lives because the energy of the fall is dissipated over a much larger area than the area of a bullet. But if you ask around, it's usually easy to find a friend or acquaintance who has suffered a broken bone from a fall of a similar height. Elderly people, in particular, are vulnerable to such falls. Each additional meter of height is like adding the kinetic energy of another .45-caliber bullet. From a kinetic energy standpoint, a mere 6-meter (19.8 ft) fall—routine for an action hero—is similar to being simultaneously shot by six .45-caliber bullets. Suppose our hero is a 109-kilogram (240 lb) body builder instead of the wiry person mentioned in the first example. Now a 6-meter fall is like getting shot simultaneously by thirteen .45-caliber bullets at point-blank range. Indeed, it's true that the bigger they are the harder they fall. Yes, bullets are incredibly lethal because they can penetrate into vital organs and a fall on a sidewalk would lack this penetration. But, it's pretty hard to completely avoid injury from being simultaneously shot point blank six times with a .45-caliber let alone thirteen times, even when wearing a bulletproof vest. A 6-meter (19.8 ft) fall directly onto a sidewalk would almost certainly break bones even with a good landing. Increase the height beyond 6 meters, and it could easily be fatal. ### FALLING BULLETS While humans falling from great heights are almost certain to be killed, humans struck by bullets falling from great heights can survive.To help understand the reasons, we can compare the terminal velocity of a falling bullet with that of a falling human. A human skydiver will reach a terminal velocity of around 120 miles per hour (193 kph). At this point the upward air resistance force is equal in size to the downward gravitational force on the person, giving a net force of zero; hence, the person cannot accelerate to a faster speed. Traveling at terminal velocity, a 154-pound (70 kg) person has a kinetic energy of 209 .45-caliber bullets. He will literally explode when hitting an unyielding surface such as a sidewalk. By comparison, when a .45-caliber bullet is fired directly upward, it will go up at a very high velocity but come down at a terminal velocity only slightly higher than the sky diver—about 170 miles per hour (242 kph). At this speed the bullet will have a kinetic energy of only 43 joules, about 9 percent of its original kinetic energy and less than the average energy required to produce a disabling wound, 81 joules (60 ft-lb), as reported by U.S. Army ordnance expert Major General Julian S. Hatcher (Hatcher's Notebook, 1962). However, the term average implies that sometimes a lower value is sufficient to produce a disabling wound. Also chances are very high that the bullet will strike its victim in the head, and no blow to the head can be considered harmless. Indeed, doctors at the King-Drew Medical Center in Los Angeles claim to have treated 118 people for falling-bullet injuries (including 38 fatalities) between the years 1985 and 1992, mostly attributed to the massive discharge of firearms during celebrations such as New Year's Eve. These statistics suggest that about a third of the people hit by falling bullets die, but many questions have been raised about the validity of the numbers. First, minor injuries are typically not reported. Second, the criterion for listing a random falling bullet as a cause of a gunshot wound is very liberal, and witnesses are often less than forthcoming with details. There are also many factors that can increase the harmfulness of a random falling bullet. Common rifle bullets, for example, tend to be more aerodynamic and come down at higher velocities than large-diameter bullets such as those of a .45-caliber handgun. When they strike a victim, longer and thinner rifle bullets dissipate more energy per unit of area than shorter and fatter handgun bullets, and are more likely to penetrate the skin. But the single biggest increase in danger is the fact that drunken revelers firing bullets in the air are not noted for their careful aim. They often don't fire their bullets straight up into the air. Fired at even a slight angle, projectiles will come down nose first instead of base first, decreasing air resistance and increasing bullet speed in the process. If the angle is significant, the bullet can come down at a substantially higher speed. _The Mexican_ [PGP] is about the only movie to make a plot device out of a fatality caused by a falling bullet from a horde of drunken gun shooters. Okay, it's certainly possible but not predictable. On the other hand, imagine the plot possibilities for falling bullets on planets or moons with no atmospheres. An assassin pauses next to the rover parked on the moon's surface and carefully places a box beside it. He presses a button and steps back as the box silently emits puffs of smoke from its top for about two seconds. Concealed inside is a Mac 10 submachine gun with a special aiming mechanism that keeps it pointed exactly upward, and a solenoid to depress its trigger.The assassin removes the box and disappears. About 5.4 minutes later the victim starts working on the rover as thirty .45-caliber bullets rain down on his head. Since there is no air resistance, they strike the victim's space suit at the same velocity they left the barrel of the Mac 10 a few minutes earlier. They hit with a slight amount of scatter caused by the recoil-induced vibration of the submachine gun, but there is no wind to blow them off course.The lack of an atmosphere opens up all kinds of creative possibilities for plot devices. ### CARS AS WEAPONS The hero walks down the narrow alley and looks behind as 3,000 pounds (1,360 kg) of dark sedan roars toward him at thirty miles per hour (48 kph) from a distance of 100 feet. At the last instant, he jumps out of the way—or, at the last instant he is hit and rolls over the top of the sedan. In either case, he grimaces, dusts himself off, and goes on his way. He is after all the hero. One wonders why the bad guys keep trying assassination by automobile. It never works. Although the hero had a mere 2.3 seconds to assess the situation and make his move, it's no problem. He's handled worst. But the car's kinetic energy is not so easily dismissed. It is the equivalent of 254 .45-caliber bullets. This is more kinetic energy than a 154-pound (70 kg) person falling at terminal velocity (209 .45-caliber bullets). The stop isn't as sudden as hitting the sidewalk, but rolling over the top of a car is no roll in the hay. It's going to do some damage, and portraying it otherwise is going to do some damage to clear thinking. In the real world a drunken imbecile weaving his car down the road at 30 miles per hour should be greeted with even more horror than a drunken fool emptying his six-shooter skyward in the middle of the street. Maybe it's not Hollywood's place to help us put the dangers in perspective, but it certainly wouldn't hurt clear thinking if car-pedestrian interactions in movies were more injurious. #### Summary of Movie Physics Rating Rubrics The following is a summary of the key points discussed in this chapter that affect a movie's physics quality rating. These are ranked according to the seriousness of the problem. Minuses [–] rank from 1 to 3, 3 being the worst. However, when a movie gets something right that sets it apart, it gets the equivalent of a get-out-of-jail-free card. These are ranked with pluses [+] from 1 to 3, 3 being the best. [–] [–] [–] Using underpowered nuclear bombs to save humanity from certain destruction. [–] [–] [–] Contrived happy endings that have no logical or reasonable scientific basis and that help obscure real problems facing humanity. [–] [–] Having massive objects fall to Earth with only minor consequences. [–] [–] Slapping together major engineering projects in ridiculously short periods of time. [–] Humans falling from great heights and receiving no injuries. [–] Moderate- to high-speed car-pedestrian accidents without so much as a bruise on the pedestrian. [0] Fatalities from falling bullets on Earth (possible but unlikely). [+] Fatalities from falling bullets on moons or planets with no atmospheres. ## CHAPTER 12 ## MOVIE MOMENTUM: ### The Attractive Force of Glass, Rail-Gun Recoil, and Cosmic Toyotas ### SHOTGUN BLASTS AND THE ATTRACTIVE FORCE OF GLASS Sergeant Martin Riggs (Mel Gibson) stands on the sidewalk as a sinister car approaches with a shotgun protruding from the window. Suddenly he sees it, but—blam!—too late. He's blown violently off his feet and flies several feet backward through the nearest display window. Fortunately, he's wearing his bulletproof vest and survives ( _Lethal Weapon_ [PGP-13] 1987). If he were not on the sidewalk by a display window, then invariably he'd be blown into a rack of whisky bottles, a giant mirror, or some other large glass object. This happens so often in movies that Hollywood seems to have discovered a new principle of physics: the attractive force of glass. Fortunately, under normal circumstances, one needn't fear. Although remarkably reliable, the attractive force of glass only works for shooting victims and then only in movies. Still, wouldn't something as deadly as a shotgun blast at least blow a victim violently backward? At first glance it looks like it would, and that we could prove it using the law of conservation of energy. We could calculate the buckshot's kinetic energy before colliding with the victim and confidently predict that the victim would end up with this energy after being shot. If the energy were still in the form of kinetic energy, the victim's velocity could then easily be calculated. Indeed, in an elastic collision this analysis would work perfectly. The trouble is that in an elastic collision the objects that collide don't stick together. A load of buckshot hitting a vest tends to stick; hence, its collision with the victim is clearly inelastic, meaning that the kinetic energy of the victim will always be significantly less than the original kinetic energy of the buckshot. The "lost" kinetic energy is not really lost but rather altered in form. Some energy becomes a shock wave in the victim, creating bruises and possibly cracked ribs. Some energy converts immediately into heat. Predicting where all the kinetic energy goes and what it does is a daunting task, and so a kinetic-energy analysis can't determine whether a victim will be blown backward. A quantity called momentum, however, is surprisingly helpful in these calculations because it cannot change form. Momentum is a measure of how hard it is to stop an object. Conveniently, when an object, such as a bullet, collides with another object, such as a shooting victim, the bullet shares its momentum with the victim. In other words, the bullet's momentum immediately before the bullet strikes must be equal to the momentum of the bullet and victim immediately after, regardless of what happens to the kinetic energy. The phenomenon is called the law of conservation of momentum and as noted in earlier chapters, any law with the word conservation in it is about as close to absolute truth as we humans can get. Unfortunately, friction messes up conservation of momentum. So, how do we handle this pesky little force? We simply ignore it. Okay, it sounds pretty sloppy, but in reality it isn't. First, if the analysis is made immediately after the collision, friction will not have had enough time to mess things up significantly. Second, if the victim is blown off his feet, there will be little friction force present while he's flying through the air. Third, if a friction-free calculation says a victim will not be blown violently backward, then accounting for friction will make the event even less likely: the friction force would resist backward motion. #### ANALYSIS OF THE BACKWARD MOTION OF A SHOOTING VICTIM We'll assume there's no friction to impede the backward motion of the victim. This would favor the event's occurrence. To calculate the momentum of an object, we use the following equation: p = mv (EQUATION 12.1) Where: p = momentum m = mass v = velocity Before the buckshot collides with the victim, the victim's momentum is zero, since he's not moving. This means that we only have to consider the forward momentum of the buckshot. For simplicity we'll treat the buckshot as though it's a single object rather than calculating individual momentums for each pellet and adding them together. Both methods give the same result. After the collision, the victim and buckshot stick together and so, again, we only have to calculate the momentum of their combined mass. We'll assume that the combined mass of buckshot and detective is MD = 80 kilograms, and the momentum after the collision as PD even though it's really the momentum of both the detective and buckshot stuck together. From conservation of momentum: or Substitution yields: Note that the velocity of the detective is proportional to the ratio of the buckshot's mass to the detective's mass. This ratio is going to be tiny. If we run a momentum analysis (see "Analysis of the Backward Motion of a Shooting Victim") on the hapless Sergeant Riggs, we find he's blasted backward at the momentous speed of 0.4 miles per hour. Keep in mind that humans can walk briskly at about 4 miles per hour. Since the analysis was done with assumptions that favor being blown backward, it's clear that not just Sergeant Riggs but shooting victims in general aren't going to be blown backward by the force of a shotgun blast. Here's another way to analyze the situation: apply the law of conservation of momentum to the shooter similar to the way it was applied to the victim. In other words, recoil from firing a weapon will give a shooter backward momentum equal to the forward momentum of the buckshot and hot gasses (from burning gun powder) exiting the shotgun's barrel. (Note: buckshot will also include a light-weight, fibrous wad placed between the powder and buckshot.) Unless the muzzle of the shotgun is pressed against the victim, he will receive only the buckshot's momentum. The magnitude of the victim's backward momentum will be less than the magnitude of the shooter's because the victim will not be hit by the hot gasses propelling the buckshot out of the gun barrel. Also, thanks to air resistance, the buckshot will be moving slower and have less momentum than when it first exited the gun. If the recoil momentum from discharging a firearm doesn't throw the shooter backward through the nearest window, then certainly the buckshot's momentum won't. Sometimes Newton's third law is incorrectly evoked as an explanation for why a shooting victim is not blown violently backwards. These explanations claim that the recoil force acting on the shooter and the buckshot's force acting on the victim are an action-reaction pair. To qualify as an action-reaction pair the two forces must Occur simultaneously Be equal in magnitude Be opposite in direction The recoil force and the buckshot's force fail the first two requirements. The recoil force begins as soon as the buckshot starts moving down the gun barrel. Recoil force is smaller, although it lasts a longer time than the buckshot's force. The buckshot's force does not happen until the buckshot hits its target. The force is very brief but also very large in magnitude compared to the recoil force. There's no way that the force the buckshot creates on the victim and the recoil force acting on the shooter can possibly be an action-reaction pair. There is one other possible explanation for a victim being blown backward through a window: involuntary muscle contraction. The victim could be so stunned by being shot that he involuntarily tenses his muscles, causing him to jump backward. But it's nearly impossible to jump from a standing position without first bending the knees, which would require one to momentarily relax the leg muscles. Even after bending the knees, it's normally not possible to jump backward by more than 2 or 3 feet (about 1 m). Such a puny jump does not even come close to the distances traveled by Hollywood shooting victims. ### RAIL-GUN RECOIL "They said the physics was impossible" (and it is), yet two bad guys lurk in the shadows watching through impossible x-ray vision scopes mounted on impossible rail-guns as they zero in on their prey, Lee Cullen (Vanessa Williams) and John Kruger (Arnold Schwarzenegger) in the 1996 movie _Eraser_ [RP].The shiny new rail-guns come equipped with LED indicator lights on their sides and green beams of light emitted from their scopes— perfect for those stealthy sniper missions where one must not be seen. When their victims attempt to flee, the assassins send aluminum bullets zinging through the walls at nearly the speed of light, narrowly missing their targets who take refuge behind a refrigerator. Are the assassins' scopes out of whack? Did they jerk their triggers? Unlike ordinary bullets, bullets traveling near the speed of light would arrive on target almost the instant they were fired. There would be no time for wind, gravity, or motion of the target to create differences between the point of aim and the point of impact. The assassins are within 100 yards (91 m) of their targets. At these distances the misalignment caused by jerking the trigger or the inaccuracies from shooting a shoddy rifle would not usually cause a shooter to completely miss a human-sized target. Even if we imagine that the rail-gun physics make sense, the scene does not. The rail-gun physics also makes no sense. First, there's the issue of recoil. Yes, even rail-guns would have recoil. It's not necessary to have exploding gunpowder for recoil. The hot gasses from burning gunpowder propelling a normal bullet do add to the recoil, but these gasses exit at about 1.5 times the velocity of the bullet and have far less mass. In a high-powered rifle cartridge such as the 7.62 NATO, the mass of the gunpowder is less than one-third the mass of the bullet. Propelling the bullet at the same speed without using gunpowder would reduce the recoil momentum by about one-third—a significant amount.With a handgun cartridge like the .45-caliber ACP, the gunpowder is only about 4 percent of the mass of the bullet. Here, propelling the bullet without gunpowder would make little difference in recoil. Recoil is caused by sending highvelocity mass out the end of the gun barrel. It does not matter if the mass is a bullet or the gasses from burning gun powder. Likewise, it does not matter whether the force propelling the bullet is from gas pressure or an electromagnetic field. The big difference in _Eraser_ ' _s_ rail-gun recoil comes from the claim that the bullet travels at nearly the speed of light. Einstein's theory of relativity must be used to calculate the momentum of the bullet at such speeds, making the bullet's momentum far higher than at lower speeds. If we assume the aluminum bullet exits at 90 percent of the speed of light and weighs 0.26 grams or one-tenth as much as a .22-caliber rim-fire bullet, the backward velocity of the shooter (mass = 100 kg) must be a whopping 1,610 meters per second— about 4.7 times the speed of sound in air—for his momentum to be the same size as the forward momentum of the bullet. Obviously, such recoil is going to impart more than a sore shoulder. It's going to be fatal. #### CALCULATING RECOIL WITH BULLET VELOCITIES NEAR THE SPEED OF LIGHT According to Einstein, when the speed of an object approaches the speed of light, the object's momentum is calculated using the Lorentz factor as follows: Where: p = momentum γ = Lorentz factor m 0 = mass at rest u = velocity Where: c = speed of light For the bullet in _Eraser_ : Substituting into equation 12.2 yields: From conservation of momentum, the backwards momentum of the shooter (ps) must be equal to the forward momentum of the bullet as follows: or The bullet from the magical rail-gun in _Eraser_ would also have an unmanageably high kinetic energy—equivalent to several kilotons of TNT. (Note again that Einstein's equations must be used for calculating the kinetic energy.) The bullet is not going to zing through the walls. It's going to demolish the walls, along with the assassins outside and everything else in the immediate vicinity. At distances under 100 yards, the shooter can have his choice: death by the rail-gun's recoil or death by the bullet's impact with the target. At long distance it's only death by recoil. An aluminum bullet is not magnetic—this point is often cited as a rail-gun physics flaw, but in fact it is not. Such a bullet only has to be conductive. Roughly speaking, a rail-gun works by passing a large current through the bullet from one rail to the other. In the process, a strong magnetic field is generated between the rails at a right angle to the current passing through the bullet. This creates a force acting on the bullet in the direction of the barrel points. Since the bullet is free to move, it accelerates down the barrel and exits as a projectile. The key problem with aluminum is its somewhat-low melting temperature. The electrical current used for acceleration can vaporize the bullet. If the aluminum bullet does make it out the end of the barrel, heat generated at ultra-high velocity by air resistance can also vaporize it or cause it to combust when in contact with air. Excessive recoil problems can be solved and excessive kinetic energy problems reduced by dramatically lowering bullet mass. But even if the bullet's mass in _Eraser_ is reduced to 1/10,000 the size of a .22-caliber rim-fire bullet, the kinetic energy is still going to be the equivalent of over 1,000 pounds of TNT. An aluminum bullet smaller than a speck of dust going at 90 percent of the speed of light will overheat from air resistance and disintegrate the instant it leaves the rail-gun (assuming it doesn't vaporize in the barrel). As it disintegrates, the bullet's kinetic energy will be converted into heat, causing a rather nasty explosion a couple of feet (less than a meter) in front of the shooter's face. There's just not a happy ending available for this device. In _Eraser_ , the rail-gun bullet has huge amounts of momentum that hurls victims horizontally backward great distances. But even here the depiction is bogus. As shown in the movie, the rail-gun bullets are capable of zipping through walls. With such penetration, a human victim would offer almost no resistance to slow the projectile's velocity. Since the bullet has almost exactly the same momentum when it exits the victim, conservation of momentum would still be satisfied even if the victim quietly drops to the floor where he or she is standing. The force of a bullet striking its victim occurs in an extremely short period of time, so it has to be extremely high if it is going to send a person flying backward across an entire room. Such high forces would more likely tear the person apart. Getting hit by a high-energy projectile such as a .50-caliber machine-gun bullet has a gruesome effect on people. It can blow a person in half. It's hard to imagine that a far more energetic projectile from a rail-gun would only throw a person backward. So how is a victim actually blown backward through windows and across rooms in movies without injury? The actor wears a specially designed harness hidden under his shirt with a rope or wire attached to the back. He is then pulled slightly upward and backward through the window or across the room. The force required to do this is fairly low because it is applied continuously as the person flies backward. ### THE COSMIC TOYOTA It's time to blast off. The hero has been visiting a planet in a distant galaxy (for some heroic purpose) and decides to leave. It's clear that this is an Earth-like planet because the hero can breathe and walk around in just a jumpsuit. The gravity is comparable to Earth and, of course, the planet's higher life forms all speak English. He steps into his spacecraft—about the size of a Toyota—fires the thrusters, and zips off into the cosmos. Assuming the craft has a mass of 1,000 kilograms, it will take the energy equivalent of about 1,400kg (3,100 lb) gallons of gasoline to reach the escape velocity of this Earth-like planet—25,000 miles per hour (40,300 kph), a paltry speed by cosmic standards. None of this, however, is going to strain the cosmic Toyota's fuel supply. The cosmic Toyota obviously isn't running on gasoline. It has some exotic energy source—say, antimatter. Combining 2.2 pounds (1 kg) of antimatter with 2.2 pounds (1 kg) of ordinary matter would release the energy of about 1.5 billion gallons of gasoline. But there are a few problems. First, storage: antimatter instantly explodes if it contacts ordinary matter. Second, source: there isn't any. Oh well, surely these can be solved in a distant time and galaxy. So, what's the real problem? In a word: thrusters. Thrusters require an energy source, but they also need a supply of mass to produce the thrust. They work using conservation of momentum. Blast some high-velocity mass out the back of the cosmic Toyota's thrusters, and the craft will gain the same momentum in the forward direction as the expelled mass has in the opposite. The thrust force developed is as follows: Thrust = (velocity of exhaust) (mass flow rate of exhaust) Using a very optimistic expelled mass velocity of 50,000 m/s, the Konstantin Tsilokovsky rocket equation predicts that a 1,000 kg Cosmic Toyota will have to expel 800 kg or 80 percent of its mass to reach escape velocity. But the need for mass is actually much worse when blasting off a planet against gravity and air resistance forces. Air resistance does drop to zero outside the atmosphere but is substantial for the first few minutes of liftoff. All these factors together make the mass required for liftoff huge, explaining why NASA needed a behemoth rocket 95 feet 4 inches (29 m) long and 10 feet (3 m) in diameter just to launch the first American, John Glenn, into a relatively low Earth orbit at considerably less than escape velocity. To send three astronauts and their supplies to the moon, NASA required a 363-feet-(111-m-) long 33-feet-(10-m-) diameter Saturn V. Forget energy requirements, a vehicle designed to leave an Earth-sized planet is going to need an enormous mass supply to do so. As long as it's in an atmosphere, the cosmic Toyota could intake air in the front and exhaust it out the back at a higher velocity, similar to the way a ramjet engine works. Unfortunately, atmospheres tend to be remarkably shallow compared to the distance one must travel to reach escape velocity. So, the supply of mass provided by the atmosphere quickly runs out. Getting a Toyota-sized vehicle off an Earthlike planet using thrusters is impossible without a way to store large quantities of mass. Once liberated from the Earth-like planet, the cosmic Toyota could cruise around in outer space on a more limited tank of mass, since it would no longer have to overcome a gravity force or air resistance, but it's still going to be a mass hog if its driver is an acceleration freak. If cosmic Toyotas became the rage, the galaxy might become dotted with mass stations. Assuming the cosmic Toyotas came with a few years' supply of antimatter, their thrusters could use just about any form of matter. It might be possible to run them on water or discarded banana peels. Hollywood could go wild over the opportunities for specialeffects scenes. Wreck a cosmic Toyota and its 22-pound (10 kg) fuel tank would explode with the energy of 4.3 nuclear bombs rated at 100 megatons TNT each (the biggest nuclear bombs ever built). An entire disaster movie could be based on a single chase scene and a single wreck. One could hope that in the faraway time and galaxy heretofore undiscovered, principles of physics or breakthroughs in engineering might solve the problem of the excessive mass needed for escaping from a planet, not to mention the problems of antimatter storage and supply. Sadly, barring such luck, the cosmic Toyota is just too small for shuttling personnel between a planet's surface and an orbiting mother ship, not to mention interstellar travel. #### Summary of Movie Physics Rating Rubrics The following is a summary of the key points discussed in this chapter that affect a movie's physics quality rating. These are ranked according to the seriousness of the problem. Minuses [–] rank from 1 to 3, 3 being the worst. However, when a movie gets something right that sets it apart, it gets the equivalent of a get-out-of-jail-free card. These are ranked with pluses [+] from 1 to 3, 3 being the best. [–] [–] Recoil-free rail-guns. [–] [–] Shuttle craft the size of Toyotas using thrusters with the ability to escape from an Earth-like planet's gravity. [–] [–] Shooting victims blown backward large distances, especially when they crash into glass. ## CHAPTER 13 ## JFK AND MOMENTUM: ### Hollywood's Conspiracy to Assassinate History ### BACK AND TO THE LEFT As the open-top limousine cruises silently into view, the president appears to grasp his throat, and is then struck in the head by an assassin's bullet. His head moves back and to the left, its motion captured in shocking detail by the Zapruder film—a bystander's film of the actual events—embedded in Oliver Stone's controversial 1991 movie _JFK_ [RP]. During Stone's depiction of the Clay Shaw (Tommy Lee Jones) trial for conspiring to assassinate the president, the scene of Kennedy's head moving back and to the left is repeated again and again as District Attorney Jim Harrison (Kevin Costner) hammers away that it conclusively proves there was a second shooter firing from a position in front of the limousine and not just the lone shooter, Lee Harvey Oswald, firing from behind. His premise is that the victim's head will always be blasted in the opposite direction from the shooter. The physics say otherwise. #### ANALYSIS OF KENNEDY'S HEAD MOTION If the bullet that hit Kennedy in the head had remained embedded in his skull causing no exit wound, Kennedy's head motion would have been easy to analyze with a simple conservation of momentum equation. The analysis would have predicted a forward head motion away from the direction of the shooter. But when the bullet exited the head along with a significant amount of high-velocity tissue, the situation became far more complex. While a simple analysis can no longer be considered conclusive, it can establish if it's possible for the head to move backward instead of forward when struck in the back. We will model the motion as though the head rotated about a pivot at the base of the neck and will use conservation of rotational momentum. A rotational momentum analysis is slightly different than the linear momentum analysis used in the previous chapter, but both obey a conservation of momentum law. Officially, Kennedy was shot in the back of the head by a 10.37-gram full-metal jacketed bullet fired from a 6.5 × 52- millimeter Italian Carcano WWII surplus military rifle. The bullet's velocity would have been about 552 meters per second at 100 yards distance. We calculate the bullet's rotational momentum as though the bullet is rotating around the base of the neck the instant before it hits as follows: Where: L = rotational momentum I = rotational inertia ω = angular velocity Assume all objects in the analysis can be modeled as point masses. The rotational inertia for a point mass is Where: m = mass r = distance from pivot Let LB1 = The momentum of the bullet before collision LB1 = IB1 ωB1 But Substitution of 13.2 and 13.3 into equation 13.1 yields: L = (m • r2) • (v / r) The military-style bullet that struck Kennedy's head broke into several fragments that cracked the windshield and dented metal trim inside the limousine. Let's assume that the fragments retained 33 percent of the bullet's initial rotational momentum when it exited. A human head weighs about 11 pounds (5 kg). Assume that about 10 percent of the head's mass (or 0.5 kg) of brain, blood, and bone tissue exited the head wound in the forward direction after the bullet exited the head. Also assume that the neck's rotational inertia is minor or negligible compared to the head, and the dimensions of the head are as shown in Figure 20. Zapruder's camera was running at about 18 frames per second, or roughly one frame every 0.057 seconds. The shutter would have been open for about 0.025 seconds during each frame [Zavada, Roland J. "Dissecting the Zapruder Bell & Howell 8mm Movie Camera," <http://www.jfk-info.com/zavada1.htm>, 10/24/98]. While this sounds like a very short time, it's enough to blur moving objects, making them harder to see. A moving particle, for example, would look like a blurry streak. To calculate an object's average velocity, a researcher would have to estimate how far it displaced and how much time it took to move, then divide displacement by time. But, there would be no good way to know exactly when the motion started. If the motion started halfway through the time the shutter was open, the average velocity would be twice as high as if it had started at the beginning of the shutter opening, assuming the blurry streak was the same length. Even worse, in every frame, the shutter would close for about 0.032 second so the film could be advanced. No photographic record would be made during this time. These facts alone place limits on the amount of information available for analysis of the bullet's high-speed collision with its target. There is no evidence of the head shot in frame 312 of the Zapruder film. Frame 313 clearly shows tissue expelled in a forward direction from a head wound. It also shows that a particle was ejected from the wound at an upward angle a distance of over 1.5 meters. It's probably a rotating bone or bullet fragment with at least one reflective side. Its image on film looks like a series of evenly spaced dots (probably corresponding to instances when the reflective side rotated so that it caught the light) connected by a blurry line extending all the way from Kennedy's head. This implies the particle exited the wound after frame 313 had begun. If the particle had exited before the shutter opened, it would have been some distance from Kennedy's head when the photographic record of frame 313 began. There would have been a gap between the President's head and the starting point of the particle's image. Assuming that 0.5 kg of mass exited the wound and traveled 30 cm (11.8 in) during the 0.025 second the shutter was open in frame 313 gives an average velocity of 12 m/s (26.8 mph or 43.2 kph). The forward rotational momentum of the exiting mass would be as follows: Let Lm = The rotational momentum of the mass exiting the wound. From equation 13.4: Let LB2 = The momentum of the bullet after collision Let LH = The momentum of the head after collision From conservation of momentum: Therefore, the head would have had to move backward for conservation of momentum to be true. But In two frames of the Zapruder film, this would have been a motion of about 22 degrees in 0.11 seconds, which is enough to give the perception that the head was being snapped backward (see Figure 21). Admittedly, the model is too simplistic to be considered conclusive, but it does indicate that a backward motion of the head could be caused by a shot from behind—a possibility that's not even considered in Stone's film. Conservation of momentum equations—similar to those demonstrating that a shotgun blast won't blow a shooting victim violently backward—can also show that blasting open a head can make it move in the opposite direction of the bullet's motion (see "Analysis of Kennedy's Head Motion"). In the Kennedy assassination, a significant amount of brain, blood, and bone tissue (there's no way to say it delicately) exited the president's head wound with a forward and to-the-right velocity. This jet of exiting tissue acted like a thruster pushing the president's head back and to the left. In addition, when Kennedy was shot in the back prior to the head shot, he raised his hands toward the exit wound in his throat and elevated his right shoulder causing him to lean slightly to the left. This lean may have assisted the leftward motion of the head. OK, it takes a lot of simplifications and estimations to make these momentum calculations, and so by themselves the numbers presented above are not conclusive. However, experiments with paint-filled skulls, shown in a November of 1988 NOVA program on PBS, agree that if the bullet passes through the skull and expels fluid at high velocity out the exit hole, the skull will consistently move in the opposite direction of the bullet. Experiments with objects such as melons (Penn and Teller among others have performed this demo), turkey carcasses, and an assortment of other objects have been repeated many times and have shown similar results. Material ejected in the same direction as the bullet acts like a small rocket thruster or jet that pushes the object it was ejected from in the opposite direction. This head motion explanation has become known as the "jet effect." Normally speaking, exit wounds are significantly larger than entry wounds. Certainly in the Zapruder film, the wound toward the front of Kennedy's head appears much larger than any wound in the back. There are no signs of expelled tissue out the back of the head. This means that if Kennedy were shot in the front of the head, the bullet should have been found in his skull. But if bullet fragments had mysteriously exited from the back of his head with little or no blood spray, they would have fallen in the street since Kennedy was sitting in the back of the limousine. The only bullet fragments found from the head shot were recovered in the front seat area of the car, suggesting that they entered the head from the back and exited from the front, as is consistent with a shot fired from behind. Still, Kennedy's head motion may have had little to do with conservation of momentum. It may have been nothing more than a random reflex reaction. The analysis of the backward motion of a shooting victim (see Chapter 12) as well as the above analysis shows that victim motion caused by bullets is subtle. Being shot in the head has a tendency to stimulate random nerve impulses. These may have caused Kennedy's neck muscles to involuntarily snap his head back and to the left. The claim that the back and to the left motion of Kennedy's head proved that a second shooter located in front of the limousine fired the head shot is an unsupported conjecture. #### How Movies Distort Judgment about Shootings In films, bullet impacts are generally simulated with "bloodpacks," exploded when the victim is supposedly shot. The explosion often sprays a noticeable amount of simulated blood toward the shooter (the opposite direction of the bullet's motion). Exit wound blood splatter is often not simulated. (Why waste a perfectly good blood pack on the victim's back where it's hard to see?) By contrast, in real life there is some blood spray out the entry wound, but the majority of blood and tissue are expelled at higher velocity out the exit wound. On this basis alone, the Zapruder film indicates that Kennedy was shot in the back of the head and the bullet exited the front. But a person whose only knowledge of gunshot effects comes from movies would likely not be convinced by the spray pattern. Such a person would have seen simulated shooting victims blown violently off their feet and sent flying backward in movies many, many times—pure nonsense according to physics. A movie-indoctrinated person would expect body motion to always be in the direction of the bullet's motion. To this person, any backward motion, such as the backward motion of Kennedy's head, would be convincing evidence that he had been shot from the front. Again, the physics casts doubt. Could there have been a conspiracy as suggested by the movie _JFK_? Who knows? The motion of the president's head certainly does not support the theory of a second shooter in front of the limousine, which is a key element in the movie's conspiracy theory. Like most things Hollywood, _JFK_ seems to have been far more concerned with generating ticket-sale-increasing hype than with presenting insightful analysis. ### COUNTING SHOTS (AGAIN) After over forty years, available forensic evidence still indicates that a lone gunman fired three shots from the fifth floor of the Book Depository Building, two of which hit President Kennedy. The first hit—now known as the magic bullet—is where much of the conspiracy fun begins. This bullet struck Kennedy in the upper back, exited his throat, and struck Texas Governor John Connelly in the torso, wrist, and thigh.The bullet was later found lying on a stretcher. At first glance, it looks like it's in pristine condition, but closer examination reveals that it is significantly flattened on one side. The bullet was a full-metal-jacketed type, specifically designed for military use requiring maximum penetration with minimal deformation, as required by the Hague Convention of 1899. For humanitarian reasons, this convention banned easily deformed expanding bullets for military use. The magic bullet lost a large part of its kinetic energy when it passed through Kennedy's neck but had little deformation because it struck no major bones. While passing through Connelly's torso, the bullet glanced off Connelly's ribs, losing more of its velocity in the process. It had tumbled sideways by the time it eventually collided with a major bone in Connelly's wrist; this explains why the bullet was flattened on one side. Careful analysis of the magic bullet's path by a number of investigators has shown that Kennedy's throat wound does indeed line up with Connelly's numerous wounds. These investigators used photographic evidence for their analysis, including the Zapruder film and 3-D computer graphics simulations. Sophisticated FBI testing with neutron-activation analysis in 1964 and again in the late 1970s showed that the lead alloy in the magic bullet was consistent with lead fragments collected from Connolly's wounds.The testing also showed that bullet fragments found in the limousine matched with fragments taken from Kennedy's head wound. There's no evidence to suggest that any other bullets struck objects in the limousine. Both the magic bullet and other bullet fragments could be traced to Oswald's rifle. Yes, some conspiracy buffs still reject all of the above evidence, but to do so usually requires them to claim that the evidence was faked or modified. Many—including Oliver Stone—think the magic bullet was planted. This means conspirators had to fire bullets through Oswald's rifle ahead of time in such a way that the bullets tumbled sideways and were flattened on one side. Confederates with the proper credentials to approach wounded victims would then have needed to wait near possible hospitals for just the right moment and then plant one of the faked bullets. They would have needed to know that none of the real bullets ended up in a recoverable form. Planting an extra bullet would have created all kinds of problems if all the real ones were found. The additional shooters who supposedly shot Kennedy from the front would have needed disappearing bullets. Any recovered bullet with a caliber other than 6.5 millimeters or micro-scratch marks different from those made by Oswald's rifle would have been a dead giveaway that another shooter was involved. Controlling the final position and condition of a bullet once it's fired would have been problematic at best. If sophisticated conspirators had set Oswald up as the lone assassin, why would they have given him a $12.78 rifle mounted with a supposedly defective $4.58 scope, which according to Stone's movie could not possibly have made the shots? At the time, military surplus semiautomatic M1 carbines mounted with scopes and thirty-round magazines were popular and readily available for under $75—not a huge investment for a group of conspirators. One of these rifles could have spit out at least eight bullets in the time it took Oswald to fire three with his bolt-action rifle. Certainly, an M1 carbine would have been at least as accurate as the 6.5 52-millimeter Italian Carcano and far easier to shoot in rapid fire, hence, far less controversial. Had Oswald rapidly fired eight or more shots, witnesses could not possibly have kept an accurate count. It would have been easy to fire a couple of extra shots undetected from a different location, if needed. Some conspiracy buffs also claim the crime's Rosetta Stone— the Zapruder film—has been deliberately modified as part of a coverup along with x-rays of the president's head, autopsy photographs, and various other forms of evidence. Again, who knows? All this data modification and faking would have required a coordinated effort by all kinds of government groups and individuals, but so what. These are, after all, the same type of groups and individuals who thwarted the Japanese plan to bomb Pearl Harbor, pulled off the Bay of Pigs invasion of Cuba, prevented the 9-11 terrorist attacks, and coordinated the timely hurricane Katrina relief efforts in New Orleans, to name a few known highlights. How did the Jim Garrison character count shots in the movie? Why, in true Hollywood fashion, of course. According to him there were six, not three, shots fired resulting in seven wounds (he counts entrance and exit points as two wounds). In the movie, Garrison argues against the magic bullet theory using a blatantly incorrect diagram. It shows Connelly seated directly in front of Kennedy at the same height—a position where the so-called magic bullet would have needed to make impossibly sharp turns to have caused the "seven" wounds. In reality, Connolly was seated in a folding jump seat, 3 inches lower and 6 inches to the left of Kennedy.These seats were used inside the limousine to accommodate the president's entourage but were placed lower so that people seated in them would not block an onlooker's view of the president. Just before he was wounded, Connelly had also turned noticeably to his right. As for the bullet fragment analysis, the movie has Garrison ranting that " . . . the government says it can prove [the single-bullet theory] with some fancy physics in a nuclear laboratory. Of course they can. Theoretical physics can prove an elephant can hang from a cliff with its tail tied to a daisy . . ." What an insightful comment. Obviously, all forensic experts who use theoretical physics to guide their conclusions are simpletons. So what are they supposed to use? We're never told, but perhaps it's an ultra reliable tool like personal opinion. The movie's most brilliant analysis occurs when Garrison and an assistant are shown peering out the window of the book depository building overlooking the assassination site. Their dialogue informs us that the Zapruder film established that three shots were fired in 5.6 seconds. (Careful analysis of the Zapruder film indicates that the last two shots were fired within about eight seconds of the first.) The assistant, pretending to be Oswald, then aims, dry-fires, and cycles a rifle identical to Oswald's as Garrison times him. Garrison announces that the time is between six and seven seconds. If you actually time the scene, however, it turns out that the assistant fired the simulated shots in the 5.6 seconds that was supposedly impossible. In a serious moment, comicmagicians Penn and Teller conducted the same dry-firing experiment in under 3.5 seconds. Keep in mind that the clock starts with the first trigger pull, hence, it's only necessary to cycle and aim the rifle twice during the time interval. Naturally, one also wonders about the other three of the six shots Garrison later claimed were fired. If the Zapruder film established that three shots were fired, then what happened to the others? ### IT'S ONLY A MOVIE—THE JFK RESPONSE Inaccuracy in the movie _JFK_ goes beyond stupid movie physics, matters of artistic license, or even of interpretation. The movie's problems mired it in controversy even before it was released. It was attacked in the _New York Times_ , _Washington Post,_ and _Time_ magazine while still in production. Entire Web sites have been devoted to debunking virtually every scene in the film.For example, the movie insists that the president's motorcade route was secretly altered at the last minute to slow the motorcade with a sharp turn and guide the president directly into a killing zone at Dealey Plaza. Yet, the route was not only unaltered but widely publicized ahead of time. It was the only way the motorcade could get from Dallas's Main Street to their desired exit route down the Stemmons Freeway. The movie centers on Jim Garrison's investigation of an alleged conspiracy to assassinate President Kennedy. Garrison once described the assassination as a homosexual thrill killing and, at various other times, indicated that the CIA, FBI, NASA (yes, the space guys), secret service, Cuban exiles, aerospace industry, Dallas police, Lyndon Johnson, neo-Nazis, and many others too numerous to mention had had a role in the assassination and/or coverup. Of all the suspects he named, he was only able to bring one, Clay Shaw, to trial.The jurors found Garrison's evidence against Shaw so compelling that they took a whopping forty-five minutes to acquit him. Not to be outdone as a conspiracy theorist, Stone not only tries to convince us that the Kennedy assassination was a conspiracy, but that Lee Harvey Oswald was nothing but a patsy who was unjustly vilified. The movie goes beyond absolving Oswald of guilt as the lone assassin—it actually tries to create reasonable doubt that Oswald murdered police officer J. D. Tippit. When Tippit tried to question Oswald following the assassination, Oswald pulled out a revolver and cold-bloodedly shot Tippit multiple times, finishing him with a shot to the head as he lay helpless on the street. Never mind that it was in broad daylight in front of numerous witnesses; never mind that at least six people picked Oswald out of a lineup and at least two others identified him from pictures; never mind that he had the murder weapon on him when arrested; and never mind that he tried to use it on a second policeman during the arrest—Stone would have us believe that Oswald might have been framed. And what does Stone offer for creating reasonable doubt? Two witnesses who either couldn't or wouldn't identify Oswald, a less-thansterling job of crime scene investigation by the police, and an unusually large number of police officers showing up for Oswald's arrest. The police presence probably had something to do with the numerous officers already in the neighborhood investigating the Tippit murder, the possibility that many Dallas policemen wanted the distinction of collaring the president's killer, and the radio call that an assassination suspect had entered a nearby theater. Hollywood responded to the film's controversy by giving it Academy awards for Best Cinematography and Best Film Editing, along with nominations for Best Actor in a Supporting Role (Tommy Lee Jones), Best Director, Best Music: Original Score, Best Sound, Best Writing: Screenplay Based on Material from Another Medium, and, of course, Best Picture. As for the audience, they awarded the film with over $205 million in earnings during its initial movie run. Naturally, everyone who saw the film dismissed it saying, "It's only a movie." Oddly however, Congress rammed through a bill that formed the U.S. Assassination Records Review Board (ARRB) shortly after the film came out—what a coincidence.The ARRB consumed taxpayer money for about six years and made many government documents on the assassination more accessible to the public, including at least some of the previously sealed materials, but was not mandated to draw conclusions and didn't. Did Stone's movie unravel a conspiracy, help us understand the assassination, or have any impact whatsoever? Historian Michael Beschloss summarized its impact like this: "the problem that I and most historians would have with Oliver Stone is not his talent—he's a wonderful filmmaker—but that he's used this to put certain myths into the American blood stream that abide to this day." #### Summary of Movie Physics Rating Rubrics The following is a summary of the key points discussed in this chapter that affect a movie's physics quality rating. These are ranked according to the seriousness of the problem. Minuses [–] rank from 1 to 3, 3 being the worst. However, when a movie gets something right that sets it apart, it gets the equivalent of a get-out-of-jail-free card. These are ranked with pluses [+] from 1 to 3, 3 being the best. [–] [–] Using bad physics as justification for defective historical analysis. [–] [–] Using Hollywood depictions of shootings as though they were real forensic analysis. [–] [–] Assuming a shooting victim will always be blown in the same direction that the bullet is moving. ## CHAPTER 14 ## SCENES WITH REAL GRAVITY: ### Celebrating Disasters with Happy Hollywood Endings ### ESCAPE VELOCITY ON ASTEROIDS When killer chunks of space junk threaten Mother Earth, what should we do? Dial NASA, slap together a mission, land a spacecraft on the offender, and nuke it. In _Armageddon_ it's a Texassized rock. In _Deep Impact_ a 7-mile-long rock filled snowball. Thanks to gravitational effects, both pose considerable challenges to landing parties. The daring crew in _Armageddon_ had to land on a foreboding spike-covered asteroid. Their choice of landing craft: a space shuttle, of course. At the Kennedy Space Center landing such a craft requires a 15,000-foot-(4,572-m-) long, 300-foot-(91.4-m-) wide specially constructed runway and parachutes for a touchdown at speeds of 213 to 226 miles per hour (343–364 kph). Who knows what the shuttle's speed was in the movie, but a closing speed of over 200 miles per hour was well within reason. The main shuttle boosters were pointed backward, so the shuttle had no means of slowing down upon landing other than applying brakes or running into rock formations. Certainly, parachutes would have been worthless since there was no atmosphere. Airliners touching down on smooth water at similar speeds routinely disintegrate, but not— by golly—our hope-of-all-humanity space shuttle when landing on misshapen rock formations. Once on the asteroid, crew members walked around normally in spite of the reduced gravity. In fact, gravity would have been about 10 percent of the level on Earth, assuming the asteroid's density was the same as Earth's. By comparison, the moon's gravity is only 17 percent of Earth's—an amount less than the smaller-sized asteroid due to the moon's lower density. #### G-FIELD BASICS According to Newtonian mechanics, any mass, such as a planet, creates a gravitational force field around it. The strength of the force field is usually represented by the symbol g, generally referred to as the acceleration due to gravity. Although g has units of acceleration, an object's acceleration in a gravitational field will only be equal to g when it is free falling. The gravitational force acting on an object will be mg (where m is the object's mass) regardless of whether the object is freefalling with an acceleration of g or sitting on the ground with an acceleration of zero. It's more accurate to refer to g as the gravitational field strength. #### GRAVITATIONAL OR WEIGHT FORCE ON A PLANET, MOON, OR ASTEROID To find the gravitational force acting on an object, in other words its weight, multiply its mass times g as follows: Where: F = force due to gravity m = mass of the object in a gravitational field g = the strength of the gravitational field (g = 9.8 m/s2 for Earth) #### GRAVITATIONAL FIELD STRENGTH—AROUND A PLANET, MOON, OR ASTEROID For any spherical-shaped celestial object, the gravitational field strength g at a specific location on or above the surface can be calculated as follows: Where: G = the universal gravitational constant MP = the mass of the planet r = the distance from the center of the planet Note that if the distance from the center of the planet is doubled, the gravitational force decreases by a factor of 4. Gravitational field strength drops quickly as one moves away from the planet. #### GRAVITY FIELD STRENGTH—INSIDE A PLANET If a shaft is drilled into the interior of the planet, g can be found as follows (assuming that the density of the planet remains constant): Where: RP = the radius of the planet Note that the gravity level actually increases as one moves away from the center of the planet, that is, until reaching the surface. Then, at the surface, equation 15-2 takes over and the gravity level starts dropping. The movie at least has one of the two shuttles crash, but, of course, all hands are not lost. The surviving crew members set out in a rover hoping to join up with members of the intact shuttle. Faced with crossing a deep chasm, they simply rev up the rover and roar over the side.With the low gravity and no air resistance, the rover supposedly goes into a close-to-surface orbit, easily crossing the chasm without falling into it. If an object close to the surface has no horizontal velocity and is dropped, it will fall straight down. Give it a horizontal velocity, and it will fall in a parabolic arc. Give it enough horizontal velocity, and it will "fall" in a stable circular orbit. Yes, such an orbit is possible on the surface of a planet or asteroid and requires a much lower horizontal velocity on the asteroid than on Earth. On our Texas-sized asteroid, however, the rover would have to travel at a speed of 1,800 miles per hour (2,900 kph) to reach the required critical velocity—a little fast for the typical rover. Astronauts on the surface of the Texas-sized asteroid could jump up and down as much as they wanted with no danger of reaching escape velocity and accidentally floating off into space. Escape velocity is proportional to the square root of the gravitational field strength and, surprisingly, the gravitational field of the asteroid would be a little stronger than on the Moon, assuming the asteroid's density matched that of Earth rather than the lower value of the moon. On Earth escape velocity is slightly over 25,000 miles per hour (40,000 kph). On the asteroid it's greatly reduced but still over 2,500 miles per hour (4,000 kph). Taking off from the surface in a horizontal direction would make reaching escape velocity a real challenge. #### CRITICAL VELOCITIES RELATED TO GRAVITY There are two critical velocities related to gravity that determine how and if an object orbits a celestial body. (A celestial body in this case refers to a spherical body like a planet.) #### LOWEST CIRCULAR ORBIT VELOCITY An object could conceivably orbit a planet a fraction of a millimeter off the surface, if the planet were perfectly spherical, uniform in density, and had no air resistance to slow the object's speed. The horizontal velocity required for the lowest possible circular orbit defines the first critical velocity. This velocity is perpendicular to a radial line drawn from the center of the celestial body. If a spacecraft attempts to take off in a horizontal direction on a celestial body that has no atmosphere, the craft's velocity will have to exceed the first critical velocity. Without a lengthy wellmaintained runway, a horizontal takeoff is next to impossible, which is why missions to asteroids, moons, or planets with thin atmospheres will require vertical takeoffs and landings. On Earth, airplanes can take off at relatively low horizontal velocities thanks to the atmosphere, which provides lift. In a circular orbit, the force of gravity acting on an object acts as the centripetal force. The velocity required for a circular orbit is calculated as follows: Where: G = the universal gravitational constant M P = the mass of the planet r = the distance from the center of the planet The first critical velocity V C1 would be found by substituting the radius of the planet rp as follows. #### ESCAPE VELOCITY Escape velocity is the second critical velocity value. This is the minimum velocity required to escape from the gravitational pull of the celestial body. If an object is moving with a tangential velocity between the first and second critical speeds, it will move in an elliptical orbit. The escape velocity is derived from energy equations. The work required to move an object from a planet's surface to infinity is set equal to the object's kinetic energy. This results in the following expression: Note that although the escape velocity is derived in a different manner, it's simply the circular orbit velocity multiplied by the square root of 2. When a space vehicle slingshots around a planet or moon, it has to be going at or above the escape velocity to avoid being captured in an orbit or—worse—crashing into the surface (if the vehicle is below the circular orbit speed). Slingshotting allows a spacecraft to make a turn without using fuel. Normally, turns consume large amounts of fuel. #### SUMMARY OF THE EFFECTS OF A TANGENTIAL VELOCITY AROUND A PLANET First critical velocity—the lowest velocity possible for taking off from a celestial body with no atmosphere. Second critical velocity—the lowest possible velocity for escaping a celestial body's gravity. If the booster motors were vectored with a downward angle, they would push the shuttle's tail upward. Unfortunately, this would also rotate the shuttle's nose downward. Yes, the shuttle would have small thrusters in its front, which in theory could counteract some of the nose's downward rotation. But they would be low-powered devices used for positioning the shuttle when in orbit.They would not be designed for assisting a horizontal liftoff. Keep in mind that on the asteroid the gravitational attraction force on an empty space shuttle would be over 16,000 pounds (7,300 kg). With no air, there would be no lift generated by the shuttle's wings. Getting the shuttle to rise off the surface using booster motors pointed in a horizontal direction would be a major feat. There are two critical velocities associated with gravity: the velocity required for a circular orbit at the surface and the escape velocity. If the shuttle is moving horizontally with no lift force, it would have to exceed the velocity required for circular orbit at the surface before it could hope to lift off. As mentioned earlier in the rover discussion, this velocity is 1,800 miles per hour (2,900 kph)—a new land-speed record for humanity if not for Earth. Once off the surface, the shuttle is going to have to ramp up its speed to over 2,500 miles per hour (4,000 kph) in order to escape the asteroid's gravity. Even if the shuttle did miraculously manage to leave the spike-covered asteroid, it would likely not survive reentry into Earth's atmosphere. The space shuttle Columbia burned up during reentry due to damage sustained when its wing hit a chunk of foam insulation that broke off its fuel tank during launch. How are a shuttle's heat tiles going to survive scraping against and smashing into an asteroid's rock formations? _Deep Impact_ was far more realistic than _Armageddon_ Its 7-mile-long comet would have had only about 0.09 percent of Earth's gravity level, and the movie portrayed it that way. Astronauts on the surface were attached to tethers to keep them from floating off. Even here, a person could not easily reach the escape velocity of 22 miles per hour (36 kph) simply by jumping. But escape velocity was still way too low for comfort. The astronauts touched down on the comet in a specially designed lander rather than bulldozing a landing strip with a space shuttle. Naturally, nuclear bombs had to be drilled into the comet's surface not at 75 feet, but at exactly 100 feet.This drilling had to be done at some distance from the landing craft so that the craft could almost run out of fuel as it raced to pick up the tardy drilling crew—just in the nick of time. Even then, the comet had rotated into the sunlight, causing an astronaut to be blown into space by a violent out-gassing of comet material instantaneously vaporized by the sunlight's heat. It's not that the astronauts were dawdling. The digging device got stuck, and a brave astronaut had to selflessly climb down the 75-foot-deep hole then jump up and down on the digger to get it working. This took longer than the allotted time, but a bomb was successfully planted. Back on the ship, the bomb was detonated. After all the bravery, the ingenuity, and the close calls, the mission failed. The bomb was supposed to merely alter the course of the comet. Instead, the explosion split the comet into two pieces—a big and a little one. Both of these parts continued on a path toward Earth, with the little guy racing ahead of the big one. The split comet was a nice touch that illustrated one of the problems involved with trying to save Earth from an impact disaster. For the small piece to remain separated from the large one and speed ahead of it, the small piece would have needed to reach escape velocity, which would have been less than 22 miles per hour since the large piece had less mass after the small piece broke off.To reach such a velocity, the small piece would have needed to pick up the kinetic energy equivalent of about 10 megatons of TNT (assuming the small piece was 20 percent of the comet). The total explosive energy of the eight 2-megaton nuclear bombs carried by the spacecraft would have been marginal for providing it. Failing to reach escape velocity, the little piece would have been pulled back to the larger piece. Okay, it probably would not completely fuse back together. And maybe it would still be possible to shatter the big piece at the last minute by crashing the space ship into it as depicted in the movie. Still, if a nuclear bomb planted on the surface couldn't effectively break up the comet, it's doubtful that crashing a spaceship loaded with still other nuclear bombs of the same size would do much better. ### KILLER TIDES Let's digress back to _Armageddon_ and assume success in spite of all the space shuttle problems. It's a momentous occasion. The Texas-sized asteroid on a collision path with Earth has just been split in half. The parts pass on either side of the Earth within a mere 400 miles of the surface. But why are people joyful? The oceans would have sloshed out of their basins and sent walls of salt water smashing across the world's coastal areas. Places like Florida would be submerged. The water walls would be so heavy they would destabilize fault lines, setting off earthquakes and volcanic eruptions. When the oceans finally quit sloshing back and forth and the water receded, the sea in coastal areas would be filled with all kinds of sediment and contaminants. On land in coastal areas, dead marine life and people would be scattered everywhere, water systems contaminated, crops destroyed, and major cities demolished—not a cause for celebration. Tides are normally created by shifting gravity forces that the Moon and, to a lesser extent, the Sun exert on the oceans.The mass of one-half of the asteroid would be about 3 × 1021 kilograms as compared to 7 × 1022 kilograms for the Moon. In other words, the moon is about 23 times more massive than the asteroid half, and gravity forces are directly proportional to mass. So what's the big deal? Unfortunately, the gravity force is also inversely proportional to the square of the distance between the centers of mass of the objects causing them. The distance between the Earth's center and the moon's center is about fifty times longer than the distance between the Earth's center and the asteroid half's center. Taking into account all of the differences, the gravity force acting on Earth caused by half an asteroid is almost one hundred times higher than the gravity force on the moon. But there are two of these forces, one acting on each side of Earth. From the standpoint of tides these tend to reinforce each other. Keep in mind that ordinary tides caused by the Moon are around 10 feet (3 meters) and take several hours to rise. The asteroid-produced tides would rise much higher in much less time. Water, however, is only one source of devastation.There's also wind. Normally the atmospheric tides created by the Moon are so small that they have almost no effect on weather. But increase these forces by a factor of 100 on opposite sides on the globe, and the result would be high winds over the entire surface of Earth. Underneath the passing asteroid halves, the winds could easily act like continent-sized hurricanes, adding major-sized storm surges to the already incredibly high tides. The asteroid pieces would pass around Earth and collide back together on the other side in about half a day. They would then fly off into the cosmos. The gravitational pull of the asteroid mass would diminish quickly as it moved away from Earth. Within just a few hours the pull would be negligible. Unfortunately, the disastrous problems on Earth would persist for some time.The back and forth sloshing action of the ocean would last for hours if not days. High winds and erupting volcanoes with sloshing oceans could disrupt weather patterns for decades if not centuries, not to mention that such a large mass passing close to Earth and the moon could disrupt their orbits with unknown consequences. Earth would be a mess. ### THE DIRECTION AND STRENGTH OF "INNER" GRAVITY Imagine digging a shaft from the surface of Earth all the way through the center and out the other side (sounds like a movie plot already). Of course, there would be some minor problems such as extreme heat and pressure, but suppose these could be overcome. If a group of people descended into the hole in some type of elevator and stopped every so often to measure the force of gravity, they would find that it slowly decreased to zero at the center of the world and then increased back to its normal level as the elevator passed the center and ascended to the surface on the opposite side. If the density of Earth were constant, gravity force would be directly proportional to the distance from the center of Earth. When the inner core was reached, the gravity force would be one-sixth of its value at the surface. _The Core_ does not depict this reduction in gravity force as the crew of the _Virgil_ bores down toward Earth's core. The inner core, however, is 4.5 times denser than the surface, and so the gravitational attraction force at the inner core would only be reduced by around 25 percent—not enough difference to mention. Where the movie fails is in its depiction of gravity's direction. Until the center of Earth was reached, the force of gravity would always be downward. Yet the _Virgil_ is configured like a vertical subway train. Its crew walks around in their ship as though the gravity force were rotated by ninety degrees. They never have to climb ladders to go from the front of the ship (its lowest point) to the back (its highest point). As the ship passed its lowest depth inside Earth and started heading back out, the gravity force direction should have flipflopped, but this was also not depicted. When the _Virgil_ 's crew was in training for the mission, the movie indicated that the crew compartments could be rotated so that gravity remained pointed in the right direction. But this still did not solve the problem of moving from compartment to compartment. The design would have to be more complex than the simple subway-type design depicted in the movie. The movement between compartments would have to be done by climbing up and down ladders inside tubes connecting the pieces. The connecting tube would have to be located to one side of the compartments like a backbone so that each compartment could be rotated 180 degrees. Clearly, the moviemakers did not waste time working out such details. In a sense they had a point: why worry about minor details like the direction of gravity when the whole premise of the movie was ridiculous. #### Summary of Movie Physics Rating Rubrics The following is a summary of the key points discussed in this chapter that affect a movie's physics quality rating. These are ranked according to the seriousness of the problem. Minuses [–] rank from 1 to 3, 3 being the worst. However, when a movie gets something right that sets it apart, it gets the equivalent of a get-out-of-jail-free card. These are ranked with pluses [+] from 1 to 3, 3 being the best. [–] [–] Assuming that a near miss by a gigantic asteroid would cause no harm to Earth. [–] [–] Space shuttles landing in impossible situations without damage. [–] [–] Paying no attention to the direction of gravity. [–] [–] Space shuttles taking off in impossible situations. [–] [–] Underestimating or overestimating the gravity levels, surface orbit velocity, and escape velocity of an asteroid. ## CHAPTER 15 ## SCENES WITH ARTIFICIAL GRAVITY: ### The Good, Bad, and Ugly Space Stations ### THE VOMIT COMET The person who said, "crime doesn't pay," never watched a space movie. While some movies are upstanding, most are lawbreakers—laws-of-physics breakers, that is—especially when it comes to gravity. Trying to simulate the lack of or apparent lack of gravity takes creativity and hard work—an anathema to the prospects of easy money. _Apollo 13_ [GP] (1995) pulled the simulation off beautifully using NASA's "Vomit Comet" (the KC-135A aircraft similar to the Boeing 707 commercial airliner). During a parabolic dive cycle, this aircraft provides about twenty-five seconds of apparent weightlessness but unfortunately cycles between the sensation of zero and elevated gravity—a cycle that drives the inner ear bonkers, producing mild to extreme nausea, hence, the nickname Vomit Comet. When the _Apollo 13_ movie crew needed to film a space flight scene, they didn't do lunch, they risked redoing lunch. The result, however, was worth the indigestion: _Apollo 13_ was the third highest grossing film in 1995, with two academy awards and seven additional academy award nominations. At the start of a parabolic cycle, the Vomit Comet climbs upward at a forty-five-degree angle. As it rounds the top section of a parabolic arc, the aircraft and all its contents are in freefall, which feels like zero gravity. The sensation is sometimes incorrectly referred to as zero-gravity, but, in reality, it's not: the gravity force is just as high as it would normally be. The condition is also sometimes referred to as zero gs, but gs are a unit of acceleration and the acceleration of the aircraft is 1.0 g downward, even when simulating weightlessness. The sensation occurs only because the aircraft is in freefall. As the aircraft heads toward the ground, the pilot has to pull it upward and the sensation of gravity returns with a vengeance. At the bottom of the dive a person will feel as though they are 80 percent heavier. ### CREATING ARTIFICIAL GRAVITY For filmmakers with finicky stomachs, artificial gravity is the cure. It requires no unsettling parabolic cycles, but to do it right requires some understanding of physics. Keep in mind that artificial gravity is not really gravity at all. To understand it, we first must understand which force causes the sensation of weight for a person standing on the ground. It's not the gravity force. It's something called a normal force. Obviously, there's a gravitational force pulling the person downward, but since the standing person is not moving or sinking into the ground, there must be another force of the same size pushing the person upward. The two forces cancel each other out. The upward force is called a normal force and is simply the upward force the ground creates on the person. Okay, the idea of the ground pushing upward may seem outlandish, but it does. The person's feet push downward on the ground; the ground pushes upward on the person. It's an actionreaction pair. The normal force always acts perpendicular (or normal) to the surface that creates it, hence the name normal force. Since there are actually two forces acting on a person standing on the ground—a gravity force and a normal force—one, the other, or both must cause the sensation of weight. Let's run a little mind experiment to find out which it is. First, let's spring a trap door on a person and cause him to fall into a bottomless pit. In other words, remove the normal force but leave the gravity force. Other than the emotions from falling down a bottomless shaft, how does the person feel? Weightless. In fact, anyone in free fall will feel weightless. Clearly, the normal force is required for having a sensation of weight. #### THE BASIS OF ARTIFICIAL GRAVITY Artificial gravity has nothing to do with gravity. In reality, it is the normal force acting as a centripetal force in a rotating cylinder, disk, or doughnut-shaped spacecraft that produces the effect. The normal force pushes upward on the inhabitants standing on the rotating floor. It is derived as follows: F C = maC Where: F C = centripetal force m = the mass of the object or person subjected to the artificial gravity a C = centripetal acceleration Centripetal acceleration is calculated as follows: a c = v2/r Where: v = the object's tangential velocity r = the distance from the center of rotation to the object's center of mass The centripetal force or normal force must be equal to a person's weight on Earth to make the person feel like he or she is in an Earth-like gravity field. Hence, the centripetal acceleration must be equal to 1.0 g (9.8 m/s2). In equation form: g = v 2/r Solving for velocity gives: However, it's inconvenient to talk about rotation in terms of tangential velocity. Revolutions per minute (RPM) is a more common way to quantify rotation. Assume that v is in units of meters per second and r is in units of meters. The object travels the circumference of the circle (2 r) in each revolution. Then the number of revolutions per second (RPS) is as follows: Substituting for v using equation 15.1 yields: For Earth g = 9.8 m/s2 For the 400-meter diameter space station in _2001: A Space Odyssey_ the rotational speed would be calculated as follows: Next, let's pull the imaginary giant gravity switch in the sky to the "off" position. Yeah, yeah, it sounds like something in a movie, but doing physics often requires imagination. Our person again feels like he's weightless. So, it seems that a gravity force is also needed. But wait. When the gravity force was turned off, the normal force also ended. Unfortunately, we still don't know if we need gravity to have a sensation of weight.To answer the question we have to create an experiment with a normal force but no gravity force. If the person still feels the sensation of weight, then it's obvious that a normal force is required but a gravity force is not. To run this experiment, we can have subjects stand against the wall inside an amusement park ride—the kind that is a large hollow cylinder that spins around a vertical axis at its center. When the ride is spinning at full speed and the riders are pressed against the cylindrical wall, the bottom drops out. This results in some screaming, but no one falls out. They feel like they have a large gravity force pressing them against the wall so firmly that they can't slide out. But there is no gravity force in the horizontal dimension. What they are feeling is the normal force between the cylindrical wall and the back sides of their bodies. This force acts as the centripetal force that makes the subjects speed around in a circular path. A normal force acting without a gravity force can indeed produce the sensation of weight. The conclusion: normal force, not gravity, is responsible for the sensation of weight. Okay, at this point someone invariably says "but what if a person is hanging from a cable? There is no normal force." The answer is that a normal force is simply the force a surface exerts on an object—in this case a person. To hold the person up, the surface of the cable or the surfaces of a harness attached to it must be in contact with the person. Add up all the normal forces from the cable or harness, and it will equal the force of gravity but act in exactly the opposite direction. In other words, the normal force does still exist and is indeed the primary force causing the sensation of weight. Someone will invariably also argue that the amusement ride described above does not turn off the force of gravity. However, the sensation of weight described was in the horizontal dimension corresponding to the normal force exerted by the cylindrical wall. Gravity is in the vertical dimension. Seal the ends of the cylinder, provide it with a life support system, transport it to outer space, spin it up to speed with the people against the wall, and they will still feel a weight-like sensation. If the cylinder has a large diameter—say 440 yards (400 m) so that it looks disk shaped—and is spinning at exactly the right speed, the people will be able to stand on the cylindrical wall and walk around just like they were standing on Earth. If one of them drops a coin, it will appear to fall to the floor (the cylindrical wall) just like a coin would on Earth. The effect is called artificial gravity. In reality it is an artificially produced normal force. There is no gravity force involved. The normal force is providing a centripetal force in the direction of the center of the cylinder. This centripetal force keeps people rotating around inside the disk. When a coin is dropped, the centripetal force is momentarily removed and the coin falls to the floor, which then reestablishes the centripetal force. The rotating cylinder needs to have a large diameter for two reasons: it makes the floor's curvature less noticeable, and it makes the artificial gravity effect on the person more uniform. With artificial gravity the centripetal force provides the artificial normal force needed for the sensation of gravity. Unfortunately, centripetal force depends on one's distance from the center of rotation, or in this case, the center of the disk-shaped space station. It will be zero at the center and 1.0 g at the floor people stand on. (Keep in mind that the floor is the cylindrical wall of the disk.) If the space station had a diameter of 12 feet (3.7 m) and was rotating fast enough so that objects on the floor would experience 1.0 g of acceleration, six-foot-tall people standing on the rotating floor would experience 1.0 g in their feet and 0 g in their heads. The result: who knows? But nausea, lightheadedness, and disorientation would be good bets, especially if a person bent over, sat down, or stood up. ### THE GOOD PORTRAYAL OF ARTIFICIAL GRAVITY A realistic space station with artificial gravity would look like a gigantic rotating bicycle wheel with large spokes—just like the space station in _2001: A Space Odyssey_ [GP] (1968).Yes, _2001_ has some out-there stuff, such as the monoliths, which have about as much scientific basis as magic wands, not to mention the movie's colorful but incomprehensible ending (reading the book was required to make any sense of it). But when a scene calls for realistic Newtonian physics, the movie delivers. Its realism created a mood that has never been duplicated. _2001_ won an academy award for visual effects, is listed number twenty-two in the American Film Institute's 100 Greatest Movies list (<http://www.afi.com/tvevents/100years/movies.aspx>), made $56.7 million (270 million in 2004 dollars), and developed a cult following; and yet it ranks as one of Hollywood's least copied movies. If influence over other films were measured in height above sea level, _2001_ would be in the Marianas Trench. Why? Hollywood has yet to understand its success let alone develop a formula for cloning it. Still, a few aspects of the movie have stuck, such as the vague notion that something has to rotate to produce artificial gravity. ### THE BAD PORTRAYAL OF ARTIFICIAL GRAVITY To give itself credibility, _Mission to Mars_ [RP] (2000) had its spaceship rotate to produce artificial gravity and its inhabitants correctly walk around on the inside of its outer wall. The ship, however, was only about 24 feet in diameter (7.3 m). When standing on the floor in this ship, the feet of people six feet tall would experience 1 g while their heads would experience 1/2 g. If they sat down, the acceleration of their heads would increase by 50 percent.When they climbed the ladder leading to the center of the ship, their centripetal acceleration would have decreased to near zero, yet none of these changes produced even the slightest nausea. ### THE UGLY PORTRAYAL OF ARTIFICIAL GRAVITY _Armageddon_ [RP] (1998) took the foolishness even further. They had an astronaut press a button in a Mir-type Russian space station (mass = 124,340 kg) and spin it up to full artificial gravity level in a matter of seconds. The stresses from the high acceleration required to spin up so quickly would have torn the space station apart. Inside the space station the distance from the axis of rotation varied from 39.4 feet (12 m) to as little as 6.6 feet (1 m), yet the gravity level was always the same in any part of the station. Both the station inhabitants and its visitors experienced no discomfort when their heads were located at 0 g and their feet at 1.0 g. The artificial gravity was so remarkable that it always acted in the correct direction even when the visitors were climbing through tubes pointed directly away from the axis of rotation. _Red Planet_ [RP] (2000) takes the award for most muddled understanding of artificial gravity. The spaceship in it looks like an oversized shoebox with large counterrotating rings on each end that seem like they belong on a carnival ride with neon lights. While it's not completely clear, the main crew quarters seem to be located in the nonrotating section of the shoebox. So it's a mystery how the crew can walk around inside it just like they were on Earth. The box-like shape of the central ship also makes no sense— assuming it's pressurized for human habitation. The internal pressure inside it would tend to make the sides bulge outward. A sphere or a cylinder with spherical ends would be a far better shape for containing internal pressure. Having the rings counterrotate with a stationary shoebox in between means the rings must have large-sized bearings and seals to prevent air loss. Thanks to seal friction, the rings would have to constantly be driven by electric motors—a power drain on long space voyages. Compare this to the elegance of the _2001_ space station in which the entire space station rotates. Once it's turning, it will rotate indefinitely with no further power input. There is no air resistance or friction in space to slow it down, nor are there any bearings or seals required. When a solar flare disables the _Red Planet_ spaceship, the counterrotating rings stop moving, causing the artificial gravity to fail. The rings on the ship would have a huge amount of rotational inertia, and yet they are brought to a halt in seconds. The accelerations required to do this would likely tear the rings apart. A large spacecraft would likely not be designed for unexpectedly high stresses, since every pound of material used to build it would cost thousands of dollars just to lift it off Earth and send it into space for assembly. As the rings stop, loose objects aboard the ship begin to float about. But why? They would still be moving in the direction of rotation. Quickly stopping the rings should send objects tumbling into the nearest wall in the direction of their motion—that is, if the crew quarters were correctly set up in the rotating rings. When the rings are again restarted, artificial gravity is instantly restored and all the randomly floating objects immediately drop to the floor. If they really were gently floating inside a stationary ring, the objects would also be stationary. When the ring started rotating, the wall opposite of the one they had previously tumbled into would appear to move forward and bump into all the floating objects. As the rings accelerated the objects would slide toward the floor and pile up on top of each other. Artificial gravity on the starship _Enterprise_ in the _Star Trek_ movie series is beyond the categories of good, bad, and ugly because no attempt is made to use centripetal force as the source. _Star Trek_ proposes that humanity is so advanced, a spaceship can be built that manipulates gravity in a similar way as it manipulates other phenomena such as electricity—once considered esoteric. The series offers no mumbo-jumbo explanations. If the _Enterprise_ couldn't generate its own gravity, the entire movie series would have to be rethought. The stretch is forgivable but in a begrudging manner. Had the writers used reliable Newtonian physics to generate artificial gravity, the _Enterprise_ would have looked different and the stories been altered, but it still would have had the _Star Trek_ flavor. At first glance, a rotating ring like the huge _2001_ space station flying through space sounds weird, but why not? As long as the vehicle is neither required to land nor take off, there's no reason for making it aerodynamic. It will encounter no air resistance. The ship will have no fuel-guzzling liftoffs, and once it's up to cruising speed it will need no energy to keep it there. Hence, small size is not critical. Such a ship would still have a great deal of screen presence. Robert Zubrin's highly creative proposal for a Mars ship would break all cinematic paradigms in spaceship design. He suggests that a section of used-up booster could be tethered several hundred meters from the living quarters of the Mars ship and the two rotated around a point in the middle. In a military version both sections could hold living quarters. Imagine the spectacle of an invading army in hundreds of tethered ships spinning as they silently traveled through space. Realistic artificial gravity does impose design constraints on cinematic spaceships, but even in the world of reality there's still plenty of room for creativity and gee-whiz effects. #### Summary of Movie Physics Rating Rubrics The following is a summary of the key points discussed in this chapter that affect a movie's physics quality rating. These are ranked according to the seriousness of the problem. Minuses [–] rank from 1 to 3, 3 being the worst. However, when a movie gets something right that sets it apart, it gets the equivalent of a get-out-of-jail-free card. These are ranked with pluses [+] from 1 to 3, 3 being the best. [–] [–] Depictions of spacecraft in which rotating parts produce artificial gravity (AG) but the part of the craft with the gravity does not rotate. [–] [–] Depictions of AG in which the direction of the AG does not match with the direction of centripetal force. (Note: centripetal force always points at the center of rotation.) [–] [–] Depictions of AG in which peoples' heads are subjected to totally different AG conditions than their feet. [–] [–] Starting or stopping rotation in massive spacecraft parts in a matter of seconds. [–] Objects falling straight to the floor when interrupted AG produced by rotation is restored. [+] Astronauts becoming dizzy and possibly vomiting when they climb ladders taking them from high rotationally produced AG to low AG. [+] [+] Using a Zubrin design for producing AG. ## CHAPTER 16 ## THE MOVIE MERRY-GO-ROUND: ### How Filmmakers Create Ridiculous Spin ### MARTIAL ARTS It's possibly the most famous movie kick ever.Trinity leaps in the air, arms extended like the wings of a white crane about to fly. For a moment time stops. When it resumes, she falls toward Earth slamming her foot forward and slightly downward into a fat cop's chest. He flies horizontally backward across the room and crashes into a wall ( _The Matrix_ [RP]).The action does take place inside a computer simulation, and Trinity has supposedly mastered altering the simulation's physics, but what about the fat cop? Surely, he hasn't. He's part of the simulation and should have rotated backward and crashed into the ground a short horizontal distance from where he got kicked. Increasing the power of the kick would cause the hapless cop to slam into the ground harder, but would have little effect on the distance he flies backward. In fact, at some point the extra power will mostly go into crushing the rib cage and collapsing the lungs rather than increasing the victim's kinetic energy. The only way a victim can be sent straight backward is to apply a horizontal force through or, in other words, lined up with the victim's center of mass. Even so, the force must have a slightly upward direction to knock the victim's feet off the ground, thereby eliminating the friction force between the victim's feet and the floor. Since Trinity's kick does not act through the center of mass, the friction force would otherwise cause backward rotation. The force from Trinity's kick obviously did not match the conditions required for translation (moving in a linear fashion), so why did the cop fly such a long horizontal distance? Run the scene in slow motion, and it's possible to see the glint of a horizontal wire pulling the hapless cop backward. Indeed, the laws of movie physics always require the hapless victim to fly backward—if he or she is going to be thrown horizontally at all— because slamming a stunt person front wise, even into a fake wall, tends to be hard on the nose, not to mention that pulling people forward tends to bend their backs harmfully backward. #### The Basics of Torque Torque is a twisting action that causes an object to rotate similar to the way a force causes an object to translate (move in a linear fashion). A force F applied at a ninety-degree angle to a lever arm or moment arm r creates a torque as follows: τ = F (r) #### The Rules of Rotation/Translation An object's motion can be categorized as translation, rotation, or some combination of the two. Translation is motion along a smooth path. Rotation is a spinning motion around a pivot point. If the object can move freely, the pivot point will be its center of mass. The center of mass is like a balance point. For example, a child's seesaw will balance if the pivot is located at or under the center of mass. Like forces, torques can counteract each other. For example, a torque that causes a twisting action in a clockwise direction can be counteracted by one causing a twisting action in the counterclockwise direction. When all the torques are added up, the result is called the net torque; and if the net torque is not zero, the object will have rotational acceleration. To understand what torques and forces do, let's see what happens when we apply them to a stationary object that could otherwise move freely. Like many things in physics, the resulting motion can be reduced to a few simple rules: A net force (the result of adding up all the forces) acting on an object will always cause translation in the direction of the force regardless of whether the object rotates or not. A net force that does not act through the object's center of mass or pivot point will cause translation and will create a torque that causes the object to rotate. (Assuming no other torques counteract it. See A.) An object will translate without rotation (see B) if the net force on it acts through the center of mass. An object will rotate without translation (see C) if the net force acting on it is zero but the net torque is not. Concepts such as center of mass, rotation, and translation are key to understanding many martial arts. Practitioners of Aikido (considered the primary martial art of Steven Segal) actually spend time meditating on their centers of mass in order to remain balanced while sending their opponents flying. Attackers foolish enough to charge headlong at an Aikido master will likely find their linear velocity tuned into head over heels rotation. Up to a point, the same mastery of applied physics can be simulated with clever camera and wire tricks that make even moderately trained actors look like martial artists. If overdone, however, the wire and camera stunts merely make the actors look like cartoon parodies. ### KNIFE THROWING Why would anyone in a life-or-death struggle want to throw away a perfectly good knife? Unlike a gun, a knife never runs out of bullets. Kept in the hand it can be used to attack or defend again and again.When thrown it has to stick in the target to do any real harm, but that's just the first requirement.There's a reason killers often stab their victims multiple times, and it's not just viciousness. Stab wounds, even well-placed ones, are usually not immediately fatal. So, of course, knife throwing is a routine staple of action movies and invariably drops its victims instantly. The first problem with knife throwing can be summed up in a word: rotation. Typically, a knife thrower will grasp the blade near the tip and raise the knife slightly over his head so that the hilt is pointed slightly backward. As the knife thrower swings his arm downward and forward, the hilt will be pointed toward the target just before release. The knife will have generally rotated at least a fourth of a turn during the act of throwing, even before it leaves the knife thrower's hand. To get this rotation, a knife thrower has to create a force on the knife that does not act through the knife's center of mass. Some knife throwers prefer to grip the hilt rather than the blade during throwing. Either way, the knife will be rotating in what could be called a forward direction as it leaves the hand and flies toward the target. To stick the knife, the tip has to rotate more or less forward (within ±30°) when the knife strikes its target, or the knife may as well be a stone. Knifethrowing performers generally train themselves to throw their knives so that the blades rotate at a repeatable rate. Throwers then position themselves at a known distance from the target. Using this system along with a lot of practice, good knife throwers can stick their blades consistently. Place knife throwers at a different distance, and they lose at least some of their advantage. They can still stick a knife but have to estimate the distance and alter the way they throw enough to make their knives rotate properly. By holding the knife at the hilt and snapping the wrist correctly as the knife is thrown, it's actually possible to make a knife rotate backward from its normal direction of rotation as it travels toward its target.This would usually be considered a mistake, but done with moderation it can reduce the knife's overall rotation rate. So-called spear-style or rotation-free knife throwers use heavy knives usually 1 foot (30 cm) or more in length to minimize the tendency to rotate. By adjusting their grip, wrist snap (as mentioned above), and release point, along with lots of practice, they can significantly reduce the rate of rotation. Even then, however, their knives usually rotate at least one-fourth of a turn before striking the target.The stronger the throwing arm and the higher the linear velocity of the knife, the farther it travels before overrotating and failing to stick. Spear-style knife throwing can produce consistent results at distances under 15 feet (4.6 m). By contrast, the Olympic javelin throw record was 321.1 feet (98.49 m) by Jan on May 25, 1996. A well-designed spear thrown by a less talented person would not travel as far but could easily be "stuck" at distances on the order of 100 feet without any worry of rotation. Spears can be easily thrown and stuck in targets without rotating while knives cannot because the throwing force applied to a spear almost has to act through its center of mass. In addition, there's something called rotational inertia. Inertia is defined as resistance to a change in motion. With linear or translational motion (motion along a smooth curve or line) inertia is equal to an object's mass. Rotational inertia, or the resistance to changes in rotation, is more complex. Like its linear cousin, it is directly proportional to mass but is also related to how the mass is distributed. Different shapes have different rotational inertia values even when their masses are equal. A knife or spear has a shape similar to a rod, which yields a rotational inertia as follows: (rotational inertia) = 1/3 (mass)(length)2 According to the above equation, a six-foot-long spear is going to have at least thirty-six times more rotational inertia than a onefoot-long knife just from length alone. In most cases the spear will also have more mass than the knife, making the spear's rotational inertia even higher. If the force used to throw the spear is slightly misaligned with the center of mass, the spear's rotational inertia will resist the tendency to rotate far better than the knife would in the same situation. The second problem with knife throwing's effectiveness is bone; bone is hard to penetrate and tends to show up in inconvenient places for the knife thrower—for example, as protective armor for vital organs. A thrown knife delivers a single stab wound (assuming it sticks in the victim). If the knife hits bone, it may not penetrate far enough to inflict substantial damage. If it does penetrate, it may not disable a victim fast enough to prevent him or her from fighting back or calling for help. Even if stabbed directly in the heart, a victim can remain conscious for about 10 seconds. A highly motivated, adrenaline-fueled, or drugged victim can continue to fight back during at least some of this time. Stabbings are not at all like they're depicted in the movies: victims don't just quietly accept their demise the instant they are stabbed. Although throwing a knife significantly reduces its effectiveness, it does extend its range—by at least a few meters. If a wildeyed terrorist across the room announces murderous intentions and brandishes a loaded AK-47, then by all means hurl a dagger at him. Why not? It might disrupt his aim. Rush him and hopefully wrestle away his weapon. But, other than desperate situations or circus acts, it's best to hold on to one's blade.Yes, having multiple knives helps, but even then, a thrown knife is more feasible as a distraction than an actual killing technique. The movie _Cellular_ [PGP] (2004) cleverly illustrates how a blade can be used effectively as a weapon. In the movie Jessica Martin (Kim Basinger) is kidnapped and left in a room with a smashed phone. She manages to piece it together well enough to make a highly improbable call to a random stranger's cell phone. He (Chris Evans) spends the rest of the movie trying to rescue her. Not one to helplessly wait for Prince Charming, Basinger— a high school science teacher (not a good person to mess with)— knows anatomy and slices one of her kidnaper's major arteries when he attacks her. As he quickly weakens, she stays just out of range from his grasp long enough for him to bleed to death, a satisfying moment for the audience. While having a knife incurs a significant advantage over an unarmed opponent, the problem with knife fights is that both opponents have them. At the close range of knife fights, cutting an opponent is easy, but stabbing one in the vitals is hard. On the other hand, the main difference between slicing blood vessels in the arms and legs versus stabbing a vital organ is mostly the amount of time it takes for one's opponent to lose enough blood to pass out or give up. The key to winning a serious knife fight is to make your opponent bleed faster than you do. ### FIREARM SPIN In movies, skill with firearms is as remarkable and common as knife-throwing ability. Shooting from the hip, as discussed in Chapter 2, has long been a Hollywood specialty, but now there is an even cooler handgun technique appearing in movies: the horizontal grip. Hollywood has spun yet another cliché without considering the physics of rotation. Normally a handgun is gripped with the fist in a vertical position. This enables one to use the gun sights—a handy feature if one wants to hit something. When a handgun is fired in the vertical position, the gun barrel is above the fist and the recoil creates a force that pushes backward above the wrist joint, creating a twisting action on the fist that rotates both it and the gun barrel upward. Conveniently, gravity helps rotate it back, more or less to its original position. This up-and-down rotation can cause aiming errors in the vertical dimension. But the vital area on a personsized target is about twice as high vertically as it is wide horizontally. If a shooter is going to have an aiming problem, it's best to have it in the vertical dimension. #### Torque and Rotation of Firearms The barrel of any type handgun will typically be located above the pivot point in the wrist and will generate a torque equal to the recoil force times the distance r, as shown in the diagram. This torque will rotate the gun barrel upward as shown. Grip a handgun, turn the fist horizontally, and it's oh so cool, but all of the advantages mentioned above disappear. The first to go is the ability to effectively use gun sights. The head is in the wrong position. It's too high. Raise the fist above shoulder level and it's possible to get the sights to a usable level, but it places the arm in an awkward position. The handgun's sights must also be adjusted for shooting with a horizontal grip, or accuracy is going to suffer. When the shooter fires using a horizontal grip, the recoil will rotate the handgun horizontally and—guess what—there is no horizontal gravity to help restore it to its original position. Resulting errors are going to scatter shots horizontally, where they are more likely to miss a person-sized target. Okay, so maybe Billy Bob out in the Texas Panhandle has mastered the technique after years of practice on rattlesnakes. But it still doesn't change the fact that a horizontal handgun grip is ridiculous for most people. It's a good way to accidentally shoot an innocent bystander. The confusion about rotation and translation (moving in a linear fashion) doesn't just apply to handgun grip but also to how victims—hopefully bad guys—react when shot. Although conservation of momentum (see Chapter 13) rules out the cliché of shooting victims being blown off their feet and sent flying backward through the nearest glass object, the conditions required for translation also cast doubt on this scenario. To throw a person violently backward and slightly upward, a shotgun or handgun blast (as depicted below) has to hit in line with the person's center of mass (about 2 in. below the navel). This means it has to be fired by a long-armed chimpanzee who can hold the weapon below knee level and fire it in a slightly upward direction. Shooting a person above the belt would tend to rotate him backward. Shooting him in the shoulder would add a spin similar to an ice skater's spin but much more mild. Neither of these effects would send a person flying backward. ### ROTATING CARS Although people can theoretically act in unpredictable ways, inanimate objects such as cars cannot. Yet, even here Hollywood has difficulty. Watch a few hours of reality TV filmed by policecar-dashboard cameras, and it's clear that cars rarely go airborne when they crash. Watch a few hours of Hollywood chase scenes, and cars routinely go airborne while doing more twists than an Olympic platform diver. Even when colliding with the backside of a parked car, the front end of the moving car invariably flips upward, sending it airborne with a half twist that causes it to land on its roof several car lengths in front of the parked vehicle. To get the entire car airborne, the net force on it has to be large and upward. To flip up the car's front, an upward force has to act on the front to cause it to vertically rotate around the car's center of mass. To twist or rotate the car like a huge slow-moving bullet so that the car ends up on its top, a force has to be applied to one side of the car. Driving a car at high speed up a ramp gives it the large upward force needed to get it airborne. Adding a kicker plate gives the front end an upward rotation. (Kicker plates are short ramps that act only on the front wheels and then fall away.) Using the kicker primarily on one side gives the car the twisting motion that causes it to end up landing on its top. Placing the camera in front of the parked car hides the ramps, kicker plates, and so forth. Air cannons can also be used to provide missing forces. These are large-diameter, short-barreled devices that are specially mounted inside cars and aimed at the ground. They generally shoot a section of a telephone pole propelled by air pressure. These act like large super-fast hydraulic jacks that almost instantly elevate the vehicle. While it might sound odd to use sections of telephone poles, they are just about the right size and weight, not to mention readily available. Some of the cannons are designed to use black-powder charges when fire and smoke are needed during a crash. If a moving car is supposed to roll over sideways, the cannon is mounted to the right of the driver where a passenger would normally sit. If the moving car is to flip with the car's trunk rotating upward and forward over the cars' hood, the cannon is installed near the center of the car's trunk. By moving the cannon around relative to the car's center of mass, it's possible to get just about any type of rotation desired. When combined with ramps and a high forward speed, the stunt director can choreograph whatever type of motion is needed. Roaring down the highway, pursued by submachine-gun wielding albino twins ( _Matrix II_ ), Trinity triggered one of the most famous car wrecks in cinematic history. To pull off this scene, some of the stunt cars actually towed ramps behind them as they sped down the road. When the stunt drivers in ramptowing cars slammed on their brakes, cars behind them continued up the ramps and went airborne over the ramp-towing cars. Various combinations of air cannons and ramps had cars rolling, twisting, and flipping, all at the same time, in every conceivable manner. It was a veritable physics ballet—impressive and entertaining but not realistic. It's impossible not to admire the technical skill and daring that goes into spectacular car-wreck scenes. The individuals designing them are applied physicists, who must possess a finely tuned understanding of forces. The stunt drivers performing them are risk takers who must put their very lives in danger. Yet movies based entirely on spectacular car wrecks are like restaurants based on food fights. While experiencing them might be fun, they leave one hungry for sustenance. #### Summary of Movie Physics Rating Rubrics The following is a summary of the key points discussed in this chapter that affect a movie's physics quality rating. These are ranked according to the seriousness of the problem. Minuses [–-] rank from 1 to 3, 3 being the worst. However, when a movie gets something right that sets it apart, it gets the equivalent of a get-out-of-jail-free card. These are ranked with pluses [+] from 1 to 3, 3 being the best. [–] Above-the-belt kicks and punches that throw victims horizontally backward significant distances. [–] Throwing one's knife as anything other than a pastime, circus stunt, or last-ditch tactic. Having multiple knives helps, but even then, a thrown knife is more effective as a distraction than an actual killing technique. [–] The horizontal handgun grip used at any distance other than point blank. [–] Spectacular car wrecks that could not happen in reality without ramps and air cannons. [+] Winning a knife fight in an understated manner by severing an artery other than the carotid. ## CHAPTER 17 ## HOLLYWOOD DISASTERS: ### Global Warming, Tsunamis, Tornadoes, and Other Big Winds ### GLOBAL EXAGGERATION It's the ultimate science experiment: dump trillions of tons of CO2 into the atmosphere for decades and see what happens. It takes a while but then, according to _The Day After Tomorrow_ [RP] (2004), snow blankets Bombay, super-sized hail hammers Hong Kong, and terrible twisters trash Los Angeles (F5s on a scale of F1 to F5). Dare to engage in extramarital sex or, worse yet, inane live news coverage as one of these tornadoes approaches, and your demise is certain. But that's just the beginning. The north polar ice cap suddenly melts, shutting down Atlantic currents and in the process triggers a massive hurricane-like blizzard covering North America. Since the North Pole's ice cap floats, melting it does little to raise ocean levels, but then apparently ice sheets in Antarctica and Greenland also suddenly melt causing an immediate change in ocean level. This immediate change sends a super-tsunami selectively sweeping into New York City. Frigid upper layers of the atmosphere plummet downward and freeze people midconversation, and then comes the snow—biblical amounts of it. In reality, the whole state of California—it's definitely not Kansas, Toto—has never recorded a tornado rated greater than an F2, but there's no law of physics that says it can't. An ice age in North America from the season's first snowstorm is also far-fetched, but again there's no law against it. Why, however, would New York City be a magnet for super-tsunamis that apparently hit nowhere else? The scientific explanation is obvious: the Statue of Liberty. It washed up on the beach symbolizing the decline of insensitive and thoughtless humans replaced by apes in _Planet of the Apes_ (1968). It protruded from a frozen New York Harbor in _A.I_. (2001), symbolizing the decline of insensitive and thoughtless humans replaced by skinny robots. So, what could be better for symbolizing the decline of insensitive and thoughtless fossil-fuel-burning fools? Have the old gal get slapped in the kisser by a global-warming-induced super tsunami; that should do it. But destroy her—never! It would destroy all hope of a happy ending. So the movie leaves her protruding from the frozen harbor, still standing, as a symbol of hope. At 305 feet (93 m) tall (including the pedestal), the venerable lady also puts things in perspective. Judging from its level on the statue, the tsunami has to be around 240 feet (72.8 m) high. This height means that the statue's feet will be under nearly 90 feet (27.4 m) of water. Unless the statue instantly fills with water, its feet will be subject to about 2.7 atmospheres of water pressure, enough to crush the statue's 0.09375-inch-thick (0.237 cm) copper sheet metal walls. Keep in mind that each square foot of the thin sheet metal in the base of the statue would have to resist a total force of over 5,700 pounds (25,000 N). Add the massive impact of the wave, and the grand lady's days of symbolizing are over. She's going to be a twisted sunken wreck. When it hits the shore, the giant 240-foot- (72.8-m-) high wave would again be far more devastating than depicted. By comparison the Indian Ocean tsunami on December 26, 2004, was as much as 115 feet (35 m) high as it rolled ashore in Sumatra near the epicenter of the earthquake that caused it, killing about 320,000 people. In Thailand the tsunami was down to at most 34.7 feet (10.6 m) high with a death total of 14,000 people. By the time it reached India, the tsunami was less than 8 feet (2.4 m) high—a mere shadow of its younger self—yet still caused about 22,000 deaths. Overall, more than 400,000 people died as a result of the tsunami's devastating power. A 240-foot- (72.8-m-) high super-tsunami hitting New York City is going to make the December 2004 tsunami look mild in terms of death and destruction. Static water pressure would be 7.25 atmospheres (atm) at the bottom of a 240-foot wave as compared to an estimated pressure of 4.1 atmospheres under the Hiroshima atomic bomb blast. Like the Statue of Liberty, a building would be unaffected by the static water #### SUPER-TSUNAMI MATHEMATICS Mathematically predicting the destructive potential of the super-tsunami would be extremely complex. However, we can get a rough idea of its destructive potential by comparing it to a wind with similar kinetic energy. The famous Bernoulli equation indicates that when a moving fluid such as a wind or water flow is stopped, say, by running into a wall, the kinetic energy of the flowing fluid will be converted into pressure acting on the wall. Obviously, if the pressure is too high the wall collapses. To approximate how the pressure created by flowing water compares with wind, we can use the kinetic energy term from Bernouli's equation and solve for the velocity of air as follows: Using the above relationship, a sedate water velocity of ten miles per hour will be equal to an air velocity of 290 miles per hour from a kinetic energy standpoint—the equivalent of the wind speed in a category F5 tornado. Ramp the water velocity up to thirty-five miles per hour and the available kinetic energy would be equivalent to a 1,000 miles per hour of wind, similar to the wind speed under the Hiroshima bomb blast, estimated at 980 miles per hour (1,580 kph)26. Since anyone attempting to measure it would likely be killed, good data for the velocity of a tsunami after coming ashore is hard to find; however, it's typically estimated to be between ten and thirty-five miles per hour. A 240-foot-high wave would probably be faster. pressure if the interior and exterior water levels rose at the same rate, but that's unlikely. The first wall to be hit by the wave would be instantaneously submerged, while the wall on the opposite side of the building remained dry.This condition, however, would not last long. A wave traveling thirty-five miles per hour (56 kph) will cover a distance of 51 feet (15.5 m) in a second. With the exterior water level rising around the building's entire perimeter in a matter of seconds, the resulting exterior water pressure would be more than enough to simultaneously implode windows and sections of walls. The water gushing in would act like a giant piston compressing air in the building into a high-pressure shock wave that would travel upward, blowing out windows and sections of wall as it progressed. It would be followed by a water hammer gushing upward though every possible path. The resulting structural damage could bring the building down, but that's only part of the picture. From a kinetic energy standpoint, a wall of water traveling 35 miles per hour would be equivalent to a 1,000-mile-per-hour (1600 kph) wind! Since the wind speed directly beneath the Hiroshima bomb blast was estimated to be 980 miles per hour (1,580 kph), it's clear that a 240-foot-high super-tsunami would be horrendously destructive. By comparison, the highest tornado wind speed ever measured was 318 miles per hour (512 kph). Wind pressures act on almost the entire side of a building from top to bottom, while wave action will affect mostly the lower part, so comparisons of relative kinetic energy don't necessarily correlate with damage. However, weakening a building's support at its base is an invitation for collapse. The combination of static pressure from the depth of water and dynamic pressure from the wave's motion would likely cause structural failure in the affected high-rise buildings with the possibility of a domino-like collapse. Even if a building did not collapse into one of its neighbors, the collapse would cause a local tsunami as falling building materials slammed into the water. Few structures would be capable of withstanding the abuse of being hit by a super-tsunami followed by the wave action of local minitsunamis. New York City would largely lie in ruins. #### Why Buildings Collapse The collapse of the twin towers on 9-11 due to airplane impact and resulting fires, along with the destruction of the Alfred P. Murrah Federal Building in Oklahoma City from a truck bomb, have demonstrated to most people that modern buildings are not as indestructible as they seem. Yet conspiracy buffs seem convinced that only explosives planted on the inside can bring a modern building down. For the Murrah Building, conspiracy theories generally go something like this: _The buildings were constructed of such and such materials rated for thousands of pounds per square inch, how could an explosion outside the building with far less pounds per square inch demolish it? Obviously, explosives were planted inside_. Simply put, the "thousands of pounds per square inch" refers to the maximum internal stress the material can handle before failing catastrophically, not the maximum external pressure, pressure that might be caused by a bomb blast. Stress and pressure are very different quantities, although they use the same units (psi). Stresses are internal and depend on an object's material and shape as well as the load applied to it. Pressure is a type of external load. Calculating stresses is too involved to describe in anything less than a text book, but suffice it to say that the internal stresses on the structural parts of buildings are usually far higher than the external pressures on them. For example, the maximum wind pressure loads buildings are designed to withstand are generally less than 0.74 pounds per square inch (0.05 atm). Although this load sounds miniscule, such a pressure would have created a sideways force of about 270,000 pounds on the vertical wall of each floor in the Murrah Building for a total force of over 2.4 million pounds on the building. To produce such pressures and forces with natural phenomenon would require something like a recordbreaking hurricane or a direct hit by a tornado. The Oklahoma bomb blast pressure was easily higher. Elastic stability or buckling resistance of the columns supporting a building's load is also a factor in collapse. Cut a soda straw about 3 inches long and compress it like a column running between your index finger and thumb. The straw will withstand a considerable force before it buckles. Repeat the experiment, only this time push lightly sideways on the straw as you compress it. The straw will quickly buckle. Sideways forces applied to support columns by explosions or walls of water are a very bad idea if the goal is to keep a building standing. Similar conspiracy theories—multiple bombs planted by insiders—exist for the twin towers. According to conspiracy theorists, the fire inside the towers could not have melted the steel structure that supported the top floors, thereby leading to their collapse, and here the theorists are right. The steel support beams would not have melted, because they didn't have to. At around 800 degrees Fahrenheit (430ºC) steel beams or trusses begin to significantly lose both their strength and stiffness. In the twin towers most of the supporting steel columns were located in the outer walls and were connected together by long, light-weight steel trusses in the floors. With fire temperatures inside the towers easily exceeding 800 degrees Fahrenheit, the floor trusses sagged. Stiff trusses normally create little sideways force on the steel columns in the outer walls. But let the trusses sag, and they become more cable-like and capable of creating sideways forces many times the downward weight of forces acting on them. As a result of these forces, the outer wall's columns were pulled inward until they snapped, sending the whole top of each tower careening down on the floors below in a chainreaction collapse. Conspiracy buffs counter by claiming that no modern building has collapsed due to fire. Maybe it has something to do with the fact that, except for the twin towers, no modern building has ever been hit at full speed by a fuel-laden jumbo jet that destroyed a significant part of the building's support structure and caused parts of the floors in the impact zone to collapse on those below, not to mention leaving the weight of many jumbo jet parts scattered on the floor in the burning inferno. From the beginning, the floors and structures in the impact area were overloaded. The conspiracy buffs continue by asking how a few collapsing floors could bring down an entire building. Of course, they fail to note that the "few" collapsing floors (thirty-three floors for tower two, and seventeen for tower one) would have been tall enough in themselves to be major buildings in many communities. Floors are usually designed for higher-pressure loads (not including the weight of the floor itself) than walls, but the maximum pressure is still generally less than 0.05 atmospheres. Pile the concrete and steel debris from several collapsed floors atop a good one, and its pressure rating is easily exceeded. But, in the twin tower collapse, the chunks of debris were not just piled, they fell with considerable impact. The result was an almost instant failure of the floor being struck. The floors might have simply pancaked to the bottom, leaving the walls standing like a huge hollow tube, except that the floors were firmly attached to the walls. Overloading a floor enough to make it sag and collapse would have produced a substantial sideways force on the walls, pulling them inward, similar to the effect of making the floors sag from high temperature only on a much faster time scale. The result: structural steel in the walls would have buckled and snapped as the floors failed. Conspiracy theorists continue by asking how a building collapse could pulverize the structure's concrete and give the appearance of a blast wave emanating outward. The answer is straightforward: Energy used to lift building materials over a construction period lasting years was stored in the buildings as potential energy—an amount roughly equal to 500,000 pounds of TNT (230,000 kg TNT) per tower, easily enough to pulverize much of the building's concrete. When each tower collapsed, all the energy was released. As top floors fell they acted like a gigantic piston compressing the air in the floors below. This compressed air had no way to escape except by blasting outward and downward, taking anything loose with it, such as concrete dust. By the time the building approached the ground, the velocity of the escaping air was high enough to throw hapless victims violently sideways. Placing a few thousand pounds of explosives inside the building would have made little difference. Since the super-tsunami in _The Day After Tomorrow_ does relatively little damage to the Statue of Liberty, the statue once again provides a useful reference point when the water eventually recedes. Allowing for about 20 feet (6.07 m) of snow, the water level had to remain over 150 feet (45.5 m) higher than normal after the tsunami had receded. To raise ocean levels by 150 feet (45.5 m), about 75 percent of Antarctica's ice would have to melt. That would take about 2.6 years, assuming that all solar energy available to Earth went entirely into melting Antarctica's ice and that the ice was already warmed up to 0 degrees Celsius Obviously, this is only a fraction of the time required for melting, and so a super-tsunami with an immediate 150-foot increase in ocean level caused by melting ice is absurd. The super-tsunami depicted in the movie could have been a storm surge brought on by high winds, but that's also ridiculous. At 240 feet (72.8 m) high, the super-tsunami is about 215 feet (65.2 m) higher than the unusually high storm surge that occurred in Louisiana during hurricane Camille (1969). That surge was caused by maximum wind speeds near 200 miles per hour (322 kph). A 240-foot- (72.8-m-) high storm surge would be virtually impossible without help from a catastrophic event such as an asteroid strike or massive land slide. Even then it's unlikely that New York City would be inundated while Washington, D.C., was left untouched (as depicted in the movie). On the one hand, the giant wave produced far less damage in the movie than would have been experienced in reality had such a wave existed. On the other hand, there were no conditions in the movie that could have caused the wave in the first place. It's classical Hollywood logic: two conflicting mistakes equal perfection. Serious as it is, global-warming effects are not going to make the same dramatic entrance on the world's stage as they did in _The Day After Tomorrow_. The behemoth globalwarming-induced wave is nothing more than a global-sized exaggeration; the potential long-term dangers of global warming are not. ### THE ULTIMATE ANTI-CHAOS THEORY The biggest surprise in _The Day After Tomorrow_ is the total lack of reference to chaos theory. The theory had its roots in meteorology, and while far too rich to explain in a few paragraphs it can be partly understood by defining the "butterfly effect," a term coined in the 1960s by Edward Lorenz. According to Lorenz, chaotic systems such as the weather are extremely sensitive to initial conditions, and even slight changes in initial conditions can radically change such a system's behavior over time. Weather is so sensitive that, theoretically, air currents caused by a butterfly flapping its wings in Beijing could eventually cause a tornado in Kansas. Imagine what a radical change such as global warming could do. It's not as though Hollywood is unaware of chaos theory— in _Jurassic Park_ [PGP-13] (1993) Malcolm (Jeff Goldblum) babbles endlessly about it. Although his arguments were muddled, they indicated that dinosaurs brought back to life in the movie would eventually become able to reproduce in spite of precautions to the contrary. Sure enough they did, but big deal. If humanity could wipe out everything from the woolly mammoth to the carrier pigeon, then surely a few hundred dinosaurs couldn't be all that hard to annihilate. It's not like they would be hard to find. Although _The Day After Tomorrow_ does offer some explanation for how global warming can trigger an ice age, the paradox doesn't make sense at a gut level. That's not to say the concept is wrong, but rather an ice age would have seemed more plausible in the context of chaos theory. In that setting, unexpected or even opposite results seem reasonable. But referring to chaos theory would have made the magical weather predictions of the movie's climatologist hero look silly. Weather accuracy is very sensitive to data available at the time a weather forecast is made—the greater the amount and accuracy of data, the greater the accuracy of the prediction, but only up to a point. Lorenz claimed that weather predictions could never be accurately made more than about two weeks ahead because that was the limit of humanity's ability to collect and analyze the required data. Extending beyond that time span would quickly require a forecaster to know the condition of every atom in the universe, he claimed. Nevertheless, the movie's climatologist nailed his forecast of a deadly ice-age-producing storm days ahead of time by using a computer simulation based on a few ice samples from Antarctica—what a guy. With such a dire prediction in hand, what can be done? Why, of course, evacuate the entire southern United States to Mexico— northerners are doomed, but they may actually be the lucky ones. Imagine this joy: being trapped for endless days in a traffic-snarl hundreds of miles long during a major blizzard. What a great problem-solving idea: the ultimate antichaos theory—death. #### Summary of Movie Physics Rating Rubrics The following is a summary of the key points discussed in this chapter that affect a movie's physics quality rating. These are ranked according to the seriousness of the problem. Minuses [–] rank from 1 to 3, 3 being the worst. However, when a movie gets something right that sets it apart, it gets the equivalent of a get-out-of-jail-free card. These are ranked with pluses [+] from 1 to 3, 3 being the best. [–] [–] Highly exaggerated storm conditions. [–] [–] Seriously underestimating the damage that would be caused by highly exaggerated storm conditions. [–] [–] Seriously overestimating or underestimating damage done to structures by natural phenomena or acts of terrorism. (Movies should use computer simulations and engineering studies to make these estimations.) [–] Scientists spouting dramatic and authoritativesounding solutions or pronouncements that make no sense from a logical or scientific perspective (such as evacuating vast territories in the middle of a blizzard). [–] Evacuating vast territories in the midst of foul weather. (Please, didn't hurricane Katrina teach us anything?) [–] Incredible computerbased predictions of chaotic systems, such as weather systems or the stock market, made in ridiculously short periods of time and based on flimsy amounts of data. ## CHAPTER 18 ## THE MOVIEMAKER'S COOKBOOK: ### Cigarettes as Lighters, Exploding Cars, Burning Bugs, and Other Recipes for Foolishness ### CIGARETTES AS LIGHTERS Call them cancer sticks, smokes, or whatever, but by any name, cigarettes are an amazing piece of technology—deliberately designed for reliable failure. Obviously combustible, they fail to burst into flame, even when burning at temperatures in excess of 1,000 degrees Fahrenheit (540°C). By design they smolder. Pull air through them, and they smolder really brightly and really quickly, but that's all they do. They just don't burst into flame. Light the wrong end (the filter), and it burns like a candle with a bright yellow-orange flame. But let a cigarette burn down to the filter and, remarkably, the tobacco smoldering at over 1,000 degrees Fahrenheit does nothing. It reliably fails to light the filter's combustible cellulose acetate fibers. So what happens when a movie villain flicks his cigarette into a puddle of gasoline for some nefarious purpose? It bursts into flame. Try the same experiment in the real world, and the gasoline will snuff out the cigarette as soon as it lands in the liquid. Okay, it's vapor, not liquid, that burns. The cigarette, however, has to pass through a combustible mixture of gasoline vapor and air before it lands in the puddle. Even if a smoker draws gasoline-vapor laced air through it, a cigarette will still not reliably ignite the vapor. #### It's Not So Simple—The Fire Triangle Just about every grade school kid learns about the fire triangle and the three requirements for creating or putting out a fire. Although the triangle is a good starting point, actual combustion is not so simple. The three conditions needed for fire have to meet a number of conditions of their own. This is why it's difficult (if not impossible) to ignite gasoline with either bullets (especially handgun bullets) or cigarettes. Combustion is a multistep process that first depends on the formation of free radicals. Free radicals are atoms or molecules with one or more unpaired electrons that provide a reaction site. After formation, the right free radicals have to bump into each other at the right moment in the right way—by a random process—so that they can bond and release energy. For example, an O2 molecule must absorb enough energy to break the double bond holding the two oxygen atoms together in order to form two free radicals— one of many types that must form. In turn, these O free radicals must bump into a carbon free radical to form CO or into a CO free radical to form CO2 or an H to form OH or any number of other free radicals to form other interim compounds. In the end, a hydrocarbon fuel (made of Cs and Hs) becomes CO2 and H2O—that is, if enough activation energy is present to start the process and enough excess oxygen to sustain it. When heat is liberated during combustion, it must provide the energy to continue activating the various steps in combustion, or the fire will go out. Simply diluting the reactants so that heat is transferred to nonreacting molecules instead of reacting ones can be enough to stop a combustion process. Interfering with the free radicals formed in interim steps can also end a combustion process. When heated, halogenated compounds such as Halon 1211 (CF2BrCl) form their own free radicals that effectively mop up the free radicals in combustion processes and extinguish fires. Generally, Halon is effective in concentrations of only 5 percent to 10 percent. Unfortunately, such compounds are also highly effective at destroying the ozone layer and have pretty much been banned. All in all, starting and maintaining a fire is not as simple as it looks. Unconvinced by testimony from several sources, a group of staff and volunteers at Intuitor.com tested the gasoline-igniting ability of cigarettes over three hundred times without a single success. They tried tossing lit cigarettes into a small puddle of gasoline, holding them (with really long tongs) in the vapor-air mixture at various distances above the puddle, placing up to forty smoldering cigarettes in and around the puddle, and using gasoline-soaked paper towels instead of a puddle, all with no effect. They devised a smoking machine and smoked numerous cigarettes directly over the puddle. Using the machine, they blew air backward through smoldering cigarettes, making sparks fly off the brightly glowing tip into the gasoline—but still no ignition. They lit an unfiltered cigarette and placed the unlit end in the gasoline. The flammable fluid wicked its way to the smoldering end and snuffed it out. In distress, the experimenters began thinking the gasoline was defective. They held a match above the puddle (at the end of a long pole) and—poof—the fuel burst into flame. They repeated this process several times, always with the same result. Clearly, cigarettes were just not reliable igniters even though matches were. The myth of cigarettes reliably igniting gasoline pervades popular culture so deeply it has worked its way into novels. In _The Partner_ , John Grisham has a character splash gasoline around his vehicle (ironically, a Chevy Blazer), light a cigarette, and throw it in the gas, igniting an inferno.Tell a group of friends that the lit cigarette wouldn't have ignited the gasoline, and invariably at least one will offer, "but they do it in movies." (A few words of advice for aspiring novelists: don't use movies for source material. The real-life experiences touted by writing teachers are actually much better.) So, how does a cigarette ignite a gasoline puddle in a movie? It doesn't. At the right moment, a special-effects technician pushes a button that fires an electronic igniter located appropriately near the fuel. The camera is placed so the igniter can't be seen. Sometimes, the fuel is lit by a trick cigarette containing combustible compounds other than tobacco. It is never, however, lit with anything as unreliable as an ordinary cigarette. The explosive or flammable range for gasoline is only about 1.4 percent to 7.6 percent gasoline vapor in air (21 percent oxygen). Concentrations below 1.4 percent don't give off enough heat to sustain the chain reaction of combustion. Concentrations above 7.6 percent don't have enough oxygen to sustain combustion. Outside these very narrow limits, gasoline cannot be ignited. Nevertheless, even the right mixture of gasoline vapor and air needs some activation energy for igniting, similar to the way some pressure is needed for tripping a mousetrap. At 536 degrees Fahrenheit (280°C) a combustible gasoline-air mixture already has enough internal energy to trigger combustion with no further energy input. Having a gasoline-air mixture contact an object at 536 degrees Fahrenheit (280°C) or higher, however, does not automatically heat the mixture to 536 degrees Fahrenheit (280°C). Heat must be transferred from the high-temperature object into the vapor-air mixture to elevate it to 536 degrees Fahrenheit before ignition occurs. Heat the gasoline-air mixture outside the cigarette and as soon as it gets warm, the vapor-air mixture will rise and mix with colder air, preventing it from reaching ignition temperature. A similar effect prevents firewalkers from burning their feet as they walk across glowing coals. If their feet contact the hot coals briefly, the heat transfer is too slow to cause burns, but stand on the coals too long and the feet get fried. Is there any other example of a combustion process that will not ignite a combustible fuel-air mixture? Yes, the Davy safety lamp. In the 1800s coal mines could only be illuminated with some sort of flame—better for igniting the mine's methane gas than for illuminating the mine's dark tunnels. The Davy lamp solved this problem by surrounding the flame with a fine wire screen. A flammable methane and air mixture could enter the lamp and make it burn brighter, but the flame would not propagate outward through the screen. Presumably, the screen disrupted heat transfer from the flame to the methane-air mixture and prevented it from reaching its ignition temperature. Can a cigarette ever light gasoline vapors? Yes, under special conditions, and it makes a convincing fire-safety demonstration in the process. A firefighter sets an object that looks like a skinny chrome-plated metal vase on the table. It has a square base with an 18-inch-long (45.5 cm) vertical tube, about 2 inches (5 cm) in diameter, welded to the base and open on the other end. He fills the tube with pure oxygen (not air), adds a few drops of gasoline, heats the outside slightly to vaporize the fuel, drops a lit cigarette in the open end, and—BOOM!—the gasoline explodes. So, yes, cigarettes can ignite gasoline vapors; yes, one should never risk smoking near gasoline; and yes, smoking is dangerous. But then there aren't many gas stations, warehouses, or fuel dumps with pure oxygen environments. If anything, the exploding vapor demonstration shows that altering oxygen concentration makes a big difference in how gasoline vapors do or don't ignite. Lower the oxygen content enough to the minimum oxygen concentration (MOC, about 12 percent for gasoline), and the gasoline vapor cannot ignite regardless of its concentration. If there's a chance of an explosive mixture forming in the empty space of a storage tank, the chemical company that owns it will keep the empty space below the MOC of the tank's contents, often by diluting the empty space's air with nitrogen. Cigarettes are designed to deliberately create an oxygen-poor, fuel (tobacco) rich environment in order to produce smoke. Draw a combustible mixture of gasoline and air into the smoldering tip, and the burning paper, which has a combustion temperature of 451 degrees Fahrenheit (233°C), along with the tobacco will greedily gobble up most of the available oxygen, lowering oxygen content below gasoline's MOC of 12 percent before the gasoline vapors get to their ignition temperature of 536 degrees Fahrenheit (280°C). What happens to the oxygen? It mostly becomes CO2, the same stuff that's in CO2 fire extinguishers. Diluting air's oxygen content with CO2 is even more effective for fire suppression than diluting it with nitrogen. Past the glowing tip, fresh air will indeed seep in through the cigarette's porous sides—boosting the oxygen content back up to around 13 percent coming out of the filter. But in the process, it also lowers the temperature well below the gasoline vapor ignition point. Neither theory nor experiments can totally rule out the possibility of igniting a fire with an oddball cigarette combined with a special set of weather conditions and an unusual blend of gasoline. But there's certainly enough theoretical and experimental information to show that cigarettes won't reliably ignite gasoline—probably due to a combination of poor heat transfer and low oxygen content in the burning tip. What's more, moviemakers know this. So, naturally, it makes perfect sense for them to continue filming clichéd scenes falsely depicting it. ### CARS AS BOMBS Movie bullets can be as effective as cinematic cigarettes for setting off gasoline. Shoot a car's gas tank, and it explodes in a fireball. But how? It's actually not as easy as it looks. First, automobile gas tanks aren't put in exposed locations. They're usually sandwiched between heavy frame members and surrounded by one or more layers of sheet metal in the car's body. The tanks are hard to see, let alone to shoot. Second, if there's any gas in the tank, gasoline is so volatile that enough of it would vaporize to ensure that the fuel-to-air ratio in the tank was too high for combustion. Stop a bullet suddenly, and it gets really hot because its kinetic energy changes into heat. In theory, a high-powered rifle bullet can reach high enough temperatures to set off a combustible mixture of gasoline vapor and air. But it's just about impossible to stop a bullet abruptly enough when shooting a gas tank. The gas tank doesn't offer enough resistance. The bullet will likely plow right through. If it is stopped inside, it's because it has already lost most of its kinetic energy by penetrating the car's body, frame, or gas-tank wall and will likely not have enough kinetic energy left to ignite anything. Sometimes, a bullet can cause a spark, especially if the bullet has steel parts or a static electric charge on it, but these are not the bright fiery flashes of light caused by overuse of pyrotechnic compounds in bullet impact special effects. They are modest sparks that are neither effective at starting fires nor clearly visible in normal daylight. For one thing, the sparks will likely occur outside the gas tank—where there are no combustible vapors—when the bullet first contacts the gas tank's wall. For another, most bullets are made of lead or copper-jacketed lead, both materials that can be ground with high-speed grinders without producing any visible sparks, as opposed to grinding steel, which produces a shower of sparks. Sparks produced by grinding steel are generally orange-yellow in color, indicating a temperature of over 1,832 degrees Fahrenheit (1,000°C), way above the autoignition temperature of gasoline vapor (280°C). Will they ignite gasoline? Typically, no. Again, the doubters at Intuitor.com tested the gasoline-igniting ability of sparks from grinding steel by repeatedly grinding over a small pan of gasoline. The sparks showered into the pan for several minutes with no ignition. Again, to prove that a combustible mixture existed over the gasoline, a lighted match (on the end of a long pole) was held above it, and the mixture burst into flame. Although the sparks themselves were well above the autoignition temperature of a combustible gasoline vapor and air mixture, they did not contain the right amount of thermal energy to heat the combustible mixture around them to a high enough temperature for ignition. Once again it should be emphasized that neither theory nor experiments can totally rule out the possibility of igniting gasoline with sparks from a grinding operation, and so grinding near a puddle of gasoline has to be considered a very unsafe activity. However, sparks from a normal grinding operation are not a reliable source of ignition. This casts doubt on whether sparks from a steel bullet would be any more effective. If a vehicle's gas tank is shot with a machine gun and gasoline leaks out, and it forms a combustible mixture, and a bullet just happens to hit in such a way that it makes a spark with just the right amount of energy inside the combustible mixture, then— poof! But that's not likely. Even heavy .50-caliber machine guns in WWII airplanes were found to be unreliable for starting fires of this type. Incendiary bullets were invented to remedy the problem. They contain a pyrophoric material, which bursts into flame when it hits an object and burns like white phosphorus. Although the fire is very brief, it's also very hot and highly effective at igniting flammable materials. Tracer bullets can also sometimes light fires but are less effective. The tracer compound is designed to produce a streak of light as the bullet flies toward its target so that gunners can see where their shots are going.The tracer compound does not burn as intensely as incendiary material, and it is often largely or entirely used up by the time the bullet reaches its target. Incendiary bullets are the only type capable of creating the large bright flashes of light on impact commonly portrayed in movies. Outside the military, virtually no one uses incendiary bullets in gunfights. The overdone bullet impact flashes in movies can be traced to _Raiders of the Lost Ark_ [PGP-13] (1981). Bullet impact pyrotechnics were overused in this movie to create excitement. The bright flashes certainly give the impression that bullets would be effective fire starters. The movie was a hit and—as is Hollywood's habit—was widely emulated. But that doesn't change the fact that, on impact, real bullets don't make such fiery flashes and very rarely start fires. Movie car crashes also routinely trigger infernos. Drive a car off a cliff, and it's certain to burst into flame, sometimes even before it hits the ground. A character can flip, roll, and smash his car into the shape of an accordion, and yet walk away without so much as a broken nose. But if it's time to kill him off, he's going to get the fireball. Sometimes for dramatic effect he's granted a few moments to ponder his fate while trapped upside down in the car as a puddle of gasoline ominously oozes beneath him. Nevertheless, a fiery end is assured—sometimes at the hands of a villain who sneers as he tosses a cigarette in the puddle. Yes, cars can catch on fire and sometimes even explode, but it's rare. The narrow flammable limits of gasoline vapor in air make it unlikely. Not only does the gas tank have to rupture— hardly preordained—but a source of ignition has to occur in combination with an explosive mixture of gasoline and air. ### BURNING BUGS After crash landing on Mars, finding their habitat destroyed, and running out of air, the crew in _Red Planet_ [RP] (2000) runs into a locust-like swarm of flesh-eating nematodes that can bore right through their space suits. But it's not all bad news. The nematodes made the oxygen atmosphere, which kept the crew alive when they removed their helmets as their air tanks ran dry. The voracious little guys are also highly flammable and, therefore, easily exterminated. Light one on fire and it bursts into flame, setting off a chain reaction with its nearby cousins in a veritable fireworks display. Apparently, viewers are supposed to believe that the nasty little critters not only make oxygen from Mars's otherwise CO2 atmosphere, but also store it in their bodies under high pressure. According to Robert Zubrin, if Mars were terriformed so that it had a breathable atmosphere, the pressure would only be about five pounds per square inch (1/3 atm). Although it would be nearly pure oxygen—a condition favoring rapid combustion—the partial pressure of oxygen would be about the same as on Earth, a condition favoring normal combustion rates. Most of the oxygen needed for making the nematodes burn like fireworks would have to be stored inside them. The oxygen concentration outside the little guys would not be high enough for such spectacular combustion. It takes at least 3.45 grams of oxygen to completely burn 1 gram of paraffin wax (assuming a composition of C30H62). Oxygen free radicals have to "bump into" free radicals from fuel molecules for combustion to occur. As oxygen is consumed, these collisions become less and less likely. So, in reality, significantly more than 3.45 grams of oxygen must be available to insure complete combustion. Assuming that burning nematode carcasses consume as much oxygen as candle wax, the little guys would need to compress and store large quantities of oxygen at high pressure to be so flammable. The stored oxygen would weigh more than 3.45 times the critter's deflated body weight. If the voracious little guys gave off oxygen as a waste product—enough to create an entire oxygen atmosphere—then why would they want to store and tote around such a heavy load of it? Producing oxygen from CO2 is a very expensive process from an energy standpoint, but plants are clearly willing to pay. The process is about the only way they can get the carbon they need for growth. Since plants can't move around, they have to let the carbon come to them as CO2 carried by the wind. Plants have lots of surface area in their leaves for collecting solar energy, and so it's no problem for them to collect the payment for their energy bills. Small mobile critters such as the nematodes have neither the means nor the need for withdrawing carbon from air or energy from sunlight. They can get all the carbon and energy they need from munching on plants. So, naturally, it makes all kinds of sense for them to waste energy creating an oxygen atmosphere for assisting possible competitors—such altruism. Ironically, the nematode scenes required that moviegoers remember enough science to know things burn better in pure oxygen. The scenes then sought to kill all further scientific reasoning with the yuck factor—seeing little critters with the charm of cockroaches crawl out of a dead person's nose—along with the shock effect of seeing a burning critter cause a chain reaction of flaming nematodes shooting from random holes in a corpse. After that combination, who's going to notice that the science is silly? By the end of _Red Planet_ , the crew has mostly been eaten, murdered, or otherwise destroyed; the surface of Mars incinerated; the years of effort to establish oxygenating plant growth wiped out; and the hope of a new habitat for people gone. Clearly, the required happy ending is at risk, not to mention the future of humanity. But fear not! Having survived the ordeals, the two remaining crewmembers (a man and a woman) are headed back to Earth. They have not only found romance but a solution to Earth's critical overcrowding and pollution problems: bring a flesh-eating, oxygen-producing nematode back to Earth— certainly the cure for overcrowding if not for pollution. #### Summary of Movie Physics Rating Rubrics The following is a summary of the key points discussed in this chapter that affect a movie's physics quality rating. These are ranked according to the seriousness of the problem. Minuses [–] rank from 1 to 3, 3 being the worst. However, when a movie gets something right that sets it apart, it gets the equivalent of a get-out-of-jail-free card. These are ranked with pluses [+] from 1 to 3, 3 being the best. [–] [–] Spectacular combustion scenes, such as burning nematodes, that have no logical or reasonable scientific basis. [–] [–] Contrived happy endings with no logical or reasonable scientific basis. [–] [–] Lighting gasoline puddles by tossing in lit cigarettes. [–] [–] Blowing up cars by shooting the gas tank, especially when it's done with a handgun bullet. [–] Clichéd brightly flashing bullet impacts. [–] Clichéd fiery car crashes. ## CHAPTER 19 ## WARS VERSUS TREK: ### Forgiving versus Forgetting ### FORGIVENESS Interstellar space travel even remotely similar to anything in _Star Trek_ or _Star Wars_ would require a much deeper understanding of physics—possibly even the discovery of as-yet-unknown principles of physics—not to mention far more advanced engineering capability. Such travel makes for great stories but may be completely impossible. Certainly, with the existing knowledge of physics, the speed and energy required for these space flights are too high and the length of a human lifetime too short (see Chapters 7 and 10). Any movie in the space-travel genre automatically ventures into the hostile depths of insultingly stupid movie physics (ISMP). Venturing into such depths is not, however, automatically fatal; it's like scuba diving—take the right gear, respect the dangers, and survive. Find some sunken treasure (for a movie: a good story line) and prosper. Under the right conditions, even the depths of ISMP are capable of forgiveness, but there must be reasons for it—good reasons. ### GOING WHERE NO MAN HAS GONE _Star Trek_ has been plagued by plenty of half-correct science and mumbo-jumbo explanations, not to mention inconsistencies, yet is not just redeemable but also groundbreaking, at least for movies and television. To understand its significance requires a temporary digression from movies to TV in order to look at the conditions when _Star Trek_ first appeared. The TV series that spawned the _Star Trek_ movies made a an inventive shift from movie-TV tradition by featuring large unaerodynamic spaceships, built in outer space and designed to stay there, thereby eliminating the enormous fuel resources needed to lift such ships off the surface. By never entering the atmosphere, the ships did not need to be aerodynamic. The large ship size stemmed from the large travel times and distances of interstellar space travel, requiring enormous amounts of resources. _Star Trek_ spacecraft again broke with movie-TV tradition by not using conventional rocket thrusters for propulsion. The starship Enterprise's impulse engines are indeed thrusters but are supposedly powered by a fusion process similar to that used in the hydrogen bomb, albeit in a much more controlled manner. The ship's warp drives were also a movie-TV innovation, barely conceivable within the known boundaries of physics. Still, the drives were created in recognition of the fact that conventional rocket thrusters—even upgraded fusion-powered devices—could not possibly provide the incredibly high speeds needed for interstellar space travel. _Star Trek_ broke with movie-TV tradition yet again by fueling its spacecraft with the ultimate energy source: antimatter. True, using such a fuel is extremely unlikely but, at least, conceivable. It is also about the only conceivable energy source condensed enough to power an enormous spacecraft on lengthy interstellar space journeys. Some fictional inventions, such as inertial dampers and transporters, have no basis in known physics. The principles behind them are not even conceivable. However, without inertial dampers, it would take months to speed up, slow down, and make turns, even when traveling at rather sedate speeds like one-fourth the speed of light in a vacuum (see Chapter 10). Travel from the surface of a planet to orbiting spacecraft with any small-sized craft is already nearly inconceivable, so from a scientific standpoint, beaming up via a transporter is not much worse. From a story standpoint, beaming up is far better. It accelerates the plot. #### Shields Up! There is no known mechanism capable of producing the shields depicted in the _Star Trek_ and _Star Wars_ movies, yet without them every space battle would be a suicide mission. In fact, even space travel itself might be hampered. If a ship finds itself in an asteroid belt or other space junk yard, no problem: up go the shields and all is well. Since shields are so critical to the entire space-movie genre, let's assume they do exist. A space battle is raging, and a fighter craft is now attacking a large battle cruiser protected by such a shield. The fighter would likely have a mass of around 15,600 pounds (7,091 kg), similar to an Earthbound F-16 fighter, and be approaching kamikazestyle at, say, one-tenth the speed of light—a sedate velocity for spacecraft. The fighter's kinetic energy would be the equivalent of 763 megatons of TNT, or 7.63 of the largest-sized nuclear bomb ever made. Unquestionably, the fighter would be blown up before it got close enough to launch its weapons, but the debris from the fighter would continue forward and impact the cruiser's shields. Naturally, the shields would stop the debris, but what about the kinetic energy they contain? It would have to be turned into something, and about the only choice is heat— enough to convert the debris into plasma—and a giant electromagnetic pulse (EMP) containing every form of electromagnetic radiation from radio to gamma waves. In the best case, the plasma and EMP would temporarily render the cruiser's sensors useless. In the worst case, it would wipe them out along with the rest of the cruiser's electronic equipment and crew who would be zapped by the gamma rays in the EMP. Energy, however, is not the only quantity that must be conserved. Momentum also must be conserved. The result is that even if the shields hold, the cruiser is going to get a mighty jolt. At best, the jolt will knock the cruiser out of position; at worst, it will send shock waves into its hull, tearing up equipment and injuring crew members in the process. In short, even if shields did exist, there would still be major problems to overcome. After the TV series debuted in 1966, _Star Trek_ slowly developed as a cultural phenomenon. The TV debut happened at a time of widespread racial inequality—Martin Luther King had delivered his famous "I Have a Dream" address only three years before. Yet not only were the Enterprise's crewmembers multicultural and multiracial, but if a character was Asian, the actor was Asian. By contrast, the famous TV series _Kung Fu_ , from 1972, featured a half-Asian, half-Caucasian main character wandering the Old West in America armed only with well-honed martial art skills. A Caucasian with no previous martial arts background, David Carradine, was chosen for the role over world-renowned martial artist, Bruce Lee, an Asian. _Star Trek_ used space exploration as a stage for exploring all kinds of human issues, including the effects of technology on people. The series exemplified equality and harmony existing in the midst of diversity. Yes, women did initially wear miniskirts, but they were also portrayed in nontraditional roles. Keep in mind that the second-wave feminist movement had just begun around 1960. From the beginning, _Star Trek_ was closer to the more forgiving genre of science fantasy than science fiction. #### Quick Comparison: Star Wars versus Star Trek The two franchises include many different media; for brevity, the following will address only movies. There are significant differences between the first series of _Star Wars_ movies and the final series, but they are not evaluated separately. Figure 38: Star Wars vs. Star Trek That's not to say that _Star Trek_ was always consistent with its own visionary understanding of the future, at least not from a technical standpoint. For example, in _Star Trek IV_ , Kirk and crew hijack a Klingon Bird-of-Prey, time-travel back to the twentieth century, land in San Francisco's Golden Gate Park, capture a pair of humpback whales, and fly off with them (a serious break with the tradition of keeping large ships in space) all without being detected by local residents. Okay, the Bird-of-Prey was supposedly cloaked and, hence, invisible when sitting in the park, but does no one walk their dog? Wouldn't Fido be offended by having a spaceship in the middle of his relief area? Wouldn't he, at least, want to mark it? Still, the movie remembers its survival gear, things like scintillating dialog and interesting characters. The movie prospers because it finds that most valued of treasures: humor with heart. It features, among other things, an outer-space alien, Spock—the epitome of logic and reason— wandering around unnoticed in a city with a reputation for creative illogic and a Russian (Chekov) claiming he's a starship officer when caught stealing nuclear energy aboard an aircraft carrier during the height of the cold war—all in a movie about saving whales. _Star Trek's_ much used WWII submarine warfare model is conceivable but not overly imaginative. According to the model, large ships launch powerful weapons such as torpedoes against other similar ships. While these weapons frequently jostle the inhabitants—similar to a WWII depth-charge attack—the targets are rarely destroyed on the first shot. Such close-range battles would be little more than toe-to-toe slugfests, with few tactical possibilities, although the movies pretend to have them. About the only available battle tactics would be putting up shields and firing weapons. Once in a while, one of the combatants would be able to use trickery or hide in a plasma cloud, but that's about it. More realistic space battles would likely be fought at great distances in a far more imaginative way (see Chapter 5). Still, although the lack of imaginative battles is a disappointment, it's not enough to trigger a fall from grace. ### . . . IN A GALAXY FAR, FAR AWAY . . . On the other hand, the entire WWII aircraft-carrier battle model used by _Star Wars_ is flawed, if not outright ridiculous. But in the original _Star Wars_ trilogy, it worked. Why? Because the original was an inside joke designed to poke fun at Hollywood. The first movie came out in 1977, only three years after the Watergate scandal compelled President Richard Nixon to resign in shame, and only four years after United States involvement ended in the divisive Vietnam War. At the time America's selfimage, as the land of eternal good guys, lay shattered, oozing self-doubt—an image reflected in movies. Characters, even heroes, had to be mixtures of good and bad. Seemingly, nothing could ever again be portrayed in simple terms. _Star Wars_ landed on the era's cynical pop culture like an artillery shell. The movie presented everything in the purest of black-or-white, good-orevil terms. Arguably, the greatest movie villain ever created— Darth Vader—for example, was totally black and totally evil (at least in the first movie). Although Han Solo may have seemed to be a mix, on closer examination he was merely a purehearted hero with attention deficit disorder. He might be distracted by personal interests, but given a chance to focus he'd risk everything for the cause. The original _Star Wars_ trilogy was deliberately modeled after obsolete 1930s movie theater serials and used a WWII battle model from the most heroic moment in U.S. history along with light-saber-wielding knights as high-tech updates from classics such as _Seven Samurai_ (1954) [NR] and Errol Flynn swashbucklers. These elements were extensions of both the trilogy's positive tone and tongue-in-cheek humor. On that basis alone, movies from the original _Star Wars_ trilogy deserve ISMP forgiveness. While they might look like science fiction, in reality they are a mix of parody and fantasy—a humorous yet heroic and altogether ISMP-forgivable mythology. ### THE MOTHER OF ALL ISMP LAND BATTLES Unfortunately, the second trilogy did not follow in the first's footsteps. _Episode I_ kicked off the downward decline with a clear case of amnesia. The movie forgot the source of its forgiveness: its roots with the original trilogy. For openers, it offered an unnecessary biological explanation for how the Jedi tap into the Force: "midichlorians," a type of interstellar microbe. The little guys grant access to the Force after planting themselves in one's cells—the more the better. Does this mean swilling a microbe-laced cocktail could make a person stronger in the Force? What about injections? Is the microbe airborne or sexually transmitted, and if so, why are Jedi required to be celibate? Apparently midichlorians fathered Anakin Skywalker. Did they also father the Force, or did the Force father the midichlorians? Was it all some happy cosmic coincidence? By explaining how the Force works, _Episode I_ raised more questions than a child does in the fourth year of life. It moved the Force into the glare of scientific and logical analysis and, in the process, evicted the film from the forgiving genre of mythical fantasy. Having badly weakened its case for forgiveness, _Episode I_ proceeded to take one of the goofiest characters ever created, a flop-eared Gungan called Jar Jar Binks, give him a major role, and then build the ISMP classic of all land battles around him and his species. The battle pits the bumbling Gungans against heavily armed, high-tech droids. The Gungans have a sophisticated forcefield technology capable of shielding their army on the battlefield, yet they ride around on beasts of burden. They have explosive devices that look like giant blue marbles but have to launch them with ancient-looking catapults. Do they put their knowledge of explosives to work and modify them into propellants for rockets and firearms? No, they use spears. Do they rely on stealth, harassment, or guerrilla warfare—tactics that, at times, have actually worked against technologically superior forces? No, they face off head-to-head with the droids on open ground—a tactic that's usually disastrous when used against technologically superior forces. When droid tanks fire, their shots bounce off the Gungan force field. Yet droids can walk through the shield effortlessly. Apologists explain that the shields are somehow tuned to block high-energy blasts but allow everything else to pass. Okay, then why didn't a few kamikaze droids loaded with explosives walk through and blow up the Gungans? Why didn't the tanks drive up, poke their barrels through the shields, and blast the Gungans? There are dozens of ways the droids could have improved their battle tactics but didn't. Yet, even with droid bungling, their superior technology eventually proves invincible: the Gungans face annihilation—then they win. And how does this miracle occur? When the droids' mother ship is destroyed, the droids shut down. Keep in mind that the droids use audible language over their radios to relay information and acknowledge commands. Aside from the illogic of quitting when winning, there was no one in the mother ship capable of giving the command to shut down, so why did they? Apologists answer that given the capability for independent action, droids might have rebelled against their leaders. Yet this doesn't seem to have been a problem for Hitler, Napoleon, Genghis Khan, or most other leaders of major-sized military forces. _Episode I_ clearly slipped from the state of grace established by the _Star Wars_ franchise. On the other hand, with Gungan battles and characters like the flop-eared Jar Jar Binks, the movie looks too much like a Bugs Bunny cartoon to ever be taken seriously. ### THE MOTHER-OF-ALL ISMP SPACE BATTLES _Episode II_ featured the usual assemblage of impossible gizmos, including small-sized craft capable of flying through the atmosphere, landing on their footprint, and making interstellar flights in less time than it takes to drive across Texas. When Senator Padmé Amidala (Natalie Portman) needed to go into hiding to avoid being assassinated, who does she entrust with her senatorial duty of defending the known universe from chaos? Jar Jar Binks (who, unfortunately, was not a candidate for assassination). Fortunately, we are otherwise spared from having to endure him. When Obi Wan Kenobi (Ewan McGregor) wishes to travel to a mysterious distant planet and can't find a record of it in the archives, he consults not the venerable Yoda, but a class of younglings (future Jedi). They give him their profound insight: "someone deleted it from the archives." Gosh, do you think so? And then there is the movie's theme: love is blind. Anakin Skywalker (Hayden Christensen) gets the girl, while incessantly whining and throwing tantrums. (What does Padmé see in this guy?) _Episode II_ offered nothing unique with respect to ISMP, but then it offered nothing that made it forgivable. The movie's worst break with its traditions was the inclusion of an unappealing main character—Anakin Skywalker, a mixture of good and evil. _Episode III_ resumed the downward spiral in its opening scene with what is, arguably, movie history's most ridiculous space battle. The evil General Grievous (voiced by Matthew Wood), along with a major armada of space craft, has somehow slipped into town and kidnapped the head of the Senate, Supreme Chancellor Palpatine (Ian McDiarmid). As the evil general, along with his armada, is escaping into the blackness of outer space high above the capital, Obi-Wan Kenobi and Anakin Skywalker, along with their own armada, race to the rescue. There's, of course, the trademark WWII aircraft carrier battle stuff, but it's embellished. Obi-Wan, Anakin, and company must fly through exploding flak that leaves little black clouds of smoke. Anywhere near the edge of outer space, these smoke particles would have an outward velocity and essentially no air resistance to slow them down since there's virtually no air. Under such conditions the smoke would almost instantly dissipate. Enemy forces counter attack with everything from vulture-like droids, to droids that fasten onto Obi-Wan's spacecraft and attempt to drill holes in it. Here's a thought: since bullets are cheap and droids are expensive, why not shoot a whole mess of bullets and have them drill the spacecraft? Large spacecraft using eighteenth century sailing ship tactics, deliver close range broadsides with twentieth-century-like cannons, ejecting empty shells out the back as they recoil. Who knows what they shoot, but whatever it is certainly explodes when it hits. Whether or not these were conventional cannons, blowing up an enemy ship at close range would likely be suicidal. The damaged ship's entire fuel supply— an amount designed to provide the humongous energy needs of interstellar travel—could detonate. During the battle Anakin Skywalker (Hayden Christensen) and Obi-Wan Kenobi (Ewan McGregor) board a huge enemy spacecraft in order to rescue Supreme Chancellor Palpatine. First, the two Jedi fly their fighters through an open entryway and crashland in a hanger room—without depressurizing the larger spacecraft! After much lightsaber slashing and yada-yada, they rescue the politician just in time for the seriously damaged ship to upend and fall straight toward the planet it had previously been moving away from in an outward, spiraling orbit. (What happened to its orbital velocity?) This dive sends everyone aboard, including the two Jedi, their trusty droid, and the slimy politician they've just rescued, sliding toward the falling end of the ship. Okay, maybe "a long time ago in a galaxy far away" they understood gravity well enough to pump it like central heating fluid through the floors of spacecraft. But if they did, why would the artificial gravity change direction with respect to the floor when the ship fell toward a planet? It seems like the artificial gravity's direction would remain perpendicular to the floor regardless of the ship's position. Keep in mind that the planet's gravity force never changed direction and cannot be "felt" by an observer on the ship, regardless of whether the ship is falling straight down or orbiting. Both are a form of free fall, which feels like zero gravity. To make things more complex, the spacecraft was attempting to escape into the vastness of outer space. To do this, it would have needed to accelerate until it exceeded escape velocity. The movie depicted the spacecraft as moving in a horizontal direction relative to the ground. As the spacecraft accelerated, its orbit would have tended to spiral outward. People onboard would have felt as though a force was pushing them toward the back of the ship in the opposite direction of the acceleration. An artificial gravity system would not only have needed to compensate for the feeling of zero gravity, but also for the effects of forward acceleration. That's some system! If the ship were damaged so that it started spiraling downward toward the planet, and the artificial gravity was disrupted, the occupants would have floated as though in zero gravity conditions. Luckily, General Grievous gets the ship back under control, but following another round of yada-yada and light saber slashing, along with taking additional hits on his ship, he decides to abandon it. In the process he jettisons all the escape pods, leaving Palpatine, R2D2, and the two Jedi stranded as the ship once again takes a nose dive. On descent and reentry the ship—now piloted by Anakin Skywalker—glows red amid a superheated cloud of plasma, breaks in half, and catches fire—yet lands at the nearest spaceport where the plucky rescue team and freed hostage depart uninjured. (If only NASA guys watched movies, just think what they could do.) Can the miraculous descent be explained away by the ship's shields? Not likely; they were at least partly disabled when the Jedi boarded. Can such a wonder ever be explained? Why, yes, it must be the midichlorians! Okay, the _Star Wars_ apologists say that the enemy's armada was not really in orbit but in the extreme upper atmosphere— accounting for the contrast of a black sky with daylight conditions directly below—traveling at suborbital speed. However, the actual kidnapping would have been done by a small group of covert operators. They would have killed Palpatine's body guards, and most likely have been immediately detected. With luck and split-second timing, they could have made their way to a nearby space craft (no doubt a Cosmic Toyota) and blasted off, but not before attracting a swarm of police pursuers. Fearing they'd hit Palpatine, the police would have held their fire, giving the abductors time to travel some distance from the surface. At that moment the previously undetected hostile armada would have dropped out of hyper space (assuming there was such an option) into orbit, and promptly zapped all the pursuers, enabling the abduction to succeed. Needless to say, the armada would be in serious jeopardy and not want to slow down or linger any longer than absolutely necessary before making its way back into space. The idea that an entire armada would land on the surface to kidnap a single politician is preposterous. Even if the armada temporarily dropped below orbital velocity in the extreme upper atmosphere, staying in a horizontal position without falling toward the surface would require aerodynamic lift or downward thrusters. The thrusters don't seem to be there, leaving aerodynamic lift as the only possibility, but at the edge of the atmosphere there's almost no air. A large spacecraft would have to be going extremely fast and be highly aerodynamic to have any lift at all. If the craft intended to escape into outer space, as mentioned earlier, it would have to accelerate to a speed higher than that required for a circular orbit in order to spiral outward in an ever increasing orbit. Keep in mind that the apparent lack of gravity for orbiting objects is not caused by being outside the atmosphere, but by having the object moving at the correct speed, in the correct direction, for the given distance above the surface. In theory a spacecraft could be in orbit a centimeter away from the surface, if the planet were perfectly spherical and had no surface imperfections such as mountains. Even if the planet had an atmosphere, a spacecraft with powerful thrusters could overcome air resistance and give its inhabitants the feeling of zero gs just by traveling at the correct orbital velocity in a horizontal direction. People in an outward spiraling spacecraft would feel as though the weight force were directed backwards, in the opposite direction of the craft's horizontal velocity. With a very slow outward spiral, the apparent weight force would be mild or even imperceptible. The sensation of weight would otherwise not be present. In the extreme upper atmosphere, opening an entryway large enough to admit fighter craft would not only partly depressurize the larger spacecraft, but likely destabilize it. Air rushing out would act like a thruster which could roll the craft upside down or turn it sideways. If the craft were moving at high velocity in the upper atmosphere, the opening itself would cause a horrendous change in aerodynamic properties, possibly enough to send the craft out of control. When the craft fell it would still not have fallen straight down, thanks to its high horizontal velocity. Assuming that the craft was free falling, and not wildly spinning or tumbling, its occupants would still have felt weightless during the fall. However, the ships thrusters were firing during the fall, which could have caused the equivalent of a power dive, accelerating the ship downward at a faster rate than the acceleration of gravity. Under such circumstances, people and objects in the ship would have appeared to "fall" upwards toward the tail of the ship. When General Grievous pulled out of the dive, the craft's occupants would have been subjected to accelerations greater than one g. Anything not tied down would have likely slammed into walls. ### THE EVIL DATA AND BAD DUNE BUGGY It would be nice to say that _Star Trek_ has retained its originality and remembered that it belonged not just in an action genre, but the last movie installment, _Nemesis_ [RP] (2003), gives pause. The movie forgot what an original—let alone, good—script was, and offered a rehash of older _Star Trek_ plots—in particular, _The Wrath of Khan_ (1982).This time Khan was replaced by a megalomaniac Captain Picard clone called Shinzon (Tom Hardy), who, aside from his shaved head, bore no resemblance to Picard. At best, Shinzon resembled a younger Picard's evil twin. Shinzon takes over Romulus and decides—what else—to annihilate humanity. (If he sounds strangely like a machine, it's because he has the charm of a wood chipper.) On the way to Romulus, Data finds a missing older brother called B4 (he was made before Data), and completely forgets what happened previously when he found his last missing brother Lore—his evil twin. So what does Data do? Why, of course, he downloads all his memory banks into B4, including exhaustive details of how the Enterprise operates—no risk there. Surprise, surprise, B4 turns out to be a quisling. _Nemesis_ doesn't feel like a _Star Trek_ installment—superstoic Klingon-tough-guy Warf, at a wedding celebration, whining about the side effects of Romulan ale? Give us a break. The movie clearly forgot that the franchise is not about hangover clichés, fight scenes, and other mindless crowd pleasers, but about the human condition and the future impact of technology on the mental and material aspects of our lives. _Nemesis_ serves up mostly nonstop action, with everything from hand-to-hand combat, to a lengthy spacecraft battle. The movie even includes a highly contrived "car chase scene." When the _Enterprise_ detects B4's signals emanating from a distant planet, Picard thumbs his nose at regulations and drives around the planet's surface in a newly created dune buggy, searching for the signal's source. And why does he insist on personally driving a dune buggy instead of sending others in a shuttle? Is he breaking rules to save his crew or to successfully complete his critical mission? Is he breaking them in service to a higher cause or morality? No, no, and no; he's breaking them because it's more fun. Naturally, bad guys in similar dune buggies give chase, along with copious quantities of poorly aimed blaster fire and wrecks (bad guys only). The away team survives by driving off a cliff, flying through the air, and miraculously landing in the back of their shuttle craft, which has been maneuvered into just the right position by Data using a handheld remote. ### THE MOST FORGIVABLE Both _Star Trek_ and _Star Wars_ have descended into the depths of ISMP and, at times, forgotten their breathing gear. The _Star Trek_ franchise with ten movies and five TV series, compared to six _Star Wars_ movies, is the more vulnerable of the two franchise based on size alone. Indeed, _Star Trek_ has had more problems with inconsistent script quality than _Star Wars_ , but this is not necessarily a compliment. Following the consistently good quality of the first three _Star Wars_ movies, the last three have been consistently disappointing. Overall, the _Star Trek_ universe and story lines have been more diverse, and its exploration of future scientific innovations more thought provoking and detailed than those of the _Star Wars_ franchise. In their own way, both franchises are gemstones, but _Star Trek_ has the edge on deserving forgiveness for ISMP slipups, although its edge is razor thin. ## CHAPTER 20 ## ALL-TIME STUPID MOVIE PHYSICS CLASSICS: ### "They Said the Physics Were Impossible . . ." ### THE PINNACLE OF BADNESS It's easy to make a movie with bad physics, but to reach the pinnacle—beyond the merely insultingly stupid—of classically stupid requires artistry. Though many aspire, few achieve. Clearly discernible technical blunders, such as disobeying the first law of thermodynamics, are critical to this category, as is the generous use of bad physics' clichés. Creative physics badness is even better, but the movie must also possess illogical problem solving, inconsistency, and out-of-character or stereotyped scientists, engineers, and other sorts of techies. A few pithy but ridiculous lines of dialogue help immensely, but in the end nothing makes physics flaws shine brighter than a movie which takes itself seriously and is monotonous, clichéd, or lifeless from an artistic standpoint. Mere illogic or exaggeration is insufficient; a true classic must be scientifically unfixable and artistically bland (with the exception of spectacular special effects—these help). ### TERRESTRIAL WANNABES The _Matrix_ flirted with becoming an insultingly stupid movie physics (ISMP) classic, but failed. Its explanation of why the machines keep humans as a power source (see Chapter 3) shredded the first and second laws of thermodynamics, and ranks as the ISMP classic for first and second law blunders! The movie followed with mindless nonstop action scenes, but alas, it failed to reach overall ISMP classic status. The first half of the movie was an artistic and science fiction masterpiece, which subsequently spoiled all hope for ISMP classic status. _Matrix_ sequels fared better, especially the third which served up the ISMP classic of indoor battle scenes: the loading dock battle described in Chapter 5. The unprotected warriors strapped to gigantic robotic devices (called APUs) would have slaughtered themselves with ricochets and falling debris by blasting an impossibly high number of automatic cannon shells toward the concrete roof over their heads. Survivors would have succumbed due to inhaling the smoke from cannon blasts and collateral fires set by exploding shells. Alas, even this nonsense was not enough to grant the movies ISMP classic status. The pithy line, "they said the physics were impossible . . ." (certainly an ISMP classic), which was followed by defying the conservation of momentum, not to mention the first and second laws of thermodynamics, immediately identified _Eraser_ [RP] as a contender. But honestly, even given its physics flaws, the movie has Arnold Schwarzenegger, and who can dislike the big guy. There's a reason he was elected governor and it probably wasn't just his super-duper plan for saving California. The movie was a viable action adventure and its flaws, though grievous, could have been fixed with little (if any) negative impact on the story. The movie failed to achieve the elevated ISMP classic status because its main premise was just not absurd enough. _The Day After Tomorrow's_ trailer alone created significant Internet buzz. Could this be the one, the ISMP colossus? Certainly, early buzz is a good sign. The special effects budget— a major component of any ISMP contender—was huge. The giant wave crashing against the Statue of Liberty, the LA tornados, and the feeble attempts at dialogue all contributed to its candidacy. It had the enchanted tent. When the movie's hero and a group of friends trudge through a once-in-the-history-of-Earth blizzard to rescue the hero's son, they find solace in the enchanted tent.The wind may howl and the snow may drift, but all is well in the enchanted tent. One can't even see one's breath. This movie looked like a contender. But once again, it was mostly mere exaggeration—nothing especially creative. ### DOWN-TO-EARTH OUTER SPACE TRAVEL WANNABES One might think that near-Earth space travel would offer few opportunities for ISMP classic status. After all, humanity has traveled to the Moon, built space stations, and flown the Space Shuttle. Such ventures have become almost routine. Still, it seems that ISMP opportunities abound even in this almost down-to-Earth environment. _Armageddon_ certainly rose to the ISMP challenge. It contained one physics flaw after another, mixed with improbability and illogic. It only took a small piece of loose insulation to fatally damage the Challenger, and subsequently over two years to get ready for the next shuttle launch. So how could we possibly train an inexperienced team, have a duel space shuttle launch, land a shuttle on an asteroid, save humanity, and safely return all in eighteen days? The whole idea that humanity can sit and do nothing to prepare for an asteroid strike disaster, then go out and save itself with a puny nuclear bomb blast against a Texas-sized asteroid—all in a matter of weeks—is worse than farcical, it's dangerous. The movie positively overflows with ISMP and improbability.Yet, many of the flaws were simply gross exaggeration. A good number were fixable, and besides, the characters were (unfortunately) likable. _Red Planet_ (RP) and _Mission to Mars_ (MM) ventured a little further into space and contained numerous examples of ISMP. Both have spacecraft with poorly conceived artificial gravity (AG) scenes. MM's AG is merely bad, whereas RP's AG is downright ugly (see Chapter 15). MM offers up an excellent ISMP scene in which a group of astronauts floating in orbit around Mars attempt to rescue Woody Blake (Tim Robbins), who has drifted off, and is at the edge of a rapidly decaying orbit and certain death. To reach him, his would-be rescuers have to continually use their thrusters and are flashed many low fuel warnings by their wrist-mounted computers. But wait, isn't this outer space? What happened to Newton's first law? Once in motion they would have no further need to use thrusters until it was time to stop. RP offered its impossibly flammable alien life forms and homicidal robot, but neither movie had truly groundbreaking levels of ISMP. _Independence Day_ brings interstellar space travel down to Earth as aliens arrive and attempt a hostile takeover. Even if the movie's premise were accepted—that gargantuan spacecraft could travel to Earth as depicted—when the spaceships were shot down, the resulting explosions as they fell to Earth would destroy the planet's environment (see Chapter 11). There'd be no happy ending. But although the movie delivers some scientific whoppers, it lacks the nonstopbadness that the ISMP all-time classic should possess. _War of the Worlds_ also showed promise with its alien invasion. Making a gigantic mechanical vehicle—filled to capacity with nasty aliens and high-powered weapons—balance, let alone walk around on the spindliest of legs, would be some trick. Yet, not only did these massive mechanical monsters move, they did so after being stored under a few feet of soil for eons. (Wow, that's some set of batteries!) What's more, they were stored undetected in locations that ended up in the middle of major cities. Did no one dig holes? Did no one have a metal detector? Were there no curious nerds around? After all that planning and preparation for invading and inhabiting an entire world, these super-intelligent aliens apparently neglected to do an environmental study. What were they thinking? Did they really believe they would be safe? Did they misinterpret all the TV ads for cold remedies and antibacterial soap—intercepted by their version of SETI? Furthermore, when the aliens do show up in their tripods and start killing everyone, why would a human such as Tom Cruise think he would be safe by fleeing to Boston? Wouldn't heinous aliens bent on turning humanity into fertilizer start with the most dangerous group of all—MIT students? These people are not just nerds, they're uber-nerds. Give them free time and a large-domed building, and for entertainment they do things like put police cars and Wright Brothers' airplanes atop it, or morph it into various new forms, such as a giant pumpkin or an oversized robot. Imagine what they'd do with a bunch of spindlylegged tripods! But disrupting the power for their cool toys (computers), closing down their calculus classes, and threatening the continued existence of humanity is enough to make them mad. Do the invaders recognize this danger and respond by putting the Cambridge and Boston area at the top of their destruction list? No! These aliens are dumber than Tom Cruise's movie character. They deserve to die. Alas, though the movie offers plenty of ISMP, there are moderating influences. The tripod engineering problems could conceivably be solved by a super-advanced species. Such intelligent critters could possibly even screw up one or two important details when planning an invasion; certainly, such things have happened on Earth. After all, humans—upon sinking the unsinkable Titanic—discovered, to their chagrin, that not only had they failed to plan for enough lifeboats, but had failed to fill even the ones available. In total, _War of the Worlds_ just doesn't measure up. Many of its flaws are simple illogic, some are forgivable, and none are creatively spectacular. ### AND THE WINNER IS . . . It seems the choice for the ISMP classic would be tough amid such competition and yet it isn't. There is one that stands at the top of the heap, that is the pick of the pack, and that leads the rest. As mentioned in Chapter 1, its premise is absurd, its science unfixable, and its artistry uninspiring—its name: _The Core_. The movie explains an impending world horror during a meeting of top military brass, in which geophysicist Dr. Josh Keyes (Aaron Eckhart) makes a presentation. He tells the military that the core's rotation is messed up and about to cause Earth's magnetic field—all that stands between us and microwave radiation from the sun—to disappear. And why should this cause immediate panic and distress? Keyes, always one to gauge his audience, keeps the explanation moronic: he lights the aerosol from a can of hair spray and torches a peach representing Earth. A flaming peach? There's a way to impress. Never mind that the audience—leaders of an organization whose technology level and research budget makes NASA look like a club for hobbyists—might actually prefer a few scientific details. Never mind that Earth's magnetic field does nothing to reduce solar microwave radiation arriving at the Earth's surface. Microwaves are a minor part of the sun's total radiation that hit us, magnetic field or not. Never mind that the planet has never been incinerated when it has previously experienced temporary magnetic field loss during the magnetic pole flipflops that occur about every hundred thousand years. Never mind all the illogic and ISMP, a burnt peach just plain stinks. Okay, the Sun does periodically emit dangerous quantities of plasma during solar flares, which are made up mostly of protons and electrons with high amounts of kinetic energy. These particles can, indeed, be deflected by magnetic fields. However, even without a magnetic field the atmosphere would still shield us from most of this radiation. Over hundreds of millions of years the lack of a magnetic field could be disastrous. Mars, for example, lacks a magnetic field, which is thought to be the reason it also lacks an atmosphere. Mars' unprotected atmosphere was apparently slowly blown away by solar winds. The movie continues with other insightful glimpses of scientific and technically trained professionals. Ask any group of high school students to name a recent Nobel Prize-winning physicist and you'll most likely get a blank stare. When it comes to the pop culture scene, world class scientists are a no-show. So, Dr. Zimsky (Stanley Tucci) is, of course, depicted as having a massive ego, star appeal, and the look of a 1930s movie star as he signs autographs and is hounded by a bimbo.There's the genius inventor who lives alone on a vast facility in the middle of the desert and invents technological miracles, all without assistants or outside funding. There are the astronauts who engage in juvenile arguments about who should land the Space Shuttle—an almost entirely automated task. There's the likable philosophical French scientist, with that oh-so-engaging accent—who is also a nuclear weapons expert—who provides just the right amount of sadness when he dies. And, of course, there's the quintessential computer geek, Rat (D. J. Qualls) who can not only hack into a supersecret government facility, but can take over the U.S. power grid, all in a matter of minutes via the Internet. How does this plucky group of technical people solve the movie's dire nonproblem? Why, of course, by traveling in a manned craft that bores into the planet, and restarts Earth's core with a nuclear firecracker (see Chapter 11). An unmanned craft could never suffice. _The Core_ is a wonder. It would take an entire book to cover all its ISMP details. Will it ever be surpassed? Who can say? But certainly, at least for the foreseeable future, it deserves special status as the ISMP classic. It's so bad, it's good. ## NOTES . "The Core, A Filmbug Special," <http://www.filmbug.com/specials/thecore>, 3/28/2003. . Feynman, Richard, _Six Easy Pieces_ , Perseus Books Group, 1996), 69. . Frank L. Lambert, Professor Emeritus, Occidental College, "The Second Law of Thermodynamics," <http://www.secondlaw.com>. . Ohba, Mitsuru, and Benson, John. "Introduction: About the A-Bomb," <http://www.csi.ad.jp/ABOMB/data.html>, © 1998 by A-Bomb WWW project. . "To the Moon," NOVA, <http://www.pbs.org/wgbh/nova/transcripts/2610tothemoon.html>, original PBS airdate: July 13, 1999. . "The Numbers—U.S. Movie Market Summary for 2006," <http://www.the-numbers.com/market/2006.php>, 1997–2007 Nash Information Services, LLC. . Buell, Harold L, _Dauntless Hell Drivers_ (New York: Orion Books, 1991) 37. . Jennings, Ed, "Crosley's Secret War Effort: The Proximity Fuze," <http://www.navweaps.com/index_tech/tech-075.htm>, updated February 1, 2001. . "Could a seat belt have saved Diana?" <http://www.cnn.com/WORLD/9709/05/crash.analysis/>, CNN, original air date: 9/5/1997. . "The Freefall Research Page," <http://www.greenharbor.com/fffolder/ffallers.html>, © 2001–2003, Green Harbor Publications. . "How to jump into water from a height," <http://www.everything2.com/index.pl?node=How%20to%20jump%20into%20water%20from%20a%20height>, updated 11/14/2002. . "Could a seat belt have saved Diana?" <http://www.cnn.com/WORLD/9709/05/crash.analysis/>, CNN, original air date: 9/5/1997; and "Acceleration that Would Kill a Human," The Physics Fact Book, edited by Glenn Elert, <http://hypertextbook.com/facts/2004/YuriyRafailov.shtml>. . Ohba, Mitsuru, and Benson, John, "Introduction: About the A-Bomb," <http://www.csi.ad.jp/ABOMB/data.html>, © 1995, 1996, 1997, 1998 by A-Bomb WWW project. . Levoy, Jill, and Vanessa Hua, "Fighting Bullets on New Year's Eve," _Los Angeles Times_ , 12/30/1999. . Yee, Danny, "Average Weight of a Human Head," <http://danny.oz.au/anthropology/notes/human-headweight.html>, updated 7/8/07. . Zavada, Roland J, "Dissecting the Zapruder Bell & Howell 8mm Movie Camera," <http://www.jfkinfo.com/zavada1.htm>, updated 10/24/98. . "Video of Richard Trott shooting a melon," <http://mcadams.posc.mu.edu/melon-sh.mpg>, accessed 7/8/07; McAdams, John. "Dealey Plaza," <http://mcadams.posc.mu.edu/dealey.htm>, accessed 7/8/07; Penn & Teller, "Jet Effect," <http://video.google.com/videoplay?docid=745248745546892501>, accessed 7/8/07. . Meyer, Dale K, "Secrets of a Homicide," <http://www.jfkfiles.com/jfk/html/intro.htm>, accessed 7/8/07; Jennings, Peter. ABC News, _The Kennedy Assassination—Beyond Conspiracy_ DVD, 2004. . Penn & Teller, "Jet Effect," <http://video.google.com/videoplay?docid=745248745546892501>, accessed 7/8/07. . McAdams, John, "The Assassination Goes Hollywood," <http://mcadams.posc.mu.edu/jfkmovie.htm>, accessed 7/8/07; and Reitses, David. "The JFK 100—One Hundred Errors of Fact and Judgment in Oliver Stone's JFK," <http://www.jfk-online.com/jfk100menu.html>, accessed 7/8/07. . Posner, Gerald, _Case Closed, Lee Harvey Oswald and the Assassination of JFK_ , ([AU: Please provide place of publication]:Anchor Books, 2003), 273–284. . The apparent zero gravity occurs because the orbiting object is in freefall. If an object has a horizontal velocity, it will fall in a parabolic path and hit the ground, but if the horizontal velocity is high enough and there's a significant gravity force to act as a centripetal force, the object will fall in a stable orbit and never hit the ground (assuming no air resistance). . "California Tornadoes 1880–2000," <http://www.tornadoproject.com/alltorns/catorn.htm>, the Tornado Project, accessed 7/8/07. . "The Staten Island Web," <http://www.siweb.com/Statue.html>, accessed 7/8/07. 25. Ohba, Mitsuru, and John Benson. "A-Bomb WWW Museum," <http://www.csi.ed.jp/ABOMB/data.html>, © 1995, 1996, 1997, 1998 by A-Bomb WWW Project. . "If the Polar Ice Caps Melted, How Much Would the Oceans Rise?" How Stuff Works Web site, <http://science.howstuffworks.com/question473.htm>, (c) 1998–2007 HowStuffWorks, Inc.; "Volume of Earth's Polar Ice Caps," The Physics Factbook, edited by Glenn Elert, written by his students. . <http://hypertextbook.com/facts/2000/HannaBerenblit.shtml>, 2003; and "Power Density of Solar Radiation," The Physics Factbook, edited by Glenn Elert, written by his students. <http://hypertextbook.com/facts/1998/ManicaPiputbundit.shtml>, 1998. . Gleick, James, _Chaos: Making a New Science_ , ([AU: provide place of publication]: Penguin Books, 1988). . "What is the Temperature at the Tip of a Lit Cigarette?" Physics and Astronomy Online, <http://www.physlink.com/education/askexperts/ae1.cfm>, © 2007 PhysLink.com. . "Ignition Temperature of Gasoline," The Physics Factbook, edited by Glenn Elert, written by his students, <http://hypertextbook.com/facts/2003/ShaniChristopher.shtml>, 2003. . "Reducing the Health Consequences of Smoking—25 Years of Progress: A Report of the Surgeon General," 1989 Executive Summary, 79. 32. Gustin, Emmanuel, "The Fighters," <http://users.skynet.be/Emmanuel.Gustin/fgun/fgunfi/html>, © 1998–1999. ## INDEX A Acceleration, 147 constant, 140 injuries from, 158 measure of changing velocity of, 147 requirement, high, 151 in _Star Wars Episode III_ , 298 Action hero, 17–21 and ammunition, weight of, 16 in _The Matrix Revolution_ [NR] (2003), 18–20 and machine gun overheating, 16 Action-reaction force pairs, 84, 184 ground and human, 232–233 in _Lethal Weapon_ [PGP-13] (1987), 184 as normal force, 231–237 three qualifications for, 184 Aerodynamic lift, 139 Air compression, 263 in building during tsunami, 262–264 Aircraft , 122 height of, 122 range of, 122 velocity of, 122 Air resistance, 139, 192, 302 and shrapnel, 70–72 approximated, 142 exerting horizontal force, 125 in space, 72 and projectile trajectory, 72 in _Star Wars Episode III_ , 298 Air pressure escaping into space, 95 in spaceship, 75 Air resistance and downward acceleration by gravity, 125 All-time stupid movie physics classics, 308 _Armageddon_ , 309–310 _Eraser_ , 308 _Independence Day_ , 310 _Mission to Mars_ , 310 _Red Planet_ , 310 _The Day after Tomorrow_ , 309 _The Matrix_ , 308 _War of the Worlds_ , 310 worst movie physics winner, 312–313 American Film Institute's 100 Greatest Movies Web site, 237 Antiaircraft cannon's projectile fired upward arc of projectile, 122 downward force of gravity on projectile, 122 Antimatter, 191, 288 _Apollo 13_ [GP] (1995), 229–232 vomit comet, 120, 121, 229–230 Area, 53 in _Honey, I Shrunk the Kids_ [NR] (1989), 52–57 _Armageddon_ [RP] (1998), 99–100, 167–170, 213–220, 222–224, 238 asteroid, 167 artificial gravity, instant, 238–240 Artificial gravity, 231, 232–233, 238–240 basis, 232–234 centripetal acceleration, 233 centripetal force, 233 creating, 231–242 instant, 238 mass 233 Artistic license and rule breaking, 2 as ambulance license, 2 Asteroid in Armageddon, 167–170 Asteroid-produced atmospheric tides, 223 Asteroid strike, 101 Atmospheric tides, asteroid-produced, 223 Attractive force, in _Lethal Weapon_ [PGP-13] (1987), 179–184 Attractive force of glass, 179 B _Band of Brothers_ , 112 Bernouli's equation and velocity, 262 _Blackhawk Down_ [GP] (2001), gunfights and movie physics, 28 Blast wave, 166 from falling spaceship, 165 Bomb, and downward-sloping parabolic path, 125 Bomb drop calculations, 120 Bombs-fall-straight-down myth in _Pearl Harbor_ , 117 Building collapse, 264, 267 potential energy from, 267 reasons for, 264–268 released energy from, 267–268 Bullet drift, horizontal, 26 Bullet penetration in _Young Guns II_ [PGP] (1990), 78–79 Bullets air resistance and, 174 counting shots, 203–208 incendiary, 282 in outer space, 175 kinetic energy, 280 lighting gasoline, 274 motion of object passed through, 201 speed of, 174 tracer, 282 Bullet trajectory and geometry of aiming sniper rifles, 25–27 Bus jump, 133–139 center of mass, 134 downward acceleration due to gravity, 136 ramp and ramp angel, 134, 136 takeoff velocity, 136 torque to rotate, 135 Butterfly effect, 269 C Car, airborne air cannon, 255 kicker plates, 254–255 _Matrix II_ , 255 net force, 254 Carnot efficiency heat loss, 39 friction, 39 Cars as weapons, 175–176, 280 kinetic energy, 176 _Cellular_ [PGP] (2004), 250–251 Center of mass, 233, 245–246 in martial arts, 246 and pivot point, 245 and spear throwing, 249–251 Center of rotation, 233 Centripetal acceleration and aircraft, 159–160 fatal turns by spacecraft, 158–160 Centripetal force, 233, 236 Change of motion, 67 Changing velocity and acceleration, 147 Chaos theory, in _Jurassic Park_ , 270 Cigarettes as lighters, 273–290 Circumference, 233 _Collateral Damage_ [PGP] (2002), 114 Collision with concrete dome falling debris, 77 ricochet, 77 Combustion and free radicals, 274–275 Comic book adaptation, 5 Compression in _Honey I Blew up the Kids_ ,62 Conservation of momentum, 253 with handgun, 252 Constant density approach in _Honey I Blew up the Kids_ , 56–63 Counting gunshots in _Dirty Harry_ ,18 Critical velocities related to gravity, 217 Cyclist jump, 129 downward-sloping parabolic path, 125 D D-cell batteries, 43 _Deep Impact_ [PGP-13] (1998), 213, 220–222 Density, 52–63, 156, 214 falling, 156 _Honey I Blew up the Kids_ , 56–63 _Honey I Shrunk the Kids_ , 52–57 _Dirty Harry_ [PGP] (1971) counting gunshots, 18 and movie mathematics, 18 Distance, 108, 196 explosions, 108 of asteroid, 223 Distortion of judgment about shooting, 202–203 Distribution of force, 94 Downward acceleration by gravity and air resistance, 125 Driving geometry, 28–30 E Elastic stability, 61, 265 and building collapse, 266–267 experiment, 62 in _Honey I Shrunk the Kids_ , 52–57 Empire's Death Star, 103–104 Energy concentrated versus dispersed, 42 and conservation, 290 Equal and opposite "touching force," 86 _Eraser_ [RP] (1996), 185–190 Explosion propagation effects, 101 and blast front, 101 and electromagnetic pulse, 102 Explosions in _Collateral Damage_ , 114 and resulting fireball, 108–113 and infrared radiation (IR), 111 in shafts and tunnels, 113–114 outrunning, 108 shock wave from, 102, 111 F Falling, 153–156 bullets, 173 density, 156 gravity constant (g) and, 172 humans, 171–172 spaceship, 165 in _The Mexican_ , 175 in _XXX State of the Union_ , 155 Fantasy cartoons, 5 Fighter aircraft (machine guns act as thrusters), 90 Fire, conditions needed for, 274–275 Fireball from explosions, 108–113 First law of thermodynamics, 34 and _A.I.: Artificial Intelligence_ ,44 and bullet penetration, 79 conservation of energy, 34 converting mass into energy and back, 36 E = MC2, 35 in _Honey I Shrunk the Kids_ , 52–57 in _The Hulk_ [NR] (2003), 36 in _Spider-Man_ ,37 Force, 215 normal, 231–237 Fragmentation grenade, 112 and shrapnel, 113 Free-body diagram and Newton's third law, 84–86 Free radicals, 274–275, 284 combustion of , 275 oxygen, contact with fuel, 284 Friction and momentum, 181 in _Lethal Weapon_ , 181 Friction force, in _Speed II: Cruise Control_ , 150 Fuel, 299 in _Star Wars Episode III_ , 298 Fuel, mass of, 46, 192 in _A.I.: Artificial Intelligence_ ,46 required for liftoff, 192 for robots, 46 Fusion process, powered by, 288 Enterprise's impulse engines are thrusters, 288 G Galileo, rate of fall independent of mass, 138 Gasoline and flammable temperature range, 277 Geometry of driving, 28–30 Getting gunfights right in _Blackhawk Down_ ,28 Glass attractive force of, 179 safety, laminated, 87–89 Gravitational attraction in _Armageddon_ , 169 Gravity, 139, 224 artificial, 160, 231–242 direction of, 225 sensation of, 299–300 in _Star Wars Episode III_ , 298 in _The Core_ , 225 Gravity acceleration and air resistance, 125 Grenade, white phosphorous, 112 gs, 151–153, 224, 230 and falling, 172 and fatal turns by spacecraft, 158–160 and feeling of zero gravity, 302 inside Earth, 215 on planet, moon, or asteroid, 214–215 in _Speed II: Cruise Control_ , 150, 153 strength of, 215 as unit of acceleration, 152 Gun recoil and acting, 89–90 of .50-caliber machine gun, 90 in _Pearl Harbor_ ,90 Gunshots, counting, in _Dirty Harry_ ,18 H High acceleration requirement, 151 High-energy particle beams behavior in space, 73 deflection of, 75–76 and magnetic field shield, 74 straight trajectory of, 73 High pressure and spaceship falling, 165 High temperature, 166 and spaceship falling, 165 High velocity impact in space, 72 _Honey I Blew up the Kids_ [NR] (1992), 56–63 compared to large and small humans, 57–58 constant density approach, 59 density, 58 _Honey I Shrunk the Kids_ [NR] (1989), 52–57 remove molecules, 53–54 Hulk jumping 140 I Incendiary bullets, in _Raiders of the Lost Ark_ , 282 _Independence Day_ [RP] (1996), 164–168 blast wave, 166 high pressure, 166 high temperature, 166 wind velocity, 165 Indoor gun battles, 76 _The Matrix Revolution_ ,76 Inertia, 196–199 rotational, 196–199 Inertial dampers, 160–161 _Star Trek_ , 160 Inter- and intramolecular space, 56 _Honey I Blew up the Kids_ , 56–63 J Japanese zeros' cannons recoil complicates aim, 90 _JFK_ [RP] (1991) 27, 195, 203 Oswald's gun and skill, 27 Joule-Thompson effect, 75 Jumps and Hulk, 140 Jump vehicle. See Vehicle jump, most famous _Jurassic Park_ [PGP-13] (1993), 270 K Kennedy's head motion, analysis of, 196–200 _King Kong_ [PGP-13] (2005), 60–61 Kinetic energy, 169, 188, 263, 280, 290 bullet, 280 falling bullets, 173 falling humans, 171 heat, 280 in _Armageddon_ , 169 in space debris, 289–290 in _The Core_ , 171 in tsunami, 263 loss of, 280 Knife throwing, 247–249 L Laminated safety glass, 87–89 Lasers, behavior in space, 73 Law of conservation of momentum, 180 Law of inertia: mass resists a change in motion, 67 _Lethal Weapon_ [PGP-13] (1987), 179–184 Lift, 301, in _Star Wars Episode III_ , 301 Lorentz factor, 187 M Machine guns acting as thrusters for fighter jets, 90 Magnetic field rail-gun, 188 as shield, 74 Magnetic field, Earth's and earthquake weapon in _The Core_ [XP] (2003), 9–10 Magnetic field shield, 74, 75 high velocity charged-particle beam, 74 Make-believe movie history in _Pearl Harbor_ [PGP-13] (2001), 11–13 Martial arts and Newton's third law, 92 Mass, 54, 192, 215, 233 acceleration, 192 in _Honey I Shrunk the Kids_ , 52–57 at rest, 187 Mathematics, super-tsunami, and Bernoulli's equation, 261–262 _Mission to Mars_ [RP] (2000), and spaceship rotation, 238 Models of physics, 34 Momentum, 180, 290 backward, 187 of bullets, 180–181 conservation of, 196, 200–202 forward, 187 and friction, 181 human, 180–181 in _Lethal Weapon_ , 180–185 need for conservation of, 290 rotational, 196–199 shooting victim's, 183 shooter's, 183 speed of light, 187 Motion of target, 26 Movie mathematics, 18–19 Movie physics done right in _2001: A Space Odyssey_ , 237 in _Band of Brothers_ , 112 in _Cellular_ , 250 in _Pushing Hands_ , 93 in _Saving Private Ryan_ , 112 in _The Road to Perdition_ , 79 Physics models, 34 Movies as good physics teaching tools, 2 Muscle strength to weight ratio in _King Kong_ , 60–61 N NASA's first working space walk, 96–98 and Newton's third law, 96 Net force, 254 car, airborne, 254 pushing and resistance forces, 68 Net torque, 245–246 and rotational acceleration, 245 Newton's first law, 68, 151 in _Speed II: Cruise Control_ , 151 Newton's second law, (second law of thermodynamics), 151 Newton's third law in _2001: A Space Odyssey_ ,94 and boxers, 83 and glass, 86 explained, 84 gun recoil, 89 shooting victim, 183 in _Star Wars Episode II_ ,91 Yoda's force on the rocks equal to their weight, 91 Newtonian martial arts, 92 Normal force, 231–237, 232–237, 236 artificially produced, 236 centripetal force, 236 in space, 236–247 sensation of weight, 235 Nuclear bomb, 103, 163, 170 in _Independence Day_ [RP] (1996), 164 in _The Core_ , 170–171 used to save earth, 103, 163–165 O Opposing forces (equal and opposite), 84 Orbital velocity, 301 in _Star Wars Episode III_ ,30 Outrunning fiery explosions, 108–113 P Painters breaking laws of physics, 45 Parody and bad physics, 5 Pearl Harbor [PGP-13] (2001), 90 bombs-fall-straight-down myth, 117 and make-believe movie history, 11–13 and physics of bomber flight, 12 and physics of dog-fighting, 12 Perpetual motion machine, and frictionless environment, 40 Physics clichés becoming obsolete, 7 Physics of bomber flight in _Pearl Harbor_ ,12 Physics of bombing, 117–124 and bomb's velocity, 119 and downward-sloping parabolic path, 119 and gravity, 119 Physics of dog-fighting in _Pearl Harbor_ ,12 Potential energy, 171, 267 and building collapse, 267 and falling humans, 171 President Kennedy assassination, 203–210 Pressures and temperatures, 264, 265 in building collapse, 265 from water depth, 263–264 in _Honey I Shrunk the Kids_ , 52–57 in _The Core_ [XP] (2003), 9–10 in _The Day After Tomorrow_ , 260 in _Star Wars Episode III_ , 298 and type of external load, 264 of water, 260 Projectile trajectory, 73–79 deterioration due to gravity, 72–78 downward curving, 73 WWII versus space, 73 Properties of similar triangles in handgun shooting, 20 _Pulp Fiction_ [PGP] physics precision and artistic ambiguity, 21 movie physics done right, 21 _Pushing Hands_ [GP] (1992), 93 R Radioactive contamination, 52 Radius, car turning in _The Italian Job_ , 28–30 _Raiders of the Lost Ark_ [PGP-13] (1981), and incendiary bullets, 282 Rail-gun, 185–190 Realistic space battles and spaceship depressurization, 75 Reality, feeling of, 6 Recoil as backward momentum, 183 calculating, 187 cause of, 186 in _Eraser_ , 185–190 of rail-gun, 185–190 in _Star Wars Episode III_ , 298 _Red Planet_ [RP] (1998) artificial gravity, 238–240 burning bugs, 283–285 Repulsion forces between atoms, in _Honey I Shrunk the Kids_ , 52–57 Resistance, 280, 302 cars, 280 in outer space, 71 of body in _Eraser_ , 189 Revolutions per minute (RPM), 233 Ricochet in indoor gun battles, 76 in _The Matrix Revolution_ ,76 Rifle bullet trajectory, 23–27 detuning to different vibration pattern, 25 disassembling and reassembling, 25 geometry of, 23–26 sniper, 25 Robots _A.I.: Artificial Intelligence_ [XP] (2001), 46 fuel, weight of, 46 heat from nuclear fuel, 47 machine used overtime, 47 perpetual motion machines, 44 Rotation, 247, 254 air cannons, 255 cars, 254–256 handgun, 252 kicker plates, 254–255 knife throwing, 247–249 Rotational inertia, and spear throwing, 249–251 S Safe movie physics guidelines, 5–6 Safety glass, laminated, 87–89 _Saving Private Ryan_ , [GP] (1998), 7, 112 Scaling machinery, 63 Second law of thermodynamics, 38 _A.I.: Artificial Intelligence_ , 44 definition, 38 electrical energy, 38 mechanical energy, 38 thermal energy, 38–40 Sensation of weight and normal force, 232–237 Shooting from the hip and laser pointer experiment, 21 mathematics of, 21–22 recoil, bullet drop, hand tremors, and body misalignment, 20 Shrapnel, 113 SMASH! Plastic "glass," 88 Sniper rifles, aiming. See also rifle bullet trajectory, 23–27 geometry of, 23–26 Spear throwing, 249–251 rotational inertia in, 249 Spaceship falling, 164, 165 blast wave from, 166 depressurization and temperature, 75 high pressure and, 166 high temperature and, 166, wind velocity and, 166 Spaceships air resistance to, 192 antimatter and, 191 car-sized, 190–192 cloaking and stealth devices of, 76 fuel supply for, 191 mass required for liftoff of, 192 rotation and _Mission to Mars_ [RP] (2000), 238 thrusters on, 191–192, 288 Space shuttle _Armageddon_ , 213 stopping in space, 213–214 Space travel, speed of, 106 _Speed_ [PGP-13] (1994), famous vehicle jump in, 8 _Speed II_ : Cruise Control [PGP], 149–153 Speed of light, 187 Speed = distance/time and movie calculation, 99 _Spider-Man_ [NR] (2002), 37 _Star Trek_ , 107, 160, 287, 288 inertial dampers, 160–161 and _Nemesis_ , 303 warp drives, 288 warping space, 107–108 Web strands, 37 _Star Trek IV_ and time travel, 293 _Star Trek_ movie series, 240 artificial gravity in, 241 _Star Wars_ , 287 _Star Wars Episode I_ , land battles in, 295 _Star Wars Episode II_ [NR] (2002), 91 space battles in, 297 _Star Wars Episode III_ , 298–306 air resistance, 298 lift, 301 orbital velocity, 301 space battles, 297 thrusters, 301 velocity, 299 Yoda's force on rocks equal to their weight, 91 _Star Wars_ versus _Star Trek_ , 291–293 Stress dependent on object's material and shape, 264–265 Stretching physics to the remotely possible, 6 Sugar-pane "glass," 88 Superheated plasma, 300 in _Star Wars Episode III_ , 298 Surviving windows, 86 explosive charges break glass, 89 laminated safety glass, 89–91 SMASH! Plastic "glass," 89 Sugar-pane "glass," 90 T Takeoff ramp, 137 horizontal component for forward motion, 137 and takeoff velocity, 140 and vertical velocity, 137 Tangential velocity around planet, effects of, 219 Target motion, 26 Temperatures and pressures in spaceship, 75 in _The Core_ , 9–10 Target, moving, 26 Technology, out of control, 52 in _Honey I Shrunk the Kids_ , 51–56 Terminal velocity, 128 _The Core_ [XP] (2005), 170–171 as all-time stupid movie, 312–314 and earthquake weapon, 9 probe into Earth's core, 10–11 scientist consultants, 9–10 _The Day After Tomorrow_ [RP] (2004), 259, 269 effect of water pressure on Statue of Liberty, 259 storm surge, 268–269 _The Italian Job_ [PGP-13] (2003) and car turning radius, 28–30 _The Matrix_ [NR] (1999), 40–42, 243 human bioelectrical energy, 41 humans 25,000 btus/sec, 41–42 simulation physics altered, 243–245 victim's center of mass, 244 _The Matrix Revolutions_ [NR] (2003), 80 action hero in, 16 ammunition in, 16 machine gun, overheating, 16 _The Mexican_ [PGP] (2001), 175 Theory of relativity in Eraser, 186 _The Road to Perdition_ [GP] (2002) and bullet penetration, 79–80 Thermal energy and car bombs, 281 Thermite grenades and heat of blast, 112 Thrusters, 191, 201 _Enterprise_ 's impulse engines are thrusters, 288 machine guns acting as (on fighter jets), 90 in _Star Wars Episode III_ , 301 Tides in _Armageddon_ , 222–224 asteroid-produced, 223 atmospheric, 222 moon's gravity and, 222 Time and explosions, 108 Time travel, 2–5 in _Star Trek IV_ , 293 in _The Terminator_ ,4 Torque, 245–246, 252 Toxic waste, 51 Translation, 254 and horizontal aim of handgun, 251–254 Transporter as plot acceleration device, 289 _True Lies_ and motorcycle jump calculations, 126–128 Tsunami, 260–264 and air compression, 263 and kinetic energy, 263 _2001: A Space Odyssey_ [GP] (1968), 94, 237 V Vehicle jump in _Speed_ [PGP-13] (1994), 8 ramp required for, 9 Velocity, 72, 187, 196, 233 angular, 196 and Bernouli's equation, 262 of escape, 218 of explosions, 108 of flames, 100 horizontal, 155 and lowest circular orbit, 217 in _Star Wars Episode III_ , 298 of takeoff velocity, 140 vertical, 155 Volume in _Honey I Shrunk the Kids_ , 52–57 Vomit comet, 120, 121, 229–230 W WWII–style space battles air resistance, 72 projectile trajectory, 72 resistance force, 71 Warping space in _Star Trek_ , 107–108 Weight in _Honey I Shrunk the Kids_ [NR] (1989), 52–57 Weightlessness and normal force, 232–237 White phosphorous grenade, 112 Wind velocity, 166 and falling spaceship, 165 World wide explosions, speed of, 99 X _XXX State of the Union_ [RP] (2005) Y _Young Guns II_ [PGP] (1990), bullet penetration, 78–79 ## ABOUT THE AUTHOR Tom Rogers is the founder and creator of the wildly popular website Insultingly Stupid Movie Physics. He has a bachelors degree in mechanical engineering from Arizona State University and a Master of Business Administration degree from Clemson University. He worked as an engineer for eighteen years and currently lives in Greenville, South Carolina.	{ "redpajama_set_name": "RedPajamaBook" }	4,698
{"url":"https:\/\/zbmath.org\/?q=an%3A0236.34064","text":"## The functional-differential equation $$y'(x)=ay(\\lambda x)+by(x)$$.(English)Zbl\u00a00236.34064\n\n### MSC:\n\n 34K10 Boundary value problems for functional-differential equations 34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)\nFull Text:\n\n### References:\n\n [1] L. Fox, D. F. Mayers, J. R. Ockendon and A. B. Tayler, On a functional differential equation, J. Inst. Math. Appl. (to appear). \u00b7 Zbl\u00a00251.34045 [2] Kurt Mahler, On a special functional equation, J. London Math. Soc. 15 (1940), 115 \u2013 123. \u00b7 Zbl\u00a00027.15704 [3] Proceedings United States-Japan Seminar on Differential and Functional Equations, Held at the University of Minnesota, Minneapolis, Minn., June 26-30, 1967. Edited by William A. Harris, Jr. and Yasutaka Sibuya, W. A. Benjamin, Inc., New York-Amsterdam, 1967. [4] N. G. de Bruijn, The asymptotically periodic behavior of the solutions of some linear functional equations, Amer. J. Math. 71 (1949), 313 \u2013 330. \u00b7 Zbl\u00a00033.27002 [5] N. G. de Bruijn, On some linear functional equations, Publ. Math. Debrecen 1 (1950), 129 \u2013 134. \u00b7 Zbl\u00a00036.19501 [6] N. G. de Bruijn, The difference-differential equation F\u2019(x) = e. I, II, Nederl. Akad. Wetensch. Proc. Ser. A 56 = Indag. Math. I5 (1953), 449-464. MR 15, 629. \u00b7 Zbl\u00a00053.38703 [7] E. W. Bowen and G. R. Morris, private communication. [8] Paul O. Frederickson, Global solutions to certain nonlinear functional differential equations, J. Math. Anal. Appl. 33 (1971), 355 \u2013 358. \u00b7 Zbl\u00a00191.15302 [9] P. O. Frederickson, Analytic solutions for certain functional-differential equations of advanced type (to appear). \u00b7 Zbl\u00a00191.15302 [10] Richard Bellman and Kenneth L. Cooke, Differential-difference equations, Academic Press, New York-London, 1963. \u00b7 Zbl\u00a00105.06402 [11] Laurent Schwartz, Th\u00e9orie des distributions, Publications de l\u2019Institut de Math\u00e9matique de l\u2019Universit\u00e9 de Strasbourg, No. IX-X. Nouvelle \u00e9dition, enti\u00e9rement corrig\u00e9e, refondue et augment\u00e9e, Hermann, Paris, 1966 (French). \u00b7 Zbl\u00a00962.46025\nThis reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.","date":"2022-12-03 06:32:03","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.5686087012290955, \"perplexity\": 1824.9439071105378}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-49\/segments\/1669446710924.83\/warc\/CC-MAIN-20221203043643-20221203073643-00712.warc.gz\"}"}	null	null
Published January 11, 2017 2:14pm EST Opinion: Immigration overreach is not the answer to a permanent solution By Nelson Balido , \| Fox News Following the recent Republican romp in the fall elections, Ariz. Sen. John McCain was in no mood to spike the football. Yes, he was happy that the GOP was poised to assume the Senate majority and that he would soon take over as the chairman of the Senate Armed Services Committee, but a looming policy decision had him more concerned. The Thursday after Election Day, Sen. McCain was reacting to rumblings that President Obama was prepared to act via executive order on immigration. No serious Democrat or Republican can argue that our byzantine visa system, overly bureaucratic guest worker program and patchwork worker verification scheme is effective or makes any sense. — Nelson Balido On MSNBC, McCain said that he was "pleading with the president not to act. Give it a chance. We've got a new Congress. We've got a new mandate. Let's let the House of Representatives decide if they want to move forward on immigration reform or not." The president apparently wasn't in a mood to wait around for Congress or take advice from the one member of the opposite party who bears more scars from the immigration fights of the last decade than any other. On Wednesday, the White House released via Facebook a video of the president in the Oval Office dressed casually in shirtsleeves announcing that he would address the nation Thursday night to lay out the details of an executive order focusing on the steps he could take "to start fixing our broken immigration system." Leaning up against his desk in the same office where Ronald Reagan would never take off his suit jacket, the president was signaling a monumental shift in national policy with all the seriousness of renaming a post office. As for the president's contention that our immigration system is broken, on that there is bipartisan agreement. No serious Democrat or Republican can argue that our byzantine visa system, overly bureaucratic guest worker program and patchwork worker verification scheme is effective or makes any sense. If the president needs validation that our immigration system is a mess, I'm happy to acknowledge that fact from my corner of the U.S.-Mexico border. But the president's executive order demonstrates the arrogance of a leader who has surrounded himself with sycophants who are either too timid to challenge their boss or who failed to learn anything from Election Day. For years, president Obama repeatedly told the American people that he did not have the authority to act unilaterally, what changed his mind? One would assume he doesn't need reminding, but this president would be well served to remember that he has very little credibility on Capitol Hill, even within his own party. The liberal New York Times earlier this summer documented what West Virginia Democrat Sen. Joe Manchin described as a "fairly nonexistent" relationship with the president. Going it alone on immigration and going around Congress isn't going to engender more warm feelings on the other end of Pennsylvania Avenue. If the president is angling to get more Christmas cards from Capitol Hill, this isn't going to work. Actions such as these demonstrate a complete disregard for the American people. Americans want to see immigration reform, but they want Congress involved Instead the president should look to work with the new Republican majority on areas where both parties can make substantive reforms to immigration. For example, in some states, the use of the E-Verify worker verification system is more prevalent than others. Congress and the president could ensure all employers use the system. The agriculture community does not have enough labor to ensure domestic production meets the nation's needs. Congress and the president could expand and simplify the H-2A visa allocation process. Our border security strategy over the past 10 years has focused mostly on driving up the Border Patrol's personnel numbers. Congress and the president could ensure a more rational allocation of resources between Border Patrol and the Customs and Border Protection officers who guard the ports of entry and are just as integral to the ongoing battle against human trafficking and smuggling. These are just a few areas where both sides can get a win and demonstrate to the American public that Washington might be mostly dysfunctional, but not hopelessly so. With a few small but important reforms, the ground might just be more fertile to take on the thornier issues of how to regularize the presence of over 11 million individuals not in the U.S. in a legal status. Faced with an American public that soundly rejected his governance, this president has instead doubled down. Where voters asked for the humility, the president has delivered hubris. It's too bad. He might have just derailed any hope of real immigration reform. Get the recap of top opinion commentary and original content throughout the week. Arrives Daily	{ "redpajama_set_name": "RedPajamaCommonCrawl" }	4,793
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Marathos or Marathi is a small Greek Island in the Aegean sea lying east of Patmos island, southwest of Arkoi island, and northwest of Leipsoi island. It is part of the Dodecanese archipelago. It is a small island with and area of but there are a couple of tavernas and few rooms to let. Population 1991 - 2 2011 - 5 References Islands of the South Aegean Islands of Greece Dodecanese Populated places in Kalymnos (regional unit)	{ "redpajama_set_name": "RedPajamaWikipedia" }	4,081
\section{Introduction} \label{sec1} Superconducting metamaterials comprising Superconducting QUantum Interference Devices (SQUIDs), are artificial materials that exhibit exceptional properties not found in nature, such as negative magnetic permeability, dynamic multistability \cite{Jung2014a,Zhang2015}, broadband tunability, and self-induced broadband transparency \cite{Zhang2015}. Some of these extraordinary properties have been predicted theoretically both for the quantum \cite{Du2006} and the classical regime \cite{Lazarides2007,Lazarides2013,Lazarides2018}. They can be implemented and studied in various designs and arrangements, both in one and two dimensions \cite{Trepanier2013,Zhang2015,Zhang2016,Butz2013,Jung2014a,Jung2014b, Ustinov2015,KIS19}. Recently, the degree of spatio-temporal coherence of SQUID metamaterials was examined experimentally and numerically using microwave transmission measurements~\cite{Trepanier2017}. Moreover, its quantum counterpart, the qubit, has been proposed as an important ``building block'' of quantum computers~\cite{SAI13,SHU18}. Apart from their technological applications, SQUID metamaterials provide a unique testbed for exploring complex spatio-temporal dynamics. A SQUID metamaterial is in essence a system of nonlinear coupled oscillators with inertia, which are driven, damped, and are characterized by a nonlinear term which enters through the Josephson effect \cite{Josephson1962}. A very prominent dynamical feature of SQUID metamaterials are dissipative breathers~\cite{LAZ08}, which emerge as a result of their discreteness, the weak coupling between their elements and the Josephson nonlinearity. In this work, we will study the collective behavior beyond these localized states, in a dynamical regime where the whole lattice is oscillating and is capable of creating Turing-like patterns \cite{Turing1952}. Pattern forming systems have been in the center of scientific research for decades in a rich variety of natural and laboratory scenarios~\cite{CRO93}. These include oscillatory chemical reactions governed by reaction-diffusion dynamics~ \cite{SHO15}, static and excitable biological media~\cite{KOC94}, dissipative spatio-temporal solitons in nonlinear optics~\cite{ARE99}, and many more. Here, we will use synchronization measurements in order to explore pattern formation in two-dimensional (2D) SQUID metamaterials. Another phenomenon related to synchronization which has been observed in SQUID metamaterials are chimera states, where domains of coherent and incoherent motion coexist in an otherwise symmetric network of identical oscillators~ \cite{KUR02a,ABR04,panaggio:2015,YAO16,OME18}. SQUID chimeras have mainly been studied in one-dimensional (1D) arrays~\cite{LAZ15,HIZ16a,HIZ16b,BAN18b}. Here we will explore this phenomenon for locally coupled SQUIDs on a tetragonal lattice. Higher-dimensional chimeras have been the subject of recent works involving networks of Kuramoto and neuronal oscillators~\cite{MAI15,SCH17,KAS18,ARG19}. The interplay, however, between chimeras and Turing-like patterns has not been addressed sufficiently and this a new element that our work focuses on. Note that the system under study is a physical, technologically relevant example of a \emph{forced} system, where such dynamics is still to be investigated ~\cite{DUD16,CLE18}. \section{Single SQUID dynamics} A SQUID consists of a superconducting ring interrupted by a Josephson junction (JJ) as shown schematically inside the dashed box of Fig.~\ref{fig1}(a). When placed in a perpendicular, spatially uniform magnetic field $H$, a current $I$ is induced which is the sum of the supercurrent $I_s$ flowing through the JJ and the quasiparticle current. Then, the magnetic flux $\Phi$ threading the loop of the SQUID is given by: \begin{eqnarray} \label{eq1} \Phi =\Phi_{ext} +L\, I , \end{eqnarray} where $L$ is the self-inductance of the SQUID ring and $\Phi_{ext} =\Phi_{dc} +\Phi_{ac} \, \cos( \omega t )$ is the external flux applied to the SQUID, containing both a constant (dc) flux bias $\Phi_{dc}$ and an alternating (ac) flux of amplitude $\Phi_{ac}$ and frequency $\omega$. \begin{figure}[ht] \includegraphics[width=\columnwidth]{fig1.jpg} \caption{ (a) Schematic of a two-dimensional SQUID metamaterial in a magnetic field $H(t)$ and (b) equivalent electrical circuit of the single SQUID (marked by the dashed box in (a)) in the RCSJ framework.} \label{fig1} \end{figure} \begin{figure}[] \includegraphics[width=\textwidth]{fig2.jpg} \caption{Resonance curves of a single SQUID for various dc flux values: (a) $\phi_{dc}=0.0$, (b) $\phi_{dc}=0.3$, and (c) $\phi_{dc}=0.5$. The vertical line marks the value of the geometric resonance frequency and the insets show the corresponding stable periodic solutions at that value. Other parameters are: $\phi_{ac}=0.06$, $\gamma=0.024$ and $\beta=0.1369$.} \label{fig02} \end{figure} The current $I$ in the SQUID is given by the resistively and capacitively shunted junction (RCSJ) model of the JJ \cite{Likharev1986}, schematically shown in Fig.~\ref{fig1}(b): \begin{eqnarray} \label{eq2} I =-C\frac{d^2\Phi}{dt^2} -\frac{1}{R} \frac{d\Phi}{dt} -I_c\, \sin\left(2\pi\frac{\Phi}{\Phi_0}\right), \end{eqnarray} where $C$ is the capacitance of the JJ of the SQUID, $R$ is the resistance, $I_c$ is the critical current which characterizes the JJ, $\Phi_0$ is the flux quantum, and $t$ is the temporal variable. Combining Eqs. (\ref{eq1}) and (\ref{eq2}) we get: \begin{eqnarray} \label{eq3} \ddot{\phi} +\gamma \dot{\phi} +\phi +\beta \sin\left( 2\pi \phi \right) = \phi_{dc}+ \phi_{ac} \cos(\Omega \tau), \end{eqnarray} where all fluxes have been normalized to the flux quantum, $\phi=\Phi/\Phi_0$, $\phi_{ac,dc}=\Phi_{ac,dc}/\Phi_0$, while the frequency and time variable have been normalized to the inductive-capacitive SQUID frequency, $\omega_{LC}=1 / \sqrt{L C}$ and its inverse, respectively, i.~e. $\Omega={\omega}/{\omega_{LC}}$ and $\tau=t/\omega_{LC}^{-1}$. The parameter $\beta=LI_c/\Phi_0 =\beta_L/2\pi$ is the so-called rescaled SQUID parameter and $\gamma=\omega_{LC} L/R$ corresponds to the loss coefficient. Typical values of the design parameters of a SQUID~\cite{Trepanier2013,Zhang2015} provide the dimensionless coefficients $\beta \simeq 0.1369$ ($\beta_L \simeq 0.86$) and $\gamma \simeq 0.024$ which appear in the normalized Eq. (\ref{eq3}) for the flux $\phi =\Phi / \Phi_0$ through the loop of the SQUID. They also provide experimentally plausible values $f_{LC} =\omega_{LC} /(2\pi) \simeq 13.9 ~GHz$ ($\Omega \simeq 1$) and $f_{SQ} =\omega_{SQ} /(2\pi) \simeq 18.9 ~GHz$ ($\Omega =\Omega_{SQ} \simeq 1.364$) for the geometric and the linear resonance frequency of the SQUID, respectively~ \cite{Butz2013,Trepanier2013,Zhang2015}. The values of the externally controlled parameters $\phi_{dc}$, $\phi_{ac}$, and $\Omega$ used here, are within the range of the experimentally accessible values, i.~e., $\phi_{dc}$ in the interval $[-1, 2]$ \cite{Trepanier2013}, $\phi_{ac}$ in the interval $[0.001, 0.18]$ \cite{Zhang2015}, and $\Omega$ in the interval $\frac{2\pi}{\omega_{LC}} [10, 22.5] ~GHz$ \cite{Trepanier2013}. By expanding the sine nonlinearity in Eq.~\ref{eq3} in a Taylor series and keeping the cubic term only, the SQUID model reduces to the famous driven Duffing oscillator. The latter is known to exhibit a nonlinear frequency response, bistability, hysteresis phenomena, and chaotic behavior. Similarly, the SQUID is capable of demonstrating complex dynamics, but with additional features owing to its higher-order nonlinear term. For a certain range of parameters the SQUID exhibits a ``snake-like'' resonance curve in which multiple stable and unstable periodic orbits coexist and vanish through saddle-node bifurcations of limit cycles~\cite{HIZ16a,HIZ18,DIM82}. The detailed bifurcation structure for zero and finite dc flux was first reported in ~\cite{HIZ16a,HIZ18}. Here we significantly further this analysis and explore the stability of solutions in the \emph{full} $(\phi_{dc},\Omega)$ parameter space. \begin{figure} \includegraphics[width=\textwidth]{fig3.jpg} \caption{ Left: Bifurcation diagram in the $(\phi_{dc},\Omega)$ plane of the single SQUID oscillator. Blue and red lines correspond to saddle-node bifurcations of limit cycles and period doubling bifurcations, respectively. The inset shows a blowup around $\Omega=1$. Right: Value of the synchronization measure $\langle g_0 \rangle$ in the $(\phi_{dc},\Omega)$ parameter space for a $30 \times 30$ SQUID lattice with coupling strength $\lambda=-0.01$. The black and cyan curves correspond to saddle-node bifurcation lines of the reduced system for $\lambda=0.0$ and $\lambda=-0.01$, respectively. Other parameters are: $\phi_{ac}=0.06$, $\gamma=0.024$ and $\beta=0.1369$. \label{fig03} } \end{figure} Figure~\ref{fig02} shows the resonance curves of the single SQUID as the dc flux increases from 0 to 0.5. A saddle node bifurcation of limit cycles occurs at each turning point of the curve where stable and unstable branches merge ~\cite{HIZ16a,HIZ18}. The vertical line marks the geometric resonance frequency and the insets show the phase portraits of the corresponding \emph{stable} periodic solutions at that particular value of $\Omega$. As the dc flux increases, the ``center'' of these solutions shifts to the right and the number of coexisting limit cycles at $\Omega_{LC}$ changes. For $\phi_{dc}=0.0$ (Fig.~\ref{fig02}(a)) we have five coexisting periodic solutions of different amplitudes, centered around the origin. As the dc flux increases, the number of coexisting orbits gradually shrinks to one, at $\phi_{dc}=0.30$, while new subresonances~\cite{MAR18,HIZ18} make an appearance at lower frequencies (Fig.~\ref{fig02}(b)). At $\phi_{dc}=0.50$ the SQUID is again multistable with four coexisting periodic solutions (Fig.~\ref{fig02}(c)) and, at the same time, the occurring saddle-node bifurcations have transformed from subcritical to supercritical and vice versa~\cite{HIZ18}. This scenario repeats itself periodically with the resonance curve moving back and forth, with respect to $\Omega_{LC}$, as we vary $\phi_{dc}$. This ``rocking'' of the snake-like resonance curve and, consequently, periodic appearance and disappearance of solutions around the geometric resonance frequency, is better visualized in the video SM1 of the Supplementary Material. All of the aforementioned features are reflected in Fig.~\ref{fig03}(a), where the co-dimension 2 bifurcation diagram in the $(\phi_{dc},\Omega)$ plane is depicted. The bifurcation lines have been obtained using a very powerful software tool that executes a root-finding algorithm for continuation of steady state solutions and bifurcation problems~\cite{ENG02}. Cyan and red lines denote saddle-node bifurcations of limit cycles and period-doubling bifurcations, respectively. The bifurcation structure is extremely delicate and periodic in $\phi_{dc}$ with a period of unity. This periodicity can be proven as follows: Assuming that $\phi$ is a solution of the single SQUID equation and by plugging $\phi \pm1$ into Eq.~\ref{eq3} we get: $d^2(\phi \pm 1)/dt^2 +\gamma d(\phi \pm 1)/dt +(\phi \pm 1) +\beta \sin\left( 2\pi \phi \pm 2\pi \right)=\phi_{dc}+\phi_{ac} \cos(\Omega \tau)$. After simple manipulations we obtain: $\ddot{\phi}+\gamma \dot{\phi} +\phi +\beta \sin\left( 2\pi \phi \right) =(\phi_{dc}\pm 1)+\phi_{ac} \cos(\Omega \tau)$. Therefore, $\phi$ satisfies Eq.~\ref{eq3} also for a dc flux $\phi_{dc}\pm 1$, and $\phi_{dc}\pm 2$, and so on. Looking at Fig.~\ref{fig03}(a) again, for fixed $\phi_{dc}$ values and moving in the $\Omega$ direction, we can recreate the resonance curves shown in Fig.~\ref{fig02} and the video SM1 of the Supplementary Material: The multiple and interwoven cyan lines correspond to the multiplicity of solutions around the geometric resonance frequency (better visible in the inset), while the red lines around $\phi_{dc}=0.5$ (and its symmetric $\phi_{dc}=-0.5$) are related to the subresonances that make their appearance for those dc flux values. The bifurcation diagram of Fig.~\ref{fig03}(a) presents additional, long period-doubling bifurcation branches extending to higher $\Omega$ values, which are not captured in the resonance curves of Fig.~\ref{fig02}. The period doubling lines are symmetrical around $\phi_{dc}=\pm0.5$ and for higher ac flux values are associated with corresponding chaotic regions, as shown in \cite{HIZ18}, where the maximum Lyapunov exponent was calculated in the $(\phi_{dc},\Omega)$ plane. \section{Two-dimensional SQUID lattices} In this work, we will focus on two regimes of the driving frequency: The vicinity of $\Omega_{LC}$, and at lower values around $\Omega=0.3$. Through the single SQUID complex dynamics, we aim at interpreting the collective behavior of the 2D SQUID lattice. We consider a planar $N\times N$ SQUID array consisting of identical units as shown in Fig.~\ref{fig1}(a), arranged in an orthogonal lattice with a constant distance $d$ in both $x$ and $y$ directions. The induced current $I_{nm}$ produces a magnetic field which couples each SQUID with all the others due to magnetic dipole-dipole interactions through their mutual inductance. To a good approximation, we may assume that the SQUIDS are coupled only to their nearest neighbors, neglecting further-neighbor interactions. The dynamic equations for the normalized flux through the ring of the $(n, m)$-th SQUID, $\phi_{nm}$, are given by~\cite{LAZ08}: \begin{eqnarray} \label{eq04} &&\ddot{\phi}_{nm} +\gamma \dot{\phi}_{nm} +\phi_{nm} +\beta \sin\left( 2\pi \phi_{nm} \right) \nonumber \\ &=&\lambda( \phi_{n-1,m} +\phi_{n+1,m}+\phi_{n,m-1} +\phi_{n,m-1} ) \nonumber \\ &+&(1 -4\lambda) (\phi_{dc}+\phi_{ac} \cos(\Omega \tau)), \quad n,m=1\dots N, \end{eqnarray} where $\lambda\equiv M /L$ is the coupling constant between any two neighboring SQUIDs, coupled through their mutual inductance $M$. The value of $M$ is negative due to the fact that the magnetic field generated by one SQUID crosses the neighboring SQUID in the opposite direction. In the following, we will study the nature of the synchronization-desynchronization transitions and will identify the collective states that emerge in relevant regimes of the parameter space. The latter involves the two parameters which can be easily tuned in an experiment, namely the dc flux and the frequency of the ac flux, with the other parameters (ac flux amplitude $\phi_{ac}$, $\gamma$ and $\beta$) kept constant. Equations~(\ref{eq04}) are integrated numerically in time using a standard fourth-order Runge-Kutta algorithm with a time-step equal to $0.02$ and periodic boundary conditions, i.~e., $\phi_n(\tau)=\phi_{N+n}(\tau)$ for all $n$. This particular choice of boundary conditions does not affect the dynamics significantly. By using instead, e.~g., free-end boundary conditions, only slight differences would have been observed which account for $1-2\%$ deviations of the corresponding $g_0$ value. Moreover, if nonlocal interaction between SQUIDs were assumed, a slight suppression of global synchronization would have been observed with both periodic and free-end boundary conditions. The initial conditions for the $\phi_{nm}$ values follow a Gaussian random distribution in the interval $[-3,3]$ and $\dot \phi_{nm}=0.0$. We will employ a quantification measure, originally introduced for the classification for chimera states~ \cite{kevrekidis}, the \emph{local curvature}, which is calculated at each time instance by applying the absolute value of the discrete Laplacian on the spatial data of the magnetic flux: \begin{eqnarray} \label{eq5} \hat L\phi_{nm}(t) &=&L_{nm}(t)= 4 \phi_{n,m}(t)-\phi_{n+1,m}(t) -\phi_{n-1,m}(t) \nonumber \\ &-&\phi_{n,m+1}(t)-\phi_{n,m-1}(t), \quad n,m=1\dots N. \end{eqnarray} The local curvature is a measure for \emph{amplitude} synchronization and in the synchronization regime it is close to zero while in the asynchronous regime it is finite and fluctuating. If $g$ is the normalized probability density function of $\|\hat L\|$, then $g(\|\hat L\|=0)$ measures the relative size of spatially coherent regions in each temporal realization and characterizes the entire lattice. For a fully synchronized system $g(\|\hat L\|=0)=1$, while for a totally incoherent system it holds that $g(\|\hat L\|=0)=0$. An intermediate value of $g(\|\hat L\|=0)$ indicates the coexistence of synchronous and asynchronous SQUIDs and, therefore, potentially interesting collective behavior. From $g$, which is time-dependent, we calculate the spatial extent occupied by the coherent SQUIDs which is defined by the integral: $g_{0}(t)=\int_{0}^{\delta}g(t,\|\hat L\|)d\|\hat L\|$, where $\delta=0.01L_{\mathbf{max}}$ is a threshold value distinguishing between coherence and incoherence and is related to the maximum local curvature ($L_\mathbf{max}$). In order to correspond one single value to each realization, we calculate the time-average $\langle g_{0}(t)\rangle$, and we plot it in the $(\phi_{dc},\Omega)$ parameter space. The result is shown in~Fig.~\ref{fig03}(b) for a coupled lattice with $\lambda=-0.025$. Yellow (bright) and purple (dark) regions denote a synchronized and desynchronized lattice, respectively. The cyan lines mark two (for visualization simplicity) of the saddle-node bifurcation lines of the single SQUID system of Fig.~\ref{fig03}(a). By comparing the two plots, it is evident that the bifurcation lines of the single SQUID almost mark the borders between synchronization and desynchronization of the coupled system. For relatively weak coupling, which is the case in Fig.~\ref{fig03}(b), this is plausible: When the single SQUID has one stable solution we may claim that the whole lattice acts like one SQUID and therefore the solution for the coupled system is the fully synchronized state. However, when the single SQUID loses its stability through the bifurcations shown in Fig.~\ref{fig03}(a), each node of the lattice may behave differently resulting, thus, in a desynchronized state. For stronger coupling strengths (not shown here), the regions of incoherence around $\phi_{dc}=\pm0.5$ broaden, while the one around $\phi_{dc}=0$ shrinks. The structure of the parameter space (symmetry and periodicity), however, is maintained. In terms of mean field theory, the weak coupling case essentially corresponds to the single SQUID limit, where the collective and single SQUID behavior are seen to be in close correspondence. In the other extreme of strong coupling (not addressed in this work) one may possibly introduce an order parameter and proceed in analyzing the system from the point of view of collective phenomena. \subsection{Pattern formation} \label{subsec:patterns} Based on Fig.~\ref{fig03} we will study the collective dynamics emerging near the synchronization-desynchronization transition. Additionally, based on the resonance curve of the single SQUID (Fig.~\ref{fig02}), we select the two $\Omega$ regimes that show the most interesting behavior: One around the geometric resonance frequency where the single SQUID is extremely multistable through successive saddle-node bifurcations of periodic solutions, and one at lower frequencies where period-doubling takes place. We prepare the lattice such that the initial conditions for the $\phi_{nm}$ values follow a Gaussian random distribution in the interval $[-3,3]$ and $\dot \phi_{nm}=0.0$. As a control parameter we consider the coupling strength $\lambda$, which, in principle, can be tuned in an experiment by increasing or decreasing the distance between the SQUIDs. \begin{figure}[] \includegraphics[width=\textwidth]{fig4.jpg} \caption{ Top: Snapshots of the spatio-temporal patterns of the magnetic flux in a $n \times m$ SQUID lattice ($n=m=30$), corresponding to the cases \Romannum{1}-\Romannum{4} marked on Fig.~\ref{fig03}(b): (a) $\Omega=0.345$, $\phi_{dc}=0.5$ and $\lambda=-0.025$ (case \Romannum{1}), (b) $\Omega=0.345$, $\phi_{dc}=0.5$ and $\lambda=-0.039$ (case \Romannum{2}), (c) $\Omega=1.06$, $\phi_{dc}=0.3$ and $\lambda=-0.032$ (case \Romannum{3}), and (d) $\Omega=1.06$, $\phi_{dc}=0.23$ and $\lambda=-0.05$ (case \Romannum{4}). Other parameters are: $\phi_{ac}=0.06$, $\gamma=0.024$ and $\beta=0.1369$. (See videos SM2(a)-(d) of the Supplementary Material for the corresponding videos). Middle: Corresponding Fourier Power Spectra in the 2D $k$-space. Bottom: Radially Averaged Power Spectrum (RAPS) in $\lambda_k$.} \label{fig04} \end{figure} The results are shown in Fig.~\ref{fig04}: The top panels (a-d) show snapshots of the spatial distribution of the magnetic fluxes for the points (\Romannum{1}-\Romannum{4}) marked in the parameter space in Fig.~\ref{fig03} (b). Figures ~\ref{fig04} (a) and (b) correspond to a low driving frequency value ($\Omega=0.345$) i.~e. far from the geometric resonance, where the single SQUID obtains low-amplitude periodic solutions and undergoes period doubling. For a coupling strength $\lambda=-0.025$ the SQUID lattice self-organizes into a labyrinthine-like pattern (Fig.~\ref{fig04}(a)), while for a stronger coupling (Fig.~\ref{fig04} (b)) the collective state is a striped pattern, where smaller ``zigzag'' patterns exist within each stripe. As mentioned previously, these patterns emerge from a completely random magnetic flux initialization and are, therefore, a result of the nonlinearity of the single SQUID and the collective dynamics of the coupled system. In the middle panels, the two-dimensional Fourier power spectra $\|\tilde{\phi_k}\|^2$ are plotted in the inverse space domain. The maximum values of the power spectra correspond to the characteristic wavenumber $k=\sqrt{k^2_x+k^2_y}$ of each pattern. From $\|\tilde{\phi_k}\|^2$ we obtain the 1D Radially-Averaged Power Spectrum (RAPS) \cite{Wang2007} in terms of the wavelength $\lambda_k=2\pi/k$, shown in the lower panels of Fig.~\ref{fig04}. From the peaks of these RAPSs we can extract the characteristic wavelength of each pattern. For example, for the pattern in Fig.~\ref{fig04}(a) this value is $\simeq 3.53$, which is roughly the distance between two stripes in the $m$-direction of the corresponding plot in the top panel, in other words, the spatial period of the pattern. In the case of Fig.~\ref{fig04} (b), on the other hand, the RAPS obtains two maxima: The first one reflects the distance within the ``zigzag'' patterns inside the stripes ($\simeq 2$) and the second one, the distance between the stripes themselves ($\simeq 3.53$). Similarly, Figs.~\ref{fig04}(c) and (d) show the patterns, and the corresponding Fourier power spectra in $k$-space and RAPS, obtained near the geometric resonance, where the single SQUID may achieve high magnetic flux values through saddle-node bifurcations of limit cycles. The pattern in Fig.~\ref{fig04} (c), similar to Fig.~\ref{fig04} (a), is labyrinthine-striped, but with, evidently, a higher characteristic wavelength $\simeq 5.45$. For stronger coupling and a smaller $\phi_{dc}$ value, the emerging pattern consists of spots, with a characteristic wavelength equal to $4$ (Fig.~\ref{fig04} (d)). The patterns of Fig.~\ref{fig04} are spatio-temporal, and apart from a spatial period they also have a temporal period and corresponding frequency. These characteristic frequencies are given by the peaks of the Fourier power spectra in the inverse time domain, shown in the upper panels of Fig.~\ref{fig05}. Figures~\ref{fig05}(a) and (b) refer to Figs.~\ref{fig04} (a) and (c) (we have omitted the spectral analysis of cases Fig.~\ref{fig04} (b) and (d) because they are identical to Fig.~\ref{fig04} (a) and (c), respectively). We have plotted the spectra of all the SQUIDs in the lattice as well as their average (thick blue line). For the case of the pattern Fig.~\ref{fig04} (a), the spectra are very similar and the lattice is highly synchronized in frequency. As expected, the dominant frequency is that of the driving force, marked with the vertical dashed line. Moreover, the spectra are rather ``noisy'' and they possess multiple secondary frequencies. This is typical for quasiperiodic motion as demonstrated by the phase diagrams in the lower panels of Fig.~\ref{fig05}(a). The situation is similar, but ``cleaner'' for the pattern in Fig.~\ref{fig04} (c). As seen in the power spectra of Fig.~\ref{fig05}(b), the SQUIDs in the lattice are almost perfectly frequency-locked with the dominant frequency again being that of the driving force. The corresponding phase diagrams show, again, quasiperiodicity but the motion now is closer to harmonic since we are very close to the geometric resonance. \begin{figure}[] \includegraphics[width=.9\textwidth]{fig5.jpg} \caption{ Top: Fourier power spectra in the frequency domain of all the SQUIDs and their average (thick blue line) for the spatio-temporal patterns of (a) Fig.~\ref{fig04} \Romannum{1}, (b) Fig.~\ref{fig04} \Romannum{1}, and (c) the chimera state of Fig.~\ref{fig06}(a). Bottom: Phase diagrams of some typical timeseries in the SQUID lattice.} \label{fig05} \end{figure} In correspondence with the traditionally discussed Turing patterns in Reaction-Diffusion systems, the 2D SQUID metamaterials can be characterized as partially cross-diffusive systems whose two components are the magnetic fluxes threading the loops of the SQUIDs and their time-derivatives. This can be readily inferred by taking the continuous limit of Eqs.~\ref{eq04}. Although our system exhibits similarities with classical Reaction-Diffusion systems, it also exhibits differences, with the most important being the presence of the driving force. The emergence of Turing-like patterns in forced, discrete, 2D systems such as the one considered here has not been addressed very often in the literature, see e.~g.~\cite{MUR99}. Due to the forcing term in the dynamic equations, the simple procedure to identify Turing instabilities cannot be applied. The main reason is the multistability of the individual SQUIDs, that results in a large number of periodic solutions for the SQUID metamaterial, even in the uncoupled case. Some of these solutions may be synchronized for $\lambda=0$ and may not be destroyed as the coupling is switched on. As a result, they may coexist with Turing-like patterns, indicating a complexity which cannot be handled by the simple analysis applied in classical Reaction-Diffusion systems. \subsection{Chimera states} \label{subsec:chimeras} Chimeras are known to coexist with the fully synchronized state and, therefore, in many cases, they can be very sensitive to initial conditions. This holds for our system too, where chimeras can be achieved only for certain spatial distributions of the initial values of $\phi$. For example, in the locally coupled 1D SQUID array \cite{HIZ16a}, a ``sine wave'' magnetic flux distribution was used for the initial conditions. It was shown that the SQUIDs that were prepared at lower values formed the coherent clusters of the chimera state, while those that were initially set at higher magnetic flux values, oscillated incoherently. Moreover, as the ``wavelength'' of the initial magnetic flux distribution increased, so did the chimera state multiplicity (number of (in)coherent clusters). Note that in our system, since the frequency of the SQUID oscillators is imposed by the external driving, we are dealing with \emph{amplitude} chimera states~\cite{BAN18}. \begin{figure}[ht] \includegraphics[width=0.5\textwidth]{fig6.jpg} \caption{3D snapshots of the magnetic flux (left) and the normalized discrete Laplacian (right) of a $30 \times 30$ SQUID lattice, for gradient initial conditions, $\lambda=-0.025$, $\Omega=1.007$ and different dc flux values: (a) $\phi_{dc}=0.0$ (see Supplementary Material for the corresponding video SM2(e)), (b) $\phi_{dc}=0.3$, and (c) $\phi_{dc}=1.0$. Other parameters are: $\phi_{ac}=0.06$, $\gamma=0.024$ and $\beta=0.1369$.} \label{fig06} \end{figure} Here we will employ a set of different initial conditions, inspired by experimental feasibility. In particular, we will use a spatial gradient for the magnetic fluxes $\phi_{nm}=\frac{n-1}{N-1}\phi_{\mathbf{max}}$, where $\phi_{\mathbf{max}}=1.5$ is the slope of the gradient, and zero values $(\dot \phi_{nm}=0)$ for their derivatives. Another important factor for achieving robust chimeras in our system is the choice of the driving frequency. As reported in \cite{HIZ16a}, it is crucial to be near the geometric resonance where the phenomenon of ``attractor crwoding''~\cite{HIZ16a} favors the emergence of such states. From section~\ref{sec1}, however, we know that by varying the dc flux, the snake-like form of the resonance curve shifts, resulting in loss of the SQUID multistability. It is interesting, therefore, to see what the effect of $\phi_{dc}$ will be on the creation of chimera states. Figure~\ref{fig06} shows 3D snapshots of the magnetic flux (left), and their corresponding normalized local curvature values, when the SQUID lattice is prepared with gradient initial conditions. In Fig.~\ref{fig06}(a) the dc flux is zero and the incoherent cluster forms at the part of the lattice which is initially set at high magnetic flux values. On the other hand, the left half of the lattice is coherent and performs low-amplitude oscillations (better vizualized in the video SM2(e) of the Supplementary Material). By changing the $\phi_{dc}$ value to 0.3, the chimera state is destroyed and the collective state exhibits no spatio-temporal structure (Fig.~\ref{fig06}(b)). This is due to the fact that for this dc flux value, the single SQUID is no longer multistable and chimera states are not possible. By further increasing $\phi_{dc}$ to unity, where the single SQUID is again multistable, the chimera reappears. Interestingly, comparing to Fig.~\ref{fig06}(a), we observe a ``swap'' in the position of the (in)coherent clusters, although the initial conditions are unchanged. This is due to the fact that for $\phi_{dc}=1$ the ``center'' of the periodic solutions has shifted by $1$ and the situation is reversed compared to Fig.~\ref{fig06}(a) where $\phi_{dc}=0.0$. Apart from the single chimeras of Fig.~\ref{fig06}, we can also achieve multichimera states (with more than one (in)coherent clusters), simply by increasing the slope of the initial conditions gradient. For instance, for a slope of $3.5$, a multichimera state with two (in)coherent domains is formed (not shown here). Recently, this mechanism for the generation of chimera states was reported, for \emph{non-identical} coupled SQUIDs, where the gradient was in the dc flux distribution rather than in the initial conditions~\cite{LAZ19}. Such chimeras are similar to the equivalent one-dimensional structures \cite{HIZ16a}, extended in the second spatial dimension. For different special initial conditions, other types of chimeras are also possible, which are specific to the 2D geometry and are not present in the one-dimensional array. Here, however, we chose to focus on the ``stripe'' chimeras of Fig.~\ref{fig06}, since the gradient flux initialization is easy to achieve experimentally. Finally, we take a look at the Fourier power spectrum of the chimera state, namely that of Fig.~\ref{fig06}(a), in the frequency domain. As we can see in Fig.~\ref{fig05}(c), the sharpest peak is located at the value of the driving frequency, and there are secondary broader peaks at higher frequencies too. The corresponding phase diagram in the panel below shows some typical solutions of SQUIDs in the lattice. It is clear that the coexistence of smaller and bigger amplitude attractors (which is absent in the patterns discussed in Subsection~\ref{subsec:patterns}) is the key to the emergence of chimera states in our system. It should be noted that the emergence and form of chimera states does not depend crucially on the particular lattice geometry, as long as the dimensionality of the SQUID metamaterial is the same and the same initial conditions are used. For example, chimera states similar to those demonstrated in~\cite{LAZ18} for a 2D SQUID metamaterial on a Lieb lattice can be obtained for the 2D tetragonal lattice considered here, when the same initial conditions are used. \subsection{Interplay of patterns} As demonstrated in the previous sections~\ref{subsec:patterns} and~\ref{subsec:chimeras}, our system is capable of exhibiting Turing-like patterns associated with the single SQUID bifurcation structure in the low coupling limit, as well as chimera states when the driving frequency is chosen close to the geometric resonance frequency. Chimeras emerge through special initial conditions and may disappear and reappear as the dc flux varies; Turing-like patterns, on the other hand, can be obtained for a random lattice initialization and a wider parameter range. Naturally, the question arises, under which circumstances do these different patterns coexist and how do they interact with each other as the system parameters change. \begin{figure}[ht] \includegraphics[width=.5\textwidth]{fig7.jpg} \caption{Classification of 2D patterns in the $(\phi_{dc},\lambda)$ parameter space for $\Omega=1.03$. ``SYNCH'' stands for synchronized state, ``TL'' for Turing-like state, ``CH'' for chimera state, and ``FL'' for formless state. Points \textbf{a} and \textbf{b} correspond to $(\phi_{dc},\lambda)=(0.2,-0.03)$ and $(0.17,-0.025)$, respectively. Other parameters are: $\phi_{ac}=0.06$, $\gamma=0.024$ and $\beta=0.1369$.} \label{fig07} \end{figure} Figure~\ref{fig07} shows a map of the possible patterns observed in our system, in the $(\phi_{dc},\lambda)$ parameter space, for a driving frequency close to the resonance ($\Omega=1.03$). We distinguish areas of synchronized states (SYNCH), chimera states (CH), Turing-like states (TL), and states with no clear pattern structure which we will refer to as ``formless'' states (FL). There are regions where different patterns may coexist, depending on the choice of initial conditions. We highlight two such examples, marked by points a and b. The corresponding coexisting states are shown in Fig.~\ref{fig08}(a) and (b): In Fig.~\ref{fig08}(a) a Turing-like patterns (left) coexists with a chimera state (right). Note that the unsychronized part of the chimera has an evident spatial structure, resembling a ``half'' Turing-like pattern. On the other hand, in Fig.~\ref{fig08}(b), the chimera state (right) has a rather formless desynchronized domain and coexists with an unstructured pattern shown in the left. \begin{figure}[ht] \includegraphics[width=.5\textwidth]{fig8.jpg} \caption{(a) Coexisting ``TL'' state (left) and ``CH'' state (right) for point \textbf{a} of Fig.~\ref{fig07}. (b) Coexisting `FL`` state (left) and ``CH'' state (right) for point \textbf{b} of Fig.~\ref{fig07}. Plots (c)-(d) show the evolution of the ``CH'' state of (b), as $\lambda$ increases along the arrow in Fig.~\ref{fig07}. Specifically: (c) $\lambda=-0.024$, (d) $\lambda=-0.022$, and (e) $\lambda=-0.02$. Other parameters are: $\Omega=1.03$, $\phi_{ac}=0.06$, $\gamma=0.024$ and $\beta=0.1369$.} \label{fig08} \end{figure} These coexisitng patterns are robust and do not transform between each other, as our long simulations (of the order of $10^4$ periods) can confirm. The transformation between states, however, can be achieved by varying the system parameters, namely the coupling strength and the dc flux, as shown in Fig.~\ref{fig07}. Specifically, a chimera state may evolve into a Turing-like pattern, but not the reverse since chimeras require special initial conditions in order to occur. Additionally, a formless state may also change into a Turing-like pattern and vice versa. By performing a continuation of states while varying the coupling strength $\lambda$ in the direction of the arrow in Fig.~\ref{fig07}, we can see that the chimera state of Fig.~\ref{fig08}(b) loses its structure and becomes a formless state in Fig.~\ref{fig08} (c). In turn, this state, by further increase of $\lambda$, evolves into a Turing-like pattern as depicted in Figs.~\ref{fig08} (d) and (e). Interestingly, the coexistence of chimeras and Turing-like patterns has been reported before in two-dimensional networks of nonlocally coupled neurons in the low coupling limit~\cite{SCH17} but, in general, is a question yet to be explored. \section{Conclusions} In conclusion, we have shown that a 2D SQUID lattice with nearest neighbor interactions is capable of exhibiting a rich menagerie of Turing-like pattern forming states. In the low coupling limit, this collective behavior emerges near the transition from synchronization to desynchronization where the single SQUID undergoes complex bifurcations. Moreover, near the geometric resonance, we observe 2D chimera states, as a result of the extreme multistability of the single SQUID. What is interesting is that by proper choice of initial conditions and tuning of the dc flux of the driving force, we are able to control the multiplicity and position of the chimera states, respectively. Additionally, in certain regions of the parameter space, chimeras may coexist with Turing-like patterns and also evolve into such, by proper tuning of the relevant parameters. Recent experiments~\cite{ZHU19} on the imaging of collective states in SQUID metamaterials through laser scanning microscopy (LSM technique), are very promising in terms of verifying our theoretical findings in the lab. \section{Supplementary Material} See Supplementary Material for the videos corresponding to Fig.~\ref{fig02}, the patterns of Fig.~\ref{fig04}, and the chimera state of Fig.~\ref{fig06}(a). \section*{Acknowledgement} This work was financially supported by the Ministry of Education and Science of the Russian Federation in the framework of Increase Competitiveness Program of NUST ``MISiS'' (grant No. K3-2018-027). JH and NL acknowledge support by the General Secretariat for Research and Technology (GSRT) and the Hellenic Foundation for Research and Innovation (HFRI) (Code: 203). JH would also like to thank Jan Sieber for helping with the continuation tool.	{ "redpajama_set_name": "RedPajamaArXiv" }	7,250
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Q: Limit Tags display and ad Drop Down Menu Does anyone have any idea on how i can limit the number of tags shown in a post and if there is more it's a drop down menu. Here's an example of what i mean. Se where it sats "More On" those are the tags, I want to be able to show only 3 tags and then after that a drop down menu for the rest of the tags. Is this possible, If so how can I do this. Only Tags Attached To The Post A: This can be a start... <?php $tags = wp_get_post_tags($post_id); $html = '<div class="post_tags">'; $i=1; foreach ( $tags as $tag ) { $tag_link = get_tag_link( $tag->term_id ); if($i>3) { if($i==4) { $html .= '<ul class="post_tags_menu">'; } $html .= "<li><a href='{$tag_link}' title='{$tag->name} Tag' class='{$tag->slug}'>"; $html .= "{$tag->name}</a><li>"; } else { $html .= "<a href='{$tag_link}' title='{$tag->name} Tag' class='{$tag->slug}'>"; $html .= "{$tag->name}</a>"; } $i++; } if($i>4) { $html .= "</ul>"; } $html .= '</div>'; echo $html; ?> How to get post tags http://codex.wordpress.org/Function_Reference/wp_get_post_tags	{ "redpajama_set_name": "RedPajamaStackExchange" }	7,237
Q: Organizing a CSV file with missing columns Problem I have a .csv file that was not filled in properly, which has missing column information. The file looks something like this (whitespace is for clarity): C1, C2, C3, C4, R1C1,R1C2,R1C3,R1C4, R2C1,R2C3, , , R3C1,R3C4, , , ... Where Cx is the column header and shares a string value with RyCx. For example, Name , Date , Address , Email , Name Alex, Date Sept 3, Address 123 Madeup, Email Alex@mail.com, Name Jenn, Date Sept 4, Email Jenn@mail.co, , Where now Email Jenn@mail.co is incorrectly in the Address column. There is any number of null spaces after the data. The data is laid out so that each row is in order [R1C1,R1C2,R1C3 ...] unless the data does not exist - in which case the columns shift left but their tag Cx does not change. This is because the program outputting the data did not create null cells. There are no other patterns to this data. I would like to reorganize this data into the appropriate column as: C1, C2, C3, C4, R1C1,R1C2,R1C3,R1C4, R2C1, ,R2C3, , R3C1, , ,R3C4, ... or in the example as Name , Date , Address , Email , Name Alex, Date Sept 3, Address 123 Madeup, Email Alex@mail.com, Name Jenn, Date Sept 4, , Email Jenn@mail.co , I cannot go back to where the information was gathered, it's older supercomputer simulation results. Solution Thanks to FKEinternet and urcodebetterznow. while IFS= read -r line; do # read input line by line IFS=, read -ra fields <<<"$line" #separate fields by commas j=0; for i in $(cat headers.txt); do #I wrote the headers to a different file if [ "${fields[j]}" == "$i" ]; then #replaced with grep -o result because fields are not exact matches for the header, but contain exact matches val="${fields[j]}"; : $((j += 1)); else val=''; fi; printf '%s,' "$val"; #I later used sed to erase the redundant information already in the header done done < datafile.txt > solution.csv where a file headers.txt looks like: a b c d e f g h And the data looks like datafile.txt: a,b,c,d,e, a,c,e b,d,f,g,h c,d,g,h d,h b,f,g a,d,f,g Running the bash script I get (whitespace for clarity): a,b,c,d,e, , , , a, ,c, ,e, , , , ,b, ,d, ,f,g,h, , ,c,d, , ,g,h, , , ,d, , , ,h, ,b, , , ,f,g, , a, , ,d, ,f,g, , which was the desired result. A: Your rewritten question is now conceptually pretty easy to answer: You have an array of tags that may or may not be present in each row of data. You want to read in each row, and go through the columns in order, checking to see if the tag in that column is the one that's expected. If not, insert a blank cell, and check the next column. Once you get to the end of the list of expected tags, emit the reconstructed row. Here's some pseudocode, which you can implement in the language of your choice: read the first row split the text on commas to create the array of expected tags read the next row if no more data, exit split the text on commas to create a row data array for each expected tag check the current column in the row's data if the tag matches write the column data to the output advance the current column in the row data else write a blank column to the output terminate the output line A: I just noticed that each column of your data actually begins with the name of the column. I must have missed that when I first saw your question. That makes it not only possible but fairly easy to reformat the data. #!/usr/bin/perl use strict; my @headers; # array to hold the headers in the order they were seen. my @search; # array to hold a copy of @headers sorted by string length while(<>) { chomp; # remove newline character at end-of-line if ($. == 1) { next if (scalar @headers); # only process headers for first file # Split the first line into @headers array, removing any # leading or trailing spaces from each column @headers = split '\s,\s'; # In case one key might be a substring of another key, copy the # @headers array, sorted by length, so we can compare the data # with the longest header names first. @search = sort { length($b) <=> length($a) } @headers; print join(",", @headers), "\n"; } else { my %columns = (); # Loop over each column of the input line (row), inserting it into # the %columns hash, using the appropriate column name as the key. foreach my $c (split '\s,\s') { my $found = 0; foreach my $h (@search) { # If the current column ($c) begins with a header # name ($h), we've found the right key for it. if ($c =~ s/^$h\s+//i) { # match and remove header from column #if ($c =~ m/^$h\s+/i) { # or just match without removing header $columns{$h} = $c; $found = 1; }; }; warn "Unknown column '$c' in line $. of $ARGV\n" if ($c ne '' && ! $found); }; # Output every column in the same order as in the header line. # Columns not actually present in a row are output as an empty field print join(",", @columns{@headers}), "\n"; }; # Reset the line counter at the end of each input file if # there's more than one close(ARGV) if eof; } The regular expressions to match each column are matched case-insensitively. If your data has columns with upper and lower or mixed case versions of the same name, then remove the /i modifier from the regexes. Save this with a suitable name, e.g. ./fix-data.pl, and make it executable with chmod +x ./fix-data.pl. Sample output: $ ./fix-data.pl datafile.txt Name,Date,Address,Email Alex,Sept 3,123 Madeup,Alex@mail.com Jenn,Sept 4,,Jenn@mail.co or, using the commented-out alternative if statement: $ ./fix-data.pl datafile.txt Name,Date,Address,Email Name Alex,Date Sept 3,Address 123 Madeup,Email Alex@mail.com Name Jenn,Date Sept 4,,Email Jenn@mail.co I don't know why anyone would want this second format because the column names are already in the headers line, and every output row has every column in the right order....but it was easy enough to do if that's what you want. BTW, you can format the output as a table with same-width columns by piping it into column: $ ./fix-data.pl datafile.txt \| column -t -s , -o ', ' Name, Date , Address , Email Alex, Sept 3, 123 Madeup, Alex@mail.com Jenn, Sept 4, , Jenn@mail.co Using column with ' \| ' as the output separator is IMO more human-readable (and still easily imported into a spreadsheet or parsed by other programs) $ ./fix-data.pl datafile.txt \| column -t -s , -o ' \| ' Name \| Date \| Address \| Email Alex \| Sept 3 \| 123 Madeup \| Alex@mail.com Jenn \| Sept 4 \| \| Jenn@mail.co column can even output the data as valid json, for example: $ ./fix-data.pl datafile.txt \| tail -n +2 \| column --json -s , \ --table-columns "$(sed -n -e '1s/ , /,/gp' datafile.txt)" { "table": [ { "name": "Alex", "date": "Sept 3", "address": "123 Madeup", "email": "Alex@mail.com" },{ "name": "Jenn", "date": "Sept 4", "address": null, "email": "Jenn@mail.co" } ] } (On Debian, at least, column is in the bsdextrautils package. On other distros, it's probably in util-linux) miller and datamash are also useful command-line tools for working with your data once you've got it into a sane format. NOTE: The script assumes that the data is just a simple comma-delimited format, not properly-formed CSV (see, e.g., RFC 4180 - Common Format and MIME Type for Comma-Separated Values (CSV) Files) with the possibility of quoted string fields and even embedded commas within quoted fields. If any of rows have quoted columns, you'd need to use a CSV parser instead of simply splitting each input line on commas. e.g. perl's Text::CSV module. I don't think this is likely to be needed as your data is in a weird not-actually-CSV format apparently invented by whoever generated it (and if they knew about CSV they would probably have used it...or messed up the data even worse than it already is). This caveat would apply to any implementation in any language, because the issue would be a result of the janky data, not the code. column won't work with CSV containing embedded commas, either.	{ "redpajama_set_name": "RedPajamaStackExchange" }	9,426
Charles Martinelli, nom de scène de Charles Émile Louis Alphonse Martinet, est un acteur français né le dans le de Paris, ville où il est mort le en son domicile dans le . Biographie Charles Martinelli était l'époux de la chanteuse d'opéra Germaine Martinelli depuis 1908 et le père du comédien Jean Martinelli. Filmographie 1921 : Les Trois Mousquetaires de Henri Diamant-Berger : Porthos 1923 : Gonzague de Henri Diamant-Berger 1923 : Le Mauvais Garçon de Henri Diamant-Berger : le père 1923 : Jim Bougne, boxeur d'Henri Diamant-Berger : M. Martinet 1923 : L'Affaire de la rue de Lourcine d'Henri Diamant-Berger 1923 : Paris qui dort de René Clair : le savant fou 1924 : Le Roi de la vitesse de Henri Diamant-Berger : Cecco 1924 : Un fil à la patte de Robert Saidreau 1926 : La Tournée Farigoule de Marcel Manchez : Farigoule 1933 : Don Quichotte, de Georg Wilhelm Pabst : le chef des gendarmes 1933 : Tambour battant 1938 : Un fichu métier de Pierre-Jean Ducis Autres Opéra : Panurge (1913) de Jules Massenet : Pantagruel Notes et références Liens externes Charles Martinelli sur lesgensducinema Acteur français de cinéma Naissance en avril 1882 Naissance dans le 5e arrondissement de Paris Décès en août 1954 Décès dans le 1er arrondissement de Paris Décès à 72 ans	{ "redpajama_set_name": "RedPajamaWikipedia" }	1,315
Q: Надо ли закрывать файл после чтения и записи .xlsx? Надо ли закрывать доступ к файлу после чтения, записи файлов .xlsx, как по аналогии с чтением текстовых файлов через file handle? Открываю excel: import pandas as pd file = 'expru1.xlsx' df = pd.read_excel(file, 'Лист1', header=None) Необходимы ли дальше какие-либо действия, если сам файл 'expru1.xlsx' больше не нужен? Или можно работать с данными дальше? Тот же самый вопрос - что делаем после записи файла: df.to_excel('C:\\Users\\guzairovt\\forecast.xlsx', index=False) Конец скрипта, или надо как-то закрывать доступ? A: После того как команда pd.read_excel(filename) отработает и вернет прочитанный DataFrame filename будет автоматически закрыт. Тоже самое происходит после того как отработает команда df.to_excel(...). Более того если вы хотите записать сразу несколько Excel листов (sheets), то делать это надо так: if you wish to write to more than one sheet in the workbook, it is necessary to specify an ExcelWriter object: >>> df2 = df1.copy() >>> with pd.ExcelWriter('output.xlsx') as writer: # doctest: +SKIP ... df1.to_excel(writer, sheet_name='Sheet_name_1') ... df2.to_excel(writer, sheet_name='Sheet_name_2')	{ "redpajama_set_name": "RedPajamaStackExchange" }	487
from sqlalchemy import Column, Float, Integer, Text, ForeignKey, Boolean from sqlalchemy.orm import relationship, validates from planner.model import Base, ValidationError class Engagement(Base): __tablename__ = 'Engagement' id = Column(Integer, autoincrement=True, primary_key=True) name = Column(Text, nullable=False) revenue = Column(Integer, nullable=False) proposal = Column(Text) backlog = Column(Text) isrnd = Column(Boolean) ponumber = Column(Text) teamid = Column(Integer, ForeignKey('Team.id')) team = relationship("Team") clientid = Column(Integer, ForeignKey('Client.id')) client = relationship("Client") statusid = Column(Integer, ForeignKey('Status.id')) status = relationship("Status") complexityid = Column(Integer, ForeignKey('Complexity.id')) complexity = relationship("Complexity") probabilityid = Column(Integer, ForeignKey('Probability.id')) probability = relationship("Probability") sustainabilityid = Column(Integer, ForeignKey('Sustainability.id')) sustainability = relationship("Sustainability") alignmentid = Column(Integer, ForeignKey('Alignment.id')) alignment = relationship("Alignment") expenses = relationship("Expense") actualiterations = relationship("EngagementIteration") estimatediterations = relationship("EstimatedEngagementIteration") class Expense(Base): __tablename__ = 'Expense' id = Column(Integer, autoincrement=True, primary_key=True) value = Column(Integer, nullable=False) trackerid = Column(Text, nullable=False) paid = Column(Boolean, nullable=False) engagementid = Column(Integer, ForeignKey('Engagement.id')) typeid = Column(Integer, ForeignKey('ExpenseType.id')) type = relationship("ExpenseType") @validates('value') def validate_value(self, key, address): if address < 0: raise ValidationError return address class ExpenseType(Base): __tablename__ = "ExpenseType" id = Column(Integer, autoincrement=True, primary_key=True) name = Column(Text, nullable=False, unique=True) class Status(Base): __tablename__ = 'Status' id = Column(Integer, autoincrement=True, primary_key=True) name = Column(Text, nullable=False, unique=True) class Alignment(Base): __tablename__ = 'Alignment' id = Column(Integer, autoincrement=True, primary_key=True) value = Column(Float, nullable=False, unique=True) name = Column(Text, nullable=False, unique=True) @validates('value') def validate_value(self, key, address): if address not in [0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0]: raise ValidationError(str(address) + ' is invalid') return address class Sustainability(Base): __tablename__ = 'Sustainability' id = Column(Integer, autoincrement=True, primary_key=True) value = Column(Float, nullable=False, unique=True) name = Column(Text, nullable=False, unique=True) @validates('value') def validate_value(self, key, address): if address not in [0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0]: raise ValidationError(str(address) + ' is invalid') return address class Probability(Base): __tablename__ = 'Probability' id = Column(Integer, autoincrement=True, primary_key=True) value = Column(Float, nullable=False, unique=True) name = Column(Text, nullable=False, unique=True) @validates('value') def validate_value(self, key, address): if address not in [0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0]: raise ValidationError(str(address) + ' is invalid') return address class Complexity(Base): __tablename__ = 'Complexity' id = Column(Integer, autoincrement=True, primary_key=True) value = Column(Float, nullable=False, unique=True) name = Column(Text, nullable=False, unique=True) guide_revenue = Column(Integer) @validates('value') def validate_value(self, key, address): if address not in [0.1, 0.5, 1.0, 2.0]: raise ValidationError(str(address) + ' is invalid') return address	{ "redpajama_set_name": "RedPajamaGithub" }	457
\section{Introduction} With access to large-scale labeled data, deep neural networks have achieved state-of-the-art performance among a variety of machine learning problems and applications \cite{krizhevsky2012imagenet, oquab2014learning, donahue2014decaf, yosinski2014transferable, ren2015faster, he2016deep, he2017mask}. However, with intolerably time-consuming and labor-expensive costs, it is hard for a target domain of interest to collect enough labeled data for model training. One solution is to transfer a deep neural network trained on a data-sufficient source domain to the target domain where only unlabeled data is available. However, this learning paradigm suffers from the shift in data distributions across different domains, which brings a major obstacle in adapting predictive models for the target task. Domain Adaptation (DA) \cite{pan2009survey, yang2020transfer} aims to learn a high-performance learner on a target domain via utilizing the knowledge transferred from a source domain, which has a different but related data distribution to the target domain. A number of DA methods aim to bridge the gap between source and target domains so that the classifier learned in the source domain can be applied to the target domain. To achieve this goal, recent DA works can be grouped into two main categories: \textit{distance-based} methods \cite{ben2007analysis, ben2010theory, zhuang2015supervised, tzeng2014deep, long2015learning, courty2016optimal, sun2016return, sun2016deep, zellinger2017central, chen2019joint} and \textit{adversarial} DA methods \cite{ganin2016domain, long2017conditional, pei2018multi, tzeng2017adversarial, saito2018maximum}. Both categories aim to learn the domain-invariant feature representations. In this paper, we mainly focus on distance-based DA methods. For distance functions adopted by DA, the first attempt is the \textit{Proxy} $\mathcal{A}$-\textit{distance} \cite{ben2010theory}, which aims to minimize the generalization error by discriminating between source and target samples. \textit{Maximum Mean Discrepancy} (MMD) \cite{gretton2006kernel} is a popular distance measures between two domains and it has been used in Deep Domain Confusion (DDC) \cite{tzeng2014deep} and Deep Adaptation Network (DAN) \cite{long2015learning}. Although numerous distance-based DA methods have been proposed, learning the domain-invariant feature representation is still challenging since distances in a high-dimensional space may be difficult to truly reflect the domain discrepancy. Moreover, all of these methods are developed by using hand-crafted network architectures. Since the difficulty levels of different DA tasks are not the same, accomplishing complex tasks may require a more sophisticated network architecture than easy tasks, hence, using the same hand-crafted network architecture may limit the capacity and versatility of DA methods. To alleviate these limitations, in this paper, we propose a new similarity function, which is called Population Correlation (PC), to measure the similarity between the source and target domains. Based on the PC function, we propose a novel domain adaptation method called Domain Adaptation by Maximizing Population Correlation (DAMPC). DAMPC aims to maximize the PC between the source and target domains so that a learning model can learn a domain-invariant feature representation. Specifically, With the PC defined as the maximum of pairwise correlations between source and target samples, the proposed DAMPC method maximize it to force the two domains to have similar distributions as well as minimizing the classification loss on the labeled source samples. Built on the DAMPC method, we design a reinforcement-based Neural Architecture Search (NAS) method called DAMPC-NAS to search an optimal network architecture for DAMPC. In this way, DAMPC-NAS can learn suitable network architectures for different DA tasks. To the best of our knowledge, the proposed DAMPC-NAS method is the first NAS framework designed for similarity-based DA methods. DAMPC-NAS is also one of few works that integrate NAS methods into deep DA methods. Our contributions are summarized as follows. \begin{itemize} \item We propose a new similarity measure, i.e., PC, to measure the domain similarity. Based on the PC, we propose a DAMPC method for DA. \item We design the DAMPC-NAS framework to search optimal network architectures for the proposed DAMPC method. \item Experimental results on three benchmark datasets demonstrate the effectiveness of the proposed methods. \end{itemize} \section{Related Work} \paragraph{Neural Architecture Search} NAS aims to design the architecture of a neural network in an automated way. Comparing with manually designed architectures of neural networks, NAS has demonstrated the capability to find architectures with state-of-the-art performance in various tasks \cite{pham2018efficient, lsy19, ghiasi2019fpn}. For example, the NAS-FPN method \cite{ghiasi2019fpn} leverages NAS to learn an effective architecture of the feature pyramid network for object detection. Although NAS can achieve satisfactory performance, the high computational cost of the searching procedure makes NAS less attractive. To accelerate the search procedure, one-shot NAS leverages a supergraph, which contains all the candidate architectures in the search space. In the supergraph, weights of operations on edges are shared across different candidate architectures. ENAS \cite{pham2018efficient} employs a reinforcement-based method to train a controller that samples architectures from a supergraph with a weight sharing mechanism. DARTS \cite{lsy19} search architectures with a differentiable objective function based on a supergraph that uses the softmax function to contain all candidate operations on each edge. The final architecture is determined based on the weights corresponding to the candidate operations on each edge. \paragraph{Domain Adaptation} DA aims to transfer the knowledge learned from a source domain with labeled data to a target domain without labeled data, where there is a domain shift between domains. As discussed in the introduction, recent works in DA can be mainly grouped into two categories: distance-based methods and adversarial DA methods. In this paper, we mainly focus on \textit{distance-based} methods, which minimize the discrepancy between the source and target domains via some measures, including the MMD used in DDC \cite{tzeng2014deep}, DAN \cite{long2015learning}, Weighted Domain Adaptation Network (WDAN) \cite{yan2017mind}, Joint Adaptation Networks (JAN) \cite{long2017deep}, and Deep Subdomain Adaptation Network (DSAN) \cite{zhu2020deep}, the \textit{Kullback-Leibler divergence} adopted in Transfer Learning with Deep Autoconders (TLDA) \cite{zhuang2015supervised}, the \textit{second-order statistics} utilized in CORrelation ALignment (CORAL) \cite{sun2016return, sun2016deep}, and the Central Moment Discrepancy (CMD) \cite{zellinger2017central}. \begin{figure}[htbp] \centering \includegraphics[width=0.95\linewidth]{DAMPC-NAS.pdf} \caption{Overview of the DAMPC-NAS framework. Source and target data first go through the feature extractor to extract hidden features. The controller samples cell choices for each cell and connections between the cells from search space to generate the architecture of the sampled network. Source and target data with the extracted feature representation then go through the sampled network. Finally, the cross-entropy loss is minimized and the PC is maximized. The controller's policy is updated by the reward of the negative overall loss.} \label{fig:model} \end{figure} \paragraph{Neural Architecture Search for Domain Adaptation} There are few works on NAS for DA. To improve the generalization ability of neural networks for DA, \citet{li2020adapting} analyze the generalization bound of neural architectures and propose the AdaptNAS method to adapt neural architectures between domains. \citet{li2020network} propose a DARTS-like method for DA, which combines DARTS and DA into one framework. \citet{robbiano2021adversarial} aim to learn a auxiliary branch network from data for an adversarial DA method. In this paper, different from those works, we aim to leverage NAS to search optimal neural architectures for the proposed DAMPC method. \section{Methodology} In this section, we introduce the proposed PC similarity and the DAMPC method as well as the DAMPC-NAS method. \subsection{Population Correlation} We first present the definition of PC. Here we study DA under the unsupervised setting. That is, the target domain has unlabeled data only. In DA, the source domain $\mathcal{D}_{s}=\left\{\left(\mathbf{x}_{i}^{s}, \mathbf{y}_{i}^{s}\right)\right\}_{i=1}^{n_{s}}$ has $n_s$ labeled samples and the target domain $\mathcal{D}_{t}=\left\{\mathbf{x}_{j}^{t}\right\}_{j=1}^{n_{t}}$ has $n_t$ unlabeled samples. To adapt the classifier trained on the source domain to the target domain, one solution is to minimize the domain discrepancy or equivalently maximize the domain similarity. To achieve this, we propose the PC to measure the similarity between the source and target domains. Specifically, suppose $F(\cdot)$ is the feature extraction network. Then the PC between the source and target domains can be computed based on each pair of source and target samples as \begin{equation} \label{eq:pc_loss} \begin{aligned} \mathrm{PC}(\mathcal{D}^s,\mathcal{D}^t)=&\frac{1}{n_s}\sum_{i=1}^{n_s}\max_{j\in[n_t]}\mathrm{corr}\left(F(\mathbf{x}^s_i),F(\mathbf{x}^t_j)\right)\\ &+\frac{1}{n_t}\sum_{j=1}^{n_t}\max_{i\in[n_s]}\mathrm{corr}\left(F(\mathbf{x}^s_i),F(\mathbf{x}^t_j)\right), \end{aligned} \end{equation} where $\\|\cdot\\|_2$ denotes the $\ell_2$ norm of a vector, $\mathrm{corr}(\mathbf{x}_1,\mathbf{x}_2)=\frac{\mathbf{x}_1^T\mathbf{x}_2}{\\|\mathbf{x}_1\\|_2\\|\mathbf{x}_2\\|_2}$ denotes the correlation between two vectors, and $[n]$ denotes a set of integers $\{1,\ldots,n\}$ for an integer $n$. Here we use the cosine similarity to calculate the correlation between two vectors, thus the larger the PC value is, the more similar the two domains are. \subsection{DAMPC} Built on the PC introduced in the previous section, in this section, we present the proposed DAMPC method which aims to learn a domain-invariant feature representation. For DA tasks, the hidden feature representations learned by the feature extraction network should be not only discriminative to train a strong classifier but also domain-invariant to both the source and target domains. Only maximizing the PC can help learn a domain-invariant feature representation and only minimizing the classification loss is to learn a discriminative feature representation. Therefore, we combine the classification loss and the PC to obtain the final objective function, which is formulated as \begin{equation} \label{eq:obj} \mathcal{L}_{\text{DAMPC}} = \frac{1}{n_s}\sum_{i=1}^{n_s}l(C(F(\mathbf{x}^s_i)),y^s_i)-\lambda\mathrm{PC}(\mathcal{D}^s,\mathcal{D}^t), \end{equation} where $\lambda$ is a trade-off parameter, $C(\cdot)$ denotes the classification layer, and $l(\cdot,\cdot)$ denotes the classification loss such as the cross-entropy loss. By minimizing Eq. (\ref{eq:obj}), the final learned feature representations are not only discriminative for classification but also domain-invariant for the adaptation. \subsection{DAMPC-NAS} In this section, we introduce the proposed DAMPC-NAS framework that finds an optimal architecture for the DAMPC method introduced in the previous section. An overview of the DAMPC-NAS framework is shown in Figure \ref{fig:model}. \subsubsection{Cell-based Search Space} We design the search space on the top of the Resnet-50 backbone, whose architecture is kept fixed, and hence we only search the architecture after the backbone. The search space of the DAMPC-NAS method consists of two parts: within cells and between cells. We design the cell as the composition of the fully connected layer, batch-norm layer, and dropout layer as well as the associated activation functions. Within the cell, we search for the size of the fully connected layer and the location of the skip connection. Specifically, the search choice of the fully connected layer in a cell can be `the same as input size' or `the half of input size'. The starting location of the skip connection can be chosen from the cell input, the fully connected layer, and the batch-norm layer. Between the cells, we search for input and output connections of the $N$ cells. For example, if there are three cells in the search space, i.e., $N=3$, the input of ``Cell 1'' can be chosen from the outputs of ``Backbone'' and ``Cell 0'', and the input of ``Cell 2'' can be chosen from the outputs of ``Cell 0'' and ``Cell 1'', hence the input of a cell can be chosen from the outputs of the previous two cells. The calculation of PC can be choose from one of outputs of all cells. Moreover, One of the outputs from the $N$ cells, i.e., ``Cell 0'', ``Cell 1'' and ``Cell 2'', can connect to the classifier trained on source domain data. Hence, the total search space has $(2\times3)^N2^{N-1}N^2$ configurations. An illustration of the search space in the DAMPC-NAS method is shown in Figure \ref{fig:search_space}. In experiments, for efficiency, we use the search space with $N=3$ cells for all experiments. \begin{figure}[htbp!] \centering \includegraphics[width=0.95\linewidth]{search_space.pdf} \caption{The search space of the DAMPC-NAS method. Dashed lines represent possible search choices and numbered grey circles indicate the order of choices generated from the controller.} \label{fig:search_space} \end{figure} \subsubsection{Searching optimal architecture} The searching algorithm for the DAMPC-NAS method is described in Algorithm \ref{alg:nas}. DAMPC-NAS is a reinforcement-based NAS framework which leverages a controller network to sample architectures from the search space. The controller network is a LSTM that samples search choice via a softmax classifier. We denote by $\theta$ the learnable parameters of the controller. The policy of the controller is denoted by $\pi(m;\theta)$. In each epoch, the training procedure of DAMPC-NAS consists of two phases. In the first phase, we fix parameters of the controller $\theta$ and train the shared weights $\omega$ in the search space $\mathcal{A}_{space}$. Specifically, the controller samples an architecture $\mathcal{A}_{m}$ from the search space $\mathcal{A}_{space}$ with policy $\pi(m;\theta)$. For each mini-batch from $\mathcal{D}_{s}$ and $\mathcal{D}_{t}$, $\mathcal{L}_{\text{DAMPC}}$ is computed according to Eq. (\ref{eq:obj}) and the shared weights $\omega_{m}$ of the sampled architecture are updated by minimizing $\mathcal{L}_\text{DAMPC}$. In the second phase, we fix all the shared weights $\omega$ in the search space $\mathcal{A}_{space}$ and update the parameter $\theta$ of the controller. Specifically, after one epoch of training, $-\mathcal{L}_\text{DAMPC}$ is used as the reward to update the policy $\pi(m;\theta)$ in the controller. The gradient is computed via the REINFORCE algorithm \cite{williams1992simple} with a moving average baseline. \begin{algorithm} \SetAlgoLined \SetKwInOut{Input}{Input} \SetKwInOut{Output}{Output} \SetKwInOut{Return}{Return} \SetKwComment{Comment}{// }{} \SetCommentSty{normalsize} \Input{source data $\mathcal{D}_{s}$, target data $\mathcal{D}_{t}$, the number of training epochs $n_{epochs}$} \Output{The searched architecture with learned weights} initialize controller\; \For{$i\gets0$ \KwTo $n_{epochs}$}{ sample $\mathcal{A}_{m}$ from $\mathcal{A}_{space}$ with policy $\pi(m;\theta)$\; \Comment{fix controller policy $\pi(m;\theta)$ and train $\omega$ in $\mathcal{A}_{space}$} \For{\text{mini-batch} in $\mathcal{D}_{s}$ and $\mathcal{D}_{t}$}{ compute $\mathcal{L}_\text{DAMPC}$ in Eq. (\ref{eq:obj}) with $\mathcal{A}_{m}$\; update $\omega_m$ in $\mathcal{A}_{space}$\ with $\mathcal{L}_\text{DAMPC}$\; } \Comment{fix $\omega$ in $\mathcal{A}_{space}$ and update $\theta$ in policy $\pi(m;\theta)$} calculate reward of $\mathcal{A}_{m}$ as $R_m=-\mathcal{L}_{\text{DAMPC}}$\; update $\theta$ in $\pi(m;\theta)$ with reward $R_m$\; } \Return{$\mathcal{A}_{m}$ with trained weights $\omega_m$} \caption{Overview of DAMPC-NAS} \label{alg:nas} \end{algorithm} In summary, the DAMPC-NAS method is a one-shot style NAS method. That is, the DAMPC-NAS method trains a supernet that contains all shared parameters in the search space during the searching process. The DAMPC-NAS method samples a child network in each epoch to calculate the loss function defined in Eq. (\ref{eq:obj}) and updates its shared parameters in the search space. Parameters in the controller are updated by the reward, which is the negative loss of the sampled child network. After searching, all weights of the final architecture are retained for testing. Different from two-stage one-shot NAS methods, there is no need for the DAMPC-NAS method to retrain the final architecture from scratch for testing since DAMPC-NAS can directly optimize the objective in Eq. (\ref{eq:obj}), which is just the negative reward for the controller, in an end-to-end manner. In this way, the architecture is optimized alongside child networks' parameters. Therefore, the final architecture derived from the DAMPC-NAS method can be deployed directly without parameter retraining, which improves the efficiency. \section{Experiments} In this section, we empirically evaluate the proposed method. \begin{table}[htbp] \centering \caption{Accuracy (\%) on the Office-31 dataset with ResNet-50 as the backbone.} \begin{tabular}{llccccccc} \toprule Type & Method & A$\rightarrow$D & A$\rightarrow$W & D$\rightarrow$A & D$\rightarrow$W & W$\rightarrow$A & W$\rightarrow$D & Avg \\ \midrule & ResNet-50 \cite{he2016deep} & 68.9 & 68.4 & 62.5 & 96.7 & 60.7 & 99.3 & 76.1 \\ \cmidrule(){1-9} \multirow{6}{Dist Based} & JDA \cite{long2013transfer} & 80.7 & 73.6 & 64.7 & 96.5 & 63.1 & 98.6 & 79.5 \\ & DDC \cite{tzeng2014deep} & 76.5 & 75.6 & 62.2 & 96.0 & 61.5 & 98.2 & 78.3 \\ & DAN \cite{long2015learning} & 78.6 & 80.5 & 63.6 & 97.1 & 62.8 & 99.6 & 80.4 \\ & D-CORAL \cite{sun2016deep} & 81.5 & 77.0 & 65.9 & 97.1 & 64.3 & 99.6 & 80.9 \\ & JAN \cite{long2017deep} & 84.7 & 85.4 & 68.6 & 97.4 & 70.0 & 99.8 & 84.3 \\ & MDDA \cite{wang2020transfer} & 86.3 & 86.0 & \textbf{72.1} & 97.1 & \textbf{73.2} & 99.2 & 85.7 \\ \cmidrule(){1-9} \multirow{4}{Adv Based} & DANN \cite{ganin2015unsupervised} & 79.7 & 82.0 & 68.2 & 96.9 & 67.4 & 99.1 & 82.2 \\ & ADDA \cite{tzeng2017adversarial} & 77.8 & 86.2 & 69.5 & 96.2 & 68.9 & 98.4 & 82.9 \\ & CAN \cite{zhang2018collaborative} & 85.5 & 81.5 & 65.9 & 98.2 & 63.4 & 99.7 & 82.4 \\ & DDAN \cite{wang2020transfer} & 84.9 & 88.8 & 65.3 & 96.7 & 65.0 & \textbf{100.0} & 83.5 \\ \midrule & DAMPC-NAS (Ours) & \textbf{89.16} & \textbf{93.08} & 70.36 & \textbf{98.74} & 69.05 & \textbf{100.0} & \textbf{86.69} \\ \bottomrule \end{tabular} \label{tab:office31} \end{table} \begin{table}[ht] \centering \caption{Accuracy (\%) on the Office-Home dataset with ResNet-50 as the backbone.} \resizebox{\linewidth}{!}{ \begin{tabular}{llccccccccccccc} \toprule Type & Method & Ar$\rightarrow$Cl & Ar$\rightarrow$Pr & Ar$\rightarrow$Rw & Cl$\rightarrow$Ar & Cl$\rightarrow$Pr & Cl$\rightarrow$Rw & Pr$\rightarrow$Ar & Pr$\rightarrow$Cl & Pr$\rightarrow$Rw & Rw$\rightarrow$Ar & Rw$\rightarrow$Cl & Rw$\rightarrow$Pr & Avg \\ \midrule & ResNet-50 \cite{he2016deep} & 34.9 & 50.0 & 58.0 & 37.4 & 41.9 & 46.2 & 38.5 & 31.2 & 60.4 & 53.9 & 41.2 & 59.9 & 46.1 \\ \cmidrule(){1-15} \multirow{4}{Dist Based} & JDA \cite{long2013transfer} & 38.9 & 54.8 & 58.2 & 36.2 & 53.1 & 50.2 & 42.1 & 38.2 & 63.1 & 50.2 & 44.0 & 68.2 & 49.8 \\ & DAN \cite{long2015learning} & 43.6 & 57.0 & 67.9 & 45.8 & 56.5 & 60.4 & 44.0 & 43.6 & 67.7 & 63.1 & 51.5 & 74.3 & 56.3 \\ & D-CORAL \cite{sun2016deep} & 42.2 & 59.1 & 64.9 & 46.4 & 56.3 & 58.3 & 45.4 & 41.2 & 68.5 & 60.1 & 48.2 & 73.1 & 55.3 \\ & JAN \cite{long2017deep} & 45.9 & 61.2 & 68.9 & 50.4 & 59.7 & 61.0 & 45.8 & 43.4 & 70.3 & 63.9 & 52.4 & 76.8 & 58.3 \\ \cmidrule(){1-15} \multirow{3}{Adv Based} & DANN \cite{ganin2015unsupervised} & 45.6 & 59.3 & 70.1 & 47.0 & 58.5 & 60.9 & 46.1 & 43.7 & 68.5 & 63.2 & 51.8 & 76.8 & 57.6 \\ & CDAN \cite{long2017conditional} & 46.6 & 65.9 & 73.4 & 55.7 & 62.7 & 64.2 & 51.8 & \textbf{49.1} & 74.5 & 68.2 & \textbf{56.9} & \textbf{80.7} & 62.8 \\ & DDAN \cite{wang2020transfer} & \textbf{51.0} & 66.0 & 73.9 & 57.0 & 63.1 & 65.1 & 52.0 & 48.4 & 72.7 & 65.1 & 56.6 & 78.9 & 62.5 \\ \midrule & DAMPC-NAS (Ours) & 46.53 & \textbf{68.42} & \textbf{75.24} & \textbf{58.3} & \textbf{66.3} & \textbf{67.48} & \textbf{56.94} & 44.77 & \textbf{75.33} & \textbf{69.26} & 51.94 & 80.33 & \textbf{63.4} \\ \bottomrule \end{tabular} } \label{tab:officehome} \end{table} \subsection{Setup} We conduct experiments on three benchmark datasets, including Office-31 \cite{saenko2010adapting}, Office-Home \cite{venkateswara2017deep}, and VisDA-2017 \cite{peng2017visda}. The Office-31 dataset has 4,652 images in 31 categories collected from three distinct domains: \textit{Amazon} (\textbf{A}), \textit{Webcam} (\textbf{W}) and \textit{DSLR} (\textbf{D}). We can construct six transfer tasks: \textbf{A} $\rightarrow$ \textbf{W}, \textbf{D} $\rightarrow$ \textbf{W}, \textbf{W} $\rightarrow$ \textbf{D}, \textbf{A} $\rightarrow$ \textbf{D}, \textbf{D} $\rightarrow$ \textbf{A}, and \textbf{W} $\rightarrow$ \textbf{A}. The Office-Home dataset consists of 15,500 images in 65 object classes under the office and home settings, forming four extremely dissimilar domains: \textit{Artistic} (\textbf{Ar}), \textit{Clip Art} (\textbf{Cl}), \textit{Product} (\textbf{Pr}), and \textit{Real-World} (\textbf{Rw}) and 12 transfer tasks. The VisDA-2017 dataset has over 280K images across 12 classes. It contains two very distinct domains: \textbf{Synthetic}, which contains renderings of 3D models from different angles and with different lightning conditions, and \textbf{Real} that are natural images. On this dataset, we study a transfer task: Synthetic $\rightarrow$ Real. We compare the proposed \textbf{DAMPC-NAS} method with state-of-the-art DA methods, including Joint Distribution Adaptation (\textbf{JDA}) \cite{long2013transfer}, Deep Domain Confusion (\textbf{DDC}) \cite{tzeng2014deep}, Deep Adaptation Network (\textbf{DAN}) \cite{long2015learning}, Domain Adversarial Neural Network (\textbf{DANN}) \cite{ganin2015unsupervised}, Correlation Alignment for Deep Domain Adaptation (\textbf{D-CORAL}) \cite{sun2016deep}, Residual Transfer Networks (\textbf{RTN}) \cite{long2016unsupervised}, Joint Adaptation Networks (\textbf{JAN}) \cite{long2017deep}, Adversarial Discriminative Domain Adaptation (\textbf{ADDA}) \cite{tzeng2017adversarial}, Conditional Domain Adversarial Networks (\textbf{CDAN}) \cite{long2017conditional}, Collaborative and Adversarial Network (\textbf{CAN}) \cite{zhang2018collaborative}, Manifold Dynamic Distribution Adaptation (\textbf{MDDA}) \cite{wang2020transfer}, and Dynamic Distribution Adaptation Network (\textbf{DDAN}) \cite{wang2020transfer}. The results of baseline methods are directly reported from DDAN \cite{wang2020transfer} and CDAN \cite{long2017conditional}. We use the PyTorch package \cite{paszke2017automatic} to implement all the models and leverage the ResNet-50 network \cite{he2016deep} pretrained on the ImageNet dataset \cite{russakovsky2015imagenet} as the backbone for the feature extraction. For optimization, we use the mini-batch SGD with the Nesterov momentum 0.9. The learning rate is adjusted by $\eta_p = \eta_0(1 + \alpha p)^{-\beta}$, where $p$ is the index of training steps, $\eta_0$ = 0.1, $\alpha$ = 0.001, and $\beta$ = 0.75. The batch size is set to 128 for all the datasets. \subsection{Results} \begin{figure}[ht] \centering \includegraphics[width=0.9\textwidth]{arch_drawio.pdf} \caption{Searched architecture for transfer task D$\rightarrow$W of the Office-31 dataset. Left: architectures within the three cells. Right: connections between the three cells, PC and classifier.} \label{fig:arch_dw} \end{figure} The classification results on the Office-31 dataset are shown in Table \ref{tab:office31}. As illustrated in Table \ref{tab:office31}, the proposed DAMPC-NAS method achieves the best average accuracy. In four out of six transfer tasks, DAMPC-NAS performs the best, especially on transfer tasks A$\rightarrow$D and A$\rightarrow$W, which is transferring from a large source domain to a small target domain and in the other two tasks, the DAMPC-NAS method performs slightly worse than the best baseline method, which implies that the proposed DAMPC-NAS model works well when the source data is sufficient and it is able to learn transferable feature representations for effective domain adaptation. Figure \ref{fig:arch_dw} shows the architecture found by DAMPC-NAS for the transfer task D$\rightarrow$W constructed on the Office-31 dataset. The left part of Figure \ref{fig:arch_dw} shows the search choice within the three cells found by the DAMPC-NAS method and the right part of Figure \ref{fig:arch_dw} shows the connections among the three cells, PC and classifier. In Cell 0, the DAMPC-NAS method chooses the FC layer with the same size as the input and the skip connection is connected to the batch-norm layer. In Cell 1, the choice of FC is the same as Cell 0 but the skip connection is starting from the cell input. In Cell 2, the skip connection is the same as Cell 2 but the FC layer is of half size of the input. For connections between cells, the DAMPC-NAS method chooses to use the output of Cell 0 to calculate the PC and the output of Cell 1 to calculate the classification loss. For a simple transfer task D$\rightarrow$W, the searched architecture only has two cells, which indicates that the DAMPC-NAS method can adaptively learn an architecture depending on the the complexity of the DA task. Moreover, the location of the skip connection moves forward in Cell 1 and Cell 2 when compared with Cell 0, which is to help reduce the network depth and alleviate the vanishing gradient problem. Table \ref{tab:officehome} shows the classification results on the Office-Home dataset. According to the results, we can see that DAMPC-NAS achieves the best average accuracy and performs the best in eight out of twelve transfer tasks. while transferring from a large source domain to a small target domain (i.e., Cl$\rightarrow$Ar, Pr$\rightarrow$Ar, and Rw$\rightarrow$Ar), DAMPC-NAS achieves the best performance and this phenomenon is similar to the Office-31 dataset, which again demonstrate that the proposed DAMPC-NAS model works well when the source data is sufficient. According to experimental results on the most challenging VisDA-2017 dataset as shown in Table \ref{tab:visda}, the proposed DAMPC-NAS method outperforms all the baseline methods by improving by $1.9\%$ over state-of-the-art baseline methods (i.e., CDAN) on this dataset, which again demonstrates the effectiveness of the proposed method. \begin{table}[!htbp] \centering \caption{Accuracy (\%) on the VisDA-2017 dataset with ResNet-50 as the backbone.} \resizebox{\linewidth}{!}{ \begin{tabular}{llc} \toprule Type & Method & Synthetic$\rightarrow$Real\\ \midrule & ResNet-50 \cite{he2016deep} & 45.6 \\ \cmidrule(){1-3} \multirow{3}{Dist Based} & DAN \cite{long2015learning} & 53.0 \\ & RTN \cite{long2016unsupervised} & 53.6 \\ & JAN \cite{long2017deep} & 61.6 \\ \cmidrule(){1-3} \multirow{2}{Adv Based} & DANN \cite{ganin2015unsupervised} & 55.0 \\ & CDAN \cite{long2017conditional} & 66.8 \\ \midrule & DAMPC-NAS (Ours) & \textbf{68.75} \\ \bottomrule \end{tabular} } \label{tab:visda} \end{table} \subsection{Ablation Study} Firstly, we conduct an ablation study on the Office-31, Office-Home, and VisDA-2017 datasets to demonstrate the effectiveness of the proposed PC. We compare PC with widely used distance functions, including Proxy $\mathcal{A}$-distance, Kullback-Leibler divergence (KL-divergence), Maximum Mean Discrepancies (MMD), CORrelation ALignmen (CORAL), and Central Moment Discrepancy (CMD). For fair comparison, we only replace the minus of the PC with these distance functions in Eq. (\ref{eq:obj}). Specifically, we adopt the ResNet-50 as the backbone, following with the bottleneck layer (consisting of a fully connected layer, a batch normalization layer, a ReLU activation function, and a dropout function) used for generating hidden features and a fully connected layer used for prediction. According to experimental results shown in Tables \ref{tab:ablation_study_office31}, \ref{tab:ablation_study_visda} and \ref{tab:ablation_study_officehome}, we can see that none of the distance functions can obtain performance improvement compared with no distance function used (i.e., ResNet-50). One possible reason is that the normalization layer used in the bottleneck layer has improved the performance of the ResNet-50 and adapting these distance functions can not improve the performance further. However, the proposed PC can still obtain performance improvement over ResNet-50, which indicates the effectiveness of the proposed PC. \begin{table}[!htbp] \centering \caption{Ablation Study on the Office-31 dataset with ResNet-50 as the backbone.} \resizebox{\linewidth}{!}{ \begin{tabular}{lccccccc} \toprule Measurement & A$\rightarrow$D & A$\rightarrow$W & D$\rightarrow$A & D$\rightarrow$W & W$\rightarrow$A & W$\rightarrow$D & Avg \\ \midrule None & 83.53 & 80.50 & 64.61 & 98.49 & 62.69 & 100.0 & 81.64 \\ Proxy $\mathcal{A}$-distance & 82.73 & 81.01 & 64.04 & 98.11 & 61.77 & 100.0 & 81.28 \\ KL-divergence & 83.94 & 79.75 & 63.90 & 97.86 & 63.51 & 99.80 & 81.46 \\ MMD & 83.13 & 79.25 & 64.11 & 98.74 & 63.12 & 100.0 & 81.39 \\ CORAL & 84.34 & 80.25 & 64.61 & 98.24 & 62.80 & 99.80 & 81.67 \\ CMD & 82.93 & 79.50 & 64.29 & 98.62 & 63.10 & 100.0 & 81.41 \\ \midrule PC (Ours) & 88.35 & 91.32 & 70.36 & 98.49 & 69.05 & 100.0 & 86.26 \\ \bottomrule \end{tabular} } \label{tab:ablation_study_office31} \end{table} \begin{table}[!htbp] \centering \caption{Ablation Study on the VisDA-2017 dataset with ResNet-50 as the backbone.} \begin{tabular}{lc} \toprule Measurement & Synthetic$\rightarrow$Real\\ \midrule None & 57.68 \\ Proxy $\mathcal{A}$-distance & 56.36 \\ KL-divergence & 56.27\\ MMD & 58.76 \\ CORAL & 56.66 \\ CMD & 56.65 \\ \midrule PC (Ours) & 65.25 \\ \bottomrule \end{tabular} \label{tab:ablation_study_visda} \end{table} \begin{table}[ht] \centering \caption{Ablation Study on the Office-Home dataset with ResNet-50 as the backbone.} \resizebox{\linewidth}{!}{ \begin{tabular}{lccccccccccccc} \toprule Measurement & Ar$\rightarrow$Cl & Ar$\rightarrow$Pr & Ar$\rightarrow$Rw & Cl$\rightarrow$Ar & Cl$\rightarrow$Pr & Cl$\rightarrow$Rw & Pr$\rightarrow$Ar & Pr$\rightarrow$Cl & Pr$\rightarrow$Rw & Rw$\rightarrow$Ar & Rw$\rightarrow$Cl & Rw$\rightarrow$Pr & Avg \\ \midrule None & 43.41 & 66.55 & 74.64 & 56.61 & 63.98 & 65.32 & 53.36 & 39.36 & 72.64 & 64.73 & 46.30 & 76.55 & 60.29 \\ Proxy $\mathcal{A}$-distance & 43.21 & 65.44 & 74.85 & 55.09 & 62.51 & 65.37 & 52.33 & 38.63 & 72.83 & 64.57 & 46.23 & 76.66 & 59.81 \\ KL-divergence & 44.01 & 66.75 & 74.50 & 55.75 & 63.42 & 66.51 & 52.74 & 38.14 & 73.43 & 65.84 & 44.79 & 77.13 & 60.25 \\ MMD & 43.78 & 66.28 & 74.48 & 55.62 & 64.07 & 66.19 & 53.40 & 38.30 & 73.15 & 64.89 & 45.52 & 77.43 & 60.26 \\ CORAL & 44.15 & 65.85 & 74.16 & 55.42 & 63.01 & 66.83 & 52.95 & 39.38 & 72.53 & 65.14 & 45.96 & 77.07 & 60.20 \\ CMD & 44.40 & 65.92 & 74.50 & 54.68 & 63.37 & 67.07 & 52.78 & 38.88 & 72.94 & 65.64 & 45.29 & 77.36 & 60.24 \\ \midrule PC (Ours) & 46.19 & 66.03 & 73.7 & 57.89 & 63.48 & 65.80 & 56.94 & 44.19 & 75.58 & 69.02 & 51.11 & 78.89 & 62.24 \\ \bottomrule \end{tabular} } \label{tab:ablation_study_officehome} \end{table} \begin{figure} [ht] \centering \subfigure[ResNet-50]{\includegraphics[width=0.33\textwidth]{a_d_resnet.pdf}} \subfigure[DAN]{\includegraphics[width=0.33\textwidth]{a_d_DAN.pdf}} \subfigure[DAMPC-NAS (Ours)] {\includegraphics[width=0.33\textwidth]{a_d_DAMPC.pdf}} \caption{t-SNE visualization of different methods for the transfer task A$\rightarrow$D in the Office-31 dataset.} \label{fig:visualization} \end{figure} Then we conduct another ablation study on the Office-31 dataset to demonstrate the effectiveness of the architecture searching process in the DAMPC-NAS method. Specifically, we modify Algorithm \ref{alg:nas} to search an optimal architecture for the DAN by replacing the minus of the PC with MMD in $\mathcal{L}_{\text{DAMPC}}$. According to experimental results shown in Figure \ref{fig:mmd_nas}, DAN-NAS performs comparable to and even slightly better than DAN on the six transfer tasks in the Office-31 dataset, which demonstrates the usefulness of the search process in the DAMPC method. \begin{figure}[!htbp] \centering \includegraphics[width=\linewidth]{mmd_nas.pdf} \caption{DAMPC-NAS with DAN on the Office-31 dataset.} \label{fig:mmd_nas} \end{figure} \subsection{Visualization} We visualize in Figure \ref{fig:visualization} the hidden feature representations of the transfer task A$\rightarrow$D constructed on the Office-31 dataset learned by ResNet-50 which is trained on source samples only, DAN, and DAMPC-NAS, respectively. According to Figure \ref{fig:visualization}, we can see that samples with the representations learned by ResNet-50 and DAN are not distinguishable, but those by DAMPC-NAS are more separable, which implies that the proposed DAMPC-NAS method can learn discriminative and transferable feature representations for DA. \section{Conclusion} In this paper, we propose a new DA method called DAMPC based on the proposed PC function that can measure the domain similarity. We further design the DAMPC-NAS framework that searches optimal network architectures for DA tasks. Experiments results on the Office-31, Office-Home, and VisDA-2017 datasets demonstrate the effectiveness of the proposed method. Moreover, the proposed DAMPC-NAS framework has shown its potential to search optimal architectures for other DA methods. In our future studies, we will apply the proposed the DAMPC-NAS framework to search architectures for other DA methods and other DA settings.	{ "redpajama_set_name": "RedPajamaArXiv" }	2,273
\section{Introduction} The first catalogue of simplicial hyperplane arrangements of rank~$3$ appeared in 1971~\cite{grunbaum_1971}. This catalogue included three infinite families and 90 sporadic arrangements. Since then, the catalogue has changed: certain arrangements have been found to be isomorphic while some new arrangements have also been found, bringing the number of sporadic arrangements to 95~\cite{grunbaum_2009,cuntz_greedy_2020}. The list is known to be complete for arrangements with up to 27 lines~\cite{cuntz_simplicial_2012}. The current updated list along with several invariants is available in the present article, see Table~\ref{tab:invariants} in Section~\ref{sec:invariants} and Appendices~\ref{app:lists} and~\ref{app:wd}. The following questions are still open: \emph{Is the list complete? Is there a finite list at all?} In order to answer these questions, it is natural to search for structures lurking behind the list. Simplicial arrangements can be thought of as generalizations of finite Coxeter arrangements. Furthermore, they correspond to normal fans of simple zonotopes \cite[Theorem~7.16]{ziegler_lectures_1995}. What other combinatorial/geometric/algebraic structures regulate the list? It turns out that finite Weyl groupoids provide an algebraic justification for around half of the sporadic arrangements. Finite Weyl groupoids are algebraic structures generalizing Weyl groups that were introduced to better understand the symmetries of Nichols algebras and related Hopf algebras~\cite{heckenberger_weyl_2006,heckenberger_geometric_2011,cuntz_finite_2015}. Each Weyl groupoid originates from the data of a ``Cartan graph'', leading to a so-called ``root system''. In turn, these root systems generalize the usual notion of root system of a Weyl group. Notably, they form the set of normals of certain simplicial hyperplane arrangements. Finite Weyl groupoids of rank~$3$ have been classified and account for $53$ simplicial arrangements~\cite{cuntz_crystallographic_2011}. Posets of regions form a family of combinatorial structures that encode detailed information on hyperplane arrangements and the adjacency of regions. For simplicial arrangements, the posets of regions are always lattices, no matter what the \emph{base region} of the poset is~\cite[Theorem~3.4]{bjoerner_hyperplane_1990}. Reading showed that simpliciality can be weakened to \emph{tightness}---which is a connectivity condition on facets of regions---in order to obtain lattices~\cite[Chapter~9]{reading_lattice_2016} (see Lemma~\ref{lem:bez} below). Once again, simplicial arrangements through their lattices of regions provide generalizations, this time of the weak order of finite Coxeter groups. Unlike in the Coxeter case, a simplicial arrangement may lead to several non-isomorphic lattices of regions. Apart from being lattices, much less is known about the poset of regions of simplicial arrangements. Lattice congruences of the weak order of Coxeter arrangements generate several objects of study. For example, the permutahedron is perhaps the most studied example of a simple zonotope, that comes from the braid arrangement, or Coxeter arrangement of type $A$. The corresponding poset of regions is the weak order of the symmetric group and is a lattice. Moreover, Tamari and Cambrian lattices, generalized permutahedra, and associahedra are all related to lattice congruences of the weak order~\cite{reading_cambrian_2006,postnikov_permutahedra_2009,hohlweg_permutahedra_2011}. In particular, in type~$A$ and $B$, every lattice congruence leads to a polytope~\cite{pilaud_quotientopes_2019,padrol_shard_2020}. To which extent do these constructions extend to general simplicial arrangements? We focus here on two important properties used to study lattice congruences and shard polytopes: \emph{congruence normality} and \emph{congruence uniformity}. Coxeter arrangements are congruence normal and uniform \cite{caspard_cayley_2004}. Congruence uniform lattices admit a bijection between their join-irreducible elements and the join-irreducible elements in the lattice of lattice congruences. Congruence uniform lattices are thus particularly nice lattices as they allow one to more easily study the lattice of congruences. Reading characterized congruence uniformity of posets of regions using \emph{tightness} and \emph{shards} (i.e.\ pieces of hyperplanes)~\cite[Corollary~9-7.22]{reading_lattice_2016}. Reading also showed that supersolvable hyperplane arrangements have congruence uniform posets of regions for some canonical choice of base region~\cite{reading_lattice_2003}. Congruence uniform lattices admit a combinatorial construction whose geometric aspects in this context have yet to be explored in detail. In this article, we determine congruence uniformity and normality of posets of regions of simplicial hyperplane arrangements of rank~$3$ and draw several conclusions. To do so, we approach posets of regions through the oriented matroids naturally associated to the normals of the hyperplane arrangements, which are presented in Appendix~\ref{app:lists}. Covectors of the oriented matroid can be used to encode the ``facial weak order'' of simplicial hyperplane arrangements~\cite{dermenjian_facialweak_2018}. Here, we use covectors and the \emph{intersection} operation as our main tools to elevate Reading's characterization of congruence uniformity to the level of oriented matroids (see Theorem~\ref{thm:covector_forcing} and Corollary~\ref{cor:covector_forcing}). Namely, we introduce \emph{shard covectors}---which are covectors with some ``$$'' entries---and show they are in bijection with shards (see Theorem~\ref{thm:shard_bijection}). This approach led to the following results. If a set of normals admits a \emph{root poset} with respect to a base region, then its lattice of regions is congruence normal (see Theorem~\ref{thm:constructible}). In particular, the posets of regions of hyperplane arrangements coming from finite Weyl groupoids are always congruence normal and congruence uniform (see Corollary~\ref{cor:cn_weyl}). This result provides a new proof that finite Coxeter arrangements are obtainable through a finite sequence of interval doublings (i.e. congruence uniform) \cite[Theorem~6]{caspard_cayley_2004}. We further classify the known rank-$3$ simplicial arrangements according to whether their posets of regions are always or sometimes or never congruence normal (see Table~\ref{tab:cn_part}). The approach through covectors gives a way to determine congruence normality of posets of regions without the data of the poset or resorting to polyhedral objects (i.e.\ shards). Notably, this classification could not have been carried out through the computation of the posets of regions due to their large size. Hence, this framework provides an oriented matroid approach to study congruence normality and uniformity for large posets of regions. As an interesting outcome of this classification, five arrangements have exceptional behavior. Two of the five arrangements are always congruence normal: the non-crystallographic arrangement corresponding to the Coxeter group $H_3$ and its point-line dual arrangement which has 31 hyperplanes. The three other arrangements are never congruence normal: they have yet to show any connection to other known structures. Furthermore, we provide instructive examples which give deeper insight into congruence uniformity for posets of regions. We verified that within supersolvable simplicial arrangements (by \cite[Theorem~1.2]{cuntz_supersolvable_2019} these are the arrangements in 2 of the 3 infinite families) only four are always congruence normal and all others are only sometimes congruence normal, see Theorems~\ref{thm:cn_f2} and~\ref{thm:cn_f3}. The algorithms used to carry out the verifications and the data to construct known simplicial hyperplane arrangements are available as a \texttt{Sage}-package \cite{cn_hyperarr}. The article is structured as follows. In Section~\ref{sec:prelim}, we present the necessary background notions on lattice congruences, posets of regions, congruence normality and uniformity and the theory of shards. In Section~\ref{sec:cong_norm}, we recast shards and the forcing relation using covectors. In Section~\ref{sec:simplicial}, we present the result of the application of the approach of Section~\ref{sec:cong_norm} to the known rank-$3$ simplicial hyperplane arrangements. In Section~\ref{sec:invariants}, we present combinatorial and geometric invariants of the known rank-3 simplicial hyperplane arrangements with up to 37 hyperplanes. In Appendix~\ref{app:lists}, we give normals to realize each of these arrangements. Finally, in Appendix~\ref{app:wd}, we give a wiring diagram description for these arrangements. \medskip {\bf Acknowledgements.} The authors would like to express their gratitude to Vincent Pilaud and Julian Ritter for important discussions leading to the results in this paper. \section{Preliminaries} \label{sec:prelim} We use the following notation: $\mathbb{N}=\{0,1,2,\dots\}$, $d,m\in\mathbb{N}\setminus\!\{0\}$, and ${[m]:=\{1,2,\dots,m\}}$. We use bold faced $\mathbf{n},\mathbf{p},\mathbf{x},$ etc. to denote vectors in the real Euclidean space $\mathbb{R}^{d}$ equipped with the usual dot product \mbox{$\mathbb{R}^d \times \mathbb{R}^d\rightarrow~\mathbb{R}$}. Let $\P$ denote a finite, ordered set of vectors. The linear span of $\P$ is denoted $\spa(\P)$, its affine hull by $\aff(\P)$, and its convex hull by $\conv(\P)$. To ease reading, we often abuse notation and write for instance $\spa(\mathbf{x}_1,\mathbf{x}_2)$ instead of $\spa(\{\mathbf{x}_1,\mathbf{x}_2\})$. The orthogonal complement of a linear subspace $A\subseteq \mathbb{R}^d$ is denoted~$A^\top$. The relative interior of a subset~$\P$ of $\mathbb{R}^d$ is denoted by $\inter(\P)$. In Section~\ref{ssec:latt_cong}, we review the notion of a lattice congruence. In Section~\ref{ssec:poset_region}, we define hyperplane arrangements and posets of regions. In Sections~\ref{ssec:cong_normal} and~\ref{ssec:cong_unif}, we discuss the notions of congruence normality and uniformity. Finally, in Section~\ref{ssec:cong_shards}, we describe Reading's characterization of congruence uniformity for tight hyperplane arrangements using \emph{shards}. The material presented in this section is mostly based on material treated in the book chapter \cite[Chapter~9]{reading_lattice_2016}. \subsection{Lattice congruences} \label{ssec:latt_cong} Let $L=(P;\wedge,\vee)$ be a finite lattice, where $P$ is a poset $(P,\leq)$. An element $j \in L$ is \defn{join-irreducible} if $j$ covers a unique element~$j_\bullet\in L$. Similarly, an element $m\in L$ is \defn{meet-irreducible} if $m$ is covered by a unique element $m^\bullet\in L$. We denote the subposet of join-irreducible elements of a lattice~$L$ by~$L_{\vee}$ and the subposet of meet-irreducible elements by $L_{\wedge}$. An \defn{order ideal} of a poset $P$ is a subposet ${Q \subseteq P}$ that satisfies $x \in Q$ and $y \leq x \Rightarrow y \in Q$. The order ideals of a poset $P$ can be ordered by containment to get the \defn{poset of order ideals} denoted $\mathcal{O}(P)$. When $L$ is self-dual, join- and meet-irreducible elements are canonically in bijection. The dual map therefore allows one to refine statements involving~$L$ and its irreducible elements. Join-irreducible elements (and dually meet-irreducible elements) and posets of order ideals are very useful to understand finite distributive lattices. \begin{lemma}[{\cite[Theorem~17.3]{birkhoff_combination_1933}}] \label{lem:fund_thm_dist} Let $L$ be a lattice, $L_{\vee}$ be its subposet of join-irreducible elements, and $\mathcal{O}(L_{\vee})$ be the poset of order ideals of $L_{\vee}$. If $L$ is finite and distributive, then $L$ is isomorphic to $\mathcal{O}(L_{\vee})$. \end{lemma} Recall that cosets of a normal subgroup $N \trianglelefteq G$ determine a \emph{congruence} relation, and lead to a quotient group $G/N$, which is the image of the map sending an element to its coset. Analogously, in lattice theory, intervals play the roll of cosets, and under certain conditions, they form to a \emph{quotient lattice}. In this case, the equivalence relation is called a lattice congruence. For a thorough discussion on congruences and quotient lattices, we refer the reader to \cite[Chapter~9-5 and 9-10]{reading_lattice_2016} and the references therein. \begin{definition}[Lattice congruence, see e.g. {\cite[Proposition~9-5.2]{reading_lattice_2016}}] \label{def:lat_cong} An equivalence relation on the elements of a lattice~$L$ is a \defn{lattice congruence} if the following three conditions are satisfied: \begin{enumerate} \item Every equivalence class is an interval. \item The map $\pi_\downarrow$ sending each element to the minimal element in its equivalence class is order-preserving. \item The map $\pi_\uparrow$ sending each element to the maximal element in its equivalence class is order-preserving. \end{enumerate} Given a lattice congruence, the images of $\pi_\downarrow$ and $\pi_\uparrow$ are sublattices, i.e.\ the join and meet operations are preserved on the equivalence classes, and they are referred to as \defn{quotient lattices}. \end{definition} Lattice congruences of a lattice can be numerous and the relations between them may be challenging to describe. In spite of that, the set of lattice congruences on a lattice $L$ may be partially ordered by refinement. The equivalence relation with singleton classes is the smallest lattice congruence and its associated quotient lattice is the lattice itself. Furthermore, the equivalence relation with a unique class is the coarsest lattice congruence whose associated quotient lattice has exactly one element. It turns out that under this partial order, the set of lattice congruences forms a distributive lattice which is called the \defn{lattice of congruences} and is denoted by $\Con(L)$~\cite{funayama_distributivity_1942}. The lattices of congruences we consider here are finite and therefore complete. Consequently, given any set of relations, there is a smallest lattice congruence which contains these relations \cite[Proposition 9-5.13]{reading_lattice_2016}. This makes it possible to define two important congruences related to join- and meet-irreducible elements. Consider a join-irreducible element $j\in L_{\vee}$, then there is a smallest lattice congruence $\con_\vee(j)$ such that $j$ and~$j_\bullet$ are equivalent. Similarly, for a meet-irreducible element $m$, there is a smallest lattice congruence $\con_{\wedge}(m)$ such that $m$ and the unique element $m^\bullet$ that covers it are equivalent. In this case, we say that the congruence $\con_\vee$ \defn{contracts} $j$, and that $\con_\wedge$ contracts $m$. As $\Con(L)$ is finite and distributive, we may use Lemma~\ref{lem:fund_thm_dist} to obtain that $\Con(L)$ is isomorphic to $\mathcal{O}(\Con(L)_\vee)$. That is to say that a congruence is determined by an order ideal of join-irreducible congruences, i.e., by the join-irreducibles it contracts~\cite[Corollary 9-5.15]{reading_lattice_2016}. \begin{definition} Let $\con_\vee: L_\vee \rightarrow \Con(L)$ be the map that sends a join-irreducible element $j \in L_{\vee}$ to the smallest lattice congruence in $\Con(L)$ such that $j \equiv j_\bullet$. Dually, the map $\con_{\wedge}$ is similarly defined for meet-irreducible elements. \end{definition} The image of the map $\con_\vee$ is $\Con(L)_{\vee}$, i.e., the congruence $\con_\vee(j)$ is join-irreducible in $\Con(L)$ and for every join-irreducible congruence $\alpha$ in $\Con(L)$, there exists a join-irreducible $j\in L_\vee$ such that $\con_\vee(j)=\alpha$ \cite[Proposition 9-5.14]{reading_lattice_2016}. It may happen that two distinct join-irreducibles give rise to the same congruence, i.e.\ that $\con_\vee$ is not injective, leading to an equivalence relation on join-irreducible elements in $L_\vee$. Through the map $\con_\vee$, these equivalence classes of join-irreducible elements in $L$ are in bijection with join-irreducible congruences of $L$. \subsection{Poset of regions of a real hyperplane arrangement} \label{ssec:poset_region} A \defn{(real) hyperplane}~$H$ is a co\-di\-men\-sion-1 affine subspace in $\mathbb{R}^d$: \[ H := \{\mathbf{x}\in\mathbb{R}^d~:~\mathbf{n}\cdot\mathbf{x}=a \text{ for some } \mathbf{n} \in \mathbb{R}^d \text{ and } a\in\mathbb{R}\}. \] The vector $\mathbf{n}$ is called the \defn{normal} of $H$. A \defn{finite hyperplane arrangement} $\mathdutchcal A$ is a finite non-empty set of $m$ hyperplanes. If $a=0$ for all hyperplanes in $\mathdutchcal A$, then the hyperplane arrangement is called \defn{central}. In this case, the hyperplanes are completely determined by their normals. We denote the hyperplanes in $\mathdutchcal A$ by $H_1,\dots,H_m$ and often reuse their indices to refer to objects canonically related to them. The \defn{rank} of $\mathdutchcal A$ is the dimension of the linear span of the normal vectors of the hyperplanes in $\mathdutchcal A$. The complement of the arrangement in the ambient space $(\mathbb{R}^d \setminus \bigcup_{i\in[m]}H_i)$ is disconnected, and the closures of the connected components are the \defn{regions} of the arrangement. The set of regions of $\mathdutchcal A$ is denoted by $\mathdutchcal{R}(\mathdutchcal A)$. A region is called \defn{simplicial} if the normal vectors of its facet-defining hyperplanes are linearly independent. A hyperplane arrangement is \defn{simplicial} if every region in its complement is simplicial. To proceed further, a \defn{base region} $B$ of $\mathdutchcal A$ is chosen. For each hyperplane $H_i \in \mathdutchcal A$, we fix a normal vector~$\mathbf{n}_i\in\mathbb{R}^d$ such that $\mathbf{n}_i\cdot \mathbf{x} <0$, for all $\mathbf{x}\in B$. Given a region~$R$ of $\mathdutchcal A$, the \defn{separating set} $\Sep_B(R)$ of $R$ is the set of hyperplanes $H_i\in\mathdutchcal A$ such that $\mathbf{n}_i\cdot\mathbf{x}>0,$ for all $\mathbf{x}\in R$. The separating set of a region is the set of hyperplanes that separate it from the base region $B$. \begin{definition}[{Poset of regions, $P_B(\A)$}] Let $\mathdutchcal A$ be a hyperplane arrangement with base region $B$. The \defn{poset of regions} $P_B(\A)$ of $\mathdutchcal A$ with base region $B$ is the partially ordered set $(\mathdutchcal{R}(\mathdutchcal A),\leq)$ such that \[ R_1 \leq R_2 \text{ if and only if } \Sep_B(R_1) \subseteq \Sep_B(R_2), \] for all $R_1,R_2\in \mathdutchcal{R}(\mathdutchcal A)$. \end{definition} An \defn{upper facet} of a region $R\in\mathdutchcal{R}(\mathdutchcal A)$ is a facet of $R$ which corresponds to a cover relation of $R$ in~$P_B(\A)$. A hyperplane arrangement is \defn{tight} with respect to $B$ when the upper facets of every region intersect pairwise along a codimension-$2$ face, i.e.\ they are neighbors in the facet-adjacency graph. When a hyperplane arrangement $\mathdutchcal A$ is tight with respect to every base region, we say that $\mathdutchcal A$ is tight. For convenience, when a hyperplane arrangement is tight, we also call the corresponding posets of regions tight. The usual definition of tightness also requires the dual statement to hold. As poset of regions are self-dual, we have restricted the statement to upper facets. The following lemma is a refinement of \cite[Theorem~3.4]{bjoerner_hyperplane_1990}. \begin{lemma} \label{lem:bez} Let $\mathdutchcal A$ be a finite, central hyperplane arrangement with base region~$B$. \begin{enumerate} \item If $\mathdutchcal A$ is tight with respect to $B$, then $P_B(\A)$ is a lattice. \cite[Theorem~9-3.2]{reading_lattice_2016} \item If $\mathdutchcal A$ is simplicial, then $\mathdutchcal A$ is tight. \cite[Proposition~9-3.3]{reading_lattice_2016} \end{enumerate} \end{lemma} Reading developed an approach to study congruences of lattices of regions that is thoroughly described in \cite[Chapter~9]{reading_lattice_2016}. In particular, for posets of regions, tightness is equivalent to \emph{semidistributivity} \cite[Theorem~9-3.8]{reading_lattice_2016} (see Section~\ref{ssec:cong_unif} for the definition of semidistributivity). Furthermore, in order to describe the interplay between join-irreducible elements, the combinatorial notion of ``polygonality'' of a lattice is used; in the case of posets of regions, this notion is equivalent to the notion of tightness \cite[Theorem~9-6.10]{reading_lattice_2016}. Using the polygonality property, it is possible to describe which join-irreducibles \emph{force} other ones to be contracted. This forcing relation can then be read off from the hyperplane arrangement using pieces of hyperplanes called \emph{shards} (see Definition~\ref{def:shards} in Section~\ref{ssec:cong_shards}). The interest in the notion of tightness lies in the fact that being tight and having \emph{acyclicity} on shards characterizes congruence uniformity, see Theorem~\ref{thm:charac_uniform} in Section~\ref{ssec:cong_shards}. Throughout this article, we restrict our study to finite, central, and tight hyperplane arrangements, so that the posets of regions are guaranteed to be complete lattices regardless of the choice of base regions. We refer the reader to \cite[Chapter~9-3, 9-6]{reading_lattice_2016} for further details on tightness and polygonality. \subsection{Congruence normality} \label{ssec:cong_normal} \begin{definition}[{Congruence normality, \cite[Section~1, p.400]{day_congruence_1994}}] Let $L$ be a lattice, $L_\vee\subseteq L$ be the subposet of join-irreducible elements of $L$, and $L_\wedge$ be the subposet of meet-irreducible elements of $L$. The lattice $L$ is \defn{congruence normal} if \[ j\leq m\quad \text{ implies }\quad \con_\vee(j) \neq \con_\wedge(m), \] for all $j\in L_\vee$, and $m\in L_\wedge$. A hyperplane arrangement is called \defn{congruence normal} if its lattices of regions are congruence normal for every choice of base region. \end{definition} Equivalently, finite congruence normal lattices are exactly the lattices obtained from a one-element lattice by a sequence of \emph{doublings} of \emph{convex sets} \cite[Section~3]{day_congruence_1994}, see also \cite[Theorem~3-2.39]{adaricheva_classes_2016} and \cite{geyer_generalized_1994}. The following example illustrates a local condition showing how a lattice may fail to be congruence normal. \begin{example} \label{ex:L3_non_cn} Consider the lattice $L_3$ with the Hasse diagram illustrated in Figure~\ref{fig:L3_non_cn}. The element~$c$ is join-irreducible, and the smallest congruence $\con_\vee(c)$ such that $b\equiv c$ is illustrated on the right-hand side. \begin{figure}[H] \begin{center} \begin{tabular}{c@{\hspace{1cm}$\Longrightarrow$\hspace{1cm}}c} \begin{tikzpicture}% [baseline=(c), arete/.style={thick}, vertex/.style={inner sep=3pt}, eq_class/.style={line join=round,line width=15pt,color=orange,draw opacity=0.5,line cap=round}] \def2.5{1} \def2.5{1} \coordinate (0) at (0,0); \coordinate (a) at (-2.5,2.5); \coordinate (b) at (2.5,2.5); \coordinate (c) at (2.5/2,1.52.5); \coordinate (d) at (0,22.5); \coordinate (e) at (22.5,22.5); \coordinate (1) at (2.5,32.5); \draw[eq_class] (b) -- (c); \node (L3) at (-1.22.5,22.5) {$L_3$}; \node[vertex] (v0) at (0) {$0$}; \node[vertex] (va) at (a) {$a$}; \node[vertex] (vb) at (b) {$b$}; \node[vertex] (vc) at (c) {$c$}; \node[vertex] (vd) at (d) {$d$}; \node[vertex] (ve) at (e) {$e$}; \node[vertex] (v1) at (1) {$1$}; \draw[arete] (vd) -- (v1) -- (ve) -- (vb) -- (vc) -- (vd) -- (va) -- (v0) -- (vb); \end{tikzpicture} & \begin{tikzpicture}% [baseline=(c), arete/.style={thick}, vertex/.style={inner sep=3pt}, eq_class/.style={line join=round,line width=15pt,color=orange,draw opacity=0.5,line cap=round}] \def2.5{1} \def2.5{1} \coordinate (0) at (0,0); \coordinate (a) at (-2.5,2.5); \coordinate (b) at (2.5,2.5); \coordinate (c) at (2.5/2,1.52.5); \coordinate (d) at (0,22.5); \coordinate (e) at (22.5,22.5); \coordinate (1) at (2.5,32.5); \draw[eq_class] (0) -- (a); \draw[eq_class] (b) -- (d); \draw[eq_class] (e) -- (1); \node[vertex] (v0) at (0) {$0$}; \node[vertex] (va) at (a) {$a$}; \node[vertex] (vb) at (b) {$b$}; \node[vertex] (vc) at (c) {$c$}; \node[vertex] (vd) at (d) {$d$}; \node[vertex] (ve) at (e) {$e$}; \node[vertex] (v1) at (1) {$1$}; \draw[arete] (vd) -- (v1) -- (ve) -- (vb) -- (vc) -- (vd) -- (va) -- (v0) -- (vb); \end{tikzpicture} \end{tabular} \end{center} \caption{The Hasse diagram of the lattice $L_3$ which is not congruence normal and the equivalence classes of $\con_\vee(c)=\con_\wedge(c)$.} \label{fig:L3_non_cn} \end{figure} \noindent Following Definition~\ref{def:lat_cong}, setting $b\equiv c$ forces the lattice to project onto a three-element chain. By order-reversing symmetry, the smallest congruence such that $c\equiv d$ is the same as the smallest congruence such that $b\equiv c$. Since $c$ is also meet-irreducible, we get $\con_\wedge(c)=\con_\vee(c)$ and since $c\leq c$, this lattice is not congruence normal. \end{example} This example complements Reading's example of forcing of polygons nicely, see e.g.~\cite[Example~9-6.6]{reading_lattice_2016} and the exercise on congruence normality of polygonal lattices \cite[Exercice 9.55]{reading_lattice_2016}. The intervals $[0,d]$ and $[b,1]$ intersect on more than one cover and removing~$c$ from~$L_3$ makes it congruence normal. Unfortunately, such local obstructions may not be used on lattices of regions of a hyperplane arrangement. The corresponding Hasse diagrams are isomorphic to the 1-skeleta of the associated zonotopes, and two polygons as in the example may not intersect along more than one cover relation for convexity reasons. As we shall see in Example~\ref{ex:A10_60}, there are non-congruence normal lattices of regions. \subsection{Congruence uniformity} \label{ssec:cong_unif} A lattice is \defn{join-semidistributive} if for $x,y,z \in L$, \[ x \vee y = x \vee z \text{ implies } x \vee (y \wedge z) = x \vee y. \] It is \defn{meet-semidistributive} if \[ x \wedge y = x \wedge z \text{ implies }x \wedge (y \vee z) = x \wedge y. \] A lattice that is both join-semidistributive and meet-semidistributive is called \defn{semidistributive}. \begin{definition}[Congruence uniformity, {\cite[Definition~4.1]{day_characterizations_1979}}] Let $L$ be a finite lattice. If the maps $\con_\vee$ and $\con_\wedge$ are injective, then $L$ is called \defn{congruence uniform}. \end{definition} Congruence uniformity describes the lattice of congruences of the involved lattice through the map $\con_\vee$. If $L$ is a finite congruence uniform lattice, then the map $\con_\vee$ gives a order-preserving bijection between $L_\vee$ and $\Con(L)_\vee$. Lemma~\ref{lem:fund_thm_dist} then permits to study the whole of $\Con(L)$. Congruence uniformity is a stronger condition than congruence normality in that it should be obtained from a one-element lattice by a sequence of \emph{doublings of intervals} \cite[Theorem~5.1]{day_characterizations_1979}. \begin{theorem}[{\cite[Section~2]{day_congruence_1994}}] A finite lattice is congruence uniform if and only if it is both congruence normal and semidistributive. \end{theorem} \begin{corollary} \label{cor:norm_unif} A tight poset of regions $P_B(\A)$ is congruence normal if and only if it is congruence uniform. \end{corollary} \begin{proof} By Lemma~\ref{lem:bez}, the poset of regions $P_B(\A)$ of a $\mathdutchcal A$ is a finite lattice, independent of the choice of base region $B$. Furthermore, $\mathdutchcal A$ is tight with respect to $B$ if and only if $P_B(\A)$ is semidistributive \cite[Theorem~9-3.8]{reading_lattice_2016}. \end{proof} \begin{remark} \hfill \begin{enumerate} \item Since lattices of regions are self-dual, it suffices to verify the injectivity of $\con_\vee$ to determine whether they are congruence uniform. \item Semidistributivity can be described using sublattice avoidance~\cite[Theorem~3-1.4]{adaricheva_classes_2016}. The six sublattices obstructing semidistributivity are illustrated in Figure~\ref{fig:L3_non_cn} and~\ref{fig:forbidden_sublattices}. Four out of the six non-semidistributive lattices are not congruence normal ($L_3$, $L_4$, $L_5$, and $M_3$) and share the property that two polygons share more than 1 cover. Nevertheless, semidistributivity is neither necessary nor sufficient to obtain congruence normality: $L_1$ and $L_2$ are congruence normal but not semidistributive and Example~\ref{ex:A10_60} gives a poset of regions which is semidistributive but not congruence normal. \begin{figure}[H] \begin{tikzpicture} \def2.5{6} \def2.5{0} \node at (-2.5/2,2.5) {\input{images/L2}}; \node at ( 2.5/2,2.5) {\input{images/L5}}; \node at ( -2.5, 0) {\input{images/L1}}; \node at ( 0, 0) {\input{images/L4}}; \node at ( 2.5, 0) {\input{images/M3}}; \end{tikzpicture} \caption{Five of the six sublattices that obstruct semidistributivity, the sixth is $L_3$ illustrated in Figure~\ref{fig:L3_non_cn}} \label{fig:forbidden_sublattices} \end{figure} \item Considering two polygons in a polygonal lattice, and verifying congruence normality as in Example~\ref{ex:L3_non_cn}, one realizes that $M_3$, $L_3$, $L_4$, and $L_5$ should be avoided. For poset of regions, this comes as no surprise as polygonality, tightness and semidistributivity are equivalent \cite[Theorem~9-3.8 and~9-6.10]{reading_lattice_2016}. In general, what is the relation between polygonal and semidistributive lattices? \end{enumerate} \end{remark} \begin{example}[{\cite[Figure~5]{reading_lattice_2003} and \cite[Exercise~9.69]{reading_lattice_2016}}] \label{ex:A10_60} Figure \ref{fig:A10_60} illustrates the stereographic projection of the simplicial hyperplane arrangement $\mathdutchcal A(10,60)_3$ in $\mathbb{R}^3$ with 10 hyperplanes through the intersection of 5 hyperplanes which are mapped to lines. This arrangement is $\mathcal{A}(10,1)$ in Gr\"unbaum's list \cite[p.2-3]{grunbaum_2009}, see Section~\ref{sec:simplicial}. \begin{figure}[H] \begin{center} \includegraphics[width=3.5in]{images/not_normalbw.pdf} \end{center} \caption{The simplicial hyperplane arrangement $\mathdutchcal A(10,60)_3=\mathdutchcal F_2(10)$ whose lattice of regions with the marked base region is not congruence normal} \label{fig:A10_60} \end{figure} \noindent The lattice of regions with respect to the base region marked by a black dot is thus semidistributive. In Example~\ref{ex:cycle_in_shards}, we use shards to demonstrate that this arrangement is not congruence normal, hence not uniform by Corollary~\ref{cor:norm_unif}. It is the smallest known simplicial hyperplane arrangement of rank three with that property. \end{example} Examples~\ref{ex:L3_non_cn} and~\ref{ex:A10_60} illustrate failures to be congruence normal. Example~\ref{ex:A10_60} is particularly interesting in that it does not fail to be congruence normal because of forbidden sublattices blocking semidistributivity. \subsection{Congruence normality of simplicial hyperplane arrangements through shards} \label{ssec:cong_shards} Reading characterized congruence uniformity of posets of regions via two conditions, the first one is tightness and the second is phrased using pieces of hyperplanes called \emph{shards}. When the arrangement is central, these pieces are polyhedral cones defined through certain subarrangements. \begin{definition}[{Rank-2 subarrangements and their basic hyperplanes, see~\cite[Definition~9-7.1]{reading_lattice_2016}}] Let $\mathdutchcal A$ be a hyperplane arrangement with base region $B$, and let $1\leq i<j\leq m$. The set \[ \mathdutchcal A\|_{i,j}:=\{H\in \mathdutchcal A~:~H\supset (H_i\cap H_j)\} \] is called a \defn{rank-2 subarrangement} of $\mathdutchcal A$. The two facet-defining hyperplanes of the region of~$\mathdutchcal A\|_{i,j}$ that contains $B$ are called the \defn{basic} hyperplanes of $\mathdutchcal A\|_{i,j}$. \end{definition} \begin{definition}[{Shards, see~\cite[Definition~9-7.2]{reading_lattice_2016}}] \label{def:shards} Let $H_i\in\mathdutchcal A$ and set \[ \pre(H_i):=\{H_k\in\mathdutchcal A~:~H_k \text{ is basic in }\mathdutchcal A\|_{i,k}\quad \text{ and }\quad H_i \text{ is not basic in }\mathdutchcal A\|_{i,k}\}. \] The restriction of $\pre(H_i)$ to the hyperplane $H_i$ breaks $H_i$ into closed regions called \defn{shards}. We denote shards by capital Greek letters such as $\Sigma,\Theta,\Upsilon,$ etc. The hyperplane of $\mathdutchcal A$ that contains a shard~$\Sigma$ is denoted by $H_\Sigma$. We write $\Sigma^i$ to indicate that it is contained in $H_i$. Hyperplanes in $\pre(H_i)$ are said to \defn{cut} the hyperplane $H_i$. \end{definition} \begin{example}[Example~\ref{ex:A10_60} continued] \label{ex:shards} Figure \ref{fig:shards} illustrates the 29 shards obtained from the base region marked with a dot. \begin{figure}[H] \begin{center} \begin{tikzpicture} \node at (0,0) {\includegraphics[width=4in]{images/Not_normal.pdf}}; \node at (-2.9,-.8) {$H_1$}; \node at (1.9,-2.3) {$H_2$}; \node at (-.7,-3) {$H_3$}; \node at (-3.4,-2.9) {$H_4$}; \node at (-2.9,1.1) {$H_5$}; \node at (1.3,-3) {$H_6$}; \node at (4.6,.3) {$H_7$}; \node at (3.8,-2.3) {$H_8$}; \node at (2.9,-.8) {$H_9$}; \node at (1.8,2.5) {$H_{10}$}; \node at (.7,3) {$\Sigma$}; \node at (-1.3,-3) {$\Sigma$}; \node at (-1.3,3) {$\Sigma'$}; \node at (.6,-3) {$\Sigma''$}; \end{tikzpicture} \end{center} \caption{The shards of the simplicial hyperplane arrangement $\mathdutchcal A(10,60)_3=\mathdutchcal F_2(10)$ with respect to the dotted region} \label{fig:shards} \end{figure} \noindent On the one hand, due to the particular choice of projection, it is necessary to distinguish whether two unbounded straight line-segments lying on a common line form 1 or 2 shards. For example, the unbounded line-segments on the line labeled $H_3$ form one shard $\Sigma$, and the unbounded line-segments on the line labeled $H_6$ form 2 distinct shards $\Sigma'$ and $\Sigma''$. On the other hand, it is possible to solve this by changing the projection to obtain only circles, though simultaneously losing symmetry. \end{example} The following directed graph records the cutting relation among hyperplanes. \begin{definition}[{Directed graph $\H_B(\mathdutchcal A)$ \cite[Section~3]{reading_lattice_2004}}] \label{def:directed_graph} Let $\H_B(\mathdutchcal A)$ be the directed graph whose vertices are the hyperplanes of the arrangement $\mathdutchcal A$, and whose oriented edges are such that \begin{center} $H_i \rightarrow H_j$\qquad if and only if\qquad $H_i \in \pre(H_j)$. \end{center} \end{definition} The following directed graph keeps track of the cutting relation along with the ``geometric proximity'' between shards. \begin{definition}[Shard digraph, see {\cite[Section~3]{reading_lattice_2004}\cite[Definition~9.7.16]{reading_lattice_2016}}] \label{def:shard_dig} Let $\mathdutchcal{Sh}_B(\mathdutchcal A)$ be the directed graph on the shards of $\mathdutchcal A$ such that \[ \Sigma^i \rightarrow \Sigma^j \quad \text{if and only if } \quad \begin{array}{l} \bullet\hspace{5pt} H_{\Sigma^i} \rightarrow H_{\Sigma^j}\text{ in } \H_B(\mathdutchcal A) \text{ and} \\[0.25em] \bullet\hspace{5pt} \Sigma^i \cap \Sigma^j \text{ has dimension $d-2$.} \end{array} \] \end{definition} The following theorem gives a characterization of congruence uniformity in terms of the directed graph on shards. \begin{theorem}[{\cite[Corollary~9-7.22]{reading_lattice_2016}}] \label{thm:charac_uniform} Let $\mathdutchcal A$ be a hyperplane arrangement with a base region~$B$. The poset of regions $P_B(\A)$ is a congruence uniform lattice if and only if $\mathdutchcal A$ is tight with respect to~$B$ and $\mathdutchcal{Sh}_B(\mathdutchcal A)$ is acyclic. In this case, $\mathdutchcal{Sh}_B(\mathdutchcal A)$ is isomorphic to the Hasse diagram of $\Con(P_B(\A))_\vee$. \end{theorem} By Corollary~\ref{cor:norm_unif}, the theorem implies that acyclicity of the directed graph on shards~$\mathdutchcal{Sh}_B(\mathdutchcal A)$ characterizes the normality and uniformity of tight posets of regions $P_B(\A)$. \begin{example}[{Example~\ref{ex:shards} continued}] \label{ex:cycle_in_shards} Let $\Sigma^6,\Theta^{10},\Upsilon^8$, and $\Xi^9$ be the shards illustrated in Figure \ref{fig:cycle_in_shards}. The directed graph on shards contains the cycle $\Sigma^6 \rightarrow \Theta^{10} \rightarrow \Upsilon^8 \rightarrow \Xi^9 \rightarrow \Sigma^6$. Thus, for this choice of base region, the lattice of regions is not congruence normal. \end{example} \begin{figure}[H] \begin{center} \begin{tikzpicture} \node at (0,0) {\includegraphics[width=4in]{images/shard_forcing.pdf}}; \node at (-.2,0) {$\Sigma^6$}; \node at (-.4,-1.2) {$\Xi^9$}; \node at (2.2,.2) {$\Theta^{10}$}; \node at (2.7, -1) {$\Upsilon^8$}; \end{tikzpicture} \end{center} \caption{A cycle in the shards of the simplicial hyperplane arrangement from Example~\ref{ex:A10_60}.} \label{fig:cycle_in_shards} \end{figure} \section{Congruence normality through restricted covectors} \label{sec:cong_norm} In this section, we recast shards as certain restricted covectors---which we call \emph{shard covectors}---in the point configuration dual to the arrangement~$\mathdutchcal A$. We then describe how to detect cycles in $\mathdutchcal{Sh}_B(\mathdutchcal A)$ using shard covectors. This reduces the verification of congruence normality for tight posets of regions to its simplest combinatorial expression, one that does not require the entire poset nor the usage of polyhedral objects. Furthermore, it is possible to express an obstruction to congruence normality for tight hyperplane arrangements. In Section~\ref{ssec:restrict_inter}, we introduce restricted covectors and the intersection operation. In Section~\ref{ssec:aff_point}, we define affine point configurations and their lines. In Section~\ref{ssec:shards_as_cov}, we interpret shards as covectors. In Section~\ref{ssec:forcing_on_cov}, we translate the forcing relation on shards into the language of covectors. Finally, in Section~\ref{ssec:obstruction} we describe examples of obstructions to congruence normality in terms of restricted covectors. \subsection{Restricted covectors and the intersection operation} \label{ssec:restrict_inter} For standard references on covectors and oriented matroids, we refer the reader to the books \cite{oriented_matroids,de_loera_triangulations_2010}. \begin{definition}[Covector and restricted covector] Let $\P=\{\mathbf{p}_i\}_{i\in[m]}$ be an ordered set of vectors in $\mathbb{R}^d$. A \defn{covector} on $\P$ is a vector of signs $(\mathdutchcal{c}_i)_{i\in[m]}\in \{0,+,-\}^m$ defined as \[ \mathdutchcal{c}:=(\sign(\mathbf{c}\cdot \mathbf{p}_i + a))_{i\in[m]}, \] where $\mathbf{c}\in\mathbb{R}^d$ and $a\in\mathbb{R}$. Given a subset $\mathbf{U} \subseteq \P$ and a covector $\mathdutchcal{c}$ on $\P$, the \defn{restricted covector}~$\mathdutchcal{c}\|_{\mathbf{U}}$ with respect to $\mathbf{U}$ is equal to $\mathdutchcal{c}$ on the entries $\{j~:~\mathbf{p}_j\in \mathbf{U}\}$ and contains a ``$$'' symbol in every other entry. \end{definition} Intuitively, a restricted covector ``forgets'' about certain hyperplanes while keeping them encoded. Similarly, reversing the roles of $\mathbf{c}$ and $\mathbf{p}_i$ above, covectors may be thought of as \emph{sign evaluations} of a certain vector $\mathbf{x}$ with respect to a set of vectors: \begin{definition}[Sign evaluation of a vector] Let $\P=\{ \mathbf{p}_i\}_{i\in[m]}$ be an ordered set of vectors in $\mathbb{R}^d$ and $\mathbf{x}\in\mathbb{R}^d$. The \defn{sign evaluation} of $\mathbf{x}$ with respect to $\P$ is the covector \[ \mathdutchcal{c}_\P(\mathbf{x}):=\left(\sign( \mathbf{p}_i \cdot \mathbf{x})\right)_{i\in[m]}. \] \end{definition} Inspired by the composition operation on \emph{vectors} (i.e.\ affine dependences) of oriented matroids \cite[Chapter 3]{oriented_matroids}, we define an intersection operation on restricted covectors. \begin{definition}[Intersection of restricted covectors] The commutative \defn{intersection operation} $\cap$ from \newline ${\{0,+,-,\}\times\{0,+,-,\}}$ to $\{0,+,-,\}$ is defined as \begin{center} \begin{tabular}{c@{\hspace{2cm}}c@{\hspace{2cm}}c} $+\cap+:=+$, & $+\cap-=-\cap +:=0$, & $-\cap-:=-$,\\[0.5em] $0\cap \varepsilon=\varepsilon\cap 0:=0$, & $\cap \varepsilon=\varepsilon\cap :=\varepsilon$, & \\ \end{tabular} \end{center} where $\varepsilon\in\{0,+,-,\}$. Let $\mathdutchcal{c},\mathdutchcal{d} \in \{0,+,-,* \}^m$ be two restricted covectors, then their \defn{intersection} $\mathdutchcal{c}\cap \mathdutchcal{d}$ is the vector of signs $(\mathdutchcal{c}_i\cap \mathdutchcal{d}_i)_{i\in[m]}$. \end{definition} The vector of signs $(\mathdutchcal{c}_i\cap \mathdutchcal{d}_i)_{i\in[m]}$ is not necessarily a covector, though it nevertheless records the information of the sign evaluation of points in an intersection. It is possible to interpret this intersection operation using subsets of the real numbers. That is, if one replaces the four symbols $0,+,-,$ respectively by the sets $\{0\},\mathbb{R}_{\geq0},\mathbb{R}_{\leq0},\mathbb{R}$, and consider their intersections, we get exactly the same results. The associativity of this operation then follows easily. \subsection{Affine point configurations and lines} \label{ssec:aff_point} We use duality to pass from a hyperplane arrangement $\mathdutchcal A$ in~$\mathbb{R}^d$ with a base region $B$ to an acyclic point configuration~$\mathdutchcal A_B^$, see \cite[Section 1.2]{oriented_matroids} for more detail. Indeed, the normals $\{\mathbf{n}_i \}_{i \in [m]}$ are oriented so that the linear hyperplane orthogonal to $\mathbf{v}_B\in\inter(B)$ separates them from the base region $B$, i.e.\ $\mathbf{v}_B\cdot \mathbf{n}_i<0$, for all $i\in[m]$, making the set $\{\mathbf{n}_i\}_{i\in[m]}$ acyclic. \begin{definition}[Affine point configuration relative to a base region] Let $\mathdutchcal A$ be a hyperplane arrangement in $\mathbb{R}^d$, $B\in\mathdutchcal{R}(\mathdutchcal A)$, and $\mathbf{v}_B\in\inter(B)$. Let \[ \mathbb{A}_B := \{\mathbf{x} \in \mathbb{R}^d~:~\mathbf{v}_B\cdot \mathbf{x} = -1 \}, \] and associate the point $\mathbf{p}_i:=-\frac{1}{\mathbf{v}_B\cdot \mathbf{n}_i}\cdot \mathbf{n}_i \in \mathbb A_B\subset \mathbb{R}^d$ to the normal $\mathbf{n}_i$. The ordered set of vectors $\{\mathbf{p}_i\}_{i\in[m]}$ is the \defn{affine point configuration of $\mathdutchcal A$ relative to the base region $B$} and is denoted~$\mathdutchcal A_B^$. \end{definition} Choosing a different normal vector $\mathbf{v}_B\in\inter(B)$ yields an affine point configuration which is projectively equivalent to $\mathdutchcal A_B^$. Hence, up to projective transformation, this construction does not depend on the choice of $\mathbf{v}_B$. \begin{definition}[Lines of a point configuration, $\mathdutchcal{L}(\P)$] Let $\P=\{\mathbf{p}_i\}_{i\in[m]}$ be an ordered set of vectors in~$\mathbb{R}^d$ . A subset of $\P$ consisting of all the points that lie on the affine hull of two distinct points of $\P$ is called a \defn{line}. The set of lines of $\P$ is denoted by $\mathdutchcal{L}(\P)$. \end{definition} \begin{lemma} \label{lem:lines} Let $\mathdutchcal A$ be a hyperplane arrangement in $\mathbb{R}^d$ with base region $B$, $\ell\in\mathdutchcal{L}(\mathdutchcal A_B^)$, and $\mathbf{p}_i$ and~$\mathbf{p}_j$ be the two vertices of the segment $\conv(\ell)$. \begin{enumerate}[label=\roman{enumi}),ref=\ref{lem:lines}~\roman{enumi})] \item The lines in $\mathdutchcal{L}(\mathdutchcal A_B^)$ are in bijection with the rank-2 subarrangements of $\mathdutchcal A$. \label{lem:lines_i} \item The hyperplanes $H_i$ and $H_j$ are the basic hyperplanes of the rank-2 subarrangement corresponding to $\ell$. \label{lem:lines_ii} \end{enumerate} \end{lemma} \begin{proof} \emph{i)} Let $\mathdutchcal A':=\{H_i~:~i\in\mathcal{I}\}$, for some $\mathcal{I}\subseteq[m]$. The subarrangement $\mathdutchcal A'$ is a rank-2 subarrangement if and only if \[ \dim\left(\bigcap_{i \in \mathcal I} H_i\right) = d-2\quad\text{and}\quad \dim\left(\bigcap_{i \in \mathcal{I}\cup\{j\}} H_i\right) < d-2, \text{ for every } j \notin \mathcal{I}. \] Equivalently, \[ \dim\left(\spa(\mathbf{n}_i~:~i \in \mathcal{I})\right)= 2 \quad\text{and}\quad \dim\left(\spa(\{\mathbf{n}_j\}\cup\{\mathbf{n}_i~:~i \in \mathcal{I}\})\right) > 2, \text{ for every } j \notin \mathcal I. \] By passing to the affine point configuration in the affine space$~\mathbb A_B$, the above statement is equivalent to $\{\mathbf{p}_i~:~i \in \mathcal{I}\} \in \mathdutchcal{L}(\mathdutchcal A_B^)$. Thus the map sending a rank-2 subarrangement $\mathdutchcal A'$ to the line $\{\mathbf{p}_i~:~i \in \mathcal{I} \}$ is a bijection. \emph{ii)} Let $B\|_{i,j}$ be the region of $\mathdutchcal A\|_{i,j}$ that contains $B$: \[ B\|_{i,j} = \{\mathbf{x} \in \mathbb{R}^d~:~\mathbf{p}_k \cdot \mathbf{x} \leq 0,\text{ for all } \mathbf{p}_k\in\ell\}, \] by part \emph{i)}. Let $\mathbf{p}_k$ be the normal of a facet $F$ of $B\|_{i,j}$ and $\mathbf{x}$ be contained in the relative interior of $F$ so that $\mathbf{p}_k\cdot \mathbf{x} =0$. Since $\mathbf{p}_i$ and $\mathbf{p}_j$ are the vertices of $\conv(\ell)$, we have $\mathbf{p}_k = \lambda_k \mathbf{p}_i +(1-\lambda_k)\mathbf{p}_j$, for some $0 \leq \lambda_k \leq 1$. Then \[ 0 = \mathbf{x} \cdot \mathbf{p}_k = \lambda_k (\mathbf{x} \cdot \mathbf{p}_i) + (1-\lambda_k)(\mathbf{x} \cdot \mathbf{p}_j). \] As $\mathbf{p}_i\cdot\mathbf{x} \leq 0$ and $\mathbf{p}_j\cdot\mathbf{x}\leq 0$, the above equality implies that $\mathbf{p}_k$ must be $\mathbf{p}_i$ or $\mathbf{p}_j$. \end{proof} \subsection{Shards as restricted covectors} \label{ssec:shards_as_cov} Let $\mathdutchcal A$ be a tight hyperplane arrangement with respect to a base region $B$ and $\mathdutchcal A^_B$ be its associated affine point configuration. Every shard $\Sigma$ of $\mathdutchcal A$ has a corresponding unique join-irreducible region $J_\Sigma$ \cite[Proposition~9-7.8]{reading_lattice_2016}. In the lattice of regions, $J_\Sigma$ is the meet of all regions $R$ such that \[ H_\Sigma \in \Sep(R)\quad \text{ and }\quad R \cap \Sigma \text{ has dimension }d-1. \] The next lemma shows how $\pre(H_\Sigma)$ and $\Sep(J_\Sigma)$ yield a description of the shard as the intersection of half-spaces. It is originally stated for simplicial arrangements, though the same holds true for tight hyperplane arrangements. \begin{lemma}[{see \cite[Lemma 3.7]{reading_lattice_2004}}] \label{lem:shards_Hdesc} A shard $\Sigma$ has the following description: $$ \Sigma = \bigg \{ \mathbf{x} \in H_\Sigma \, \bigg \lvert \begin{array}{l} \mathbf{n}_i \cdot \mathbf{x} \geq 0 \text{ if } H_i \in \pre(H_\Sigma) \cap \Sep(J_\Sigma) \\ \mathbf{n}_i \cdot \mathbf{x} \leq 0 \text{ if } H_i \in \pre(H_\Sigma) \setminus \Sep(J_\Sigma) \end{array} \bigg \}. $$ \end{lemma} To interpret shards on a hyperplane $H_i$ as covectors, we restrict to a certain subconfiguration containing $\mathbf{p}_i$. \begin{definition}[Subconfiguration localized at a point] Let $\mathbf{p}_i\in\mathdutchcal A_B^$. The \defn{subconfiguration~$\mathdutchcal A_{B,i}^$ of $\mathdutchcal A_B^$ localized at $\mathbf{p}_i$} contains $\mathbf{p}_i$ and the vertices of the convex hulls of lines of $\mathdutchcal A_B^$ that contain~$\mathbf{p}_i$ in their interior. \end{definition} Lemma~\ref{lem:lines_ii} and Definition~\ref{def:directed_graph} imply the following lemma. \begin{lemma} \label{lem:subconf} The subconfiguration $\mathdutchcal A_{B,i}^$ satisfies \[ \mathdutchcal A_{B,i}^=\{\mathbf{p}_i\}\cup\{\mathbf{p}_j~:~H_j\in \pre(H_i)\}. \] \end{lemma} \begin{definition}[Shard covectors of a point] Let $\mathbf{p}_i\in\mathdutchcal A_B^$. A \defn{shard covector of $\mathbf{p}_i$} is a restricted covector~$\sigma^i=\mathdutchcal{c}\|_{\mathdutchcal A_{B,i}^}$ with respect to $\mathdutchcal A_{B,i}^$ such that \begin{itemize} \item $\sigma^i_j=$\quad if and only if\quad $\mathbf{p}_j\not\in \mathdutchcal A_{B,i}^$, and \item the restriction of $\sigma^i$ to the subconfiguration $\mathdutchcal A_{B,i}^$ is a covector with exactly one zero in position ``$i$''. \end{itemize} \end{definition} \begin{example} \label{ex:A6_24} In Figure~\ref{fig:A6_24}, the left image illustrates the affine point configuration $\mathdutchcal A(6,24)^$ for the rank-$3$ braid arrangement with $6$ hyperplanes. The right image illustrates the subconfiguration of $\mathdutchcal A(6,24)^$ localized at $\mathbf{p}_6$, $\mathdutchcal A(6,24)^_{6}$. \begin{figure}[H] \begin{center} \begin{tabular}{c@{\hspace{2cm}}c} \begin{tikzpicture} [scale=0.75, point/.style={circle,fill=black,inner sep=1.5pt}, line/.style={black!20,line width=2pt}] \coordinate (1) at (0.000000000000000,0.000000000000000); \coordinate (2) at (2.00000000000000,3.46410161513775); \coordinate (3) at (4.00000000000000,0.000000000000000); \coordinate (4) at (1.00000000000000,1.73205080756888); \coordinate (5) at (3.00000000000000,1.73205080756888); \coordinate (6) at (2.00000000000000,1.15470053837925); \draw[line] (5) -- (1) -- (2) -- (3) -- (4); \node[point,label=left:{$\mathbf{p}_1$}] at (1) {}; \node[point,label=above:{$\mathbf{p}_2$}] at (2) {}; \node[point,label=right:{$\mathbf{p}_3$}] at (3) {}; \node[point,label=left:{$\mathbf{p}_4$}] at (4) {}; \node[point,label=right:{$\mathbf{p}_5$}] at (5) {}; \node[point,label=below:{$\mathbf{p}_6$}] at (6) {}; \end{tikzpicture} & \begin{tikzpicture} [scale=0.75, point/.style={circle,fill=black,inner sep=1.5pt}, line/.style={black!20,line width=2pt}] \coordinate (1) at (0.000000000000000,0.000000000000000); \coordinate (3) at (4.00000000000000,0.000000000000000); \coordinate (4) at (1.00000000000000,1.73205080756888); \coordinate (5) at (3.00000000000000,1.73205080756888); \coordinate (6) at (2.00000000000000,1.15470053837925); \draw[line] (1) -- (5); \draw[line] (3) -- (4); \node[point,label=left:{$\mathbf{p}_1$}] at (1) {}; \node[point,label=right:{$\mathbf{p}_3$}] at (3) {}; \node[point,label=left:{$\mathbf{p}_4$}] at (4) {}; \node[point,label=right:{$\mathbf{p}_5$}] at (5) {}; \node[point,label=below:{$\mathbf{p}_6$}] at (6) {}; \end{tikzpicture} \end{tabular} \end{center} \caption{The point configuration $\mathdutchcal A(6,24)^$ for the rank-3 braid arrangement and the subconfiguration $\mathdutchcal A(6,24)^_{6}$ localized at $\mathbf{p}_6$} \label{fig:A6_24} \end{figure} \noindent There are two pairs of oppositely signed shard covectors of $\mathbf{p}_6$: \begin{align} \sigma^{6,+} = (+,,+,-,-,0),\qquad\theta^{6,+} = (+,,-,+,-,0),\\ \sigma^{6,-} = (-,,-,+,+,0),\qquad\theta^{6,-} = (-,,+,-,+,0). \end{align} It is possible to obtain these shard covectors by drawing a line through $\mathbf{p}_6$ in $\mathdutchcal A(6,24)^_{6}$, and choosing a positive and a negative side. Rotating the line about $\mathbf{p}_6$ in all possible directions, and recording the sign evaluations of the points in $\mathdutchcal A(6,24)^_{6}$ relative to the line exhausts all possibilities. \end{example} We now associate a restricted covector to each shard using the sign evaluation of vectors. Let~$\Sigma^i$ be a shard contained in hyperplane $H_i$, and let $\mathbf{x}\in\inter(\Sigma^i)$. Using Lemma~\ref{lem:shards_Hdesc} and~\ref{lem:subconf}, we get \[ \mathdutchcal{c}_{\mathdutchcal A^_{B,i}}(\mathbf{x}) := \left(\mathdutchcal{c}_{\mathdutchcal A^_{B,i}}(\mathbf{x})_j= \begin{cases} 0 & \text{if } j=i,\\ + & \text{if } H_j\in\pre(H_i)\cap\Sep(J_\Sigma) \\ - & \text{if } H_j\in\pre(H_i)\setminus\Sep(J_\Sigma) \\ \end{cases} \right)_{j\in[m]\text{ and }\mathbf{p}_j\in\mathdutchcal A^_{B,i}}. \] Completing this sign evaluation to the configuration $\mathdutchcal A^_B$, we get the restricted covector \[ \sigma^i := \left(\sigma^i_j= \begin{cases} \mathdutchcal{c}_{\mathdutchcal A^_{B,i}}(\mathbf{x})_j & \text{if } H_j\in\pre(H_i)\cup\{H_i\}\\ * & \text{if } H_j\notin\pre(H_i)\cup\{H_i\} \end{cases} \right)_{j\in[m]}. \] This restricted covector is independent of the choice of vector $\mathbf{x}\in\inter(\Sigma^i)$, thanks to Lemma~\ref{lem:shards_Hdesc}, and only depends on the choice of base region $B$. \begin{theorem} \label{thm:shard_bijection} Let $\mathdutchcal A$ be a tight hyperplane arrangement with respect to a base region $B$. The map sending a shard~$\Sigma^i$ to the shard covector~$\sigma^i$ gives a bijection between the shards of $\mathdutchcal A$ with base region~$B$ and the shard covectors of $\mathdutchcal A^_B$. \end{theorem} \begin{proof} \emph{Injectivity.} Suppose $\sigma^i = \theta^i$ for two shards $\Sigma^i$ and $\Theta^i$, for some $i\in[m]$. By the definition of $\sigma^i$ and~$\theta^i$, the shard covectors are obtained from some points $\mathbf{x} \in \inter(\Sigma^i)$ and $\mathbf{y} \in \inter(\Theta^i)$ and \[ \sign(\mathbf{n}_j \cdot \mathbf{x}) = \sign(\mathbf{n}_j \cdot \mathbf{y}) \quad\text{for every } j \text{ such that } H_j\in \pre(H_i) \cup \{H_i\}. \] By Lemma~\ref{lem:shards_Hdesc}, an H-description of the shard is given by the sign evaluation of any of its points in the relative interior with respect to the hyperplanes in $\pre(H_i)$. Because $\Sigma^i$ and $\Theta^i$ are both shards on hyperplane~$H_i$, and the sign evaluation of $\mathbf{x}$ and $\mathbf{y}$ agree on all normals in $\pre(H_i)$, $\Sigma^i$ and $\Theta^i$ must be the same. \emph{Surjectivity}. Let $\mathdutchcal{c}$ be a shard covector with a unique zero at position $i \in [m]$. Considered as a sign evaluation, there is an $\mathbf{x}\in\mathbb{R}^d$ such that $\mathdutchcal{c}=\mathdutchcal{c}_{\mathdutchcal A^_B}(\mathbf{x})\|_{\mathdutchcal A_{B,i}^}$. The linear hyperplane with normal $\mathbf{x}$ separates the normal vectors in $\pre(H_i)$ as $\mathdutchcal{c}$ dictates. Thus $\mathbf{x}$ is a point in the relative interior of a shard $\Sigma^i$ of $H_i$ such that ${\sigma^i =\mathdutchcal{c}}$. \end{proof} By Theorem~\ref{thm:shard_bijection}, there is a unique shard covector associated to every shard. We therefore use lowercase Greek letters $\sigma^i$ to denote the unique shard covector corresponding to a shard~$\Sigma^i$. \subsection{Forcing relation on covectors} \label{ssec:forcing_on_cov} In this section, we use Theorem~\ref{thm:shard_bijection} and interpret the shard digraph~$\mathdutchcal{Sh}_B(\mathdutchcal A)$ using shard covectors of $\mathdutchcal A^_B$. In Definition~\ref{def:shard_dig}, the first condition to get an edge $\Sigma^i\rightarrow\Sigma^j$ translates to the shard covectors of $\mathbf{p}_j$ having a $+$ or $-$ at position~``$i$''. The second condition requires one to interpret the dimension of intersection of two shards using shard covectors. To do so, we define \defn{line covectors} of two hyperplanes. \begin{definition}[Line covector] Let $\ell\in\mathdutchcal{L}(\mathdutchcal A_B^)$. A \defn{line covector} of $\ell$ is a covector $\mathdutchcal{h}^\ell$ on $\mathdutchcal A_B^$ such that \begin{center} $\mathdutchcal{h}^{\ell}_k=0$\quad if and only if\quad $\mathbf{p}_k\in\ell$. \end{center} \end{definition} Line covectors record possible sign evaluations of non-zero points in the intersection of two hyperplanes with respect to~$\mathdutchcal A_B^$. They come in oppositely signed pairs which we denote by~$\mathdutchcal{h}^{\ell,+}$ and $\mathdutchcal{h}^{\ell,-}$. In the case of rank-3 hyperplane arrangements, these covectors are actually cocircuits of the oriented matroid. For higher-rank hyperplane arrangements, the set of $0$-indices of a line covector gives a flat of rank~$2$ in the underlying matroid. \begin{example}[Example~\ref{ex:A6_24} continued] Let $\ell=\{\mathbf{p}_1,\mathbf{p}_5,\mathbf{p}_6\}$. Since $\mathbb{A}_B$ has dimension $2$, the line $\ell$ has exactly two line covectors. From Figure~\ref{fig:A6_24}, we deduce that the line covectors of $\ell$ are: \[ \begin{aligned} \mathdutchcal{h}^{\ell,+} &= (0,+,-,+,0,0), \\ \mathdutchcal{h}^{\ell,-} &= (0,-,+,-,0,0). \\ \end{aligned} \] \end{example} \begin{lemma} \label{lem:codim2} Let $\mathdutchcal A_B^=\{\mathbf{p}_i\}_{i\in[m]}$ be an affine point configuration, $1\leq i<j\leq m$, $\ell$ be the line spanned by $\mathbf{p}_i$ and $\mathbf{p}_j$, and $\mathdutchcal{h}^\ell$ be a line covector of $\ell$. The set ${\{\, \mathbf{x}\in (H_i \cap H_j)~:~\mathdutchcal{c}_{\mathdutchcal A_B^}(\mathbf{x})=\mathdutchcal{h}^\ell\, \}}$ has dimension~$d-2$. \end{lemma} \begin{proof} Let $\mathbf{x} \in H_i \cap H_j$ with $\mathdutchcal{c}_{\mathdutchcal A_B^}(\mathbf{x}) = \mathdutchcal{h}^\ell$. For any $\mathbf{v} \in \spa(\mathbf{n}_i,\mathbf{n}_j)^\perp$ and $\varepsilon>0$, the $k$-th entry of $\mathdutchcal{c}_{\mathdutchcal A_B^}(\mathbf{x} + \varepsilon \mathbf{v})$ is equal to \begin{align} \mathdutchcal{c}_{\mathdutchcal A_B^}(\mathbf{x} + \varepsilon \mathbf{v})_k & = \sign{( \mathbf{x} \cdot \mathbf{n}_k + \varepsilon( \mathbf{v} \cdot \mathbf{n}_k))} \\ & = \begin{cases} 0 & \text{ if } k \in \{i,j \}, \\ \sign(\mathbf{x} \cdot \mathbf{n}_k + \varepsilon(\mathbf{v} \cdot \mathbf{n}_k)) & \text{ if } k \notin \{i,j\}.\\ \end{cases} \end{align} When $\varepsilon$ is chosen small enough, then \[ \mathdutchcal{c}_{\mathdutchcal A_B^}(\mathbf{x} + \varepsilon \mathbf{v})_k = \mathdutchcal{c}_{\mathdutchcal A_B^}(\mathbf{x})_k = \mathdutchcal{h}^\ell_k. \] Thus $\dim(\{\mathbf{x}\in (H_i \cap H_j)~:~\mathdutchcal{c}_{\mathdutchcal A_B^}(\mathbf{x})=\mathdutchcal{h}^\ell\}) = \dim(\spa(\mathbf{n}_i,\mathbf{n}_j)^\perp) = d-2.$ \end{proof} \begin{example}[Example~\ref{ex:A6_24} continued] Figure \ref{fig:A6_24_shards} shows a stereographic projection of $\mathdutchcal A(6,24)$ broken into shards. The shards $\Theta^{6,+}$ and $\Sigma^1 = H_1$ are thickened and one sees that~$H_1$ cuts $H_6$. The shards $\Sigma^1$ and $\Theta^{6,+}$ intersect at a point so there is an oriented edge $\Sigma^1\rightarrow\Theta^{6,+}$ in the shard digraph. \begin{figure}[H] \begin{center} \begin{tikzpicture} \node at (0,0) {\includegraphics[width=2.5in]{images/A3.pdf}}; \node at (-3.6,-.5) {$H_1 = \Sigma^1$}; \node at (2.5,.4) {$H_2$}; \node at (-1.8,2.3) {$H_3$}; \node at (-1,-1.5) {$H_4$}; \node at (1.5,-.3) {$H_5$}; \node at (-.9,0) {$H_6$}; \node at (.35,.45) {$\Theta^{6,+}$}; \end{tikzpicture} \end{center} \caption{The shards of the arrangement $\mathdutchcal A(6,24)$ shown via stereographic projection} \label{fig:A6_24_shards} \end{figure} \noindent This fact translates to a property of the corresponding shards covectors $\sigma^{1}=(0,,,,,)$ and $\theta^{6,+}=(+,,-,+,-,0)$. Indeed, consider the line $\ell=\{\mathbf{p}_1,\mathbf{p}_5,\mathbf{p}_6\}$ and the line covector $\mathdutchcal{h}^{\ell,+}=(0,+,-,+,0,0)$. Then $\mathdutchcal{h}^{\ell,+} \cap \theta^{6,+} \cap \sigma^{1} = (0,+,-,+,0,0)$. Figure~\ref{fig:shic} illustrates the affine point configuration~$\mathdutchcal A(6,24)^$ along with the three oriented lines describing the involved covectors. \begin{figure}[H] \begin{center} \begin{tikzpicture} [ point/.style={circle,fill=black,inner sep=1.5pt}, line/.style={black!20,line width=2pt}] \coordinate (1) at (0.000000000000000,0.000000000000000); \coordinate (2) at (2.00000000000000,3.46410161513775); \coordinate (3) at (4.00000000000000,0.000000000000000); \coordinate (4) at (1.00000000000000,1.73205080756888); \coordinate (5) at (3.00000000000000,1.73205080756888); \coordinate (6) at (2.00000000000000,1.15470053837925); \draw[line,dashed] (1) -- (5); \draw[line,dashed] (1) -- (2); \draw[line,dashed] (3) -- (2); \draw[line,dashed] (3) -- (4); \draw[line,blue,shorten >= -35mm, shorten <= -10mm] (1) -- (5); \draw[line,black] (2.00000000000000,1.15470053837925) -- +(2,-2); \draw[line,black] (2.00000000000000,1.15470053837925) -- +(-2.5,2.5); \draw[line,teal] (0,0) -- +(-3,3); \draw[line,teal] (0,0) -- +(1,-1); \node[point,label=below:{$\mathbf{p}_1$}] at (1) {}; \node[point,label=above:{$\mathbf{p}_2$}] at (2) {}; \node[point,label=below:{$\mathbf{p}_3$}] at (3) {}; \node[point,label=left:{$\mathbf{p}_4$}] at (4) {}; \node[point,label=below:{$\mathbf{p}_5$}] at (5) {}; \node[point,label=below:{$\mathbf{p}_6$}] at (6) {}; \node[label = right:{\textcolor{teal}{$-$}}] at (-2,2) {}; \node[label = left:{\textcolor{teal}{$+$}}] at (-2,2) {}; \node[label = left:{\textcolor{black}{$+$}}] at (0,3.15) {}; \node[label = right:{\textcolor{black}{$-$}}] at (0,3.15) {}; \node[label = above left:{\textcolor{blue}{$+$}}] at (4.5,2.625) {}; \node[label = below right:{\textcolor{blue}{$-$}}] at (4.5,2.625) {}; \node[label = below:{$\mathdutchcal{h}^{\ell,+}$}] at (6,3.46) {}; \node[label = left:{$\theta^{6,+}$}] at (-0.5,3.5) {}; \node[label = left:{$\sigma^{1}$}] at (-3,3) {}; \end{tikzpicture} \end{center} \caption{The point configuration $\mathdutchcal A(6,24)^$ and hyperplanes describing the covectors $\sigma^1$, $\theta^{6,+}$, and $\mathdutchcal{h}^{\ell,+}$, where $\ell=\{\mathbf{p}_1,\mathbf{p}_5,\mathbf{p}_6\}$} \label{fig:shic} \end{figure} \noindent It is possible to interpret the fact that the two shards intersect at a point as follows. Apply a clockwise rotation to the line labeled $\theta^{6,+}$ about the point $\mathbf{x}_6$ until it collides with the line corresponding to $\mathdutchcal{h}^{\ell,+}$. During the rotation, the line did not cross any points in $\mathdutchcal A_{B,6}^$. Similarly, applying the same with the line labeled $\sigma^1$ about $\mathbf{x}_1$ does not cross any points in $\mathdutchcal A_{B,1}^=\varnothing$. \end{example} The theorem below shows that the above equality is exactly the necessary and sufficient condition for the two involved shards to have an intersection of dimension~$d-2$. \begin{theorem} \label{thm:covector_forcing} Let $\mathdutchcal A_B^=\{\mathbf{p}_i\}_{i\in[m]}$ be an affine point configuration, $1\leq i<j\leq m$, and let $\ell$ be the line spanned by $\mathbf{p}_i$ and $\mathbf{p}_j$. Furthermore, let $\Sigma^i \subseteq H_i$ and ${\Theta^j \subseteq H_j}$ be two shards. The intersection $\Sigma^i \cap \Theta^j$ has dimension~$d-2$ if and only if there exists a line covector $\mathdutchcal{h}^\ell$ such that $\mathdutchcal{h}^{\ell}\cap \sigma^i\cap\theta^j= \mathdutchcal{h}^\ell$. \end{theorem} \begin{proof} Assume $\dim (\Sigma^i \cap \Theta^j) = d-2$. Hence there exists $\mathbf{x} \in \Sigma^i \cap \Theta^j$ such that the sign evaluation $\mathdutchcal{c}_{\mathdutchcal A_B^}(\mathbf{x})_k$ equals zero if and only if $\mathbf{p}_k \in \ell$. Therefore $\mathdutchcal{c}_{\mathdutchcal A_B^}(\mathbf{x})$ is a line covector of $\ell$. If $\mathbf{x}$ is in the boundary of $\Sigma^i$, then for $\mathbf{z} \in \inter (\Sigma^i), \mathbf{p}_k \in \mathdutchcal A_{B,i}^$, either $\sign(\mathbf{x} \cdot \mathbf{p}_k) = \sign(\mathbf{z} \cdot \mathbf{p}_k)$ or $\sign( \mathbf{x} \cdot \mathbf{p}_k) = 0$. As $\mathdutchcal{c}_{\mathdutchcal A_B^}(\mathbf{x})_k$ equals zero if and only if $\mathbf{p}_k \in \ell$, $\sigma^i_k = \mathdutchcal{c}_{\mathdutchcal A_{B}^}(\mathbf{x})_k$ for all $k$ such that $\mathbf{p}_k \in (\mathdutchcal A_{B,i}^\setminus\ell)$. Likewise, $\theta^j_k = \mathdutchcal{c}_{\mathdutchcal A_{B}^}(\mathbf{x})_k$ for all~$k$ such that $\mathbf{p}_k \in (\mathdutchcal A_{B,j}^\setminus\ell)$. Thus, \[ \mathdutchcal{c}_{\mathdutchcal A_B^}(\mathbf{x}) \cap \sigma^i \cap \theta^j = \mathdutchcal{c}_{\mathdutchcal A_B^}(\mathbf{x}). \] Assume now that there exists a line covector $\mathdutchcal{h}^\ell$ such that ${\mathdutchcal{h}^{\ell}\cap \sigma^i\cap\theta^j=\mathdutchcal{h}^\ell}$. Let $S = \{\mathbf{x} \in {(H_i \, \cap\, H_j)}~:\mathdutchcal{c}_{\mathdutchcal A_B^}(\mathbf{x}) = \mathdutchcal{h}^\ell \}$. By Lemma~\ref{lem:codim2}, $\dim(S)=d-2$. Let $\mathbf{x} \in S$, $\mathbf{y} \in \inter(\Sigma^i)$, and $\mathbf{z} \in \inter(\Theta^j)$. As $\mathdutchcal{h}^\ell \cap \sigma^i = \mathdutchcal{h}^\ell$, $\sign(\mathbf{x} \cdot \mathbf{p}_k) = \sign(\mathbf{y} \cdot \mathbf{p}_k)$ for all $\mathbf{p}_k \in \mathdutchcal A_{B,i}^ \setminus \ell$. For $\mathbf{p}_k \in \ell$, we have $\mathbf{x} \cdot \mathbf{p}_k = 0$. For $0 \leq \lambda \leq 1$, let $\mathbf{m}_\lambda = (1-\lambda)\mathbf{y} + \lambda \mathbf{x}$. Then $\mathdutchcal{c}_{\mathdutchcal A_{B,i}^}(\mathbf{m}_\lambda)_k = \sign(\mathbf{y} \cdot \mathbf{p}_k)$ for all~$k$ such that $\mathbf{p}_k \in \mathdutchcal A_{B,i}^$, and $\lambda \in [0,1)$. This shows that $\mathbf{m}_\lambda \in \Sigma^i$ for all $\lambda \in [0,1)$, and thus~$\mathbf{x}$ is contained in $\Sigma^i$. A similar argument with $\mathbf{z}$ shows that $\mathbf{x}$ is in $\Theta^j$. \end{proof} \begin{corollary} \label{cor:covector_forcing} There is a directed arrow $\Sigma^i \rightarrow \Theta^j$ in $\mathdutchcal{Sh}_B(\mathdutchcal A)$ if and only if $\theta^j_i\in\{-,+\}$ and there exists a line covector $\mathdutchcal{h}^{\ell}$ such that $\mathdutchcal{h}^{\ell}\cap \sigma^i\cap\theta^j = \mathdutchcal{h}^\ell$. \end{corollary} \subsection{Obstruction to congruence normality} \label{ssec:obstruction} \begin{example}[Example~\ref{ex:A10_60} continued] The normal vectors $\{\mathbf{n}_i\}_{i\in [10]}$ for this configuration can be chosen as follows. Let $\tau = \frac{1 + \sqrt{5}}{2}$ and $ \mathbf{n}_1=(0, 1, 0), \mathbf{n}_2=(1, 0, 0), \mathbf{n}_3=(1, 1, 0), \mathbf{n}_4=(1, 1, 1), \mathbf{n}_5=(\tau+1, \tau, \tau), \mathbf{n}_6=(\tau+1, \tau+1, 1), \mathbf{n}_7=(\tau+1, \tau+1, \tau), \mathbf{n}_8=(2\tau,2\tau,\tau), \mathbf{n}_9=(2\tau+1,2\tau,\tau), \mathbf{n}_{10}=(2\tau+2, 2\tau+1, \tau+1)$. Let $B$ be the base region containing the vector $\mathbf{v}= (-1,-1,-2)$. Figure \ref{fig:A10_60_star} illustrates $\mathdutchcal A(10,60)_{3,B}^{}{}$ along with four lines describing the shard covectors \begin{align} \begin{array}{ll} \sigma^6 = (+, , -, +, , 0, , , -, ), & \theta^8= (-, , -, +, , , , 0, , +), \\ \upsilon^9 = (, -, -, , +, , , +, 0, ), & \xi^{10} = (, -, , +, +, -, +, , -, 0). \end{array} \end{align} \begin{figure}[H] \begin{tikzpicture} [scale=1.5, point/.style={circle,fill=black,inner sep=1.5pt}, line/.style={black!20,line width=1.5pt}, rotate=-36.8698976] \coordinate (A) at (0,0); \coordinate (B) at (4,3); \coordinate (C) at (2,3/2); \coordinate (D) at (0,5); \coordinate (E) at (0,5/2); \coordinate (F) at (4/3,8/3); \coordinate (G) at ($({sqrt(5)},-{sqrt(5)}/2)+(-1,3)$); \coordinate (H) at ($({2sqrt(5)/11},-{7sqrt(5)/22})+(14/11,61/22)$); \coordinate (I) at ($({-2sqrt(5)/5},-{4sqrt(5)/5})+(2,4)$); \coordinate (J) at ($({-2sqrt(5)},{7sqrt(5)/2})+(6,-11/2)$); \draw[line] (A) -- (B) -- (C); \draw[line] (A) -- (G) -- (J); \draw[line] (A) -- (F) -- (I); \draw[line] (A) -- (D) -- (E); \draw[line] (B) -- (G) -- (H); \draw[line] (B) -- (I) -- (J); \draw[line] (B) -- (E) -- (F); \draw[line] (C) -- (D) -- (F) -- (J) -- (H); \draw[line] (C) -- (E) -- (G); \draw[line] (D) -- (G) -- (I); \draw[line] (E) -- (H) -- (I); \draw[thick, black!60!green] (H) -- +(5:2.3cm); \draw[thick, black!60!green] (H) -- +(185:3.5cm); \path (H) -- +(.4:2.2cm) coordinate (6+); \node[label={[black!60!green]north east:{+}}] at (6+) {}; \path (H) -- +(5:2.3cm) coordinate (sigma6); \node[label={below:{$\sigma^6$}}] at (sigma6) {}; \draw[thick, black!60!blue] (G) -- +(185:3cm); \draw[thick, black!60!blue] (G) -- +(5:2.5cm); \path (G) -- +(-.5:2.4cm) coordinate (9+); \node[label={[black!60!blue]north east:{+}}] at (9+) {}; \path (G) -- +(5:2.5cm) coordinate (upsilon9); \node[label={below:{$\upsilon^9$}}] at (upsilon9) {}; \draw[thick, black!60!red] (I) -- +(185:3cm); \draw[thick, black!60!red] (I) -- +(5:3.1cm); \path (I) -- +(2:3.1cm) coordinate (10+); \node[label={[black!60!red]north east:{+}}] at (10+) {}; \path (I) -- +(5:3.1cm) coordinate (xi10); \node[label={below:{$\xi^{10}$}}] at (xi10) {}; \draw[thick, black!60!orange] (J) -- +(85:3cm); \draw[thick, black!60!orange] (J) -- +(-95:2cm); \path (J) -- +(85:3cm) coordinate (8+); \node[label={[black!60!orange]left:{+}}] at (8+) {}; \path (J) -- +(85:3cm) coordinate (theta8); \node[label={{$\theta^8$}}] at (theta8) {}; \node[point,label=left:{$\mathbf{p}_2$}] at (A) {}; \node[point,label=right:{$\mathbf{p}_1$}] at (B) {}; \node[point,label=below:{$\mathbf{p}_3$}] at (C) {}; \node[point,label=right:{$\mathbf{p}_4$}] at (D) {}; \node[point,label=left:{$\mathbf{p}_5$}] at (E) {}; \node[point,label=above right:{$\mathbf{p}_7$}] at (F) {}; \node[point,label=below:{$\mathbf{p}_9$}] at (G) {}; \node[point,label=below:{$\mathbf{p}_6$}] at (H) {}; \node[point,label=left:{$\mathbf{p}_{10}$}] at (I) {}; \node[point,label=right:{$\mathbf{p}_8$}] at (J) {}; \end{tikzpicture} \caption{The point configuration $\mathdutchcal A(10,60)_{3,B}^$} \label{fig:A10_60_star} \end{figure} \noindent Let $\ell_1=\{\mathbf{p}_2,\mathbf{p}_8,\mathbf{p}_9\},\ell_2=\{\mathbf{p}_1,\mathbf{p}_6,\mathbf{p}_9\},\ell_3=\{\mathbf{p}_5,\mathbf{p}_6,\mathbf{p}_{10}\},$ and $\ell_4=\{\mathbf{p}_1,\mathbf{p}_8,\mathbf{p}_{10}\}$ and consider the four line covectors \begin{align} \begin{array}{ll} \mathdutchcal{h}^{\ell_1} = (-,0,-,+,+,-,+,0,0,+), & \mathdutchcal{h}^{\ell_2} = (0,-,-,+,+,0,+,+,0,+), \\ \mathdutchcal{h}^{\ell_3} = (+,-,-,+,0,0,+,+,-,0), & \mathdutchcal{h}^{\ell_4} = (0,-,-,+,+,-,+,0,-,0). \end{array} \end{align} As $\upsilon^9$ has a ``$+$'' in position 8, $H_8$ cuts $H_9$. Furthermore, one computes that $\mathdutchcal{h}^{\ell_1} \cap\theta^8 \cap \upsilon^9 = \mathdutchcal{h}^{\ell_1}$. By Corollary~\ref{cor:covector_forcing}, there is a directed arrow $\Theta^9\rightarrow\Upsilon^9$ in $\mathdutchcal{Sh}_B(\mathdutchcal A)$. Similar computations reveal that $\theta^8 \rightarrow \upsilon^9 \rightarrow \sigma^6 \rightarrow \xi^{10} \rightarrow \theta^8$ is a cycle in $\mathdutchcal{Sh}_B(\mathdutchcal A)$. Thus, the poset of regions of $\mathdutchcal A(10,60)_3$ with respect to the base region $B$ is not congruence normal. \end{example} \begin{example} \label{ex:min_not_CU} Removing the hyperplane $H_4$ from the arrangement $\mathdutchcal A(10,60)_3$ and taking the base region that contains the vector $\mathbf{v}=(-1,-1,2)$, one obtains a non-simplicial, tight (hence semidistributive) poset of regions with 52 regions that is not congruence normal as the cycle $\theta^8 \rightarrow \upsilon^9 \rightarrow \sigma^6 \rightarrow \xi^{10} \rightarrow \theta^8$ still occurs in the shard digraph. Figure~\ref{fig:min_not_CU} illustrates the resulting affine point configuration. Is there a tight poset of regions which is not congruence normal with at most 8 hyperplanes? \begin{figure}[H] \begin{tikzpicture} [x={(-0.875cm, 1.08253175473055cm)}, y={(2cm, 0cm)}, scale=1.25, point/.style={circle,fill=black,inner sep=1.5pt}, line/.style={black!20,line width=2pt}] \coordinate (A) at (0,0); \coordinate (B) at (4,3); \coordinate (C) at (2,3/2); \coordinate (D) at (0,5); \coordinate (E) at (0,5/2); \coordinate (F) at (4/3,8/3); \coordinate (G) at ($({sqrt(5)},-{sqrt(5)}/2)+(-1,3)$); \coordinate (H) at ($({2sqrt(5)/11},-{7sqrt(5)/22})+(14/11,61/22)$); \coordinate (I) at ($({-2sqrt(5)/5},-{4sqrt(5)/5})+(2,4)$); \coordinate (J) at ($({-2sqrt(5)},{7sqrt(5)/2})+(6,-11/2)$); \draw[line] (A) -- (B) -- (C); \draw[line] (A) -- (G) -- (J); \draw[line] (A) -- (F) -- (I); \draw[line] (B) -- (G) -- (H); \draw[line] (B) -- (I) -- (J); \draw[line] (B) -- (E) -- (F); \draw[line] (C) -- (F); \draw[line] (C) -- (E) -- (G); \draw[line] (E) -- (H) -- (I); \node[point,label=left:{$\mathbf{p}_2$}] at (A) {}; \node[point,label=right:{$\mathbf{p}_1$}] at (B) {}; \node[point,label=left:{$\mathbf{p}_3$}] at (C) {}; \node[point,label=right:{$\mathbf{p}_5$}] at (E) {}; \node[point,label=right:{$\mathbf{p}_7$}] at (F) {}; \node[point,label=below:{$\mathbf{p}_9$}] at (G) {}; \node[point,label=above left:{$\mathbf{p}_6$}] at (H) {}; \node[point,label=right:{$\mathbf{p}_{10}$}] at (I) {}; \node[point,label=above right:{$\mathbf{p}_8$}] at (J) {}; \end{tikzpicture} \caption{An affine point configuration leading to a tight, non-congruence normal hyperplane arrangement} \label{fig:min_not_CU} \end{figure} \end{example} \begin{example} \label{ex:cycle_in_H} It is possible to have cycles in $\H_B(\mathdutchcal A)$ while $\mathdutchcal{Sh}_B(\mathdutchcal A)$ is acyclic, settling the question raised in \cite[p.~203]{reading_lattice_2003}. Figure~\ref{fig:cycle_in_H} shows the affine point configuration of arrangement $\mathdutchcal A(14,116)$ with respect to the base region that contains the vector $\approx(0.38, 2.85, -7.85)$. There is a cycle $H_1 \rightarrow H_4 \rightarrow H_7 \rightarrow H_1$ in~$\H_B(\mathdutchcal A)$. However, this cycle does not lead to any cycle among shards included in these three hyperplanes as $\mathdutchcal{Sh}_B(\mathdutchcal A)$ was computed to be acyclic in this case. \begin{figure}[H] \begin{tikzpicture} [x={(1.6cm, 0cm)}, y={(0cm, 1cm)}, scale=1.25, point/.style={circle,fill=black,inner sep=1.5pt}, line/.style={black!20,line width=1pt}] \coordinate (0) at (2.84240404744278, 1.81787943172609); \coordinate (1) at (0.00000000000000, 0.00000000000000); \coordinate (2) at (2.50000000000000, 1.59889252318084); \coordinate (3) at (2.09220259843842, 1.33808283664909); \coordinate (4) at (2.50000000000000, 4.33012701892219); \coordinate (5) at (2.50000000000000, 0.79130472169025); \coordinate (6) at (2.96237314857923, 0.93765594395167); \coordinate (7) at (0.77254248593736, 1.33808283664909); \coordinate (8) at (2.13525491562421, 1.65396134562402); \coordinate (9) at (2.68237254218789, 1.33808283664909); \coordinate (10) at (1.63627124296868, 2.83410492778564); \coordinate (11) at (4.22745751406263, 1.33808283664909); \coordinate (12) at (1.34836165729158, 2.33543089740679); \coordinate (13) at (5.00000000000000, 0.00000000000000); \draw[line] (0) -- (5); \draw[line] (0) -- (8); \draw[line] (10) -- (13); \draw[line] (11) -- (12); \draw[line] (1) -- (4); \draw[line] (1) -- (11); \draw[line] (4) -- (5); \draw[line] (6) -- (10); \draw[line] (8) -- (11); \draw[line] (12) -- (13); \draw[line] (3) -- (4); \draw[line] (5) -- (12); \draw[line] (7) -- (11); \draw[line] (4) -- (13); \draw[line] (7) -- (13); \draw[line] (5) -- (10); \draw[line] (6) -- (12); \draw[line] (8) -- (13); \draw[line,red,line width=2pt,dashed] (4) -- (6); \draw[line,red,line width=2pt,dashed] (0) -- (1); \draw[line,red,line width=2pt,dashed] (3) -- (13); \node[point,label=above right:{$1$}] at (0) {}; \node[point,label=left:{$2$}] at (1) {}; \node[point,label=right:{$3$}] at (2) {}; \node[point,label=below:{$4$}] at (3) {}; \node[point,label=left:{$5$}] at (4) {}; \node[point,label=below:{$6$}] at (5) {}; \node[point,label=below:{$7$}] at (6) {}; \node[point,label=left:{$8$}] at (7) {}; \node[point,label=left:{$9$}] at (8) {}; \node[point,label=right:{$10$}] at (9) {}; \node[point,label=left:{$11$}] at (10) {}; \node[point,label=right:{$12$}] at (11) {}; \node[point,label=left:{$13$}] at (12) {}; \node[point,label=right:{$14$}] at (13) {}; \end{tikzpicture} \caption{The point configuration of arrangement $\mathdutchcal A(14,116)$ with respect to the base region containing $\approx(0.38, 2.85, -7.85)$} \label{fig:cycle_in_H} \end{figure} \end{example} \section{Congruence normality of simplicial hyperplane arrangements} \label{sec:simplicial} As the number of regions of a rank-three hyperplane arrangement grows quadratically with the number of hyperplanes, its poset of regions becomes costly to construct in practice when the number of hyperplanes gets large. Consequently, checking if a given poset of regions is obtainable through doublings of convex sets becomes impracticable. Using shards to determine congruence normality first involves computing polyhedral cones contained in each hyperplane (i.e.\ regions in restrictions of the hyperplane arrangement) and then checking the dimensions of intersection for pairs of shards. In contrast, the methods developed in Section~\ref{sec:cong_norm} make the determination of congruence normality for posets of regions of rank-$3$ hyperplane arrangements tractable and could be extended to higher dimensions given a method for determining the covectors of the oriented matroid. Additionally, the oriented matroid approach makes it possible and natural to check congruence normality for non-realizable oriented matroids. One of the motivations for studying congruence normality is to better understand simplicial hyperplane arrangements. In rank $3$, the number of simplicial hyperplane arrangements is unknown \cite{grunbaum_2009,cuntz_greedy_2020}. So far, three infinite families and 95 sporadic arrangements have been found. It is conjectured that there are only finitely many sporadic arrangements. The largest sporadic arrangement found so far has 37 hyperplanes. In this section, we apply our reformulation of shards as shard covectors to classify which of the known simplicial hyperplane arrangements of rank $3$ are congruence normal. This verification was carried out using \texttt{Sage} \cite{sagemath}. The computations took around 18 hours on $8$ Intel Cores (i7-7700 @3.60Hz). The verification for each poset of regions was computed independently, for example the cocircuits were recomputed for each reorientation of the set of normals, but the computations of intersections on covectors were cached. The computation could be further improved by applying the reorientation on cocircuits directly in order to avoid recomputing them. Our results are summarized in Table~\ref{tab:cn_part}. We use the following notation: $\mathdutchcal A(m,r)_i$ denotes the $i$-th hyperplane arrangement with $m$ hyperplanes and $r$ regions. We refer to congruence normality using the acronym \textbf{CN} and \textbf{NCN} for non-congruence normality. The normals of the $119$ arrangements from the known sporadic arrangements and two of the infinite families are listed in the Appendix~\ref{app:lists} and the corresponding wiring diagrams are listed in Appendix~\ref{app:wd}. The list includes the sporadic arrangements and the arrangements from the infinite families with at most $37$ hyperplanes. \begin{table}[H] \begin{tabular}{c@{\hspace{1.5cm}}c@{\hspace{1.5cm}}c} $P_B(\A)$ always \textbf{CN} & $P_B(\A)$ sometimes \textbf{CN} & $P_B(\A)$ never \textbf{CN} \\\toprule[1pt] Rank-$3$ Finite Weyl Groupoids & $\mathdutchcal F_2(m)$ ($m\geq 10$) & $\mathdutchcal A(22,288)$ \\ (including $\mathdutchcal F_2(m)$ ($m\leq 8$) & $\mathdutchcal F_3(m)$ ($m\geq 17$) & $\mathdutchcal A(25,360)$ \\ and $\mathdutchcal F_3(m)$ ($m\leq13$)) & 41 arrangements & $\mathdutchcal A(35,680)$ \\ $\mathdutchcal A(15,120)$ & & \\ $\mathdutchcal A(31,480)$ \\ $\mathdutchcal F_1(m)$ & & \\\bottomrule[1pt] 55 arrangements & 61 arrangements & 3 arrangements \\ see Section~\ref{ssec:always} & see Sections~\ref{ssec:sometimes} and \ref{ssec:infinite} & see Section~\ref{ssec:never} \\ and Table~\ref{tab:alwayscn} & and Table~\ref{tab:sometimescn} & and Table~\ref{tab:nevercn} \end{tabular} \caption{Classification of rank-$3$ simplicial hyperplane arrangements with at most 37 hyperplanes according to the congruence normality of their posets of regions} \label{tab:cn_part} \end{table} Table~\ref{tab:cn_part} provides material to check the veracity of \cite[Conjecture~145]{padrol_shard_2020}, which postulates the existence of certain polytopes for tight congruence normal arrangements. Section~\ref{ssec:always} looks at the arrangements that are always \textbf{CN}, Section~\ref{ssec:sometimes} at the arrangements that are sometimes \textbf{CN}, and Section~\ref{ssec:never} at the arrangements that are never \textbf{CN}. In Section~\ref{ssec:discuss} we finish by discussing these results and compiling related questions. \subsection{Always \textbf{CN} simplicial arrangements} \label{ssec:always} Fifty-five of the of $119$ arrangements are congruence normal, that is, for any choice of base region, the poset of regions is congruence normal, see Table~\ref{tab:alwayscn}. \begin{table}[H] \resizebox{\textwidth}{!}{ \begin{tabular}{c\|c\|c\|c\|c\|c} \multicolumn{6}{c}{Finite Weyl Groupoids}\\\toprule[1pt] \begin{tabular}{r@{\hspace{1mm}}l} $\mathdutchcal F_2(6)=$ & $\mathdutchcal A(6,24)$\\ & $\mathdutchcal A(7,32)$ \\ $\mathdutchcal F_2(8)=$ & $\mathdutchcal A(8,40)$\\ $\mathdutchcal F_3(9)=$ & $\mathdutchcal A(9,48)$\\ & $\mathdutchcal A(10,60)_1$ \\ & $\mathdutchcal A(10,60)_2$ \\ & $\mathdutchcal A(11,72)$ \\ & $\mathdutchcal A(12,84)_1$ \\ & $\mathdutchcal A(12,84)_2$ \\ $\mathdutchcal F_3(13)=$ & $\mathdutchcal A(13,96)_1$\\ \end{tabular} & \begin{tabular}{c} $\mathdutchcal A(13,96)_2$ \\ $\mathdutchcal A(13,96)_3$ \\ $\mathdutchcal A(14,112)_1$ \\ $\mathdutchcal A(15,128)_1$ \\ $\mathdutchcal A(16,144)_1$ \\ $\mathdutchcal A(16,144)_2$ \\ $\mathdutchcal A(17,160)_1$ \\ $\mathdutchcal A(17,160)_2$ \\ $\mathdutchcal A(17,160)_3$ \\ \phantom{} \end{tabular} & \begin{tabular}{l} $\mathdutchcal A(18,180)_1$ \\ $\mathdutchcal A(18,180)_2$ \\ $\mathdutchcal A(19,192)_1$ \\ $\mathdutchcal A(19,192)_2$ \\ $\mathdutchcal A(19,200)_1$ \\ $\mathdutchcal A(19,200)_2$ \\ $\mathdutchcal A(19,200)_3$ \\ $\mathdutchcal A(20,216)$ \\ $\mathdutchcal A(20,220)_1$ \\ \phantom{} \end{tabular} & \begin{tabular}{l} $\mathdutchcal A(20,220)_2$ \\ $\mathdutchcal A(21,240)_1$ \\ $\mathdutchcal A(21,240)_2$ \\ $\mathdutchcal A(21,240)_3$ \\ $\mathdutchcal A(22,264)_1$ \\ $\mathdutchcal A(25,336)_1$ \\ $\mathdutchcal A(25,336)_2$ \\ $\mathdutchcal A(25,336)_3$ \\ $\mathdutchcal A(25,336)_4$ \\ \phantom{} \end{tabular} & \begin{tabular}{l} $\mathdutchcal A(26,364)_1$ \\ $\mathdutchcal A(26,364)_2$ \\ $\mathdutchcal A(27,392)_1$ \\ $\mathdutchcal A(27,392)_2$ \\ $\mathdutchcal A(27,392)_3$ \\ $\mathdutchcal A(28,420)_1$ \\ $\mathdutchcal A(28,420)_2$ \\ $\mathdutchcal A(28,420)_3$ \\ \phantom{} \\ \phantom{} \end{tabular} & \begin{tabular}{l} $\mathdutchcal A(29,448)_1$ \\ $\mathdutchcal A(29,448)_2$ \\ $\mathdutchcal A(29,448)_3$ \\ $\mathdutchcal A(30,476)$ \\ $\mathdutchcal A(31,504)_1$ \\ $\mathdutchcal A(31,504)_2$ \\ $\mathdutchcal A(34,612)_1$ \\ $\mathdutchcal A(37,720)_1$ \\ \phantom{} \\ \phantom{} \end{tabular} \end{tabular}} \begin{tabular}{c\|c} \multicolumn{2}{c}{Others}\\\toprule[1pt] $H_3=\mathdutchcal A(15,120)$ & $H_3^=\mathdutchcal A(31,480)$\\ \end{tabular} \caption{List of congruence normal rank-3 simplicial arrangements} \label{tab:alwayscn} \end{table} Fifty-three of these arrangements come from finite Weyl groupoids of rank~$3$~\cite{cuntz_finite_2012}. Finite Weyl groupoids correspond to (generalized) \emph{crystallographic} root systems. In the present context, affine point configurations $\mathdutchcal A_B^$ play the role of these root systems. A root system is \defn{crystallographic} if there exists a choice of normals $\{\mathbf{n}_i\}_{i\in[m]}$ for the hyperplanes such that for any base region, all normals are integral linear combinations of normals to the basic hyperplanes~\cite[Section~1]{cuntz_crystallographic_2011}. Given a base region $B$, denote the set of rays of $\spa^+(\mathdutchcal A_B^)$ by $\Delta$ and call the elements of $\mathdutchcal A_B^$ the \defn{positive roots}. A positive root $\mathbf{p}_i\in\mathdutchcal A_B^$ is \defn{constructible} if \begin{align} \mathbf{n}_i\in\Delta \quad\text{or}\quad \mathbf{n}_i=\mathbf{n}_\alpha+\mathbf{n}_\beta, \end{align} where $\alpha,\beta\in\mathdutchcal A_B^$. We call $\mathdutchcal A_B^$ \defn{additive} if every positive root in $\mathdutchcal A_B^$ is constructible. If $\mathdutchcal A_B^$ is additive, then it is possible to define the \defn{root poset} $(\mathdutchcal A_B^,\leq)$ by \[ \mathbf{p}_i \leq \mathbf{p}_j \quad \Longleftrightarrow \quad \mathbf{n}_j - \mathbf{n}_i \in \mathbb{N}\Delta. \] The following is a fundamental result about finite Weyl groupoids. \begin{theorem}[{\cite[Corollary~5.6]{cuntz_crystallographic_2011}} and {\cite[Theorem~2.10]{cuntz_finite_2012}}] \label{thm:weyl_constr} A simplicial arrangement $\mathdutchcal A$ corresponds to a finite Weyl groupoid if and only if $\mathdutchcal A_B^$ is additive for every choice of base region~$B$. \end{theorem} \begin{theorem} \label{thm:constructible} Let $\mathdutchcal A$ be a tight hyperplane arrangement with respect to a base region $B$. If $\mathdutchcal A_B^$ is additive, then~$P_B(\A)$ is congruence normal. \end{theorem} \begin{proof} Via the contrapositive statement, having a cycle in the graph $\H_B(\mathdutchcal A)$ is a necessary condition for $P_B(\A)$ \emph{not} to be congruence normal. Such a cycle between hyperplanes yields a cycle in the order defining the root poset of $\mathdutchcal A_B^$. Hence, when $P_B(\A)$ is not congruence normal, the positive roots $\mathdutchcal A_B^$ do not lead to a root poset. Thus $\mathdutchcal A_B^$ can not be additive. \end{proof} Theorem~\ref{thm:weyl_constr} leads directly to the following corollary, which provides a new proof that finite Coxeter arrangements are congruence normal \cite[Theorem~6]{caspard_cayley_2004}. \begin{corollary} \label{cor:cn_weyl} Let $\mathdutchcal A$ be the hyperplane arrangement of a finite Weyl groupoid $\mathcal{W}$. For any choice of base region~$B$, the lattice of regions $P_B(\A)$ is congruence normal. \end{corollary} There are two additional \textbf{CN} arrangements that do not stem from finite Weyl groupoids. Arrangement $\mathdutchcal A(15,120)$ is the Coxeter arrangement for the Coxeter group $H_3$ and arrangement $\mathdutchcal A(31,480)$ is its point-line dual. As discussed in \cite{cuntz_root_2015}, there is a root poset for $H_3$ supporting the fact that its arrangement is always congruence normal. The dual arrangement $\mathdutchcal A(31,480)$ is also always congruence normal, as we verified directly. Is there a proof of congruence normality for $\mathdutchcal A(31,480)$ using duality with $H_3$? Example~\ref{ex:cycle_in_H} shows that having a root poset structure on $\mathdutchcal A_B^$ \emph{is not} necessary for $P_B(\A)$ to be congruence normal. \subsection{Simplicial arrangements that are sometimes congruence normal} \label{ssec:sometimes} Sixty-one of the $119$ arrangements are congruence normal for some base regions and not congruence normal for others, see Table~\ref{tab:sometimescn}. Among them is the arrangement $\mathdutchcal A(10,60)_3$ which appeared in Example~\ref{ex:A10_60}. \begin{table}[H] \resizebox{\textwidth}{!}{ \begin{tabular}{c\|c\|c} \begin{tabular}{r@{\hspace{1mm}}lrr} \multicolumn{2}{c}{Name} & \textbf{CN} & \textbf{NCN} \\\toprule[1pt] $\mathdutchcal F_2(10)=$ & $\mathdutchcal A(10,60)_3$ & $40$ & $20$ \\ $\mathdutchcal F_2(12)=$ & $\mathdutchcal A(12,84)_3$ & $36$ & $48$ \\ & $\mathdutchcal A(13,104)$ & $24$ & $80$ \\ $\mathdutchcal F_2(14)=$ & $\mathdutchcal A(14,112)_2$ & $28$ & $84$ \\ & $\mathdutchcal A(14,112)_3$ & $72$ & $40$ \\ & $\mathdutchcal A(14,116)$ & $40$ & $76$ \\ & $\mathdutchcal A(15,128)_2$ & $72$ & $56$ \\ & $\mathdutchcal A(15,132)_1$ & $60$ & $72$ \\ & $\mathdutchcal A(15,132)_2$ & $48$ & $84$ \\ & $\mathdutchcal A(16,140)$ & $120$ & $20$ \\ $\mathdutchcal F_2(16)=$ & $\mathdutchcal A(16,144)_3$ & $32$ & $112$ \\ & $\mathdutchcal A(16,144)_4$ & $84$ & $60$ \\ & $\mathdutchcal A(16,144)_5$ & $108$ & $36$ \\ & $\mathdutchcal A(16,148)$ & $52$ & $96$ \\ $\mathdutchcal F_3(17)=$ & $\mathdutchcal A(17,160)_4$ & $96$ & $64$ \\ & $\mathdutchcal A(17,160)_5$ & $120$ & $40$ \\ & $\mathdutchcal A(17,164)$ & $76$ & $88$ \\ & $\mathdutchcal A(17,168)_1$ & $48$ & $120$ \\ & $\mathdutchcal A(17,168)_2$ & $48$ & $120$ \\ $\mathdutchcal F_2(18)=$ & $\mathdutchcal A(18,180)_3$ & $36$ & $144$ \\ & $\mathdutchcal A(18,180)_4$ & $84$ & $96$ \\ \end{tabular}& \begin{tabular}{r@{\hspace{1mm}}lrr} \multicolumn{2}{c}{Name} & \textbf{CN} & \textbf{NCN} \\\toprule[1pt] & $\mathdutchcal A(18,180)_5$ & $120$ & $60$ \\ & $\mathdutchcal A(18,180)_6$ & $120$ & $60$ \\ & $\mathdutchcal A(18,184)_1$ & $100$ & $84$ \\ & $\mathdutchcal A(18,184)_2$ & $72$ & $112$ \\ & $\mathdutchcal A(19,200)_4$ & $120$ & $80$ \\ & $\mathdutchcal A(19,204)$ & $72$ & $132$ \\ $\mathdutchcal F_2(20)=$ & $\mathdutchcal A(20,220)_3$ & $40$ & $180$ \\ & $\mathdutchcal A(20,220)_4$ & $120$ & $100$ \\ $\mathdutchcal F_3(21)=$ & $\mathdutchcal A(21,240)_4$ & $80$ & $160$ \\ & $\mathdutchcal A(21,240)_5$ & $120$ & $120$ \\ & $\mathdutchcal A(21,248)$ & $88$ & $160$ \\ & $\mathdutchcal A(21,252)$ & $36$ & $216$ \\ $\mathdutchcal F_2(22)=$ & $\mathdutchcal A(22,264)_2$ & $44$ & $220$ \\ & $\mathdutchcal A(22,264)_3$ & $168$ & $96$ \\ & $\mathdutchcal A(22,276)$ & $60$ & $216$ \\ & $\mathdutchcal A(23,296)$ & $112$ & $184$ \\ & $\mathdutchcal A(23,304)$ & $8$ & $296$ \\ & $\mathdutchcal A(24,304)$ & $112$ & $192$ \\ $\mathdutchcal F_2(24)=$ & $\mathdutchcal A(24,312)$ & $48$ & $264$ \\ & $\mathdutchcal A(24,316)$ & $184$ & $132$ \\ \phantom{} \end{tabular}& \begin{tabular}{r@{\hspace{1mm}}lrr} \multicolumn{2}{c}{Name} & \textbf{CN} & \textbf{NCN} \\\toprule[1pt] & $\mathdutchcal A(24,320)$ & $24$ & $296$ \\ & $\mathdutchcal A(25,320)$ & $288$ & $32$ \\ $\mathdutchcal F_3(25)=$ & $\mathdutchcal A(25,336)_5$ & $48$ & $288$ \\ & $\mathdutchcal A(25,336)_6$ & $48$ & $288$ \\ $\mathdutchcal F_2(26)=$ & $\mathdutchcal A(26,364)_3$ & $52$ & $312$ \\ & $\mathdutchcal A(26,380)$ & $20$ & $360$ \\ & $\mathdutchcal A(27,400)$ & $48$ & $352$ \\ $\mathdutchcal F_2(28)=$ & $\mathdutchcal A(28,420)_4$ & $56$ & $364$ \\ & $\mathdutchcal A(28,420)_5$ & $84$ & $336$ \\ & $\mathdutchcal A(28,420)_6$ & $84$ & $336$ \\ & $\mathdutchcal A(29,440)$ & $136$ & $304$ \\ $\mathdutchcal F_3(29)=$ & $\mathdutchcal A(29,448)_4$ & $56$ & $392$ \\ & $\mathdutchcal A(30,460)$ & $240$ & $220$ \\ $\mathdutchcal F_2(30)=$ & $\mathdutchcal A(30,480)$ & $60$ & $420$ \\ $\mathdutchcal F_2(32)=$ & $\mathdutchcal A(32,544)$ & $64$ & $480$ \\ $\mathdutchcal F_3(33)=$ & $\mathdutchcal A(33,576)$ & $64$ & $512$ \\ $\mathdutchcal F_2(34)=$ & $\mathdutchcal A(34,612)_2$ & $68$ & $544$ \\ $\mathdutchcal F_2(36)=$ & $\mathdutchcal A(36,684)$ & $72$ & $612$ \\ $\mathdutchcal F_3(37)=$ & $\mathdutchcal A(37,720)_2$ & $72$ & $648$ \\ & $\mathdutchcal A(37,720)_3$ & $96$ & $624$ \\ \phantom{} \end{tabular} \end{tabular}} \caption{Simplicial arrangements that are sometimes congruence normal} \label{tab:sometimescn} \end{table} Reading proved that the poset of regions of a supersolvable hyperplane arrangements is congruence normal with respect to a canonical base region~\cite[Theorem~1]{reading_lattice_2003}. In rank~$3$, the infinite families are exactly the irreducible supersolvable ones \cite[Theorem~1.2]{cuntz_supersolvable_2019}. However, we show below that~$\mathdutchcal F_2(m)$ with $m\geq 10$ and $\mathdutchcal F_3(m)$ with $m\geq 17$ always have a base region for which the associated lattice of regions is not congruence normal. \subsection{Congruence normality for the infinite families} \label{ssec:infinite} There are three infinite families of rank-$3$ simplicial hyperplane arrangements \cite{grunbaum_1971}. The first family, $\mathdutchcal F_1(m)$ with $m \geq 3$ is the family of \defn{near-pencils} in the projective plane with $m$ hyperplanes. The second family, $\mathdutchcal F_2(m)$, for even $m \geq 6$ consists of the hyperplanes defined by the edges of the regular $\frac{m}{2}$-gon and each of its $\frac{m}{2}$ lines of symmetry. The third family, $\mathdutchcal F_3(m)$, for $m=4k+1$, $k\geq2$, is obtained from $\mathdutchcal F_2(m-1)$ by adding the line at infinity. Examples of these families are illustrated in Figure~\ref{fig:infinite_families}. \begin{figure}[H] \begin{center} \begin{tabular}{c@{\hspace{2cm}}c@{\hspace{2.5cm}}c } \begin{tikzpicture} [baseline = (D), point/.style={circle,fill=black,inner sep=1.5pt}, line/.style={black,line width=.5pt}] \def 2.5{2} \def 2.5{2} \coordinate (A) at (0,0); \coordinate (B) at (-1/22.5,2/32.5); \coordinate (C) at (1/22.5,2/32.5); \coordinate (D) at (1/22.5,1/32.5); \draw[line] (B) -- (C); \draw[line] (A) -- +(90:2.5); \draw[line] (A) -- +(-90:1/42.5); \draw[line] (A) -- +(105:2.5); \draw[line] (A) -- +(-75:1/42.5); \draw[line] (A) -- +(75:2.5); \draw[line] (A) -- +(-105:1/42.5); \draw[line] (A) -- +(60:2.5); \draw[line] (A) -- +(-120:1/42.5); \draw[line] (A) -- +(120:2.5); \draw[line] (A) -- +(-60:1/42.5); \node[label=below:{$\mathdutchcal F_1(6)$}] at (0,-7/242.5) {}; \end{tikzpicture} & \begin{tikzpicture} [baseline = (A) point/.style={circle,fill=black,inner sep=1.5pt}, line/.style={black,line width=.5pt}] \def 2.5{3} \def 2.5{3} \coordinate (A) at (0,0); \path (A) -- +(0:1/72.5) coordinate (v1) ; \path (A) -- +(72:1/72.5) coordinate (v2); \path (A) -- +(144:1/72.5) coordinate (v3); \path (A) -- +(216:1/72.5) coordinate (v4); \path (A) -- +(288:1/72.5) coordinate (v5); \draw[line, shorten <=-102.5, shorten >=-102.5] (v1) -- (v2); \draw[line, shorten <=-102.5, shorten >=-102.5] (v2) -- (v3); \draw[line, shorten <=-102.5, shorten >=-102.5] (v3) -- (v4); \draw[line, shorten <=-102.5, shorten >=-102.5] (v4) -- (v5); \draw[line, shorten <=-102.5, shorten >=-102.5] (v5) -- (v1); \draw[line, shorten <=-132.5, shorten >=-102.5] (A) -- (v1); \draw[line, shorten <=-132.5, shorten >=-102.5] (A) -- (v2); \draw[line, shorten <=-132.5, shorten >=-102.5] (A) -- (v3); \draw[line, shorten <=-132.5, shorten >=-102.5] (A) -- (v4); \draw[line, shorten <=-132.5, shorten >=-102.5] (A) -- (v5); \node[label=below:{$\mathdutchcal F_2(10) = \mathdutchcal A(10,60)_3$}] at (0,-5/122.5) {}; \end{tikzpicture} & \begin{tikzpicture} [baseline = (A), point/.style={circle,fill=black,inner sep=1.5pt}, line/.style={black,line width=.5pt}] \def 2.5{2.5} \def 2.5{2.5} \coordinate (A) at (0,0); \path (A) -- +(45:1/52.5) coordinate (v1) ; \path (A) -- +(135:1/52.5) coordinate (v2); \path (A) -- +(225:1/52.5) coordinate (v3); \path (A) -- +(315:1/52.5) coordinate (v4); \path (A) -- +(0:1/52.5) coordinate (e1); \path (A) -- +(90:1/52.5) coordinate (e2); \path (A) -- +(180:1/52.5) coordinate (e3); \path (A) -- +(270:1/52.5) coordinate (e4); \draw[line, shorten <=-102.5, shorten >=-102.5] (v1) -- (v2); \draw[line, shorten <=-102.5, shorten >=-102.5] (v2) -- (v3); \draw[line, shorten <=-102.5, shorten >=-102.5] (v3) -- (v4); \draw[line, shorten <=-102.5, shorten >=-102.5] (v4) -- (v1); \draw[line, shorten <=-152.5, shorten >=-102.5] (A) -- (e1); \draw[line, shorten <=-152.5, shorten >=-102.5] (A) -- (e2); \draw[line, shorten <=-152.5, shorten >=-102.5] (A) -- (v1); \draw[line, shorten <=-152.5, shorten >=-102.5] (A) -- (v2); \node[label=above:{$\infty$}] at (1/22.5,1/22.5) {}; \node[label=below:{$\mathdutchcal F_3(9) = \mathdutchcal A(9,48)$}] at (0,-6/122.5) {}; \end{tikzpicture} \end{tabular} \end{center} \caption{Arrangements from the three infinite families of simplicial arrangements of rank $3$ drawn in the projective plane} \label{fig:infinite_families} \end{figure} \begin{theorem} \label{thm:near_pencils} The near-pencil arrangements of $\mathdutchcal F_1(m)$ are congruence normal. \end{theorem} \begin{proof} There is exactly one rank-$2$ subarrangement with at least three hyperplanes. Thus, for any choice of base region, the length of any path in the directed graph on shards is at most one, so there are no cycles. \end{proof} \begin{theorem}\label{thm:cn_f2} The second family $\mathdutchcal F_2(m)$ is sometimes congruence normal for $m \geq 10$. \end{theorem} \begin{proof} In rank~$3$, the infinite families are exactly the irreducible supersolvable ones, thus there exists a canonical choice of base region such that the poset of regions is congruence normal \cite[Theorem~1.2]{cuntz_supersolvable_2019}. On the other hand, with respect to a certain choice of base region, there is a guaranteed four-cycle in the shards as demonstrated in Figure~\ref{fig:hexagon}. The figure shows the arrangement on two projective planes and how some of the hyperplanes intersect at infinity. Let the base region be bounded by $\mathbf{e}_1$, $\mathbf{e}_2$, and $\mathbf{r}_2$. At point~$1$, the hyperplane $\mathbf{e}_5$ is cut by~$\mathbf{r}_5$. At point~$2$, the hyperplane $\mathbf{r}_6$ is cut by $\mathbf{e}_5$. At point~$3$, the hyperplane $\mathbf{e}_4$ is cut by $\mathbf{r}_6$. At point~$4$, the hyperplane $\mathbf{r}_5$ is cut by $\mathbf{e}_4$. Thus there is a cycle in the shard digraph. Adapting this procedure when $m\geq14$ similarly provides a $4$-cycle for every member of $\mathdutchcal F_2(m)$. \end{proof} \begin{figure}[H] \begin{center} \resizebox{\textwidth}{!}{ \begin{tikzpicture} \node at (0,0) {\includegraphics[width=\textwidth]{images/hexagon.pdf}}; \node at (-1,1.2) {e$_1$}; \node at (-1,.2) {r$_5$}; \node at (-1,2) {r$_6$}; \node at (-1,-1.1) {e$_4$}; \node at (-1,-2.3) {r$_4$}; \node at (-2.1,-2.5) {e$_6$}; \node at (-3.3,-2.5) {r$_3$}; \node at (-4.4,-2.5) {e$_3$}; \node at (-5,-2.5) {r$_2$}; \node at (-5.6,-2.5) {e$_5$}; \node at (-6.2,-2.5) {r$_1$}; \node at (-7.3,-2.5) {e$_2$}; \node at (-3.8,-.3) {1}; \node at (-3.5,1.3) {2}; \node at (3.4,1.3) {3}; \node at (.5,-.2) {4}; \node at (.5,2.7) {$\infty$}; \end{tikzpicture}} \end{center} \caption{The simplicial hyperplane arrangement $\mathdutchcal A(12,84)_3$ from $\mathdutchcal F_2$ whose lattice of regions with the marked base region is not congruence normal} \label{fig:hexagon} \end{figure} \begin{theorem}\label{thm:cn_f3} The third family $\mathdutchcal F_3(m)$ is sometimes congruence normal for $m \geq 17$. \end{theorem} \begin{proof} The proof is similar to that of Theorem~\ref{thm:cn_f2}. For $m \geq 17$, a four-cycle among shards still occurs, and its location relative to the base region is illustrated in Figure~\ref{fig:octagon} for $m = 17$. The line at infinity is included in these arrangements, and one of the intersection points in the cycle occurs in a rank-2 subarrangement that includes the hyperplane at infinity. Relative to the plane graph, the cycle involves the same description as a embedded cycle for the family~$\mathdutchcal F_2$. \end{proof} \begin{figure}[H] \begin{center} \resizebox{\textwidth}{!}{ \begin{tikzpicture} \node at (0,0) {\includegraphics[width=\textwidth]{images/octagon_cycle.pdf}}; \node at (-1,1.3) {r$_8$}; \node at (-1,0) {r$_7$}; \node at (-1,-1.7) {r$_6$}; \node at (-2.3,-2.5) {r$_5$}; \node at (-3.7,-2.5) {r$_4$}; \node at (-4.8,-2.5) {r$_3$}; \node at (-5.8,-2.5) {r$_2$}; \node at (-7.2,-2.5) {r$_1$}; \node at (-7.2, 2) {e$_1$}; \node at (-7.2,.3) {e$_2$}; \node at (-4.4,2.9) {e$_3$}; \node at (-7.2,2.9) {e$_4$}; \node at (-7.2,-.5) {e$_5$}; \node at (-7.2,-2) {e$_6$}; \node at (-2.6,2.9) {e$_7$}; \node at (-5.1,2.9) {e$_8$}; \node at (-3.8,-.3) {1}; \node at (-3.6,.7) {2}; \node at (.2,1.5) {3}; \node at (-1.9,-.4) {4}; \node at (.3,.6) {$\infty$}; \end{tikzpicture}} \end{center} \caption{The simplicial hyperplane arrangement $\mathdutchcal A(17,160)_4$ from $\mathdutchcal F_3$ whose lattice of regions with the marked base region is not congruence normal} \label{fig:octagon} \end{figure} \subsection{Never \textbf{CN} simplicial arrangements} \label{ssec:never} Three of the known simplicial arrangements of rank 3 are never congruence normal, see Table~\ref{tab:nevercn}. That is, there is no choice of base region such that the lattice of regions is congruence normal. The first arrangement is an arrangement with 22 hyperplanes with normals related to $\sqrt{5}$, see Figure~\ref{fig:not_cn_22}. The second arrangement has 25 hyperplanes with normals related to $\sqrt{5}$ and is shown in Figure~\ref{fig:not_cn_25}. The third arrangement is the new sporadic arrangement found in \cite{cuntz_greedy_2020}. It is the only known arrangement with $35$ hyperplanes and is illustrated in Figure~\ref{fig:not_cn_35}. We are not aware of any geometric explanation for the provenance of these arrangements and why they are never congruence normal. \begin{table}[H] \begin{tabular}{c\|c\|c} \multicolumn{3}{c}{Never congruence normal}\\\toprule[1pt] $\mathdutchcal A(22,288)$ & $\mathdutchcal A(25,360)$ & $\mathdutchcal A(35,680)$ \\ \end{tabular} \caption{Simplicial arrangements that are never congruence normal} \label{tab:nevercn} \end{table} \begin{figure}[H] \begin{tikzpicture} [x={(3cm, 0cm)}, y={(0cm, 1.2cm)}, scale=1.5, point/.style={circle,fill=black,inner sep=0.75pt}, line/.style={black!20,line width=0.5pt}] \coordinate (0) at (2.78235500444083, 2.86296737853363); \coordinate (1) at (2.90779740156158, 2.99204418227311); \coordinate (2) at (0.00000000000000, 0.00000000000000); \coordinate (3) at (2.50000000000000, 4.33012701892219); \coordinate (4) at (1.95864408835225, 3.39247107497052); \coordinate (5) at (3.81966011250105, 0.00000000000000); \coordinate (6) at (5.00000000000000, 0.00000000000000); \coordinate (7) at (3.07052017144396, 1.36561724787068); \coordinate (8) at (3.57469660655236, 1.58985027592800); \coordinate (9) at (3.09737880796660, 2.12227294276199); \coordinate (10) at (3.05901699437495, 2.16506350946110); \coordinate (11) at (3.26639215491083, 2.23807810429496); \coordinate (12) at (3.14194292957320, 2.22375553916077); \coordinate (13) at (3.01907639967691, 2.20961512267784); \coordinate (14) at (3.12305898749054, 2.28571836357388); \coordinate (15) at (3.05696480387029, 2.30768637070836); \coordinate (16) at (3.10525430923287, 2.34413985987918); \coordinate (17) at (2.96326962737348, 2.43759490491044); \coordinate (18) at (2.98420344738630, 2.45481513101885); \coordinate (19) at (3.00317939994615, 2.47042480920960); \coordinate (20) at (3.17418082864579, 2.61109112167746); \coordinate (21) at (3.38999105559213, 2.78861729235476); \begin{scope} \clip (1.85,-0.25) rectangle (4.25,3.45); \draw[line] (1) -- (2); \draw[line] (3) -- (7); \draw[line] (4) -- (20); \draw[line] (0) -- (5); \draw[line] (0) -- (6); \draw[line] (0) -- (8); \draw[line] (0) -- (9); \draw[line] (0) -- (12); \draw[line] (0) -- (15); \draw[line] (3) -- (5); \draw[line] (4) -- (21); \draw[line] (1) -- (6); \draw[line] (1) -- (7); \draw[line] (1) -- (8); \draw[line] (1) -- (9); \draw[line] (1) -- (10); \draw[line] (1) -- (13); \draw[line] (2) -- (3); \draw[line] (2) -- (6); \draw[line] (2) -- (8); \draw[line] (2) -- (11); \draw[line] (2) -- (12); \draw[line] (2) -- (14); \draw[line] (2) -- (16); \draw[line] (2) -- (21); \draw[line] (3) -- (6); \draw[line] (3) -- (8); \draw[line] (3) -- (9); \draw[line] (3) -- (10); \draw[line] (3) -- (13); \draw[line] (4) -- (5); \draw[line] (4) -- (6); \draw[line] (4) -- (11); \draw[line] (4) -- (12); \draw[line] (4) -- (14); \draw[line] (4) -- (16); \draw[line] (5) -- (21); \draw[line] (5) -- (18); \draw[line] (5) -- (17); \draw[line] (5) -- (20); \draw[line] (5) -- (19); \draw[line] (6) -- (17); \draw[line] (6) -- (18); \draw[line] (6) -- (19); \draw[line] (7) -- (16); \draw[line] (7) -- (15); \draw[line] (7) -- (21); \draw[line] (7) -- (20); \draw[line] (7) -- (19); \draw[line] (8) -- (18); \draw[line] (8) -- (19); \draw[line] (8) -- (17); \draw[line] (9) -- (21); \draw[line] (9) -- (20); \draw[line] (10) -- (21); \draw[line] (10) -- (20); \draw[line] (11) -- (13); \draw[line] (11) -- (15); \draw[line] (11) -- (17); \draw[line] (13) -- (20); \draw[line] (13) -- (21); \node[point] at (0) {}; \node[point] at (1) {}; \node[point] at (2) {}; \node[point] at (3) {}; \node[point] at (4) {}; \node[point] at (5) {}; \node[point] at (6) {}; \node[point] at (7) {}; \node[point] at (8) {}; \node[point] at (9) {}; \node[point] at (10) {}; \node[point] at (11) {}; \node[point] at (12) {}; \node[point] at (13) {}; \node[point] at (14) {}; \node[point] at (15) {}; \node[point] at (16) {}; \node[point] at (17) {}; \node[point] at (18) {}; \node[point] at (19) {}; \node[point] at (20) {}; \node[point] at (21) {}; \end{scope} \end{tikzpicture} \caption{The point configuration $\mathdutchcal A(22,288)^$. Three points are not shown and can be obtained by continuing the line segments. } \label{fig:not_cn_22} \end{figure} \begin{figure}[H] \begin{tikzpicture} [x={(4cm, 0cm)}, y={(0cm, 1.5cm)}, scale=1.3, point/.style={circle,fill=black,inner sep=0.75pt}, line/.style={black!20,line width=0.5pt}] \coordinate (0) at (2.23606797749979, 3.87298334620742); \coordinate (1) at (2.61803398874989, 2.80251707688815); \coordinate (2) at (2.76393202250021, 2.39363534581848); \coordinate (3) at (2.57514161979123, 2.67616567329817); \coordinate (4) at (2.60785001480277, 2.56071587030622); \coordinate (5) at (2.64754248593737, 2.42061459137964); \coordinate (6) at (2.50000000000000, 2.67616567329817); \coordinate (7) at (2.02254248593737, 3.50314634611018); \coordinate (8) at (2.30327668541684, 2.88675134594813); \coordinate (9) at (2.39918693812442, 2.67616567329817); \coordinate (10) at (2.59463815113608, 2.24702255251213); \coordinate (11) at (2.33002683322360, 2.49421513157466); \coordinate (12) at (2.50000000000000, 1.93649167310371); \coordinate (13) at (2.36067977499790, 2.04440865534831); \coordinate (14) at (2.20491502812526, 2.16506350946110); \coordinate (15) at (5.00000000000000, 0.00000000000000); \coordinate (16) at (0.00000000000000, 0.00000000000000); \coordinate (17) at (2.50000000000000, 0.00000000000000); \coordinate (18) at (3.19098300562505, 3.13330934601295); \coordinate (19) at (3.09016994374947, 2.67616567329817); \coordinate (20) at (2.50000000000000, 4.33012701892219); \coordinate (21) at (2.83457635340900, 3.03431837413435); \coordinate (22) at (3.01502832395825, 2.33543089740679); \coordinate (23) at (2.63932022500210, 3.30792269124804); \coordinate (24) at (2.68237254218789, 2.99204418227311); \begin{scope} \clip (1.75,-0.15) rectangle (3.25,3.95); \draw[line] (0) -- (1) -- (2); \draw[line] (0) -- (3) -- (4) -- (5); \draw[line] (0) -- (6) -- (10); \draw[line] (0) -- (7) -- (16) -- (20); \draw[line] (0) -- (8) -- (11) -- (13) -- (17); \draw[line] (0) -- (9) -- (12); \draw[line] (0) -- (15) -- (19) -- (21) -- (23); \draw[line] (0) -- (22) -- (24); \draw[line] (1) -- (3) -- (13) -- (24); \draw[line] (1) -- (4) -- (10) -- (17) -- (23); \draw[line] (1) -- (5) -- (20); \draw[line] (1) -- (6) -- (11) -- (16) -- (21); \draw[line] (1) -- (7) -- (15) -- (22); \draw[line] (1) -- (8) -- (19); \draw[line] (1) -- (9) -- (18); \draw[line] (2) -- (3) -- (7); \draw[line] (2) -- (4) -- (6) -- (8) -- (15); \draw[line] (2) -- (5) -- (11) -- (22); \draw[line] (2) -- (10) -- (13) -- (16) -- (19); \draw[line] (2) -- (12) -- (18); \draw[line] (2) -- (17) -- (21); \draw[line] (2) -- (20) -- (23) -- (24); \draw[line] (3) -- (6) -- (9) -- (19); \draw[line] (3) -- (8) -- (22); \draw[line] (3) -- (10) -- (20); \draw[line] (3) -- (11) -- (18); \draw[line] (3) -- (12) -- (23); \draw[line] (3) -- (14) -- (21); \draw[line] (4) -- (9) -- (22); \draw[line] (4) -- (11) -- (19); \draw[line] (4) -- (12) -- (24); \draw[line] (4) -- (13) -- (21); \draw[line] (4) -- (14) -- (16) -- (18); \draw[line] (5) -- (6) -- (7); \draw[line] (5) -- (9) -- (15); \draw[line] (5) -- (10) -- (12) -- (21); \draw[line] (5) -- (13) -- (18); \draw[line] (5) -- (14) -- (19); \draw[line] (5) -- (17) -- (24); \draw[line] (6) -- (12) -- (17) -- (20); \draw[line] (6) -- (13) -- (23); \draw[line] (6) -- (14) -- (24); \draw[line] (7) -- (8) -- (9) -- (10); \draw[line] (7) -- (11) -- (12); \draw[line] (7) -- (14) -- (17); \draw[line] (7) -- (18) -- (23); \draw[line] (7) -- (19) -- (24); \draw[line] (8) -- (14) -- (20); \draw[line] (8) -- (16) -- (23); \draw[line] (8) -- (18) -- (21) -- (24); \draw[line] (9) -- (11) -- (14) -- (23); \draw[line] (9) -- (13) -- (20); \draw[line] (9) -- (16) -- (24); \draw[line] (10) -- (11) -- (15); \draw[line] (10) -- (14) -- (22); \draw[line] (12) -- (13) -- (14) -- (15); \draw[line] (12) -- (16) -- (22); \draw[line] (15) -- (16) -- (17); \draw[line] (15) -- (18) -- (20); \draw[line] (17) -- (18) -- (19) -- (22); \draw[line] (20) -- (21) -- (22); \node[point] at (0) {}; \node[point] at (1) {}; \node[point] at (2) {}; \node[point] at (3) {}; \node[point] at (4) {}; \node[point] at (5) {}; \node[point] at (6) {}; \node[point] at (7) {}; \node[point] at (8) {}; \node[point] at (9) {}; \node[point] at (10) {}; \node[point] at (11) {}; \node[point] at (12) {}; \node[point] at (13) {}; \node[point] at (14) {}; \node[point] at (15) {}; \node[point] at (16) {}; \node[point] at (17) {}; \node[point] at (18) {}; \node[point] at (19) {}; \node[point] at (20) {}; \node[point] at (21) {}; \node[point] at (22) {}; \node[point] at (23) {}; \node[point] at (24) {}; \end{scope} \end{tikzpicture} \caption{The point configuration $\mathdutchcal A(25,360)^$. Three points are not shown and can be obtained by continuing the line segments.} \label{fig:not_cn_25} \end{figure} \begin{figure}[H] \begin{tikzpicture} [x={(1.6cm, 0cm)}, y={(0cm, 1cm)}, scale=3, point/.style={circle,fill=black,inner sep=0.75pt}, line/.style={black!20,line width=0.5pt}] \coordinate (0) at (3.32768253095497, 1.74265003171565); \coordinate (1) at (1.87818397394008, 3.25311006882584); \coordinate (2) at (0.00000000000000, 0.00000000000000); \coordinate (3) at (2.15548365471666, 1.80238132300618); \coordinate (4) at (2.73751258720550, 1.43358819615121); \coordinate (5) at (5.00000000000000, 0.00000000000000); \coordinate (6) at (1.33921846697968, 2.31959442724331); \coordinate (7) at (2.40441358514015, 2.01053259167888); \coordinate (8) at (2.50000000000000, 1.78482593493031); \coordinate (9) at (2.50000000000000, 1.93649167310371); \coordinate (10) at (2.96715395795394, 2.11834133483492); \coordinate (11) at (2.69716897975906, 1.92559085838539); \coordinate (12) at (2.33345049896733, 2.03112222947948); \coordinate (13) at (2.30283102024094, 1.92559085838539); \coordinate (14) at (2.12589566933614, 1.95717465274315); \coordinate (15) at (2.18385340506974, 2.01053259167888); \coordinate (16) at (2.24975151703417, 1.74265003171565); \coordinate (17) at (2.39811018962345, 1.85756816535638); \coordinate (18) at (2.41881234809646, 1.90488764453019); \coordinate (19) at (2.32156306604063, 1.86703128316506); \coordinate (20) at (2.50000000000000, 4.33012701892219); \coordinate (21) at (2.50000000000000, 1.84497206462827); \coordinate (22) at (3.83921846697968, 2.01053259167888); \coordinate (23) at (2.37982380899965, 2.19094986840217); \coordinate (24) at (2.52377486585338, 1.88615134022947); \coordinate (25) at (2.65466206810598, 2.44397567869273); \coordinate (26) at (2.67843693395936, 2.15403390019270); \coordinate (27) at (3.07450730194470, 1.61006652449696); \coordinate (28) at (1.62793549097425, 2.81966698181200); \coordinate (29) at (2.44092434675387, 1.74265003171565); \coordinate (30) at (2.36594504411141, 1.94390312412404); \coordinate (31) at (2.27565984571700, 2.01053259167888); \coordinate (32) at (2.16690099793465, 1.88615134022947); \coordinate (33) at (2.44604987980490, 1.96714520168799); \coordinate (34) at (2.35564148800271, 1.76049631439454); \begin{scope} \clip (1.3,1.3) rectangle (3.85,3.3); \draw[line] (0) -- (1) -- (5) -- (10) -- (25); \draw[line] (0) -- (2) -- (4) -- (22) -- (27); \draw[line] (0) -- (3) -- (8); \draw[line] (0) -- (6) -- (7) -- (11) -- (12); \draw[line] (0) -- (9) -- (15); \draw[line] (0) -- (13) -- (14) -- (18) -- (24); \draw[line] (0) -- (16) -- (29); \draw[line] (0) -- (17) -- (19) -- (21) -- (32); \draw[line] (0) -- (26) -- (28); \draw[line] (0) -- (31) -- (33); \draw[line] (1) -- (2) -- (6) -- (20) -- (28); \draw[line] (1) -- (3) -- (14); \draw[line] (1) -- (4) -- (9) -- (23) -- (24); \draw[line] (1) -- (7) -- (8); \draw[line] (1) -- (12) -- (17) -- (29) -- (30); \draw[line] (1) -- (13) -- (19) -- (31) -- (34); \draw[line] (1) -- (15) -- (16); \draw[line] (1) -- (21) -- (33); \draw[line] (1) -- (26) -- (27); \draw[line] (2) -- (3) -- (7) -- (13); \draw[line] (2) -- (8) -- (10) -- (11) -- (29); \draw[line] (2) -- (9) -- (16) -- (17); \draw[line] (2) -- (12) -- (32); \draw[line] (2) -- (14) -- (15) -- (23) -- (25); \draw[line] (2) -- (19) -- (26) -- (33); \draw[line] (2) -- (24) -- (34); \draw[line] (3) -- (4) -- (5) -- (6) -- (16); \draw[line] (3) -- (9) -- (10) -- (18) -- (19); \draw[line] (3) -- (11) -- (17) -- (24); \draw[line] (3) -- (12) -- (25); \draw[line] (3) -- (15) -- (20) -- (32); \draw[line] (3) -- (21) -- (22); \draw[line] (3) -- (23) -- (31); \draw[line] (3) -- (26) -- (30); \draw[line] (3) -- (27) -- (29) -- (34); \draw[line] (4) -- (7) -- (21); \draw[line] (4) -- (8) -- (12) -- (18); \draw[line] (4) -- (11) -- (20) -- (25) -- (26); \draw[line] (4) -- (14) -- (34); \draw[line] (4) -- (15) -- (19) -- (29); \draw[line] (4) -- (17) -- (28) -- (31); \draw[line] (5) -- (7) -- (9); \draw[line] (5) -- (8) -- (13) -- (15) -- (17); \draw[line] (5) -- (11) -- (23) -- (27) -- (28); \draw[line] (5) -- (12) -- (24); \draw[line] (5) -- (14) -- (29); \draw[line] (5) -- (18) -- (21) -- (30) -- (31); \draw[line] (5) -- (20) -- (22); \draw[line] (5) -- (32) -- (34); \draw[line] (6) -- (8) -- (14) -- (19); \draw[line] (6) -- (9) -- (31); \draw[line] (6) -- (10) -- (22) -- (23) -- (26); \draw[line] (6) -- (13) -- (21) -- (27); \draw[line] (6) -- (15) -- (24) -- (30); \draw[line] (6) -- (29) -- (32); \draw[line] (7) -- (10) -- (14); \draw[line] (7) -- (15) -- (22) -- (31); \draw[line] (7) -- (16) -- (19) -- (25) -- (30); \draw[line] (7) -- (17) -- (20); \draw[line] (7) -- (18) -- (23) -- (29); \draw[line] (7) -- (24) -- (28) -- (33); \draw[line] (7) -- (26) -- (32); \draw[line] (8) -- (9) -- (20) -- (21); \draw[line] (8) -- (16) -- (22) -- (34); \draw[line] (8) -- (23) -- (33); \draw[line] (8) -- (24) -- (25); \draw[line] (8) -- (27) -- (32); \draw[line] (8) -- (28) -- (30); \draw[line] (9) -- (11) -- (14) -- (30); \draw[line] (9) -- (12) -- (27) -- (33); \draw[line] (9) -- (13) -- (22); \draw[line] (9) -- (25) -- (29); \draw[line] (9) -- (26) -- (34); \draw[line] (10) -- (12) -- (15); \draw[line] (10) -- (13) -- (30) -- (32) -- (33); \draw[line] (10) -- (16) -- (24); \draw[line] (10) -- (20) -- (27); \draw[line] (10) -- (21) -- (34); \draw[line] (11) -- (15) -- (33); \draw[line] (11) -- (16) -- (21); \draw[line] (11) -- (18) -- (22) -- (32); \draw[line] (12) -- (13) -- (16) -- (23); \draw[line] (12) -- (14) -- (26) -- (31); \draw[line] (12) -- (19) -- (20); \draw[line] (12) -- (21) -- (28); \draw[line] (13) -- (28) -- (29); \draw[line] (14) -- (16) -- (28) -- (32); \draw[line] (14) -- (17) -- (27); \draw[line] (14) -- (22) -- (33); \draw[line] (15) -- (18) -- (27); \draw[line] (15) -- (28) -- (34); \draw[line] (16) -- (18) -- (26); \draw[line] (16) -- (20) -- (31); \draw[line] (17) -- (18) -- (25) -- (33) -- (34); \draw[line] (19) -- (22) -- (24); \draw[line] (20) -- (23) -- (30) -- (34); \draw[line] (20) -- (29) -- (33); \draw[line] (21) -- (24) -- (26) -- (29); \draw[line] (22) -- (25) -- (28); \draw[line] (24) -- (27) -- (31); \draw[line] (25) -- (31) -- (32); \node[point] at (0) {}; \node[point] at (1) {}; \node[point] at (2) {}; \node[point] at (3) {}; \node[point] at (4) {}; \node[point] at (5) {}; \node[point] at (6) {}; \node[point] at (7) {}; \node[point] at (8) {}; \node[point] at (9) {}; \node[point] at (10) {}; \node[point] at (11) {}; \node[point] at (12) {}; \node[point] at (13) {}; \node[point] at (14) {}; \node[point] at (15) {}; \node[point] at (16) {}; \node[point] at (17) {}; \node[point] at (18) {}; \node[point] at (19) {}; \node[point] at (20) {}; \node[point] at (21) {}; \node[point] at (22) {}; \node[point] at (23) {}; \node[point] at (24) {}; \node[point] at (25) {}; \node[point] at (26) {}; \node[point] at (27) {}; \node[point] at (28) {}; \node[point] at (29) {}; \node[point] at (30) {}; \node[point] at (31) {}; \node[point] at (32) {}; \node[point] at (33) {}; \node[point] at (34) {}; \end{scope} \end{tikzpicture} \caption{The point configuration $\mathdutchcal A(35,680)^$. Three points are not shown and can be obtained by continuing the line segments.} \label{fig:not_cn_35} \end{figure} \subsection{Observations and consequences} \label{ssec:discuss} We make a few remarks on the verification and its implications. The number of shards do not depend on the choice of base region: indeed, \cite[Lemma~146]{padrol_shard_2020} says that in a simplicial arrangement, the number of shards is the number of rays in the arrangement minus the dimension. So, computing the number of shards leads to the number of facets of the corresponding simple zonotope. For rank-$3$ simplicial arrangements, the number of shards is one less than half the number of regions. For example, the arrangements $\mathdutchcal A(30,480)$ and $\mathdutchcal A(31,480)$ have different numbers of hyperplanes but the same number of shards and regions. Finally, we end with questions that arose from this investigation. \begin{description} \item[Question 1] What is the relationship between polygonal and semidistributive lattices? \item[Question 2] Is there a hyperplane arrangement with at most $8$ hyperplanes that yields a tight poset of regions which is not congruence normal? \item[Question 3] Is there a proof of congruence normality for $\mathdutchcal A(31,480)$ using dualty with $H_3$? \item[Question 4] Is there a geometric explanation for the provenance of the three arrangements that are never congruence normal? Are the posets of regions all isomorphic? \item[Question 5] Reading used ``signed subsets'' to describe when an edge occurs between two shards in type $A$ and $B$ \cite{reading_lattice_2004}. Can shard covectors be used in conjunction with positive roots to describe forcing on shards? \item[Question 6] Apart from being dual to 2-neighborly, what can be said about the combinatorial types of the regions in a tight hyperplane arrangement? \end{description} \section{Invariants of rank-$3$ simplicial hyperplane arrangements} \label{sec:invariants} Table~\ref{tab:invariants} gives a list of invariants for the simplicial hyperplane arrangements of rank $3$ with at most $37$ hyperplanes (excluding the reducible near-pencil arrangements). The $f$-vector consists of the numbers of $0$-, $1$-, and $2$-cells in the corresponding CW-complex, i.e.\ $f_3$ is the number of chambers. The $t$-vector contains the numbers $t_i$ of vertices which lie on exactly $i$ lines; the $r$-vector contains the numbers $r_i$ of lines on which exactly $i$ vertices lie. The automorphism groups of the CW-complexes are listed in the column AG, the automorphism groups of the matroids are listed in the column AGM; a pair $(a,b)$ represents the $b$-th group of order $a$ in the database of small groups (as included for example in the system \texttt{GAP} \cite{GAP4}). In the column EXP we list the roots of the characteristic polynomials of the arrangements when they are all integers. The column ``domain'' contains the minimal field of definition for a realization of the matroid of the arrangement in characteristic zero (as computed in \cite{p-C10b}): $\mathbb{Z}$ stands for a crystallographic arrangement (which defines a Weyl groupoid). The other domains are \begin{eqnarray} Q_i &:=& \mathbb{Q}(\zeta+\zeta^{-1}), \quad \zeta \text{ an } i\text{-th root of unity},\\ K_1 &:=& \mathbb{Q}[X]/(X^3-X+1), \\ K_2 &:=& \mathbb{Q}[X]/(X^4 - 3X^3 + 3X^2 - 3X + 1). \end{eqnarray} \clearpage {\tiny \begin{longtable}{llllllll} Name & $f$-vector & $t$-vector & $r$-vector & AG & AGM & EXP & domain \\\toprule[1pt] \iffalse $\mathdutchcal A{(6,24)}$ & $\mathcal{A}(6, 1)$ & (7, 18, 12) & (3, 4) & (0, 6) & (48, 48) & (24, 12) & (1, 2, 3) \\\hline $\mathdutchcal A{(7,32)}$ & $\mathcal{A}(7, 1)$ & (9, 24, 16) & (3, 6) & (0, 4, 3) & (48, 48) & (24, 12) & (1, 3, 3) \\\hline $\mathdutchcal A{(8,40)}$ & $\mathcal{A}(8, 1)$ & (11, 30, 20) & (4, 6, 1) & (0, 2, 6) & (16, 11) & (8, 3) & (1, 3, 4) \\\hline $\mathdutchcal A{(9,48)}$ & $\mathcal{A}(9, 1)$ & (13, 36, 24) & (6, 4, 3) & ($0^{2}$, 9) & (48, 48) & (24, 12) & (1, 3, 5) \\\hline $\mathdutchcal A{(10,60)_1}$ & $\mathcal{A}(10, 3)$ & (16, 45, 30) & (6, 7, 3) & (0, 1, 3, 6) & (24, 14) & (12, 4) & (1, 4, 5) \\ $\mathdutchcal A{(10,60)_2}$ & $\mathcal{A}(10, 2)$ & (16, 45, 30) & (6, 7, 3) & ($0^{2}$, 6, 3, 1) & (12, 4) & (6, 1) & (1, 4, 5) \\ $\mathdutchcal A{(10,60)_3}$ & $\mathcal{A}(10, 1)$ & (16, 45, 30) & (5, 10, 0, 1) & ($0^{2}$, 5, 5) & (20, 4) & (20, 3) & (1, 4, 5) \\\hline $\mathdutchcal A{(11,72)}$ & $\mathcal{A}(11, 1)$ & (19, 54, 36) & (7, 8, 4) & ($0^{2}$, 4, 4, 3) & (8, 5) & (4, 2) & (1, 5, 5) \\\hline $\mathdutchcal A{(12,84)_1}$ & $\mathcal{A}(12, 2)$ & (22, 63, 42) & (8, 10, 3, 1) & ($0^{2}$, 3, 3, 6) & (8, 5) & (4, 2) & (1, 5, 6) \\ $\mathdutchcal A{(12,84)_2}$ & $\mathcal{A}(12, 3)$ & (22, 63, 42) & (9, 7, 6) & ($0^{2}$, 3, 3, 6) & (12, 4) & (6, 1) & (1, 5, 6) \\ $\mathdutchcal A{(12,84)_3}$ & $\mathcal{A}(12, 1)$ & (22, 63, 42) & (6, 15, $0^{2}$, 1) & ($0^{2}$, 3, 3, 6) & (24, 14) & (12, 4) & (1, 5, 6) \\\hline $\mathdutchcal A{(13,96)_1}$ & $\mathcal{A}(13, 1)$ & (25, 72, 48) & (9, 12, 3, 0, 1) & ($0^{2}$, 3, 0, 10) & (24, 14) & (12, 4) & (1, 5, 7) \\ $\mathdutchcal A{(13,96)_2}$ & $\mathcal{A}(13, 3)$ & (25, 72, 48) & (10, 10, 3, 2) & ($0^{2}$, 1, 4, 8) & (8, 5) & (4, 2) & (1, 5, 7) \\ $\mathdutchcal A{(13,96)_3}$ & $\mathcal{A}(13, 2)$ & (25, 72, 48) & (12, 4, 9) & ($0^{2}$, 3, 0, 10) & (48, 48) & (24, 12) & (1, 5, 7) \\ $\mathdutchcal A{(13,104)}$ & $\mathcal{A}(13, 4)$ & (27, 78, 52) & (6, 18, 3) & ($0^{4}$, 13) & (24, 13) & (24, 12) & () \\\hline $\mathdutchcal A{(14,112)_1}$ & $\mathcal{A}(14, 2)$ & (29, 84, 56) & (11, 12, 4, 2) & ($0^{2}$, 1, 4, 4, 4, 1) & (4, 2) & (2, 1) & (1, 6, 7) \\ $\mathdutchcal A{(14,112)_2}$ & $\mathcal{A}(14, 1)$ & (29, 84, 56) & (7, 21, $0^{3}$, 1) & ($0^{3}$, 7, 0, 7) & (28, 3) & (42, 1) & (1, 6, 7) \\ $\mathdutchcal A{(14,112)_3}$ & $\mathcal{A}(14, 4)$ & (29, 84, 56) & (10, 14, 4, 0, 1) & ($0^{3}$, 4, 6, 4) & (8, 5) & (8, 3) & (1, 6, 7) \\ $\mathdutchcal A{(14,116)}$ & $\mathcal{A}(14, 3)$ & (30, 87, 58) & (9, 16, 4, 1) & ($0^{4}$, 11, 3) & (4, 2) & (4, 2) & () \\\hline $\mathdutchcal A{(15,120)}$ & $\mathcal{A}(15, 1)$ & (31, 90, 60) & (15, 10, 0, 6) & ($0^{4}$, 15) & (120, 35) & (120, 34) & (1, 5, 9) \\ $\mathdutchcal A{(15,128)_1}$ & $\mathcal{A}(15, 2)$ & (33, 96, 64) & (13, 12, 6, 2) & ($0^{2}$, 1, 4, 2, 4, 4) & (16, 11) & (8, 3) & (1, 7, 7) \\ $\mathdutchcal A{(15,128)_2}$ & $\mathcal{A}(15, 4)$ & (33, 96, 64) & (12, 14, 6, 0, 1) & ($0^{4}$, 10, 4, 1) & (8, 5) & (8, 3) & (1, 7, 7) \\ $\mathdutchcal A{(15,132)_1}$ & $\mathcal{A}(15, 5)$ & (34, 99, 66) & (9, 22, 0, 3) & ($0^{4}$, 9, 3, 3) & (12, 4) & (6, 1) & () \\ $\mathdutchcal A{(15,132)_2}$ & $\mathcal{A}(15, 3)$ & (34, 99, 66) & (12, 13, 9) & ($0^{4}$, 9, 3, 3) & (12, 4) & (6, 1) & () \\\hline $\mathdutchcal A{(16,140)}$ & $\mathcal{A}(16, 4)$ & (36, 105, 70) & (15, 15, 0, 6) & ($0^{4}$, 10, 5, $0^{2}$, 1) & (20, 4) & (20, 3) & (1, 6, 9) \\ $\mathdutchcal A{(16,144)_1}$ & $\mathcal{A}(16, 2)$ & (37, 108, 72) & (14, 15, 6, 1, 1) & ($0^{2}$, 1, 2, 4, 2, 7) & (8, 5) & (4, 2) & (1, 7, 8) \\ $\mathdutchcal A{(16,144)_2}$ & $\mathcal{A}(16, 3)$ & (37, 108, 72) & (15, 13, 6, 3) & ($0^{4}$, 10, 0, 6) & (12, 4) & (6, 1) & (1, 7, 8) \\ $\mathdutchcal A{(16,144)_3}$ & $\mathcal{A}(16, 1)$ & (37, 108, 72) & (8, 28, $0^{4}$, 1) & ($0^{3}$, 4, 4, 0, 8) & (32, 39) & (32, 43) & (1, 7, 8) \\ $\mathdutchcal A{(16,144)_4}$ & $\mathcal{A}(16, 6)$ & (37, 108, 72) & (15, 12, 9, 0, 1) & ($0^{4}$, 7, 6, 3) & (12, 4) & (6, 1) & (1, 7, 8) \\ $\mathdutchcal A{(16,144)_5}$ & $\mathcal{A}(16, 5)$ & (37, 108, 72) & (14, 16, 3, 4) & ($0^{3}$, 2, 4, 8, 0, 2) & (8, 5) & (8, 3) & (1, 7, 8) \\ $\mathdutchcal A{(16,148)}$ & $\mathcal{A}(16, 7)$ & (38, 111, 74) & (12, 19, 6, 0, 1) & ($0^{3}$, 3, 3, 2, 8) & (8, 5) & (4, 2) & () \\\hline $\mathdutchcal A{(17,160)_1}$ & $\mathcal{A}(17, 2)$ & (41, 120, 80) & (16, 16, 7, 0, 2) & ($0^{2}$, 1, 0, 6, 0, 10) & (16, 11) & (8, 3) & (1, 7, 9) \\ $\mathdutchcal A{(17,160)_2}$ & $\mathcal{A}(17, 4)$ & (41, 120, 80) & (16, 16, 7, 0, 2) & ($0^{2}$, 1, 0, 6, 0, 10) & (16, 11) & (8, 3) & (1, 7, 9) \\ $\mathdutchcal A{(17,160)_3}$ & $\mathcal{A}(17, 3)$ & (41, 120, 80) & (18, 12, 7, 4) & ($0^{4}$, 8, 0, 9) & (16, 11) & (8, 3) & (1, 7, 9) \\ $\mathdutchcal A{(17,160)_4}$ & $\mathcal{A}(17, 1)$ & (41, 120, 80) & (12, 24, 4, $0^{3}$, 1) & ($0^{4}$, 8, 0, 9) & (32, 39) & (32, 43) & (1, 7, 9) \\ $\mathdutchcal A{(17,160)_5}$ & $\mathcal{A}(17, 5)$ & (41, 120, 80) & (16, 18, 1, 6) & ($0^{4}$, 6, 8, 1, 0, 2) & (8, 5) & (8, 3) & (1, 7, 9) \\ $\mathdutchcal A{(17,164)}$ & $\mathcal{A}(17, 6)$ & (42, 123, 82) & (16, 15, 10, 0, 1) & ($0^{4}$, 6, 3, 7, 0, 1) & (4, 2) & (2, 1) & () \\ $\mathdutchcal A{(17,168)_1}$ & $\mathcal{A}(17, 7)$ & (43, 126, 84) & (13, 22, 7, 0, 1) & ($0^{4}$, 6, 0, 10, 0, 1) & (8, 5) & (4, 2) & () \\ $\mathdutchcal A{(17,168)_2}$ & $\mathcal{A}(17, 8)$ & (43, 126, 84) & (14, 20, 7, 2) & ($0^{4}$, 1, 8, 8) & (8, 5) & (8, 3) & () \\\hline $\mathdutchcal A{(18,180)_1}$ & $\mathcal{A}(18, 7)$ & (46, 135, 90) & (18, 18, 6, 3, 1) & ($0^{3}$, 3, 3, 0, 6, 6) & (12, 4) & (6, 1) & (1, 8, 9) \\ $\mathdutchcal A{(18,180)_2}$ & $\mathcal{A}(18, 3)$ & (46, 135, 90) & (19, 16, 6, 5) & ($0^{4}$, 6, 2, 6, 3, 1) & (4, 2) & (2, 1) & (1, 8, 9) \\ $\mathdutchcal A{(18,180)_3}$ & $\mathcal{A}(18, 1)$ & (46, 135, 90) & (9, 36, $0^{5}$, 1) & ($0^{4}$, 9, $0^{2}$, 9) & (36, 4) & (54, 6) & (1, 8, 9) \\ $\mathdutchcal A{(18,180)_4}$ & $\mathcal{A}(18, 2)$ & (46, 135, 90) & (18, 18, 6, 3, 1) & ($0^{4}$, 3, 3, 12) & (24, 14) & (12, 4) & (1, 8, 9) \\ $\mathdutchcal A{(18,180)_5}$ & $\mathcal{A}(18, 4)$ & (46, 135, 90) & (18, 19, 3, 6) & ($0^{4}$, 3, 9, 3, 0, 3) & (12, 4) & (6, 1) & (1, 8, 9) \\ $\mathdutchcal A{(18,180)_6}$ & $\mathcal{A}(18, 5)$ & (46, 135, 90) & (18, 19, 3, 6) & ($0^{4}$, 3, 9, 3, 0, 3) & (12, 4) & (6, 1) & (1, 8, 9) \\ $\mathdutchcal A{(18,184)_1}$ & $\mathcal{A}(18, 6)$ & (47, 138, 92) & (18, 16, 12, 0, 1) & ($0^{4}$, 5, 2, 7, 2, 2) & (4, 2) & (2, 1) & () \\ $\mathdutchcal A{(18,184)_2}$ & $\mathcal{A}(18, 8)$ & (47, 138, 92) & (16, 22, 6, 2, 1) & ($0^{4}$, 6, 0, 7, 4, 1) & (4, 2) & (2, 1) & () \\\hline $\mathdutchcal A{(19,192)_1}$ & $\mathcal{A}(19, 1)$ & (49, 144, 96) & (21, 18, 6, 0, 4) & ($0^{4}$, 4, 0, 15) & (24, 14) & (12, 4) & (1, 7, 11) \\ $\mathdutchcal A{(19,192)_2}$ & $\mathcal{A}(19, 3)$ & (49, 144, 96) & (24, 12, 6, 6, 1) & ($0^{4}$, 4, 0, 15) & (24, 14) & (12, 4) & (1, 7, 11) \\ $\mathdutchcal A{(19,200)_1}$ & $\mathcal{A}(19, 4)$ & (51, 150, 100) & (20, 20, 6, 4, 1) & ($0^{4}$, 4, 4, 4, 4, 3) & (8, 5) & (4, 2) & (1, 9, 9) \\ $\mathdutchcal A{(19,200)_2}$ & $\mathcal{A}(19, 5)$ & (51, 150, 100) & (20, 20, 6, 4, 1) & ($0^{4}$, 4, 4, 4, 4, 3) & (8, 2) & (4, 1) & (1, 9, 9) \\ $\mathdutchcal A{(19,200)_3}$ & $\mathcal{A}(19, 6)$ & (51, 150, 100) & (20, 20, 6, 4, 1) & ($0^{4}$, 6, 0, 6, 4, 3) & (8, 5) & (4, 2) & (1, 9, 9) \\ $\mathdutchcal A{(19,200)_4}$ & $\mathcal{A}(19, 2)$ & (51, 150, 100) & (21, 18, 6, 6) & ($0^{4}$, 1, 8, 6, 0, 4) & (8, 5) & (8, 3) & (1, 9, 9) \\ $\mathdutchcal A{(19,204)}$ & $\mathcal{A}(19, 7)$ & (52, 153, 102) & (21, 15, 15, 0, 1) & ($0^{4}$, 4, 3, 3, 6, 3) & (12, 4) & (6, 1) & () \\\hline $\mathdutchcal A{(20,216)}$ & $\mathcal{A}(20, 5)$ & (55, 162, 108) & (20, 26, 4, 4, $0^{2}$, 1) & ($0^{3}$, 2, 2, 0, 4, 12) & (16, 11) & (8, 3) & (1, 8, 11) \\ $\mathdutchcal A{(20,220)_1}$ & $\mathcal{A}(20, 3)$ & (56, 165, 110) & (21, 24, 6, 4, 0, 1) & ($0^{4}$, 4, 2, 4, 6, 3, 1) & (4, 2) & (2, 1) & (1, 9, 10) \\ $\mathdutchcal A{(20,220)_2}$ & $\mathcal{A}(20, 4)$ & (56, 165, 110) & (23, 20, 7, 5, 1) & ($0^{4}$, 5, 1, 4, 4, 6) & (4, 2) & (2, 1) & (1, 9, 10) \\ $\mathdutchcal A{(20,220)_3}$ & $\mathcal{A}(20, 1)$ & (56, 165, 110) & (10, 45, $0^{6}$, 1) & ($0^{4}$, 5, 5, $0^{2}$, 10) & (40, 13) & (40, 12) & (1, 9, 10) \\ $\mathdutchcal A{(20,220)_4}$ & $\mathcal{A}(20, 2)$ & (56, 165, 110) & (25, 15, 10, 6) & ($0^{5}$, 5, 10, 0, 5) & (20, 4) & (20, 3) & (1, 9, 10) \\ $\mathdutchcal A{(21,240)_1}$ & $\mathcal{A}(21, 4)$ & (61, 180, 120) & (22, 28, 6, 4, $0^{2}$, 1) & ($0^{4}$, 4, 0, 4, 8, 4, 0, 1) & (16, 11) & (8, 3) & (1, 9, 11) \\ $\mathdutchcal A{(21,240)_2}$ & $\mathcal{A}(21, 5)$ & (61, 180, 120) & (26, 20, 9, 4, 2) & ($0^{4}$, 5, 0, 3, 4, 9) & (8, 5) & (4, 2) & (1, 9, 11) \\ $\mathdutchcal A{(21,240)_3}$ & $\mathcal{A}(21, 3)$ & (61, 180, 120) & (24, 24, 9, 0, 4) & ($0^{4}$, 6, 0, 3, 0, 12) & (48, 48) & (24, 12) & (1, 9, 11) \\ $\mathdutchcal A{(21,240)_4}$ & $\mathcal{A}(21, 1)$ & (61, 180, 120) & (15, 40, 5, $0^{5}$, 1) & ($0^{4}$, 5, 0, 5, 0, 11) & (40, 13) & (40, 12) & (1, 9, 11) \\ $\mathdutchcal A{(21,240)_5}$ & $\mathcal{A}(21, 2)$ & (61, 180, 120) & (30, 10, 15, 6) & ($0^{6}$, 15, 0, 6) & (120, 35) & (120, 34) & (1, 9, 11) \\ $\mathdutchcal A{(21,248)}$ & $\mathcal{A}(21, 6)$ & (63, 186, 124) & (25, 20, 15, 2, 1) & ($0^{4}$, 1, 0, 11, 0, 8, 0, 1) & (8, 5) & (4, 2) & () \\ $\mathdutchcal A{(21,252)}$ & $\mathcal{A}(21, 7)$ & (64, 189, 126) & (24, 22, 15, 3) & ($0^{6}$, 12, 0, 6, 3) & (12, 4) & (6, 1) & () \\\hline $\mathdutchcal A{(22,264)_1}$ & $\mathcal{A}(22, 4)$ & (67, 198, 132) & (27, 25, 9, 3, 3) & ($0^{4}$, 4, 0, 6, 0, 6, 6) & (12, 4) & (6, 1) & (1, 10, 11)\\ $\mathdutchcal A{(22,264)_2}$ & $\mathcal{A}(22, 1)$ & (67, 198, 132) & (11, 55, $0^{7}$, 1) & ($0^{5}$, 11, $0^{3}$, 11) & (44, 3) & (110, 1) & (1, 10, 11)\\ $\mathdutchcal A{(22,264)_3}$ & $\mathcal{A}(22, 3)$ & (67, 198, 132) & (27, 28, 0, 12) & ($0^{6}$, 12, 0, 9, 0, 1) & (12, 4) & (12, 4) & (1, 10, 11)\\ $\mathdutchcal A{(22,276)}$ & $\mathcal{A}(22, 2)$ & (70, 207, 138) & (24, 30, 12, 3, 1) & ($0^{4}$, 1, 0, 6, 3, 9, 0, 3) & (12, 4) & (6, 1) & () \\ $\mathdutchcal A{(22,288)}$ & $\mathcal{A}(22, 5)$ & (73, 216, 144) & (12, 58, $0^{2}$, 3) & ($0^{7}$, 12, 6, 0, 4) & (48, 48) & (48, 48) & () \\\hline $\mathdutchcal A{(23,296)}$ & $\mathcal{A}(23, 1)$ & (75, 222, 148) & (27, 32, 10, 4, 2) & ($0^{4}$, 1, 0, 6, 2, 7, 4, 3) & (4, 2) & (2, 1) & () \\ $\mathdutchcal A{(23,304)}$ & $\mathcal{A}(23, 2)$ & (77, 228, 152) & (16, 56, 2, 0, 1, 2) & ($0^{6}$, 1, 8, 10, 0, 4) & (16, 11) & (16, 11) & () \\\hline $\mathdutchcal A{(24,304)}$ & $\mathcal{A}(24, 2)$ & (77, 228, 152) & (32, 32, 0, 12, $0^{2}$, 1) & ($0^{5}$, 4, $0^{2}$, 20) & (32, 39) & (32, 43) & () \\ $\mathdutchcal A{(24,312)}$ & $\mathcal{A}(24, 1)$ & (79, 234, 156) & (12, 66, $0^{8}$, 1) & ($0^{5}$, 6, 6, $0^{3}$, 12) & (48, 36) & (48, 38) & (1, 11, 12)\\ $\mathdutchcal A{(24,316)}$ & $\mathcal{A}(24, 3)$ & (80, 237, 158) & (31, 32, 9, 5, 3) & ($0^{4}$, 1, 0, 6, 1, 6, 6, 4) & (4, 2) & (2, 1) & () \\ $\mathdutchcal A{(24,320)}$ & $\mathcal{A}(24, 4)$ & (81, 240, 160) & (20, 54, 4, $0^{2}$, 2, 1) & ($0^{6}$, 2, 4, 14, 0, 4) & (16, 11) & (16, 11) & () \\\hline $\mathdutchcal A{(25,320)}$ & $\mathcal{A}(25, 5)$ & (81, 240, 160) & (36, 32, 0, 8, 4, 0, 1) & ($0^{6}$, 5, 0, 20) & (32, 39) & (32, 43) & (1, 9, 15) \\ $\mathdutchcal A{(25,336)_1}$ & $\mathcal{A}(25, 7)$ & (85, 252, 168) & (33, 34, 12, 2, 3, 0, 1) & ($0^{4}$, 2, 0, 4, 4, 4, 0, 11) & (8, 5) & (4, 2) & (1, 11, 13)\\ $\mathdutchcal A{(25,336)_2}$ & $\mathcal{A}(25, 4)$ & (85, 252, 168) & (36, 30, 9, 6, 4) & ($0^{4}$, 1, 0, 9, 0, 3, 0, 12) & (24, 14) & (12, 4) & (1, 11, 13)\\ $\mathdutchcal A{(25,336)_3}$ & $\mathcal{A}(25, 6)$ & (85, 252, 168) & (36, 30, 9, 6, 4) & ($0^{4}$, 1, 0, 6, 0, 6, 6, 6) & (12, 4) & (6, 1) & (1, 11, 13)\\ $\mathdutchcal A{(25,336)_4}$ & $\mathcal{A}(25, 2)$ & (85, 252, 168) & (36, 28, 15, 0, 6) & ($0^{4}$, 4, 0, 3, 0, 6, 0, 12) & (48, 48) & (24, 12) & (1, 11, 13)\\ $\mathdutchcal A{(25,336)_5}$ & $\mathcal{A}(25, 1)$ & (85, 252, 168) & (18, 60, 6, $0^{7}$, 1) & ($0^{6}$, 12, $0^{3}$, 13) & (48, 36) & (48, 38) & (1, 11, 13)\\ $\mathdutchcal A{(25,336)_6}$ & $\mathcal{A}(25, 8)$ & (85, 252, 168) & (24, 52, 6, $0^{3}$, 3) & ($0^{6}$, 3, 0, 18, 0, 4) & (48, 48) & (48, 48) & (1, 11, 13)\\ $\mathdutchcal A{(25,360)}$ & $\mathcal{A}(25, 3)$ & (91, 270, 180) & (30, 40, 15, 6) & ($0^{8}$, 15, 0, 10) & (120, 35) & (120, 34) & () \\\hline $\mathdutchcal A{(26,364)_1}$ & $\mathcal{A}(26, 4)$ & (92, 273, 182) & (35, 39, 10, 4, 3, 0, 1) & ($0^{4}$, 1, 1, 4, 4, 2, 2, 7, 4, 1) & (4, 2) & (2, 1) & (1, 12, 13)\\ $\mathdutchcal A{(26,364)_2}$ & $\mathcal{A}(26, 3)$ & (92, 273, 182) & (37, 36, 9, 6, 3, 1) & ($0^{4}$, 1, 0, 7, 2, 2, 1, 8, 4, 1) & (4, 2) & (2, 1) & (1, 12, 13)\\ $\mathdutchcal A{(26,364)_3}$ & $\mathcal{A}(26, 1)$ & (92, 273, 182) & (13, 78, $0^{9}$, 1) & ($0^{6}$, 13, $0^{4}$, 13) & (52, 4) & (156, 7) & (1, 12, 13)\\ $\mathdutchcal A{(26,380)}$ & $\mathcal{A}(26, 2)$ & (96, 285, 190) & (35, 40, 10, 11) & ($0^{8}$, 11, 5, 10) & (20, 4) & (20, 3) & () \\\hline $\mathdutchcal A{(27,392)_1}$ & $\mathcal{A}(27, 4)$ & (99, 294, 196) & (38, 42, 9, 6, 3, 0, 1) & ($0^{4}$, 1, 0, 5, 4, 2, 0, 7, 4, 4) & (8, 5) & (4, 2) & (1, 13, 13)\\ $\mathdutchcal A{(27,392)_2}$ & $\mathcal{A}(27, 3)$ & (99, 294, 196) & (39, 40, 10, 6, 2, 2) & ($0^{4}$, 1, 0, 6, 2, 2, 2, 5, 6, 3) & (4, 2) & (2, 1) & (1, 13, 13)\\ $\mathdutchcal A{(27,392)_3}$ & $\mathcal{A}(27, 2)$ & (99, 294, 196) & (39, 40, 10, 6, 2, 2) & ($0^{4}$, 1, 0, 5, 4, 1, 2, 4, 8, 2) & (4, 2) & (2, 1) & (1, 13, 13)\\ $\mathdutchcal A{(27,400)}$ & $\mathcal{A}(27, 1)$ & (101, 300, 200) & (40, 40, 6, 14, 1) & ($0^{8}$, 8, 8, 11) & (8, 5) & (8, 3) & () \\\hline $\mathdutchcal A{(28,420)_1}$ & $\mathcal{A}(28, 4)$ & (106, 315, 210) & (41, 44, 11, 6, 2, 1, 1) & ($0^{4}$, 1, 0, 4, 4, 2, 1, 4, 6, 6) & (2, 1) & (1, 1) & (1, 13, 14)\\ $\mathdutchcal A{(28,420)_2}$ & $\mathcal{A}(28, 5)$ & (106, 315, 210) & (42, 42, 12, 6, 1, 3) & ($0^{4}$, 1, 0, 4, 4, 1, 3, 1, 10, 4) & (4, 2) & (2, 1) & (1, 13, 14)\\ $\mathdutchcal A{(28,420)_3}$ & $\mathcal{A}(28, 6)$ & (106, 315, 210) & (42, 42, 12, 6, 1, 3) & ($0^{4}$, 1, 0, 6, 0, 3, 3, 3, 6, 6) & (12, 4) & (6, 1) & (1, 13, 14)\\ $\mathdutchcal A{(28,420)_4}$ & $\mathcal{A}(28, 1)$ & (106, 315, 210) & (14, 91, $0^{10}$, 1) & ($0^{6}$, 7, 7, $0^{4}$, 14) & (56, 12) & (84, 7) & (1, 13, 14)\\ $\mathdutchcal A{(28,420)_5}$ & $\mathcal{A}(28, 2)$ & (106, 315, 210) & (45, 40, 3, 15, 3) & ($0^{8}$, 6, 9, 13) & (12, 4) & (6, 1) & (1, 13, 14)\\ $\mathdutchcal A{(28,420)_6}$ & $\mathcal{A}(28, 3)$ & (106, 315, 210) & (45, 40, 3, 15, 3) & ($0^{8}$, 6, 9, 13) & (12, 4) & (6, 1) & (1, 13, 14)\\\hline $\mathdutchcal A{(29,440)}$ & $\mathcal{A}(29, 2)$ & (111, 330, 220) & (50, 40, 1, 14, 6) & ($0^{8}$, 5, 8, 16) & (8, 5) & (8, 3) & () \\ $\mathdutchcal A{(29,448)_1}$ & $\mathcal{A}(29, 3)$ & (113, 336, 224) & (44, 46, 13, 6, 2, 0, 2) & ($0^{4}$, 1, 0, 3, 4, 3, 0, 4, 4, 10) & (8, 5) & (4, 2) & (1, 13, 15)\\ $\mathdutchcal A{(29,448)_2}$ & $\mathcal{A}(29, 4)$ & (113, 336, 224) & (45, 44, 14, 6, 1, 2, 1) & ($0^{4}$, 1, 0, 3, 4, 2, 2, 1, 8, 8) & (4, 2) & (2, 1) & (1, 13, 15)\\ $\mathdutchcal A{(29,448)_3}$ & $\mathcal{A}(29, 5)$ & (113, 336, 224) & (45, 44, 14, 6, 1, 2, 1) & ($0^{4}$, 1, 0, 4, 2, 3, 2, 2, 6, 9) & (4, 2) & (2, 1) & (1, 13, 15)\\ $\mathdutchcal A{(29,448)_4}$ & $\mathcal{A}(29, 1)$ & (113, 336, 224) & (21, 84, 7, $0^{9}$, 1) & ($0^{6}$, 7, 0, 7, $0^{3}$, 15) & (56, 12) & (84, 7) & (1, 13, 15)\\\hline $\mathdutchcal A{(30,460)}$ & $\mathcal{A}(30, 2)$ & (116, 345, 230) & (55, 40, 0, 11, 10) & ($0^{8}$, 5, 5, 20) & (20, 4) & (20, 3) & () \\ $\mathdutchcal A{(30,476)}$ & $\mathcal{A}(30, 3)$ & (120, 357, 238) & (49, 44, 17, 6, 1, 1, 2) & ($0^{4}$, 1, 0, 3, 2, 4, 1, 2, 4, 13) & (4, 2) & (2, 1) & (1, 13, 16)\\ $\mathdutchcal A{(30,480)}$ & $\mathcal{A}(30, 1)$ & (121, 360, 240) & (15, 105, $0^{11}$, 1) & ($0^{7}$, 15, $0^{5}$, 15) & (60, 12) & (120, 36) & (1, 14, 15)\\\hline $\mathdutchcal A{(31,480)}$ & $\mathcal{A}(31, 1)$ & (121, 360, 240) & (60, 40, 0, 6, 15) & ($0^{8}$, 6, 0, 25) & (120, 35) & (120, 34) & (1, 11, 19)\\ $\mathdutchcal A{(31,504)_1}$ & $\mathcal{A}(31, 2)$ & (127, 378, 252) & (54, 42, 21, 6, 1, 0, 3) & ($0^{4}$, 1, $0^{3}$, 9, 0, 6, 0, 15) & (24, 14) & (12, 4) & (1, 13, 17)\\ $\mathdutchcal A{(31,504)_2}$ & $\mathcal{A}(31, 3)$ & (127, 378, 252) & (54, 42, 21, 6, 1, 0, 3) & ($0^{4}$, 1, 0, 3, 0, 6, 0, 3, 0, 18) & (24, 14) & (12, 4) & (1, 13, 17)\\\hline $\mathdutchcal A{(32,544)}$ & $\mathcal{A}(32, 1)$ & (137, 408, 272) & (16, 120, $0^{12}$, 1) & ($0^{7}$, 8, 8, $0^{5}$, 16) & (64, 186 & (128, 913)) & (1, 15, 16)\\ $\mathdutchcal A{(33,576)}$ & $\mathcal{A}(33, 1)$ & (145, 432, 288) & (24, 112, 8, $0^{11}$, 1) & ($0^{8}$, 16, $0^{5}$, 17) i & (64, 186 & (128, 913)) & (1, 15, 17)\\\hline $\mathdutchcal A{(34,612)_1}$ & $\mathcal{A}(34, 2)$ & (154, 459, 306) & (60, 63, 18, 6, 4, 0, 3) & ($0^{6}$, 3, 3, 3, 0, 4, 0, 6, 0, 9, 6) & (12, 4) & (6, 1) & (1, 16, 17)\\ $\mathdutchcal A{(34,612)_2}$ & $\mathcal{A}(34, 1)$ & (154, 459, 306) & (17, 136, $0^{13}$, 1) & ($0^{8}$, 17, $0^{6}$, 17) & (68, 4) & (272, 50) & (1, 16, 17)\\\hline $\mathdutchcal A{(35,680)}$ & $\mathcal{A}(35, 1)$ & (171, 510, 340) & (70, 55, 25, 21), & ($0^{12}$,25,0,10) & (20, 4) & (20, 4) & () \\\hline $\mathdutchcal A{(36,684)}$ & $\mathcal{A}(36, 1)$ & (172, 513, 342) & (18, 153, $0^{14}$, 1) & ($0^{8}$, 9, 9, $0^{6}$, 18) & (72, 17) & (108, 26) & (1, 17, 18)\\\hline $\mathdutchcal A{(37,720)_1}$ & $\mathcal{A}(37, 3)$ & (181, 540, 360) & (72, 72, 24, 0, 10, 0, 3) & ($0^{6}$, 3, 0, 6, 0, 4, $0^{3}$, 12, 0, 12) & (48, 48) & (24, 12) & (1, 17, 19)\\ $\mathdutchcal A{(37,720)_2}$ & $\mathcal{A}(37, 1)$ & (181, 540, 360) & (27, 144, 9, $0^{13}$, 1) & ($0^{8}$, 9, 0, 9, $0^{5}$, 19) & (72, 17) & (108, 26) & (1, 17, 19)\\ $\mathdutchcal A{(37,720)_3}$ & $\mathcal{A}(37, 2)$ & (181, 540, 360) & (72, 72, 12, 24, $0^{6}$, 1) & ($0^{10}$, 13, $0^{3}$, 24) & (48, 36) & (48, 17) & (1, 17, 19)\\ \fi \iffalse $\mathdutchcal A{(6,24)_?}=\mathcal{A}(6,1)$ & (7,18,12) & $(3,4)$ & $(0,6)$ & (48,48) & (24,12) & [ 1, 2, 3 ] & $\mathbb{Z}$ \\ \hline $\mathdutchcal A{(7,32)_?}=\mathcal{A}(7,1)$ & (9,24,16) & $(3,6)$ & $(0,4,3)$ & (48,48) & (24,12) & [ 1, 3, 3 ] & $\mathbb{Z}$ \\ \hline $\mathdutchcal A{(8,40)_?}=\mathcal{A}(8,1)$ & (11,30,20) & $(4,6,1)$ & $(0,2,6)$ & (16,11) & (8,3) & [ 1, 3, 4 ] & $\mathbb{Z}$ \\ \hline $\mathdutchcal A{(9,48)_?}=\mathcal{A}(9,1)$ & (13,36,24) & $(6,4,3)$ & $(0^{2},9)$ & (48,48) & (24,12) & [ 1, 3, 5 ] & $\mathbb{Z}$ \\ \hline $\mathdutchcal A{(10,60)_?}=\mathcal{A}(10,1)$ & (16,45,30) & $(5,10,0,1)$ & $(0^{2},5^{2})$ & (20,4) & (20,3) & [ 1, 4, 5 ] & $Q_{5}$ \\ $\mathdutchcal A{(10,60)_?}=\mathcal{A}(10,2)$ & (16,45,30) & $(6,7,3)$ & $(0^{2},6,3,1)$ & (12,4) & (6,1) & [ 1, 4, 5 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(10,60)_?}=\mathcal{A}(10,3)$ & (16,45,30) & $(6,7,3)$ & $(0,1,3,6)$ & (24,14) & (12,4) & [ 1, 4, 5 ] & $\mathbb{Z}$ \\ \hline $\mathdutchcal A{(11,72)_?}=\mathcal{A}(11,1)$ & (19,54,36) & $(7,8,4)$ & $(0^{2},4^{2},3)$ & (8,5) & (4,2) & [ 1, 5, 5 ] & $\mathbb{Z}$ \\ \hline $\mathdutchcal A{(12,84)_?}=\mathcal{A}(12,1)$ & (22,63,42) & $(6,15,0^{2},1)$ & $(0^{2},3^{2},6)$ & (24,14) & (12,4) & [ 1, 5, 6 ] & $\mathbb{Q}$ \\ $\mathdutchcal A{(12,84)_?}=\mathcal{A}(12,2)$ & (22,63,42) & $(8,10,3,1)$ & $(0^{2},3^{2},6)$ & (8,5) & (4,2) & [ 1, 5, 6 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(12,84)_?}=\mathcal{A}(12,3)$ & (22,63,42) & $(9,7,6)$ & $(0^{2},3^{2},6)$ & (12,4) & (6,1) & [ 1, 5, 6 ] & $\mathbb{Z}$ \\ \hline $\mathdutchcal A{(13,96)_?}=\mathcal{A}(13,1)$ & (25,72,48) & $(9,12,3,0,1)$ & $(0^{2},3,0,10)$ & (24,14) & (12,4) & [ 1, 5, 7 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(13,96)_?}=\mathcal{A}(13,2)$ & (25,72,48) & $(12,4,9)$ & $(0^{2},3,0,10)$ & (48,48) & (24,12) & [ 1, 5, 7 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(13,96)_?}=\mathcal{A}(13,3)$ & (25,72,48) & $(10^{2},3,2)$ & $(0^{2},1,4,8)$ & (8,5) & (4,2) & [ 1, 5, 7 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(13,104)_?}=\mathcal{A}(13,4)$ & (27,78,52) & $(6,18,3)$ & $(0^{4},13)$ & (24,13) & (24,12) & [] & $Q_{5}$ \\ \hline $\mathdutchcal A{(14,112)_?}=\mathcal{A}(14,1)$ & (29,84,56) & $(7,21,0^{3},1)$ & $(0^{3},7,0,7)$ & (28,3) & (42,1) & [ 1, 6, 7 ] & $Q_{7}$ \\ $\mathdutchcal A{(14,112)_?}=\mathcal{A}(14,2)$ & (29,84,56) & $(11,12,4,2)$ & $(0^{2},1,4^{3},1)$ & (4,2) & (2,1) & [ 1, 6, 7 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(14,116)_?}=\mathcal{A}(14,3)$ & (30,87,58) & $(9,16,4,1)$ & $(0^{4},11,3)$ & (4,2) & (4,2) & [] & $Q_{5}$ \\ $\mathdutchcal A{(14,112)_?}=\mathcal{A}(14,4)$ & (29,84,56) & $(10,14,4,0,1)$ & $(0^{3},4,6,4)$ & (8,5) & (8,3) & [ 1, 6, 7 ] & $Q_{5}$ \\ \hline $\mathdutchcal A{(15,120)_?}=\mathcal{A}(15,1)$ & (31,90,60) & $(15,10,0,6)$ & $(0^{4},15)$ & (120,35) & (120,34) & [ 1, 5, 9 ] & $Q_{5}$ \\ $\mathdutchcal A{(15,128)_?}=\mathcal{A}(15,2)$ & (33,96,64) & $(13,12,6,2)$ & $(0^{2},1,4,2,4^{2})$ & (16,11) & (8,3) & [ 1, 7, 7 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(15,132)_?}=\mathcal{A}(15,3)$ & (34,99,66) & $(12,13,9)$ & $(0^{4},9,3^{2})$ & (12,4) & (6,1) & [] & $\mathbb{Q}$ \\ $\mathdutchcal A{(15,128)_?}=\mathcal{A}(15,4)$ & (33,96,64) & $(12,14,6,0,1)$ & $(0^{4},10,4,1)$ & (8,5) & (8,3) & [ 1, 7, 7 ] & $Q_{5}$ \\ $\mathdutchcal A{(15,132)_?}=\mathcal{A}(15,5)$ & (34,99,66) & $(9,22,0,3)$ & $(0^{4},9,3^{2})$ & (12,4) & (6,1) & [] & $K_1$ \\ \hline $\mathdutchcal A{(16,144)_?}=\mathcal{A}(16,1)$ & (37,108,72) & $(8,28,0^{4},1)$ & $(0^{3},4^{2},0,8)$ & (32,39) & (32,43) & [ 1, 7, 8 ] & $Q_{8}$ \\ $\mathdutchcal A{(16,144)_?}=\mathcal{A}(16,2)$ & (37,108,72) & $(14,15,6,1^{2})$ & $(0^{2},1,2,4,2,7)$ & (8,5) & (4,2) & [ 1, 7, 8 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(16,144)_?}=\mathcal{A}(16,3)$ & (37,108,72) & $(15,13,6,3)$ & $(0^{4},10,0,6)$ & (12,4) & (6,1) & [ 1, 7, 8 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(16,140)_?}=\mathcal{A}(16,4)$ & (36,105,70) & $(15^{2},0,6)$ & $(0^{4},10,5,0^{2},1)$ & (20,4) & (20,3) & [ 1, 6, 9 ] & $Q_{5}$ \\ $\mathdutchcal A{(16,144)_?}=\mathcal{A}(16,5)$ & (37,108,72) & $(14,16,3,4)$ & $(0^{3},2,4,8,0,2)$ & (8,5) & (8,3) & [ 1, 7, 8 ] & $Q_{5}$ \\ $\mathdutchcal A{(16,144)_?}=\mathcal{A}(16,6)$ & (37,108,72) & $(15,12,9,0,1)$ & $(0^{4},7,6,3)$ & (12,4) & (6,1) & [ 1, 7, 8 ] & $\mathbb{Q}$ \\ $\mathdutchcal A{(16,148)_?}=\mathcal{A}(16,7)$ & (38,111,74) & $(12,19,6,0,1)$ & $(0^{3},3^{2},2,8)$ & (8,5) & (4,2) & [] & $\mathbb{Q}$ \\ \hline $\mathdutchcal A{(17,160)_?}=\mathcal{A}(17,1)$ & (41,120,80) & $(12,24,4,0^{3},1)$ & $(0^{4},8,0,9)$ & (32,39) & (32,43) & [ 1, 7, 9 ] & $Q_{8}$ \\ $\mathdutchcal A{(17,160)_?}=\mathcal{A}(17,2)$ & (41,120,80) & $(16^{2},7,0,2)$ & $(0^{2},1,0,6,0,10)$ & (16,11) & (8,3) & [ 1, 7, 9 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(17,160)_?}=\mathcal{A}(17,3)$ & (41,120,80) & $(18,12,7,4)$ & $(0^{4},8,0,9)$ & (16,11) & (8,3) & [ 1, 7, 9 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(17,160)_?}=\mathcal{A}(17,4)$ & (41,120,80) & $(16^{2},7,0,2)$ & $(0^{2},1,0,6,0,10)$ & (16,11) & (8,3) & [ 1, 7, 9 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(17,160)_?}=\mathcal{A}(17,5)$ & (41,120,80) & $(16,18,1,6)$ & $(0^{4},6,8,1,0,2)$ & (8,5) & (8,3) & [ 1, 7, 9 ] & $Q_{5}$ \\ $\mathdutchcal A{(17,164)_?}=\mathcal{A}(17,6)$ & (42,123,82) & $(16,15,10,0,1)$ & $(0^{4},6,3,7,0,1)$ & (4,2) & (2,1) & [] & $\mathbb{Q}$ \\ $\mathdutchcal A{(17,168)_?}=\mathcal{A}(17,7)$ & (43,126,84) & $(13,22,7,0,1)$ & $(0^{4},6,0,10,0,1)$ & (8,5) & (4,2) & [] & $\mathbb{Q}$ \\ $\mathdutchcal A{(17,168)_?}=\mathcal{A}(17,8)$ & (43,126,84) & $(14,20,7,2)$ & $(0^{4},1,8^{2})$ & (8,5) & (8,3) & [] & $Q_{8}$ \\ \hline $\mathdutchcal A{(18,180)_?}=\mathcal{A}(18,1)$ & (46,135,90) & $(9,36,0^{5},1)$ & $(0^{4},9,0^{2},9)$ & (36,4) & (54,6) & [ 1, 8, 9 ] & $Q_{9}$ \\ $\mathdutchcal A{(18,180)_?}=\mathcal{A}(18,2)$ & (46,135,90) & $(18^{2},6,3,1)$ & $(0^{4},3^{2},12)$ & (24,14) & (12,4) & [ 1, 8, 9 ] & $\mathbb{Q}$ \\ $\mathdutchcal A{(18,180)_?}=\mathcal{A}(18,3)$ & (46,135,90) & $(19,16,6,5)$ & $(0^{4},6,2,6,3,1)$ & (4,2) & (2,1) & [ 1, 8, 9 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(18,180)_?}=\mathcal{A}(18,4)$ & (46,135,90) & $(18,19,3,6)$ & $(0^{4},3,9,3,0,3)$ & (12,4) & (6,1) & [ 1, 8, 9 ] & $Q_{5}$ \\ $\mathdutchcal A{(18,180)_?}=\mathcal{A}(18,5)$ & (46,135,90) & $(18,19,3,6)$ & $(0^{4},3,9,3,0,3)$ & (12,4) & (6,1) & [ 1, 8, 9 ] & $Q_{5}$ \\ $\mathdutchcal A{(18,184)_?}=\mathcal{A}(18,6)$ & (47,138,92) & $(18,16,12,0,1)$ & $(0^{4},5,2,7,2^{2})$ & (4,2) & (2,1) & [] & $\mathbb{Q}$ \\ $\mathdutchcal A{(18,180)_?}=\mathcal{A}(18,7)$ & (46,135,90) & $(18^{2},6,3,1)$ & $(0^{3},3^{2},0,6^{2})$ & (12,4) & (6,1) & [ 1, 8, 9 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(18,184)_?}=\mathcal{A}(18,8)$ & (47,138,92) & $(16,22,6,2,1)$ & $(0^{4},6,0,7,4,1)$ & (4,2) & (2,1) & [] & $\mathbb{Q}$ \\ \hline $\mathdutchcal A{(19,192)_?}=\mathcal{A}(19,1)$ & (49,144,96) & $(21,18,6,0,4)$ & $(0^{4},4,0,15)$ & (24,14) & (12,4) & [ 1, 7, 11 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(19,200)_?}=\mathcal{A}(19,2)$ & (51,150,100) & $(21,18,6^{2})$ & $(0^{4},1,8,6,0,4)$ & (8,5) & (8,3) & [ 1, 9, 9 ] & $Q_{5}$ \\ $\mathdutchcal A{(19,192)_?}=\mathcal{A}(19,3)$ & (49,144,96) & $(24,12,6^{2},1)$ & $(0^{4},4,0,15)$ & (24,14) & (12,4) & [ 1, 7, 11 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(19,200)_?}=\mathcal{A}(19,4)$ & (51,150,100) & $(20^{2},6,4,1)$ & $(0^{4},4^{4},3)$ & (8,5) & (4,2) & [ 1, 9, 9 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(19,200)_?}=\mathcal{A}(19,5)$ & (51,150,100) & $(20^{2},6,4,1)$ & $(0^{4},4^{4},3)$ & (8,2) & (4,1) & [ 1, 9, 9 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(19,200)_?}=\mathcal{A}(19,6)$ & (51,150,100) & $(20^{2},6,4,1)$ & $(0^{4},6,0,6,4,3)$ & (8,5) & (4,2) & [ 1, 9, 9 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(19,204)_?}=\mathcal{A}(19,7)$ & (52,153,102) & $(21,15^{2},0,1)$ & $(0^{4},4,3^{2},6,3)$ & (12,4) & (6,1) & [] & $\mathbb{Q}$ \\ \hline $\mathdutchcal A{(20,220)_?}=\mathcal{A}(20,1)$ & (56,165,110) & $(10,45,0^{6},1)$ & $(0^{4},5^{2},0^{2},10)$ & (40,13) & (40,12) & [ 1, 9, 10 ] & $Q_{5}$ \\ $\mathdutchcal A{(20,220)_?}=\mathcal{A}(20,2)$ & (56,165,110) & $(25,15,10,6)$ & $(0^{5},5,10,0,5)$ & (20,4) & (20,3) & [ 1, 9, 10 ] & $Q_{5}$ \\ $\mathdutchcal A{(20,220)_?}=\mathcal{A}(20,3)$ & (56,165,110) & $(21,24,6,4,0,1)$ & $(0^{4},4,2,4,6,3,1)$ & (4,2) & (2,1) & [ 1, 9, 10 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(20,220)_?}=\mathcal{A}(20,4)$ & (56,165,110) & $(23,20,7,5,1)$ & $(0^{4},5,1,4^{2},6)$ & (4,2) & (2,1) & [ 1, 9, 10 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(20,216)_?}=\mathcal{A}(20,5)$ & (55,162,108) & $(20,26,4^{2},0^{2},1)$ & $(0^{3},2^{2},0,4,12)$ & (16,11) & (8,3) & [ 1, 8, 11 ] & $\mathbb{Z}$ \\ \hline $\mathdutchcal A{(21,240)_?}=\mathcal{A}(21,1)$ & (61,180,120) & $(15,40,5,0^{5},1)$ & $(0^{4},5,0,5,0,11)$ & (40,13) & (40,12) & [ 1, 9, 11 ] & $Q_{5}$ \\ $\mathdutchcal A{(21,240)_?}=\mathcal{A}(21,2)$ & (61,180,120) & $(30,10,15,6)$ & $(0^{6},15,0,6)$ & (120,35) & (120,34) & [ 1, 9, 11 ] & $Q_{5}$ \\ $\mathdutchcal A{(21,240)_?}=\mathcal{A}(21,3)$ & (61,180,120) & $(24^{2},9,0,4)$ & $(0^{4},6,0,3,0,12)$ & (48,48) & (24,12) & [ 1, 9, 11 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(21,240)_?}=\mathcal{A}(21,4)$ & (61,180,120) & $(22,28,6,4,0^{2},1)$ & $(0^{4},4,0,4,8,4,0,1)$ & (16,11) & (8,3) & [ 1, 9, 11 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(21,240)_?}=\mathcal{A}(21,5)$ & (61,180,120) & $(26,20,9,4,2)$ & $(0^{4},5,0,3,4,9)$ & (8,5) & (4,2) & [ 1, 9, 11 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(21,248)_?}=\mathcal{A}(21,6)$ & (63,186,124) & $(25,20,15,2,1)$ & $(0^{4},1,0,11,0,8,0,1)$ & (8,5) & (4,2) & [] & $\mathbb{Q}$ \\ $\mathdutchcal A{(21,252)_?}=\mathcal{A}(21,7)$ & (64,189,126) & $(24,22,15,3)$ & $(0^{6},12,0,6,3)$ & (12,4) & (6,1) & [] & $K_1$ \\ \hline $\mathdutchcal A{(22,264)_?}=\mathcal{A}(22,1)$ & (67,198,132) & $(11,55,0^{7},1)$ & $(0^{5},11,0^{3},11)$ & (44,3) & (110,1) & [ 1, 10, 11 ] & $Q_{11}$ \\ $\mathdutchcal A{(22,276)_?}=\mathcal{A}(22,2)$ & (70,207,138) & $(24,30,12,3,1)$ & $(0^{4},1,0,6,3,9,0,3)$ & (12,4) & (6,1) & [] & $\mathbb{Q}$ \\ $\mathdutchcal A{(22,264)_?}=\mathcal{A}(22,3)$ & (67,198,132) & $(27,28,0,12)$ & $(0^{6},12,0,9,0,1)$ & (12,4) & (12,4) & [ 1, 10, 11 ] & $Q_{5}$ \\ $\mathdutchcal A{(22,264)_?}=\mathcal{A}(22,4)$ & (67,198,132) & $(27,25,9,3^{2})$ & $(0^{4},4,0,6,0,6^{2})$ & (12,4) & (6,1) & [ 1, 10, 11 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(22,288)_?}=\mathcal{A}(22,5)$ & (73,216,144) & $(12,58,0^{2},3)$ & $(0^{7},12,6,0,4)$ & (48,48) & (48,48) & [] & $Q_{5}$ \\ \hline $\mathdutchcal A{(23,296)_?}=\mathcal{A}(23,1)$ & (75,222,148) & $(27,32,10,4,2)$ & $(0^{4},1,0,6,2,7,4,3)$ & (4,2) & (2,1) & [] & $\mathbb{Q}$ \\ $\mathdutchcal A{(23,304)_?}=\mathcal{A}(23,2)$ & (77,228,152) & $(16,56,2,0,1,2)$ & $(0^{6},1,8,10,0,4)$ & (16,11) & (16,11) & [] & $Q_{5}$ \\ \hline $\mathdutchcal A{(24,312)_?}=\mathcal{A}(24,1)$ & (79,234,156) & $(12,66,0^{8},1)$ & $(0^{5},6^{2},0^{3},12)$ & (48,36) & (48,38) & [ 1, 11, 12 ] & $Q_{12}$ \\ $\mathdutchcal A{(24,304)_?}=\mathcal{A}(24,2)$ & (77,228,152) & $(32^{2},0,12,0^{2},1)$ & $(0^{5},4,0^{2},20)$ & (32,39) & (32,43) & [] & $Q_{8}$ \\ $\mathdutchcal A{(24,316)_?}=\mathcal{A}(24,3)$ & (80,237,158) & $(31,32,9,5,3)$ & $(0^{4},1,0,6,1,6^{2},4)$ & (4,2) & (2,1) & [] & $\mathbb{Q}$ \\ $\mathdutchcal A{(24,320)_?}=\mathcal{A}(24,4)$ & (81,240,160) & $(20,54,4,0^{2},2,1)$ & $(0^{6},2,4,14,0,4)$ & (16,11) & (16,11) & [] & $Q_{5}$ \\ \hline $\mathdutchcal A{(25,336)_?}=\mathcal{A}(25,1)$ & (85,252,168) & $(18,60,6,0^{7},1)$ & $(0^{6},12,0^{3},13)$ & (48,36) & (48,38) & [ 1, 11, 13 ] & $Q_{12}$ \\ $\mathdutchcal A{(25,336)_?}=\mathcal{A}(25,2)$ & (85,252,168) & $(36,28,15,0,6)$ & $(0^{4},4,0,3,0,6,0,12)$ & (48,48) & (24,12) & [ 1, 11, 13 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(25,360)_?}=\mathcal{A}(25,3)$ & (91,270,180) & $(30,40,15,6)$ & $(0^{8},15,0,10)$ & (120,35) & (120,34) & [] & $Q_{5}$ \\ $\mathdutchcal A{(25,336)_?}=\mathcal{A}(25,4)$ & (85,252,168) & $(36,30,9,6,4)$ & $(0^{4},1,0,9,0,3,0,12)$ & (24,14) & (12,4) & [ 1, 11, 13 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(25,320)_?}=\mathcal{A}(25,5)$ & (81,240,160) & $(36,32,0,8,4,0,1)$ & $(0^{6},5,0,20)$ & (32,39) & (32,43) & [ 1, 9, 15 ] & $Q_{8}$ \\ $\mathdutchcal A{(25,336)_?}=\mathcal{A}(25,6)$ & (85,252,168) & $(36,30,9,6,4)$ & $(0^{4},1,0,6,0,6^{3})$ & (12,4) & (6,1) & [ 1, 11, 13 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(25,336)_?}=\mathcal{A}(25,7)$ & (85,252,168) & $(33,34,12,2,3,0,1)$ & $(0^{4},2,0,4^{3},0,11)$ & (8,5) & (4,2) & [ 1, 11, 13 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(25,336)_?}=\mathcal{A}(25,8)$ & (85,252,168) & $(24,52,6,0^{3},3)$ & $(0^{6},3,0,18,0,4)$ & (48,48) & (48,48) & [ 1, 11, 13 ] & $Q_{5}$ \\ \hline $\mathdutchcal A{(26,364)_?}=\mathcal{A}(26,1)$ & (92,273,182) & $(13,78,0^{9},1)$ & $(0^{6},13,0^{4},13)$ & (52,4) & (156,7) & [ 1, 12, 13 ] & $Q_{13}$ \\ $\mathdutchcal A{(26,380)_?}=\mathcal{A}(26,2)$ & (96,285,190) & $(35,40,10,11)$ & $(0^{8},11,5,10)$ & (20,4) & (20,3) & [] & $Q_{5}$ \\ $\mathdutchcal A{(26,364)_?}=\mathcal{A}(26,3)$ & (92,273,182) & $(37,36,9,6,3,1)$ & $(0^{4},1,0,7,2^{2},1,8,4,1)$ & (4,2) & (2,1) & [ 1, 12, 13 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(26,364)_?}=\mathcal{A}(26,4)$ & (92,273,182) & $(35,39,10,4,3,0,1)$ & $(0^{4},1^{2},4^{2},2^{2},7,4,1)$ & (4,2) & (2,1) & [ 1, 12, 13 ] & $\mathbb{Z}$ \\ \hline $\mathdutchcal A{(27,400)_?}=\mathcal{A}(27,1)$ & (101,300,200) & $(40^{2},6,14,1)$ & $(0^{8},8^{2},11)$ & (8,5) & (8,3) & [] & $Q_{5}$ \\ $\mathdutchcal A{(27,392)_?}=\mathcal{A}(27,2)$ & (99,294,196) & $(39,40,10,6,2^{2})$ & $(0^{4},1,0,5,4,1,2,4,8,2)$ & (4,2) & (2,1) & [ 1, 13, 13 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(27,392)_?}=\mathcal{A}(27,3)$ & (99,294,196) & $(39,40,10,6,2^{2})$ & $(0^{4},1,0,6,2^{3},5,6,3)$ & (4,2) & (2,1) & [ 1, 13, 13 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(27,392)_?}=\mathcal{A}(27,4)$ & (99,294,196) & $(38,42,9,6,3,0,1)$ & $(0^{4},1,0,5,4,2,0,7,4^{2})$ & (8,5) & (4,2) & [ 1, 13, 13 ] & $\mathbb{Z}$ \\ \hline $\mathdutchcal A{(28,420)_?}=\mathcal{A}(28,1)$ & (106,315,210) & $(14,91,0^{10},1)$ & $(0^{6},7^{2},0^{4},14)$ & (56,12) & (84,7) & [ 1, 13, 14 ] & $Q_{7}$ \\ $\mathdutchcal A{(28,420)_?}=\mathcal{A}(28,2)$ & (106,315,210) & $(45,40,3,15,3)$ & $(0^{8},6,9,13)$ & (12,4) & (6,1) & [ 1, 13, 14 ] & $Q_{5}$ \\ $\mathdutchcal A{(28,420)_?}=\mathcal{A}(28,3)$ & (106,315,210) & $(45,40,3,15,3)$ & $(0^{8},6,9,13)$ & (12,4) & (6,1) & [ 1, 13, 14 ] & $Q_{5}$ \\ $\mathdutchcal A{(28,420)_?}=\mathcal{A}(28,4)$ & (106,315,210) & $(41,44,11,6,2,1^{2})$ & $(0^{4},1,0,4^{2},2,1,4,6^{2})$ & (2,1) & (1,1) & [ 1, 13, 14 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(28,420)_?}=\mathcal{A}(28,5)$ & (106,315,210) & $(42^{2},12,6,1,3)$ & $(0^{4},1,0,4^{2},1,3,1,10,4)$ & (4,2) & (2,1) & [ 1, 13, 14 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(28,420)_?}=\mathcal{A}(28,6)$ & (106,315,210) & $(42^{2},12,6,1,3)$ & $(0^{4},1,0,6,0,3^{3},6^{2})$ & (12,4) & (6,1) & [ 1, 13, 14 ] & $\mathbb{Z}$ \\ \hline $\mathdutchcal A{(29,448)_?}=\mathcal{A}(29,1)$ & (113,336,224) & $(21,84,7,0^{9},1)$ & $(0^{6},7,0,7,0^{3},15)$ & (56,12) & (84,7) & [ 1, 13, 15 ] & $Q_{7}$ \\ $\mathdutchcal A{(29,440)_?}=\mathcal{A}(29,2)$ & (111,330,220) & $(50,40,1,14,6)$ & $(0^{8},5,8,16)$ & (8,5) & (8,3) & [] & $Q_{5}$ \\ $\mathdutchcal A{(29,448)_?}=\mathcal{A}(29,3)$ & (113,336,224) & $(44,46,13,6,2,0,2)$ & $(0^{4},1,0,3,4,3,0,4^{2},10)$ & (8,5) & (4,2) & [ 1, 13, 15 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(29,448)_?}=\mathcal{A}(29,4)$ & (113,336,224) & $(45,44,14,6,1,2,1)$ & $(0^{4},1,0,3,4,2^{2},1,8^{2})$ & (4,2) & (2,1) & [ 1, 13, 15 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(29,448)_?}=\mathcal{A}(29,5)$ & (113,336,224) & $(45,44,14,6,1,2,1)$ & $(0^{4},1,0,4,2,3,2^{2},6,9)$ & (4,2) & (2,1) & [ 1, 13, 15 ] & $\mathbb{Z}$ \\ \hline $\mathdutchcal A{(30,480)_?}=\mathcal{A}(30,1)$ & (121,360,240) & $(15,105,0^{11},1)$ & $(0^{7},15,0^{5},15)$ & (60,12) & (120,36) & [ 1, 14, 15 ] & $Q_{15}$ \\ $\mathdutchcal A{(30,460)_?}=\mathcal{A}(30,2)$ & (116,345,230) & $(55,40,0,11,10)$ & $(0^{8},5^{2},20)$ & (20,4) & (20,3) & [] & $Q_{5}$ \\ $\mathdutchcal A{(30,476)_?}=\mathcal{A}(30,3)$ & (120,357,238) & $(49,44,17,6,1^{2},2)$ & $(0^{4},1,0,3,2,4,1,2,4,13)$ & (4,2) & (2,1) & [ 1, 13, 16 ] & $\mathbb{Z}$ \\ \hline $\mathdutchcal A{(31,480)_?}=\mathcal{A}(31,1)$ & (121,360,240) & $(60,40,0,6,15)$ & $(0^{8},6,0,25)$ & (120,35) & (120,34) & [ 1, 11, 19 ] & $Q_{5}$ \\ $\mathdutchcal A{(31,504)_?}=\mathcal{A}(31,2)$ & (127,378,252) & $(54,42,21,6,1,0,3)$ & $(0^{4},1,0^{3},9,0,6,0,15)$ & (24,14) & (12,4) & [ 1, 13, 17 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(31,504)_?}=\mathcal{A}(31,3)$ & (127,378,252) & $(54,42,21,6,1,0,3)$ & $(0^{4},1,0,3,0,6,0,3,0,18)$ & (24,14) & (12,4) & [ 1, 13, 17 ] & $\mathbb{Z}$ \\ \hline $\mathdutchcal A{(32,544)_?}=\mathcal{A}(32,1)$ & (137,408,272) & $(16,120,0^{12},1)$ & $(0^{7},8^{2},0^{5},16)$ & (64,186) & (128,913) & [ 1, 15, 16 ] & $Q_{16}$ \\ \hline $\mathdutchcal A{(33,576)_?}=\mathcal{A}(33,1)$ & (145,432,288) & $(24,112,8,0^{11},1)$ & $(0^{8},16,0^{5},17)$ & (64,186) & (128,913) & [ 1, 15, 17 ] & $Q_{16}$ \\ \hline $\mathdutchcal A{(34,612)_?}=\mathcal{A}(34,1)$ & (154,459,306) & $(17,136,0^{13},1)$ & $(0^{8},17,0^{6},17)$ & (68,4) & (272,50) & [ 1, 16, 17 ] & $Q_{17}$ \\ $\mathdutchcal A{(34,612)_?}=\mathcal{A}(34,2)$ & (154,459,306) & $(60,63,18,6,4,0,3)$ & $(0^{6},3^{3},0,4,0,6,0,9,6)$ & (12,4) & (6,1) & [ 1, 16, 17 ] & $\mathbb{Z}$ \\ \hline $\mathdutchcal A{(35,680)_?}=\mathcal{A}(35,1)$ & (171,510,340) & $(70,55,25,21)$ & $(0^{12},25,0,10)$ & (20,4) & (20,4) & [] & $K_2$ \\ \hline $\mathdutchcal A{(36,684)_?}=\mathcal{A}(36,1)$ & (172,513,342) & $(18,153,0^{14},1)$ & $(0^{8},9^{2},0^{6},18)$ & (72,17) & (108,26) & [ 1, 17, 18 ] & $Q_{9}$ \\ \hline $\mathdutchcal A{(37,720)_?}=\mathcal{A}(37,1)$ & (181,540,360) & $(27,144,9,0^{13},1)$ & $(0^{8},9,0,9,0^{5},19)$ & (72,17) & (108,26) & [ 1, 17, 19 ] & $Q_{9}$ \\ $\mathdutchcal A{(37,720)_?}=\mathcal{A}(37,2)$ & (181,540,360) & $(72^{2},12,24,0^{6},1)$ & $(0^{10},13,0^{3},24)$ & (48,36) & (48,17) & [ 1, 17, 19 ] & $Q_{12}$ \\ $\mathdutchcal A{(37,720)_?}=\mathcal{A}(37,3)$ & (181,540,360) & $(72^{2},24,0,10,0,3)$ & $(0^{6},3,0,6,0,4,0^{3},12,0,12)$ & (48,48) & (24,12) & [ 1, 17, 19 ] & $\mathbb{Z}$ \\ \fi $\mathdutchcal A{(6,24)}=\mathcal{A}(6,1)$ & (7,18,12) & $(3,4)$ & $(0,6)$ & (48,48) & (24,12) & [ 1, 2, 3 ] & $\mathbb{Z}$ \\ \hline $\mathdutchcal A{(7,32)}=\mathcal{A}(7,1)$ & (9,24,16) & $(3,6)$ & $(0,4,3)$ & (48,48) & (24,12) & [ 1, 3, 3 ] & $\mathbb{Z}$ \\ \hline $\mathdutchcal A{(8,40)}=\mathcal{A}(8,1)$ & (11,30,20) & $(4,6,1)$ & $(0,2,6)$ & (16,11) & (8,3) & [ 1, 3, 4 ] & $\mathbb{Z}$ \\ \hline $\mathdutchcal A{(9,48)}=\mathcal{A}(9,1)$ & (13,36,24) & $(6,4,3)$ & $(0^{2},9)$ & (48,48) & (24,12) & [ 1, 3, 5 ] & $\mathbb{Z}$ \\ \hline $\mathdutchcal A{(10,60)_1}=\mathcal{A}(10,3)$ & (16,45,30) & $(6,7,3)$ & $(0,1,3,6)$ & (24,14) & (12,4) & [ 1, 4, 5 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(10,60)_2}=\mathcal{A}(10,2)$ & (16,45,30) & $(6,7,3)$ & $(0^{2},6,3,1)$ & (12,4) & (6,1) & [ 1, 4, 5 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(10,60)_3}=\mathcal{A}(10,1)$ & (16,45,30) & $(5,10,0,1)$ & $(0^{2},5^{2})$ & (20,4) & (20,3) & [ 1, 4, 5 ] & $Q_{5}$ \\ \hline $\mathdutchcal A{(11,72)}=\mathcal{A}(11,1)$ & (19,54,36) & $(7,8,4)$ & $(0^{2},4^{2},3)$ & (8,5) & (4,2) & [ 1, 5, 5 ] & $\mathbb{Z}$ \\ \hline $\mathdutchcal A{(12,84)_1}=\mathcal{A}(12,2)$ & (22,63,42) & $(8,10,3,1)$ & $(0^{2},3^{2},6)$ & (8,5) & (4,2) & [ 1, 5, 6 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(12,84)_2}=\mathcal{A}(12,3)$ & (22,63,42) & $(9,7,6)$ & $(0^{2},3^{2},6)$ & (12,4) & (6,1) & [ 1, 5, 6 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(12,84)_3}=\mathcal{A}(12,1)$ & (22,63,42) & $(6,15,0^{2},1)$ & $(0^{2},3^{2},6)$ & (24,14) & (12,4) & [ 1, 5, 6 ] & $\mathbb{Q}$ \\ \hline $\mathdutchcal A{(13,96)_1}=\mathcal{A}(13,1)$ & (25,72,48) & $(9,12,3,0,1)$ & $(0^{2},3,0,10)$ & (24,14) & (12,4) & [ 1, 5, 7 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(13,96)_2}=\mathcal{A}(13,3)$ & (25,72,48) & $(10^{2},3,2)$ & $(0^{2},1,4,8)$ & (8,5) & (4,2) & [ 1, 5, 7 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(13,96)_3}=\mathcal{A}(13,2)$ & (25,72,48) & $(12,4,9)$ & $(0^{2},3,0,10)$ & (48,48) & (24,12) & [ 1, 5, 7 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(13,104)}=\mathcal{A}(13,4)$ & (27,78,52) & $(6,18,3)$ & $(0^{4},13)$ & (24,13) & (24,12) & [] & $Q_{5}$ \\ \hline $\mathdutchcal A{(14,112)_1}=\mathcal{A}(14,2)$ & (29,84,56) & $(11,12,4,2)$ & $(0^{2},1,4^{3},1)$ & (4,2) & (2,1) & [ 1, 6, 7 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(14,112)_2}=\mathcal{A}(14,1)$ & (29,84,56) & $(7,21,0^{3},1)$ & $(0^{3},7,0,7)$ & (28,3) & (42,1) & [ 1, 6, 7 ] & $Q_{7}$ \\ $\mathdutchcal A{(14,112)_3}=\mathcal{A}(14,4)$ & (29,84,56) & $(10,14,4,0,1)$ & $(0^{3},4,6,4)$ & (8,5) & (8,3) & [ 1, 6, 7 ] & $Q_{5}$ \\ $\mathdutchcal A{(14,116)}=\mathcal{A}(14,3)$ & (30,87,58) & $(9,16,4,1)$ & $(0^{4},11,3)$ & (4,2) & (4,2) & [] & $Q_{5}$ \\ \hline $\mathdutchcal A{(15,120)}=\mathcal{A}(15,1)$ & (31,90,60) & $(15,10,0,6)$ & $(0^{4},15)$ & (120,35) & (120,34) & [ 1, 5, 9 ] & $Q_{5}$ \\ $\mathdutchcal A{(15,128)_1}=\mathcal{A}(15,2)$ & (33,96,64) & $(13,12,6,2)$ & $(0^{2},1,4,2,4^{2})$ & (16,11) & (8,3) & [ 1, 7, 7 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(15,128)_2}=\mathcal{A}(15,4)$ & (33,96,64) & $(12,14,6,0,1)$ & $(0^{4},10,4,1)$ & (8,5) & (8,3) & [ 1, 7, 7 ] & $Q_{5}$ \\ $\mathdutchcal A{(15,132)_1}=\mathcal{A}(15,5)$ & (34,99,66) & $(9,22,0,3)$ & $(0^{4},9,3^{2})$ & (12,4) & (6,1) & [] & $K_1$ \\ $\mathdutchcal A{(15,132)_2}=\mathcal{A}(15,3)$ & (34,99,66) & $(12,13,9)$ & $(0^{4},9,3^{2})$ & (12,4) & (6,1) & [] & $\mathbb{Q}$ \\ \hline $\mathdutchcal A{(16,140)}=\mathcal{A}(16,4)$ & (36,105,70) & $(15^{2},0,6)$ & $(0^{4},10,5,0^{2},1)$ & (20,4) & (20,3) & [ 1, 6, 9 ] & $Q_{5}$ \\ $\mathdutchcal A{(16,144)_1}=\mathcal{A}(16,2)$ & (37,108,72) & $(14,15,6,1^{2})$ & $(0^{2},1,2,4,2,7)$ & (8,5) & (4,2) & [ 1, 7, 8 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(16,144)_2}=\mathcal{A}(16,3)$ & (37,108,72) & $(15,13,6,3)$ & $(0^{4},10,0,6)$ & (12,4) & (6,1) & [ 1, 7, 8 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(16,144)_3}=\mathcal{A}(16,1)$ & (37,108,72) & $(8,28,0^{4},1)$ & $(0^{3},4^{2},0,8)$ & (32,39) & (32,43) & [ 1, 7, 8 ] & $Q_{8}$ \\ $\mathdutchcal A{(16,144)_4}=\mathcal{A}(16,6)$ & (37,108,72) & $(15,12,9,0,1)$ & $(0^{4},7,6,3)$ & (12,4) & (6,1) & [ 1, 7, 8 ] & $\mathbb{Q}$ \\ $\mathdutchcal A{(16,144)_5}=\mathcal{A}(16,5)$ & (37,108,72) & $(14,16,3,4)$ & $(0^{3},2,4,8,0,2)$ & (8,5) & (8,3) & [ 1, 7, 8 ] & $Q_{5}$ \\ $\mathdutchcal A{(16,148)}=\mathcal{A}(16,7)$ & (38,111,74) & $(12,19,6,0,1)$ & $(0^{3},3^{2},2,8)$ & (8,5) & (4,2) & [] & $\mathbb{Q}$ \\ \hline $\mathdutchcal A{(17,160)_1}=\mathcal{A}(17,2)$ & (41,120,80) & $(16^{2},7,0,2)$ & $(0^{2},1,0,6,0,10)$ & (16,11) & (8,3) & [ 1, 7, 9 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(17,160)_2}=\mathcal{A}(17,4)$ & (41,120,80) & $(16^{2},7,0,2)$ & $(0^{2},1,0,6,0,10)$ & (16,11) & (8,3) & [ 1, 7, 9 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(17,160)_3}=\mathcal{A}(17,3)$ & (41,120,80) & $(18,12,7,4)$ & $(0^{4},8,0,9)$ & (16,11) & (8,3) & [ 1, 7, 9 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(17,160)_4}=\mathcal{A}(17,1)$ & (41,120,80) & $(12,24,4,0^{3},1)$ & $(0^{4},8,0,9)$ & (32,39) & (32,43) & [ 1, 7, 9 ] & $Q_{8}$ \\ $\mathdutchcal A{(17,160)_5}=\mathcal{A}(17,5)$ & (41,120,80) & $(16,18,1,6)$ & $(0^{4},6,8,1,0,2)$ & (8,5) & (8,3) & [ 1, 7, 9 ] & $Q_{5}$ \\ $\mathdutchcal A{(17,164)}=\mathcal{A}(17,6)$ & (42,123,82) & $(16,15,10,0,1)$ & $(0^{4},6,3,7,0,1)$ & (4,2) & (2,1) & [] & $\mathbb{Q}$ \\ $\mathdutchcal A{(17,168)_1}=\mathcal{A}(17,7)$ & (43,126,84) & $(13,22,7,0,1)$ & $(0^{4},6,0,10,0,1)$ & (8,5) & (4,2) & [] & $\mathbb{Q}$ \\ $\mathdutchcal A{(17,168)_2}=\mathcal{A}(17,8)$ & (43,126,84) & $(14,20,7,2)$ & $(0^{4},1,8^{2})$ & (8,5) & (8,3) & [] & $Q_{8}$ \\ \hline $\mathdutchcal A{(18,180)_1}=\mathcal{A}(18,7)$ & (46,135,90) & $(18^{2},6,3,1)$ & $(0^{3},3^{2},0,6^{2})$ & (12,4) & (6,1) & [ 1, 8, 9 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(18,180)_2}=\mathcal{A}(18,3)$ & (46,135,90) & $(19,16,6,5)$ & $(0^{4},6,2,6,3,1)$ & (4,2) & (2,1) & [ 1, 8, 9 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(18,180)_3}=\mathcal{A}(18,1)$ & (46,135,90) & $(9,36,0^{5},1)$ & $(0^{4},9,0^{2},9)$ & (36,4) & (54,6) & [ 1, 8, 9 ] & $Q_{9}$ \\ $\mathdutchcal A{(18,180)_4}=\mathcal{A}(18,2)$ & (46,135,90) & $(18^{2},6,3,1)$ & $(0^{4},3^{2},12)$ & (24,14) & (12,4) & [ 1, 8, 9 ] & $\mathbb{Q}$ \\ $\mathdutchcal A{(18,180)_5}=\mathcal{A}(18,4)$ & (46,135,90) & $(18,19,3,6)$ & $(0^{4},3,9,3,0,3)$ & (12,4) & (6,1) & [ 1, 8, 9 ] & $Q_{5}$ \\ $\mathdutchcal A{(18,180)_6}=\mathcal{A}(18,5)$ & (46,135,90) & $(18,19,3,6)$ & $(0^{4},3,9,3,0,3)$ & (12,4) & (6,1) & [ 1, 8, 9 ] & $Q_{5}$ \\ $\mathdutchcal A{(18,184)_1}=\mathcal{A}(18,6)$ & (47,138,92) & $(18,16,12,0,1)$ & $(0^{4},5,2,7,2^{2})$ & (4,2) & (2,1) & [] & $\mathbb{Q}$ \\ $\mathdutchcal A{(18,184)_2}=\mathcal{A}(18,8)$ & (47,138,92) & $(16,22,6,2,1)$ & $(0^{4},6,0,7,4,1)$ & (4,2) & (2,1) & [] & $\mathbb{Q}$ \\ \hline $\mathdutchcal A{(19,192)_1}=\mathcal{A}(19,1)$ & (49,144,96) & $(21,18,6,0,4)$ & $(0^{4},4,0,15)$ & (24,14) & (12,4) & [ 1, 7, 11 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(19,192)_2}=\mathcal{A}(19,3)$ & (49,144,96) & $(24,12,6^{2},1)$ & $(0^{4},4,0,15)$ & (24,14) & (12,4) & [ 1, 7, 11 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(19,200)_1}=\mathcal{A}(19,4)$ & (51,150,100) & $(20^{2},6,4,1)$ & $(0^{4},4^{4},3)$ & (8,5) & (4,2) & [ 1, 9, 9 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(19,200)_2}=\mathcal{A}(19,5)$ & (51,150,100) & $(20^{2},6,4,1)$ & $(0^{4},4^{4},3)$ & (8,2) & (4,1) & [ 1, 9, 9 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(19,200)_3}=\mathcal{A}(19,6)$ & (51,150,100) & $(20^{2},6,4,1)$ & $(0^{4},6,0,6,4,3)$ & (8,5) & (4,2) & [ 1, 9, 9 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(19,200)_4}=\mathcal{A}(19,2)$ & (51,150,100) & $(21,18,6^{2})$ & $(0^{4},1,8,6,0,4)$ & (8,5) & (8,3) & [ 1, 9, 9 ] & $Q_{5}$ \\ $\mathdutchcal A{(19,204)}=\mathcal{A}(19,7)$ & (52,153,102) & $(21,15^{2},0,1)$ & $(0^{4},4,3^{2},6,3)$ & (12,4) & (6,1) & [] & $\mathbb{Q}$ \\ \hline $\mathdutchcal A{(20,216)}=\mathcal{A}(20,5)$ & (55,162,108) & $(20,26,4^{2},0^{2},1)$ & $(0^{3},2^{2},0,4,12)$ & (16,11) & (8,3) & [ 1, 8, 11 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(20,220)_1}=\mathcal{A}(20,3)$ & (56,165,110) & $(21,24,6,4,0,1)$ & $(0^{4},4,2,4,6,3,1)$ & (4,2) & (2,1) & [ 1, 9, 10 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(20,220)_2}=\mathcal{A}(20,4)$ & (56,165,110) & $(23,20,7,5,1)$ & $(0^{4},5,1,4^{2},6)$ & (4,2) & (2,1) & [ 1, 9, 10 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(20,220)_3}=\mathcal{A}(20,1)$ & (56,165,110) & $(10,45,0^{6},1)$ & $(0^{4},5^{2},0^{2},10)$ & (40,13) & (40,12) & [ 1, 9, 10 ] & $Q_{5}$ \\ $\mathdutchcal A{(20,220)_4}=\mathcal{A}(20,2)$ & (56,165,110) & $(25,15,10,6)$ & $(0^{5},5,10,0,5)$ & (20,4) & (20,3) & [ 1, 9, 10 ] & $Q_{5}$ \\ \hline $\mathdutchcal A{(21,240)_1}=\mathcal{A}(21,4)$ & (61,180,120) & $(22,28,6,4,0^{2},1)$ & $(0^{4},4,0,4,8,4,0,1)$ & (16,11) & (8,3) & [ 1, 9, 11 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(21,240)_2}=\mathcal{A}(21,5)$ & (61,180,120) & $(26,20,9,4,2)$ & $(0^{4},5,0,3,4,9)$ & (8,5) & (4,2) & [ 1, 9, 11 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(21,240)_3}=\mathcal{A}(21,3)$ & (61,180,120) & $(24^{2},9,0,4)$ & $(0^{4},6,0,3,0,12)$ & (48,48) & (24,12) & [ 1, 9, 11 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(21,240)_4}=\mathcal{A}(21,1)$ & (61,180,120) & $(15,40,5,0^{5},1)$ & $(0^{4},5,0,5,0,11)$ & (40,13) & (40,12) & [ 1, 9, 11 ] & $Q_{5}$ \\ $\mathdutchcal A{(21,240)_5}=\mathcal{A}(21,2)$ & (61,180,120) & $(30,10,15,6)$ & $(0^{6},15,0,6)$ & (120,35) & (120,34) & [ 1, 9, 11 ] & $Q_{5}$ \\ $\mathdutchcal A{(21,248)}=\mathcal{A}(21,6)$ & (63,186,124) & $(25,20,15,2,1)$ & $(0^{4},1,0,11,0,8,0,1)$ & (8,5) & (4,2) & [] & $\mathbb{Q}$ \\ $\mathdutchcal A{(21,252)}=\mathcal{A}(21,7)$ & (64,189,126) & $(24,22,15,3)$ & $(0^{6},12,0,6,3)$ & (12,4) & (6,1) & [] & $K_1$ \\ \hline $\mathdutchcal A{(22,264)_1}=\mathcal{A}(22,4)$ & (67,198,132) & $(27,25,9,3^{2})$ & $(0^{4},4,0,6,0,6^{2})$ & (12,4) & (6,1) & [ 1, 10, 11 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(22,264)_2}=\mathcal{A}(22,1)$ & (67,198,132) & $(11,55,0^{7},1)$ & $(0^{5},11,0^{3},11)$ & (44,3) & (110,1) & [ 1, 10, 11 ] & $Q_{11}$ \\ $\mathdutchcal A{(22,264)_3}=\mathcal{A}(22,3)$ & (67,198,132) & $(27,28,0,12)$ & $(0^{6},12,0,9,0,1)$ & (12,4) & (12,4) & [ 1, 10, 11 ] & $Q_{5}$ \\ $\mathdutchcal A{(22,276)}=\mathcal{A}(22,2)$ & (70,207,138) & $(24,30,12,3,1)$ & $(0^{4},1,0,6,3,9,0,3)$ & (12,4) & (6,1) & [] & $\mathbb{Q}$ \\ $\mathdutchcal A{(22,288)}=\mathcal{A}(22,5)$ & (73,216,144) & $(12,58,0^{2},3)$ & $(0^{7},12,6,0,4)$ & (48,48) & (48,48) & [] & $Q_{5}$ \\ \hline $\mathdutchcal A{(23,296)}=\mathcal{A}(23,1)$ & (75,222,148) & $(27,32,10,4,2)$ & $(0^{4},1,0,6,2,7,4,3)$ & (4,2) & (2,1) & [] & $\mathbb{Q}$ \\ $\mathdutchcal A{(23,304)}=\mathcal{A}(23,2)$ & (77,228,152) & $(16,56,2,0,1,2)$ & $(0^{6},1,8,10,0,4)$ & (16,11) & (16,11) & [] & $Q_{5}$ \\ \hline $\mathdutchcal A{(24,304)}=\mathcal{A}(24,2)$ & (77,228,152) & $(32^{2},0,12,0^{2},1)$ & $(0^{5},4,0^{2},20)$ & (32,39) & (32,43) & [] & $Q_{8}$ \\ $\mathdutchcal A{(24,312)}=\mathcal{A}(24,1)$ & (79,234,156) & $(12,66,0^{8},1)$ & $(0^{5},6^{2},0^{3},12)$ & (48,36) & (48,38) & [ 1, 11, 12 ] & $Q_{12}$ \\ $\mathdutchcal A{(24,316)}=\mathcal{A}(24,3)$ & (80,237,158) & $(31,32,9,5,3)$ & $(0^{4},1,0,6,1,6^{2},4)$ & (4,2) & (2,1) & [] & $\mathbb{Q}$ \\ $\mathdutchcal A{(24,320)}=\mathcal{A}(24,4)$ & (81,240,160) & $(20,54,4,0^{2},2,1)$ & $(0^{6},2,4,14,0,4)$ & (16,11) & (16,11) & [] & $Q_{5}$ \\ \hline $\mathdutchcal A{(25,320)}=\mathcal{A}(25,5)$ & (81,240,160) & $(36,32,0,8,4,0,1)$ & $(0^{6},5,0,20)$ & (32,39) & (32,43) & [ 1, 9, 15 ] & $Q_{8}$ \\ $\mathdutchcal A{(25,336)_1}=\mathcal{A}(25,7)$ & (85,252,168) & $(33,34,12,2,3,0,1)$ & $(0^{4},2,0,4^{3},0,11)$ & (8,5) & (4,2) & [ 1, 11, 13 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(25,336)_2}=\mathcal{A}(25,4)$ & (85,252,168) & $(36,30,9,6,4)$ & $(0^{4},1,0,9,0,3,0,12)$ & (24,14) & (12,4) & [ 1, 11, 13 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(25,336)_3}=\mathcal{A}(25,6)$ & (85,252,168) & $(36,30,9,6,4)$ & $(0^{4},1,0,6,0,6^{3})$ & (12,4) & (6,1) & [ 1, 11, 13 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(25,336)_4}=\mathcal{A}(25,2)$ & (85,252,168) & $(36,28,15,0,6)$ & $(0^{4},4,0,3,0,6,0,12)$ & (48,48) & (24,12) & [ 1, 11, 13 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(25,336)_5}=\mathcal{A}(25,1)$ & (85,252,168) & $(18,60,6,0^{7},1)$ & $(0^{6},12,0^{3},13)$ & (48,36) & (48,38) & [ 1, 11, 13 ] & $Q_{12}$ \\ $\mathdutchcal A{(25,336)_6}=\mathcal{A}(25,8)$ & (85,252,168) & $(24,52,6,0^{3},3)$ & $(0^{6},3,0,18,0,4)$ & (48,48) & (48,48) & [ 1, 11, 13 ] & $Q_{5}$ \\ $\mathdutchcal A{(25,360)}=\mathcal{A}(25,3)$ & (91,270,180) & $(30,40,15,6)$ & $(0^{8},15,0,10)$ & (120,35) & (120,34) & [] & $Q_{5}$ \\ \hline $\mathdutchcal A{(26,364)_1}=\mathcal{A}(26,4)$ & (92,273,182) & $(35,39,10,4,3,0,1)$ & $(0^{4},1^{2},4^{2},2^{2},7,4,1)$ & (4,2) & (2,1) & [ 1, 12, 13 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(26,364)_2}=\mathcal{A}(26,3)$ & (92,273,182) & $(37,36,9,6,3,1)$ & $(0^{4},1,0,7,2^{2},1,8,4,1)$ & (4,2) & (2,1) & [ 1, 12, 13 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(26,364)_3}=\mathcal{A}(26,1)$ & (92,273,182) & $(13,78,0^{9},1)$ & $(0^{6},13,0^{4},13)$ & (52,4) & (156,7) & [ 1, 12, 13 ] & $Q_{13}$ \\ $\mathdutchcal A{(26,380)}=\mathcal{A}(26,2)$ & (96,285,190) & $(35,40,10,11)$ & $(0^{8},11,5,10)$ & (20,4) & (20,3) & [] & $Q_{5}$ \\ \hline $\mathdutchcal A{(27,392)_1}=\mathcal{A}(27,4)$ & (99,294,196) & $(38,42,9,6,3,0,1)$ & $(0^{4},1,0,5,4,2,0,7,4^{2})$ & (8,5) & (4,2) & [ 1, 13, 13 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(27,392)_2}=\mathcal{A}(27,3)$ & (99,294,196) & $(39,40,10,6,2^{2})$ & $(0^{4},1,0,6,2^{3},5,6,3)$ & (4,2) & (2,1) & [ 1, 13, 13 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(27,392)_3}=\mathcal{A}(27,2)$ & (99,294,196) & $(39,40,10,6,2^{2})$ & $(0^{4},1,0,5,4,1,2,4,8,2)$ & (4,2) & (2,1) & [ 1, 13, 13 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(27,400)}=\mathcal{A}(27,1)$ & (101,300,200) & $(40^{2},6,14,1)$ & $(0^{8},8^{2},11)$ & (8,5) & (8,3) & [] & $Q_{5}$ \\ \hline $\mathdutchcal A{(28,420)_1}=\mathcal{A}(28,4)$ & (106,315,210) & $(41,44,11,6,2,1^{2})$ & $(0^{4},1,0,4^{2},2,1,4,6^{2})$ & (2,1) & (1,1) & [ 1, 13, 14 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(28,420)_2}=\mathcal{A}(28,5)$ & (106,315,210) & $(42^{2},12,6,1,3)$ & $(0^{4},1,0,4^{2},1,3,1,10,4)$ & (4,2) & (2,1) & [ 1, 13, 14 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(28,420)_3}=\mathcal{A}(28,6)$ & (106,315,210) & $(42^{2},12,6,1,3)$ & $(0^{4},1,0,6,0,3^{3},6^{2})$ & (12,4) & (6,1) & [ 1, 13, 14 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(28,420)_4}=\mathcal{A}(28,1)$ & (106,315,210) & $(14,91,0^{10},1)$ & $(0^{6},7^{2},0^{4},14)$ & (56,12) & (84,7) & [ 1, 13, 14 ] & $Q_{7}$ \\ $\mathdutchcal A{(28,420)_5}=\mathcal{A}(28,2)$ & (106,315,210) & $(45,40,3,15,3)$ & $(0^{8},6,9,13)$ & (12,4) & (6,1) & [ 1, 13, 14 ] & $Q_{5}$ \\ $\mathdutchcal A{(28,420)_6}=\mathcal{A}(28,3)$ & (106,315,210) & $(45,40,3,15,3)$ & $(0^{8},6,9,13)$ & (12,4) & (6,1) & [ 1, 13, 14 ] & $Q_{5}$ \\ \hline $\mathdutchcal A{(29,440)}=\mathcal{A}(29,2)$ & (111,330,220) & $(50,40,1,14,6)$ & $(0^{8},5,8,16)$ & (8,5) & (8,3) & [] & $Q_{5}$ \\ $\mathdutchcal A{(29,448)_1}=\mathcal{A}(29,3)$ & (113,336,224) & $(44,46,13,6,2,0,2)$ & $(0^{4},1,0,3,4,3,0,4^{2},10)$ & (8,5) & (4,2) & [ 1, 13, 15 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(29,448)_2}=\mathcal{A}(29,4)$ & (113,336,224) & $(45,44,14,6,1,2,1)$ & $(0^{4},1,0,3,4,2^{2},1,8^{2})$ & (4,2) & (2,1) & [ 1, 13, 15 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(29,448)_3}=\mathcal{A}(29,5)$ & (113,336,224) & $(45,44,14,6,1,2,1)$ & $(0^{4},1,0,4,2,3,2^{2},6,9)$ & (4,2) & (2,1) & [ 1, 13, 15 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(29,448)_4}=\mathcal{A}(29,1)$ & (113,336,224) & $(21,84,7,0^{9},1)$ & $(0^{6},7,0,7,0^{3},15)$ & (56,12) & (84,7) & [ 1, 13, 15 ] & $Q_{7}$ \\ \hline $\mathdutchcal A{(30,460)}=\mathcal{A}(30,2)$ & (116,345,230) & $(55,40,0,11,10)$ & $(0^{8},5^{2},20)$ & (20,4) & (20,3) & [] & $Q_{5}$ \\ $\mathdutchcal A{(30,476)}=\mathcal{A}(30,3)$ & (120,357,238) & $(49,44,17,6,1^{2},2)$ & $(0^{4},1,0,3,2,4,1,2,4,13)$ & (4,2) & (2,1) & [ 1, 13, 16 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(30,480)}=\mathcal{A}(30,1)$ & (121,360,240) & $(15,105,0^{11},1)$ & $(0^{7},15,0^{5},15)$ & (60,12) & (120,36) & [ 1, 14, 15 ] & $Q_{15}$ \\ \hline $\mathdutchcal A{(31,480)}=\mathcal{A}(31,1)$ & (121,360,240) & $(60,40,0,6,15)$ & $(0^{8},6,0,25)$ & (120,35) & (120,34) & [ 1, 11, 19 ] & $Q_{5}$ \\ $\mathdutchcal A{(31,504)_1}=\mathcal{A}(31,2)$ & (127,378,252) & $(54,42,21,6,1,0,3)$ & $(0^{4},1,0^{3},9,0,6,0,15)$ & (24,14) & (12,4) & [ 1, 13, 17 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(31,504)_2}=\mathcal{A}(31,3)$ & (127,378,252) & $(54,42,21,6,1,0,3)$ & $(0^{4},1,0,3,0,6,0,3,0,18)$ & (24,14) & (12,4) & [ 1, 13, 17 ] & $\mathbb{Z}$ \\ \hline $\mathdutchcal A{(32,544)}=\mathcal{A}(32,1)$ & (137,408,272) & $(16,120,0^{12},1)$ & $(0^{7},8^{2},0^{5},16)$ & (64,186) & (128,913) & [ 1, 15, 16 ] & $Q_{16}$ \\ \hline $\mathdutchcal A{(33,576)}=\mathcal{A}(33,1)$ & (145,432,288) & $(24,112,8,0^{11},1)$ & $(0^{8},16,0^{5},17)$ & (64,186) & (128,913) & [ 1, 15, 17 ] & $Q_{16}$ \\ \hline $\mathdutchcal A{(34,612)_1}=\mathcal{A}(34,2)$ & (154,459,306) & $(60,63,18,6,4,0,3)$ & $(0^{6},3^{3},0,4,0,6,0,9,6)$ & (12,4) & (6,1) & [ 1, 16, 17 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(34,612)_2}=\mathcal{A}(34,1)$ & (154,459,306) & $(17,136,0^{13},1)$ & $(0^{8},17,0^{6},17)$ & (68,4) & (272,50) & [ 1, 16, 17 ] & $Q_{17}$ \\ \hline $\mathdutchcal A{(35,680)}=\mathcal{A}(35,1)$ & (171,510,340) & $(70,55,25,21)$ & $(0^{12},25,0,10)$ & (20,4) & (20,4) & [] & $K_2$ \\ \hline $\mathdutchcal A{(36,684)}=\mathcal{A}(36,1)$ & (172,513,342) & $(18,153,0^{14},1)$ & $(0^{8},9^{2},0^{6},18)$ & (72,17) & (108,26) & [ 1, 17, 18 ] & $Q_{9}$ \\ \hline $\mathdutchcal A{(37,720)_1}=\mathcal{A}(37,3)$ & (181,540,360) & $(72^{2},24,0,10,0,3)$ & $(0^{6},3,0,6,0,4,0^{3},12,0,12)$ & (48,48) & (24,12) & [ 1, 17, 19 ] & $\mathbb{Z}$ \\ $\mathdutchcal A{(37,720)_2}=\mathcal{A}(37,1)$ & (181,540,360) & $(27,144,9,0^{13},1)$ & $(0^{8},9,0,9,0^{5},19)$ & (72,17) & (108,26) & [ 1, 17, 19 ] & $Q_{9}$ \\ $\mathdutchcal A{(37,720)_3}=\mathcal{A}(37,2)$ & (181,540,360) & $(72^{2},12,24,0^{6},1)$ & $(0^{10},13,0^{3},24)$ & (48,36) & (48,17) & [ 1, 17, 19 ] & $Q_{12}$ \\ \hline & & \\ \caption{Invariants for the known simplicial arrangements of rank $3$ with up to $37$ lines.} \label{tab:invariants} \end{longtable}} \clearpage \newcommand{\etalchar}[1]{$^{#1}$} \providecommand{\bysame}{\leavevmode\hbox to3em{\hrulefill}\thinspace} \providecommand{\MR}{\relax\ifhmode\unskip\space\fi MR } \providecommand{\MRhref}[2]{% \href{http://www.ams.org/mathscinet-getitem?mr=#1}{#2} } \providecommand{\href}[2]{#2}	{ "redpajama_set_name": "RedPajamaArXiv" }	474
One Dozen Berrys är ett musikalbum av Chuck Berry, utgivet 1958 på skivbolaget Chess. Här finns lite av varje, hitsinglarna "Sweet Little Sixteen" och "Rock and Roll Music", den kända "Reelin' and Rockin' ", ballader, blues och även latininspirerad musik. Låtlista Alla låtar skrivna av Chuck Berry. "Sweet Little Sixteen" "Blue Feeling" "La Jaunda (Espanola)" "Rockin' at the Philharmonic" "Oh Baby Doll" "Guitar Boogie" "Reelin' and Rockin'" "In-Go" "Rock and Roll Music" "How You've Changed" "Low Feeling" "It Don't Take But a Few Minutes" Medverkande Chuck Berry - gitarr, sång Fred Below - trummor Ebbie Hardy - trummor Willie Dixon - bas Johnnie Johnson - piano Lafayette Leake - piano Hubert Sumlin - gitarr Musikalbum 1958 Album av Chuck Berry	{ "redpajama_set_name": "RedPajamaWikipedia" }	3,668
Kapu var ett hawaiiskt tabu, att bryta emot det, även om det var oavsiktligt, ledde oftast till omedelbar död. Ordet är hawaiiska och betyder "förbjudet". Det mest kända förbudet var kontakt med hövdingar eller kungar. Det var exempelvis förbjudet att gå in i en hövdings privata område, att komma i kontakt med hans hår eller naglar, att titta rakt på honom och hålla huvudet ovanför honom. Det var också förbjudet att bära röda och gula fjädrar, då dessa ansågs som kungliga. Platser som ansågs som kapu symboliserades ofta med två korsade stavar, med en vit boll ovanpå var och en. Kapusystemet reglerade också kontakt mellan män och kvinnor. Framförallt fick män och kvinnor inte äta tillsammans, och vissa typer av mat såsom fläsk, vissa typer av bananer (då de liknade fallossymboler) och kokosnötter var förbjudna för kvinnor. Kapusystemet nyttjades fram till 1819, då kung Kamehameha II avskaffade det genom att äta en symbolisk middag bestående av förbjuden mat tillsammans med kvinnorna vid hovet (sin moder Keopuolani och sin faders drottning Kaahumanu). Kapu användes även för att reglera fiske i Hawaii för att garantera fortlevnad av fiskarter kring öarna under 1700- och 1800-talen. Vissa fiskar och/eller områden var förbjudna då överfiske kunde skada omgivningen. Dessa regler påminner om dagens fiske- och jaktrestriktioner. Lagar Mat och dryck inom religion	{ "redpajama_set_name": "RedPajamaWikipedia" }	2,913
Q: How to inject an service into module in my case? I am trying to inject an old angular 1.5 service into my angular 4 module in my angular 1.5/4 hybrid app. The MyService uses a static method because if I make it a public, I have no way to initial it with new MyService() because MyService expects a param that I don't know how to provide. My class (my-service.class.ts) import {Inject, Injectable} from '@angular/core'; @Injectable() class MyService { constructor( @Inject('myOldService') private myOldService: any) {} static getMyUrl() { console.log(this.myOldService); // complains // Property 'myOldService' does not exist on type 'typeof MyService return this.myOldService.getItemUrl(); } } export default MyService; My module import { CommonModule } from '@angular/common'; import { NgModule } from '@angular/core'; ...other import.. import MyService from './my-service.class'; console.log(MyService.getMyUrl()) //has error because getMyUrl has error. @NgModule({ 'imports': [ CommonModule ], 'declarations': [ MyComponent ], 'providers': [ MyService ] }) export class MyModule {} Basically I am not sure how to inejct my old service into a static method. Any helps? Thanks a lot! A: If you need to run code only when a module is loaded. You place that code inside the constructor of the module. You have to inject your service into the constructor of the MyModule export class MyModule { constructor(MyService service) { console.log(service.getMyUrl()); } } You also have to remove static from the service. Don't use static methods with injectable services.	{ "redpajama_set_name": "RedPajamaStackExchange" }	3,964
namespace java.util.concurrent { public partial interface Delayed : global::java.lang.Comparable<Delayed> { long getDelay(TimeUnit prm1); } }	{ "redpajama_set_name": "RedPajamaGithub" }	7,684
Q: Mockery __call() has a different signature I'm using Mockery to mock a class with a __call() magic method. The problem is my mocked object has __call() with a different signature to the real class and I get this error: ErrorException: Declaration of Mockery_10_EpiTwitter::__call() should be compatible with EpiTwitter::__call($name, $params = NULL) The following is my mocking procedure: $mock = Mockery::mock('EpiTwitter')->shouldReceive('useAPIVersion')->once()->with('1.1')->mock(); I also tried to make a partial mock but the above error still appears. A: The error is caused by the E_STRICT error level, that does not allow child methods with different arguments or access level than their parents.	{ "redpajama_set_name": "RedPajamaStackExchange" }	1,068
Louis Lamothe, född den 23 april 1822 i Lyon, död den 15 december 1869 i Paris, var en fransk målare. Lamothe var läromästare för många framstående konstnärer, exempelvis Edgar Degas, James Tissot, Jules-Élie Delaunay, Henri Lerolle och Henri Regnault. Själv var han lärjunge till Hippolyte Flandrin och Jean-Auguste-Dominique Ingres. Källor Franska målare Personer från Lyon Födda 1822 Avlidna 1869 Män	{ "redpajama_set_name": "RedPajamaWikipedia" }	2,129
<?xml version="1.0" encoding="utf-8"?> <RelativeLayout xmlns:android="http://schemas.android.com/apk/res/android" android:layout_width="match_parent" android:layout_height="match_parent"> <TextView android:layout_width="match_parent" android:layout_height="wrap_content" android:textAppearance="?android:attr/textAppearanceSmall" android:fontFamily="sans-serif-light" android:text="@string/time1" android:id="@+id/valueText" android:layout_marginTop="3dp" android:layout_marginBottom="3dp" android:gravity="center_horizontal"/> <View android:id="@+id/lineTop" android:layout_width="fill_parent" android:layout_height="0dp" android:background="@color/light_grey" android:layout_below="@id/valueText"/> <ImageView android:layout_width="match_parent" android:layout_height="@dimen/row_height" android:scaleType="centerInside" android:id="@+id/gustImage" android:layout_below="@id/lineTop" android:src="@drawable/wind_icon_0" android:layout_marginTop="6dp" android:layout_marginBottom="6dp" android:adjustViewBounds="true" /> <TextSwitcher android:layout_width="match_parent" android:layout_height="wrap_content" android:textAppearance="?android:attr/textAppearanceMedium" android:textColor="?android:textColorPrimaryInverse" android:textStyle="bold" android:id="@+id/gustSpeedSwitcher" android:gravity="center_vertical\|center_horizontal" android:layout_alignTop="@id/gustImage" android:layout_alignBottom="@id/gustImage" android:adjustViewBounds="true" /> <TextView android:layout_width="match_parent" android:layout_height="wrap_content" android:id="@+id/direction" android:text="0" android:gravity="center_vertical\|center_horizontal" android:layout_alignTop="@id/gustImage" android:layout_alignBottom="@id/gustImage" android:visibility="invisible"/> <View android:id="@+id/lineMiddle" android:layout_width="fill_parent" android:layout_height="0dp" android:background="@color/light_grey" android:layout_below="@id/gustImage"/> <ImageView android:layout_width="match_parent" android:layout_height="@dimen/row_height" android:scaleType="centerInside" android:id="@+id/windImage" android:layout_below="@id/lineMiddle" android:src="@drawable/wind_icon_0" android:layout_marginTop="6dp" android:layout_marginBottom="6dp" android:adjustViewBounds="true" /> <TextSwitcher android:layout_width="match_parent" android:layout_height="wrap_content" android:textAppearance="?android:attr/textAppearanceMedium" android:textColor="?android:textColorPrimaryInverse" android:textStyle="bold" android:id="@+id/windSpeedSwitcher" android:gravity="center_vertical\|center_horizontal" android:layout_alignTop="@id/windImage" android:layout_alignBottom="@id/windImage" android:adjustViewBounds="true" /> <View android:id="@+id/lineBottom" android:layout_width="fill_parent" android:layout_height="0dp" android:background="@color/light_grey" android:layout_below="@id/windImage"/> </RelativeLayout>	{ "redpajama_set_name": "RedPajamaGithub" }	7,662
""" Calculates differential photometry. Uses Honeycutt 1992PASP..104..435H. approach """ from __future__ import absolute_import, division, print_function __metaclass__ = type #from functools import partial import numpy as np from astropy.stats import SigmaClip from cached_property import cached_property class DiffPhot(object): """Differential photometry as in Honeycutt 1992PASP..104..435H. Parameters ---------- data : array or MaskedArray NxM array of N all stars (comparision and program) magnitudes in M observations err: array or MaskedArray NxM array of `data`'s standard deviations. Used for weighting. e.g. one can use Poisson noise: np.ma.sqrt(data) comp_stars_mask: array of bool, (optional) comparision stars, stars which variance will be minimized, default: all ref_obs: None or str or int: Reference observation. Correction for reference observation is by definition 0.0, all other frames corrections are relative to reference one. Light curves and stars magnitudes are expressed in reference frame scale. If `int`, should be an number from `-M..M-1`, for positive is an index of ref frame, for negative index is counted from the end. `None` is equivalent of `0`. There are two special string values `"min"` and `"max"` which chooses brightest ans faintest frame respectively. Value of chosen frame is available by `ref` property. """ def __init__(self, data, err, comp_stars_mask=None, lazy=True, ref_obs=None): super(DiffPhot, self).__init__() self._data = data self._err = err self._mask_stars_comp = comp_stars_mask self._ref_obs = ref_obs if not lazy: # force evaluate solution _ = self.solution @property def N(self): """Number of stars. Size of mag or err vector""" return self.data.shape[0] @property def M(self): """Number of observations.""" return self.data.shape[1] @cached_property def data(self): return np.ma.asanyarray(self._data) @cached_property def err(self): return np.ma.asanyarray(self._err) @cached_property def weights(self): w = self.err -2 return self.err -2 @cached_property def lc(self): return self.solution[1] @cached_property def lc_residuals(self): """NxM residuals: $r_{ij} = l_{ij} - m_i$ where $l$ is light curve point, and $m$ is resulting star magnitude""" return self.lc - self.mag[:, np.newaxis] @cached_property def lc_e(self): """NxM sqrt( err^2 + obs_deltas^2 )""" return np.sqrt(self.err2 + self.obs_deltas_stddev2) @cached_property def obs_deltas(self): return self.solution[2] @cached_property def obs_deltas_stddev(self): """std dev of observations deltas from residuals, weighted by err^-2""" r2w = self.lc_residuals*2 self.weights sig2o = r2w.sum(axis=0) / self.weights.sum(axis=0) * r2w.count(axis=0) / (r2w.count(axis=0) - 1.0) return np.ma.sqrt(sig2o) @cached_property def mag(self): return self.solution[0] @cached_property def mag_v2(self): WnClc = self.lc * self.weights return WnClc.sum(axis=1) / self.weights.sum(axis=1) @cached_property def mag_e(self): return (self.err -2).sum(axis=1) -0.5 @cached_property def mag_chi(self): return self._notimplemented @cached_property def mask_stars_comp(self): if self._mask_stars_comp is None: return np.ones(self.N, dtype=bool) else: return np.asanyarray(self._mask_stars_comp, dtype=bool) @cached_property def mask_stars_empty(self): try: return np.ma.getmask(self.data).all(axis=1) except: # nomask return np.zeros(self.N, dtype=bool) @cached_property def mask_obs_empty(self): try: return np.ma.getmask(self.data).all(axis=0) except: # nomask return np.zeros(self.M, dtype=bool) @cached_property def mask_obs_compempty(self): try: m = np.ma.getmask(self.data).copy() m[~self.mask_stars_comp] = True # mask all data for noncomparision stars return m.all(axis=0) except: # nomask return np.zeros(self.M, dtype=bool) @cached_property def ref(self): if isinstance(self._ref_obs, str): return self.solution[3] else: if self._ref_obs < 0: return self.M + self._ref_obs else: return self._ref_obs @cached_property def solution(self): data = self.data[:, ~self.mask_obs_compempty] data_e = self.err[:, ~self.mask_obs_compempty] weights = self.weights[:, ~self.mask_obs_compempty] comp_stars_mask = self.mask_stars_comp & ~self.mask_stars_empty # construct equations from comparision stars K = data.shape[1] # number of (nonempty) obs D = data[comp_stars_mask] W = weights[comp_stars_mask] W.unshare_mask() W[W.mask] = 0.0 # no more mask for bad values, just zero-weights A00 = np.diag(W.sum(axis=0)[1:]) A11 = np.diag(W.sum(axis=1)) A10 = W[:, 1:] A01 = A10.T A = np.block([[A00, A01], [A10, A11]]) assert not (A00.diagonal() == 0.0).any(), "Bad obs: {}".format(np.argwhere(A00.diagonal() == 0.0)) assert not (A11.diagonal() == 0.0).any(), "Bad star: {}".format(np.argwhere(A11.diagonal() == 0.0)) WD = W * D.filled(0) B1 = WD.sum(axis=0, keepdims=True).T[1:] B2 = WD.sum(axis=1, keepdims=True) B = np.block([[B1], [B2]]) X = np.vstack([np.zeros((1, 1)), np.linalg.solve(A, B)]) # obs[0] set to 0, excluded from equations O = X.squeeze()[:K] C = X.squeeze()[K:] # light curves calculation lc = data - O # add non-comparision (nC) stars S = np.ma.masked_all(self.N) S[comp_stars_mask] = C nC_mask = ~self.mask_stars_comp & ~self.mask_stars_empty WnC = weights[nC_mask] WnClc = lc[nC_mask] * WnC S[nC_mask] = WnClc.sum(axis=1) / WnC.sum(axis=1) # recreate masked fields (columns) for empty obs (observations without comaprision stars) in O and lc if self.mask_obs_compempty.any(): nO = np.ma.masked_all(self.M) nO[~self.mask_obs_compempty] = O O = nO nlc = np.ma.masked_all(shape=(self.N, self.M)) nlc[:, ~self.mask_obs_compempty] = lc lc = nlc # reference frame is 0, shift to another one if requested: ref_idx = 0 if self._ref_obs: if isinstance(self._ref_obs, str): if self._ref_obs == 'min': ref_idx = O.argmin() elif self._ref_obs == 'max': ref_idx = O.argmax() else: raise ValueError('Allowed sting values for ref_frame are "min" nad "max". Recived "{}"' .format(self._ref_obs)) else: ref_idx = self._ref_obs if self._ref_obs >= 0 else len(O) + self._ref_obs delta = O[ref_idx] S += delta lc += delta O -= delta return S, lc, O, ref_idx @property def _notimplemented(self): raise NotImplementedError('Not implemented yet') def dphot(data, stddevs, comp_stars_mask=None): """ Calculates differential photometry as in Honeycutt 1992PASP..104..435H. Parameters ---------- :param data: NxK array of N comparision data magnitudes in K observations :type data: np.ndarray or np.ma.MaskedArray :param stddevs: NxK array of N comparision data stddevs in K observations, e.g. one can use Poisson noise: np.ma.sqrt(data) :type stddevs: np.ndarray or np.ma.MaskedArray :param comp_stars_mask: stars which variance will be minimized, default: all :type comp_stars_mask: None or array-like(bool) :returns: tuple(S, L, O, sigS, sigL, sigO) N-element array of stars diff photometry NxK-element array of light curves K-element array of corrections for observations, and standard deviations for that, elements for observations without stars and stars without observations are masked out :rtype: (np.ma.MaskedArray, np.ma.MaskedArray, np.ma.MaskedArray, np.ma.MaskedArray, np.ma.MaskedArray, np.ma.MaskedArray) Notes ----- Elements for observations without stars and stars without observations are masked out. If data and stddevs are provided and are masked arrays, masks should be identical. Examples -------- >>> s = np.array([12.0, 12.6, 13.0, 13.2, 14.1]).reshape(5,1) # 5 stars magnitudes >>> o = np.array([1.0, 1.08, 0.9, 1.3]).reshape(1,4) # 4 observations deviations >>> x = s.dot(o) + np.random.normal(scale=0.1, size=[5,4]) # 5x4 noisy observations simulated >>> x array([[ 6.77523649, -2.78321445, 0.84035323, 15.88001531], [ 4.56942913, -2.11396852, 0.31539753, 16.33408252], [ 3.10018787, -3.87499686, -0.5951147 , 16.25294246], [ 4.4895964 , -2.27193403, 0.40524158, 16.81285796], [ 6.69650016, -0.89424425, 0.60376388, 17.43194032]]) >>> d = dphot(x, np.sqrt(x)) >>> d masked_array(data = [ 0. 0.98206477 -1.29619307 3.88027423], mask = False, fill_value = 1e+20) >>> diff_phot = x - d # differential photometry for x >>> diff_phot masked_array(data = [[ 11.83835643 11.91950781 12.18217253 11.72821846] [ 12.77376351 12.58305526 12.68857425 12.5437627 ] [ 13.12730035 13.04171745 12.86315952 12.93030926] [ 13.1704 13.10646413 13.14529582 13.31344976] [ 14.11213373 14.38888686 14.11465464 14.55691934]], mask = False, >>> diff_phot.mean(axis=1) # mean magnitude masked_array(data = [ 11.91706381 12.64728893 12.99062164 13.18390243 14.29314864], mask = False, fill_value = 1e+20) """ if comp_stars_mask is None: # all stars equal comp_stars_mask = np.ones(data.shape[0], dtype=bool) else: comp_stars_mask = np.array(comp_stars_mask, dtype=bool) if not isinstance(stddevs, np.ma.MaskedArray): stddevs = np.ma.masked_values(stddevs, 0) empty_str = np.zeros(data.shape[1], dtype=bool) empty_obs = np.zeros(data.shape[1], dtype=bool) if not isinstance(data, np.ma.MaskedArray): data = np.ma.masked_array(data, mask=stddevs.mask) else: m = np.ma.getmask(data) assert np.array_equal(m, stddevs.mask), "data and stddev masks must be the same" if m is not np.ma.nomask: # masked data provided, search for empty obs and stars empty_obs = m.all(axis=0) empty_str = m.all(axis=1) data = data[:, ~empty_obs] stddevs = stddevs[:, ~empty_obs] comp_stars_mask &= ~empty_str # construct equations from comparision stars K = data.shape[1] # number of (nonempty) obs D = data[comp_stars_mask] Wall = stddevs ** -2 W = Wall[comp_stars_mask] W.unshare_mask() W[W.mask] = 0.0 # no more mask for bad values, just zero-weights A00 = np.diag(W.sum(axis=0)[1:]) A11 = np.diag(W.sum(axis=1)) A10 = W[:, 1:] A01 = A10.T A = np.block([[A00, A01], [A10, A11]]) assert not (A00.diagonal() == 0.0).any(), "Bad obs: {}".format(np.argwhere(A00.diagonal() == 0.0)) assert not (A11.diagonal() == 0.0).any(), "Bad star: {}".format(np.argwhere(A11.diagonal() == 0.0)) WD = W * D.filled(0) B1 = WD.sum(axis=0, keepdims=True).T[1:] B2 = WD.sum(axis=1, keepdims=True) B = np.block([[B1], [B2]]) X = np.vstack([np.zeros((1, 1)), np.linalg.solve(A, B)]) # obs[0] set to 0, excluded from equations O = X.squeeze()[:K] C = X.squeeze()[K:] # light curves calculation lc = data - O # add non-comparision stars S = np.ma.masked_all(empty_str.size) S[comp_stars_mask] = C nC_mask = ~comp_stars_mask & ~empty_str WnC = Wall[nC_mask] WnClc = lc[nC_mask] * WnC S[nC_mask] = WnClc.sum(axis=1) / WnC.sum(axis=1) # weighted variance calculation resid = lc - S.reshape(S.size, 1) r2w = resid ** 2 * Wall # sig2(obs) from comparision only sig2o = r2w[comp_stars_mask].sum(axis=0) / W.sum(axis=0) * C.size / (C.size - 1.0) # sig2(stars) for all (nonempty) sig2s = r2w.sum(axis=1) / Wall.sum(axis=1) * O.size / (O.size - 1.0) # sig2(lc) sig2mean = sig2o / data.mask.sum(axis=0) # sig2(obs) / num of stars in obs sig2lc = stddevs 2 + sig2mean if empty_obs is not None: # recreate masked fields (columns) for empty obs nO = np.ma.masked_all(empty_obs.size) nO[~empty_obs] = O O = nO nsig2o = np.ma.masked_all(empty_obs.size) nsig2o[~empty_obs] = sig2o sig2o = nsig2o nlc = np.ma.masked_all((empty_str.size, empty_obs.size)) nlc[:, ~empty_obs] = lc lc = nlc nsig2lc = np.ma.masked_all((empty_str.size, empty_obs.size)) nsig2lc[:, ~empty_obs] = sig2lc sig2lc = sig2lc return S, lc, O, np.ma.sqrt(sig2s), np.ma.sqrt(sig2lc), np.ma.sqrt(sig2o) def dphot_filters(data, stddevs, filters_masks, comp_stars_mask=None): """ Calculates differential photometry as in Honeycutt 1992PASP..104..435H, for sets of observations The ``filters_masks`` parameter should be a list of boolean masks choosing subsets of K observations e.g. for different filters. Differential photometry will be calculated for each set independently by ``dphot`` routine. :param data: NxK array of N comparision stars** magnitudes in K observations :type data: np.ndarray or np.ma.MaskedArray :param stddevs: NxK array of N comparision data stddevs in K observations, e.g. one can use Poisson noise: np.ma.sqrt(data) :type stddevs: np.ndarray or np.ma.MaskedArray :param filters_masks: list-like of 1D K-element or 2D (FxK) array boolean masks selecting subset of observations to be processed (e.g. filter for F filters) :type filters_masks: list(np.ndarray) or list(list(bool)) or array-like :param comp_stars_mask: stars which variance will be minimized, default: all. Can be 1D N-element boolean array which indicates common set for all filters, or 2D FxN array-like with masks for each filter. :type comp_stars_mask: None or array-like(bool) or list(array-like(bool) :returns: tuple(S, L, O, sigS, sigL, sigO): list of N-element arrays of stars diff photometry in filters, NxK-element array of light curves K-element array of corrections for observations, and standard deviations for that, elements for observations without stars and stars without observations are masked out :rtype: (list(np.ma.MaskedArray), np.ma.MaskedArray, np.ma.MaskedArray, list(np.ma.MaskedArray), np.ma.MaskedArray, np.ma.MaskedArray) """ filters_masks = np.array(filters_masks, dtype=bool) if comp_stars_mask is not None: comp_stars_mask = np.array(comp_stars_mask, dtype=bool) if comp_stars_mask is not None and comp_stars_mask.ndim == 2: cmasks = comp_stars_mask else: cmasks = [comp_stars_mask] * filters_masks.shape[0] O = np.ma.masked_all(data.shape[1]) sigO = np.ma.masked_all(data.shape[1]) S = [] sigS = [] L = np.ma.masked_all(data.shape) sigL = np.ma.masked_all(data.shape) for i, mask in enumerate(filters_masks): vS, lc, vO, sS, slc, sO = dphot(data[:, mask], stddevs[:, mask], cmasks[i]) O[mask] = vO sigO[mask] = sO S.append(vS) sigS.append(sS) L[:, mask] = lc sigL[:, mask] = slc return np.ma.array(S), L, O, np.ma.array(sigS), sigL, sigO def mean_phot(lc, lc_stddev, lc_clip_sigma=1.0, stdev_clip_sigma=1.7, lc_clip_iters=2, stdev_clip_iter=2): """ Calculates stars mean magnitude and error from light curves Calculates stars mean magnitude with standard deviation from light curves using: - weights from data points erros $w=e^{-2}$ - one-side sigma clipping on errors - sigma clipping on data points :param lc: NxK array of N star magnitudes in K observations :param lc_stddev: NxK array of lc stddevs """ p = np.ma.array(lc, copy=True) pe = np.ma.array(lc_stddev, copy=True) lc_clip = SigmaClip(sigma=lc_clip_sigma, iters=lc_clip_iters) # , cenfunc=partial(np.ma.average, weights=pe-1)) err_clip = SigmaClip(sigma_lower=10.0, sigma_upper=stdev_clip_sigma, iters=stdev_clip_iter) pmask1 = err_clip(pe, axis=1, copy=False).mask pmask2 = pmask1 \| lc_clip(p, axis=1, copy=False).mask # print(f, p.mask.sum(), pmask1.sum(), pmask2.sum()) # mean, median, stddev = sigma_clipped_stats(lc[:,m], mask=mask1, axis=1, sigma=2.0) p.mask = pe.mask = p.mask \| pmask2 pw = pe -2 mean = np.ma.average(p, axis=1, weights=pw) resid = lc - mean[:, np.newaxis] stddev = np.ma.sqrt(np.ma.average(resid ** 2, axis=1)) # , weights=pw) return mean, stddev	{ "redpajama_set_name": "RedPajamaGithub" }	2,458
Theme and Grammar p4: Adverb Theme December 18, 2019 October 11, 2020 Subsurface Games Now on to Adverb Theme. If Verb Theme is how closely your decision process as a player matches that of your avatar in the game world, Adverb Theme is about the emotions that come up during that decision process, and how they match the emotions suggested by the theme. As a game designer, they're a level removed from your control, because they are, of course, dependent on the players. In the Noun theme post, I talked about the frequent criticism that some games are themeless because they could be about anything: while sometimes that's a comment on the game's setting ("Sure, you're building a medieval castle in Italy, but you could be building a Colony on Mars or a Bee Hive"), it's often about that feel. Because this subject is by nature more abstract, let's dive in what I think is a perfect example: Lost Cities. Actually, before I went with the Grammar shtick, this whole series started with what I call "Knizia theme", and Lost Cities is one of its best, and most well-known, examples. Still, a quick overview of the game if you don't know what it is: Lost Cities is a card game themed around expeditions. Players are rival entrepreneurs who fund explorers to go around exotic locales and bring fame and fortune back. Or artifacts? Or maybe it's taking pictures and posting them on Instragram. Who cares, really? The game is abstracted to the bare minimum, and many would call it abstract, with that "it could be anything!" Yet, I argue, it couldn't: that theme is the perfectest fit. Picture from BoardGameGeek Mechanically, the game offers 5 suits, each containing cards numbered 2-10, and 3 Handshake cards. You can play cards in your tableau, as long as they are higher than the number of the last card you placed in that color, with Handshakes having to be played before number cards. At the end of the hand, you score each color in which you played, adding up the cards, subtracting 20, and, if you have 1, 2, or 3 handshakes, doubling, tripling, or quadrupling, respectively -which could pay a lot, or, if you run short, could cost a lot. You also gain 20 points if you play 8 cards of a color. The game is mostly about not giving your opponent cards they need, not showing your opponent what card you need, and fighting against the clock of the deck running out. Now the noun theme is barely existent: the cards represent advancement, the handshakes represent how much funding goes into the thing. There's no money, no explorers, and the adventures are nothing but rows of cards. The verbs aren't even clear in what you're doing thematically: drawing cards and playing cards isn't what I think of when I think of planning an expedition. The game is a lot easier to understand in abstract, mechanical terms: it's almost impossible to teach it with any hint of theme. Yet, if I were to describe the experience, I'd say it's a game about taking risk, about deciding when to pull the trigger, based on incomplete information, and going from planning to action: you can't wait until you know exactly how it will end before you get started. It's a game about hedging your bets, about knowing when to go full throttle and when to take your time. It's a game where you don't directly hurt your opponent, but if you fall on something they need, you bury it deep. It's a game about sometimes digging deeper and finding a gem, but more often then not you get something of little importance. Doesn't that sound like expeditions to unknown lands? Like funding archaeological missions? Many games described as Abstract thrive on Adverb Theme. Individual mechanisms seem abstract, yet the experience the game delivers is described in terms which clearly resonate with the theme. Sure, Lost Cities could be about funding start ups in Silicon Valley, or any other situation where you take risks based on limited information. Likewise, whether it's finding cures while controlling the diseases' spreading, closing portals to Hell while fighting demons, building pumps while controlling raising water levels, or negotiating alliances with barbarian leaders while defending Rome from their attacks, Pandemic is a game about trying to progress on long term solutions when you have time in between two emergencies. Are they less thematic because the Noun theme could be changed? What do you think are other good examples of Adverb Theme, games where the actions and mechanisms are not necessarily good matches, but where the theme perfectly fits the emotional journey you go on during a game? Categories: Board Game Design Tags: grammar as theme, theme ← Theme and Grammar p3: Verb Theme Grammar and Theme p5: Adjective theme →	{ "redpajama_set_name": "RedPajamaCommonCrawl" }	9,351
\section{my outline} \section{Introduction} \label{Intro} An action of a group $G$ on a set $S$ is called $k$-transitive if, for every choice of distinct elements $x_1, ... , x_k \in S$ and every choice of distinct targets $y_1, ... , y_k \in S$, there is an element $g\in G$ such that $g(x_i)=y_i$. The term \emph{transitive} means 1-transitive; actions with $k>1$ are \emph{multiply transitive}. The number of elements in $S$ is the \emph{degree}. Transitive actions are common (for example, every group acts transitively on itself by left multiplication), while multiply-transitive actions are relatively rare. The theory is well developed; see \cite{Dixon:1996uq}. It is obvious that the isometry group of a complete finite-volume hyperbolic three-manifold induces a permutation action on the set of cusps. In this paper we call such a manifold \emph{k-transitive} if the induced action is $k$-transitive. Note that this definition is of the `inclusive hierarchy' type. For instance, a 3-transitive manifold is automatically 2-transitive, and possibly 4-transitive as well. Kojima \cite{kojima1988isometry} shows by construction that every finite group $G$ occurs as the isometry group of some closed hyperbolic 3-manifold. At one stage, the construction involves a cusped manifold, with cusps labeled by the elements of $G$. The induced permutation action on the cusp set amounts to left-multiplication of the labels by elements of $G$. Since this action is transitive, the manifold at this stage is 1-transitive by our definition, and we see that 1-transitive manifolds are plentiful and can have any number of cusps. But the action is also free, which implies that it is never 2-transitive. Hence one may begin to wonder, for $k\ge 2$, how common and how challenging to construct are the $k$-transitive manifolds? In Section \ref{Examples} we give some examples of 1-, 2- and 4-transitive manifolds, all constructed as complements of hyperbolic links in $S^3$. In Section \ref{2-trans} we show a construction that leads to our main result: \begin{theorem} \label{MainThm} For the class of 2-transitive manifolds, there is no upper bound on the number of cusps. \end{theorem} In Section \ref{Conclusion} we summarize known results and mention some open questions. \section{Examples with $k=1,2,4$} \label{Examples} All the manifolds in this section are link complements in $S^3$. The constructions are easy, so we give only brief descriptions. The key idea is that, since the geometric structure of a hyperbolic link complement is unique, symmetries of the link are always realized by isometries of the complement. Where no outside reference is given, hyperbolicity has been verified using SnapPea \cite{Weeks:1999uq}. \begin{figure}[h] \begin{center} \includegraphics[scale=0.6]{ChainLink.pdf} \end{center} \caption{Chain link with $n$ components and $t$ half-twists.} \label{ChainLink} \end{figure} \subsection{A chain construction} Consider a cycle of $n$ unknotted loops, $n\in{\mathbb Z} ^+$, linked sequentially, and having $t$ half-twists, $t\in{\mathbb Z}$, as in Figure \ref{ChainLink}. The chain itself, viewed as a single loop, must be unknotted. There is an obvious 1-transitive cyclic action on the link components. Two sub-families of such chains appear as examples in Thurston's notes, and the complete family is analyzed by Neumann and Reid \cite{neumann1992arithmetic}. They show that for $n\ge5$ the link is hyperbolic for every value of $t$, and for $n < 5$ the link is hyperbolic for all but $5-n$ values of $t$, the exceptions being the cases with the least overall twisting. \begin{figure}[h] \begin{center} \includegraphics[scale=0.5]{B5closure2} \end{center} \caption{Braid $B$ has associated permutation $(1 \,3 \,5 \,4 \,2)$. Although the closure of $B$ is the unknot, the closure of $B^5$ is hyperbolic. Shifting the diagram cyclically one step to the right gives a 1-transitive action on the five components.} \label{B5closure} \end{figure} \subsection{A braid construction} Suppose $B$ is a pseudo-Anosov braid on $n$ strands for which the associated permutation is cyclic of order $n$. Then the braid $B^n$ induces the trivial permutation on the strands, and the closure of $B^n$ is thus a link having $n$ components. Again, there is an obvious 1-transitive cyclic action. An example is shown in Figure \ref{B5closure}. The closed braid might fail to be hyperbolic. In particular, since a braid is closed by performing a $(1,0)$ Dehn filling on the braid axis, it might happen that the meridian is too short to allow a hyperbolic filling. In this case, the longer braid $(B^n)^m$ will have meridian $m$ times as long, and thus, by the `$2\pi$ theorem' of Gromov and Thurston \cite{bleiler1996spherical}, the closed braid will be hyperbolic for sufficiently large $m$. (It seems likely that the $n$th power of $B$ is already enough to guarantee a meridian longer than $2\pi$, but there may be exceptions to this.) \subsection{Two cubical constructions} Consider the four planes in ${\mathbb R} ^3$ given by $Ax + By + z=0$, with $A,B\in\{\pm 1\}$. These planes are perpendicular to the four diagonals of the cube with vertices $(\pm 1, \pm 1, \pm 1)$. Intersecting these planes with the unit sphere gives four great circles intersecting at twelve points. By resolving each intersection to an over- or under-crossing, in alternating fashion, a hyperbolic link is obtained. A planar diagram is shown in Figure \ref{CubeLink} (Left). \begin{figure}[h] \begin{center} \includegraphics[scale=0.25]{CubeLink} \end{center} \caption{Left: The complement of this link is 4-transitive. Center and right: Each vertex of a cube is replaced by three interlocking half-loops. The complement is 1-transitive, with 12 cusps.} \label{CubeLink} \end{figure} The group of orientation-preserving symmetries of the cube carries over naturally to the link components, and it is an easy exercise to check that this action is 4-transitive. This link can also be obtained by the braid construction given above, but the 4-transitivity is not so obvious. An analogous construction, where the cube is replaced by an icosahedron, yields a 2-transitive manifold having 6 cusps. The second cubical construction builds a 12-component link by following the structure of the edges of a cube, as shown in Figure \ref{CubeLink}. The complement is hyperbolic and 1-transitive. In contrast to the chain and braid examples shown earlier, the action is non-cyclic. \eat{ \subsection{A conjecture} How many cusps can a $k$-transitive manifold have? The examples shown in Section \ref{} strongly suggest that any positive number of cusps can occur in a 1-transitive manifold. For $k=2$ the situation seems more difficult, but the construction given in Section \ref{2-trans} will show that the possibilities include every prime power. The situation feels quite different for $k\ge 3$, due in part to the scarcity of groups that can act in the required way, and in part to the spatial restrictions inherent in dimension three. While hoping that it is not the case, we suspect that there is in fact an upper bound on the number of cusps whenever $k\ge 3$. } \section{A family of 2-transitive manifolds} \label{2-trans} In this section we construct an infinite family of 2-transitive manifolds for which the number of cusps increases without bound. The construction builds on a family of regular maps described by Biggs \cite{Biggs:1971kx} and further studied by James and Jones \cite{James:1985uq}. Here is an overview of the construction. Let $S$ be a surface carrying one of the regular maps of Biggs. There is a natural 2-transitive action on the $n$ faces of this map by its automorphism group. The product $S\times S^1$ is formed, and within this non-hyperbolic manifold a system of $n$ simple closed curves is specified. The curves are carefully designed to maintain the original 2-transitive symmetry. The complement of this link is the desired manifold $M$. Finally, to verify that $M$ is hyperbolic, it is viewed as a punctured-surface bundle over $S^1$ with pseudo-Anosov monodromy. \begin{figure}[h] \begin{center} \includegraphics[scale=0.63]{HelicalArc_D} \end{center} \caption{Left: Each arc is a helical segment joining the image of $x_i$ in the lower boundary to the image of $x_{i+1}$ in the upper boundary. After boundary identification, four arcs become a single closed curve. Right: The view from above, after increasing the radius so that each arc extends out to link with an arc of the neighboring face. } \label{HelicalArc} \end{figure} We now describe the construction in more detail. Let $n$ be a prime power greater than 3, and let $\textup{\sf{F}}$ be the finite field of order $n$. Biggs uses the arithmetic of $\textup{\sf{F}}$ to construct orientable regular maps (tessellations) on a closed surface. Such a map has $n$ faces, each face a $(n-1)$-gon. The genus of the surface is given by \begin{equation} g_n=\left\{ \begin{array}{ll} 1+\frac{\textstyle n(n-7)}{\textstyle 4} & \textrm{if} \;\; n\equiv 3 \mod 4\\ 1+ \frac{\textstyle n(n-5)}{\textstyle 4} & \textrm{otherwise.} \end{array} \right . \label{genus} \end{equation} The faces admit a natural labeling by the elements of $\textup{\sf{F}}$, and the automorphism group of the map is exactly the natural action of the affine group $A(1,\textup{\sf{F}})$ on the face labels. The 2-transitivity of this action is an easy exercise. The significance of this, combinatorially, is that each face of the map shares an edge with each of the remaining faces. We take $S$ to be the orientable surface carrying this regular map, endowed with the natural constant-curvature metric (see \cite{edmonds1982regular}). The case $n=5$ is used in the illustrations; the surface is a square torus tiled by five square faces. The construction continues inside a preliminary three-manifold $M_I=S\times I$, where $I$ is the unit interval. For each face $f$ of $S$, $n-1$ arcs are specified in $M_I$ as follows. First, let $P$ be the center point of $f$, and let $C$ be the circle of radius $\rho$ and circumference $\sigma$ in $S$ centered at $P$. Let the vertices of $f$ be denoted $v_i$ sequentially around the perimeter, for $0\le i\le n-2$. Let $x_i$ be the point of intersection of $C$ and the radial segment extending from $P$ to $v_i$. Now $C_I=C\times I$ is a cylinder surrounding the fiber $\{P\}\times I$ in $M_I$. The desired arcs are defined to be the helical segments $s_i$ of slope $\frac{n-1}{\sigma}$ lying on $C_I$, each extending from the image of $x_i$ in $f\times\{0\}$ to the image of $x_{i+1}$ in $f\times\{1\}$ (indices modulo $n-1$). Figure \ref{HelicalArc} illustrates this step. \begin{figure}[h] \begin{center} \includegraphics[scale=0.8]{PointPush_B} \end{center} \caption{The point-pushing homeomorphism $\mathscr{H} $. The marked points are punctures. Dashed arrows represent the point-pushing trajectories. The small dotted loop encloses two punctures; the long snaking loop is its image under $\mathscr{H} $. With further iterations it would limit on the $f_+$ foliation in the sense of Thurston \cite{thurston1988geometry}.} \label{PointPush} \end{figure} Next, $M_\circ$ is formed by identifying the two boundary components of $M_I$ by equality in the first factor; hence $M_\circ$ is the product $S\times S^1$. By this identification the cylinder $C_I$ becomes a torus, and the segments $s_i$ join end-to-end yielding a closed curve, namely, a $(n-1,1)$ torus knot. Finally, to obtain the desired link, we adjust the size of circle $C$ as follows. A face of $S$ has two characteristic radii: $r_1$, the distance from center $P$ to an edge midpoint, and $r_2$, the distance from $P$ to a vertex. By requiring the radius $\rho$ to satisfy $r_1 < \rho < r_2$, each copy of $C$ lies partly on its own face and partly on the neighboring faces. Hence each strand of the corresponding torus knot extends radially outward just far enough to link with a strand of the neighboring knot. Manifold $M$ is now defined to be the complement in $M_\circ$ of this link. \eat{ It is easy to see that $M$ is the mapping torus of a point-pushing homeomorphism $\mathscr{H}$ of a punctured surface. The fiber is just the original surface $S$, but with $n(n-1)$ points missing where the surface intersects the strands of the link. We view $\mathscr{H} $ as acting on the fiber at level $\frac{1}{2}$ with respect to the original $I$ factor, as shown in Figure \ref{PointPush}. } In $M$, each original cross section $S\times \{x\}$ (for $x\in S^1$) is now a punctured surface, since the $n(n-1)$ points of intersection with the strands of the link are now missing. For convenience in the subsequent analysis, we specify the cross section at level $\frac 1 2$ with respect to the original $I$ factor as the `base surface' and observe that $M$ is the mapping torus of a point-pushing homeomorphism ${\mathscr{H}}$ of this surface. A diagram for ${\mathscr{H}}$ is shown in Figure \ref{PointPush}. \begin{figure}[h] \begin{center} \includegraphics[scale=0.38]{pseudoAnosov4B} \includegraphics[scale=0.38]{PseudoAnosov5B} \end{center} \caption{Left: An approximation of the $f_+$ foliation, showing the 4-pronged singularities. Right: A train track for $\mathscr{H}$.} \label{TrainTrack} \end{figure} A homeomorphism is pseudo-Anosov if there exists a pair of transverse singular foliations, $f_+$ and $f_-$, invariant under $\mathscr{H} $, and an associated constant $\lambda>1$, the dilatation. The surface is stretched and compressed along the two foliations by factors of $\lambda$ and $\lambda ^{-1}$, respectively. By a result of Thurston \cite{Thurston:1982fk}, the mapping torus of a pseudo-Anosov homeomorphism is hyperbolic. \eat{ Figure \ref{TrainTrack} shows an approximation of the $f_+$ foliation for ${\mathscr{H}}$. Singularities occur at the vertices and face-centers of the underlying map; these points are fixed by $\mathscr{H}$. A train track for $\mathscr{H}$, as discussed by Bestvina and Handel \cite{bestvina1995train}, is also shown. Positive weights for the track will be computed below, along with $\lambda$. The complement of the track consists of once-punctured monogons and cusp-cornered polygons. It follows that $\mathscr{H}$ is indeed pseudo-Anosov. Details for the theory of train tracks are given by Penner and Harer \cite{Penner:1992vn}. } Figure \ref{TrainTrack} shows an approximation of the $f_+$ foliation for ${\mathscr{H}}$. Singularities occur at the vertices and face-centers of the underlying map; these points are fixed by ${\mathscr{H}}$. A train track for ${\mathscr{H}}$, as discussed by Bestvina and Handel \cite{bestvina1995train}, is also shown. The structure of the track is equivariant with respect to the symmetries of the surface. The complement of the track consists of once-punctured monogons and cusp-cornered polygons. The track captures in a discrete way the overall structure of the $f_+$ foliation, and is mapped, with appropriate stretching, onto itself by ${\mathscr{H}}$ (modulo some adjustment homotopic to the identity). Details for the theory of train tracks are given by Penner and Harer \cite{Penner:1992vn}. We turn next to the calculation of $\lambda$ and the weights associated to branches of the track. A few different approaches to this problem are possible. The underlying symmetry allows some simplifications to be made. \eat{ To compute the track weights and the dilatation $\lambda$ for $\mathscr{H}$ we refer to the diagram in Figure \ref{Dilatation}. Points labeled $A$ through $E$ are punctures, while $F$ is a fixed point of $\mathscr{H}$. Each branch of the track carries a weight. Two branches are assigned weights $w$ and $z$; the weights for all other branches are determined by symmetry and by the summation rule where branches meet. The weights correspond to a measure for transverse arcs. } In Figure \ref{Dilatation} the points labeled $A$ through $E$ are punctures, while $F$ is a fixed point of ${\mathscr{H}}$. Each branch of the track is assigned a positive weight. The weights determine a crossing measure for transverse arcs. Two branches in the diagram are assigned weights $w$ and $z$; the weights for all other branches are determined by symmetry and by the summation rule where branches merge. Thus each semicircular branch that half-surrounds a puncture has weight $w+2z$ and each very short branch found between a pair of nearest-neighbor punctures has weight $2w+2z$. \begin{figure}[h] \begin{center} \includegraphics[scale=0.7]{Dilatation} \end{center} \caption{Train track and arcs for computing the dilatation $\lambda$.} \label{Dilatation} \end{figure} Arc $\overline{AB}$ crosses 17 branches and has total crossing measure $10w+14z$. Its image under $\mathscr{H}$ is arc $\overline{CD}$, which has crossing measure $2w+2z$. One may view this as compression by ${\mathscr{H}}$ in the transverse ($f_-$) direction, resulting in the full weight $10w+14z$ being forced onto a portion of track that previously carried just $2w+2z$. Since the contraction factor for the compression is $\lambda^{-1}$, one may attribute the increased `density' to a scaling by $\lambda$; hence \begin{equation}\label{weights1}10w+14z=\lambda (2w+2z).\end{equation} Similarly, arc $\overline{DF}$ has measure $2w+3z$, while its image, arc $\overline{EF}$, has measure $z$, and we obtain \begin{equation}\label{weights2}2w+3z=\lambda z.\end{equation} With these two equations, we have enough constraints to determine the unknowns. Since weights are determined only up to a scale factor, we can set $z=1$ and solve, first obtaining $w=\sqrt{2}$, and then $$\lambda =3+2\sqrt{2}$$ and $$ \lambda^{-1}=3-2\sqrt{2}.$$ This quick solution may seem a bit ad hoc; for a more systematic view of things let us divide both sides of equation \eqref{weights1} by 2 and then subtract equation \eqref{weights2} to produce \begin{equation}\label{weights3} 3w+4z=\lambda w. \end{equation} Equations \eqref{weights2} and \eqref{weights3} together now form a linear system $$\left[\begin{array}{rr} 3 & 4 \\ 2 & 3 \\ \end{array}\right] \left[\begin{array}{r} w \\ z \\ \end{array}\right] = \lambda \left[\begin{array}{r} w \\ z \\ \end{array}\right],$$ and we see how the weights constitute an eigenvector for eigenvalue $\lambda$. A related (and the most standard) approach is based on viewing the train track as an embedded graph and analyzing the self-map induced on it by ${\mathscr{H}}$. Every branch is assigned a numerical value; these correspond to a tangential measure, and may be interpreted simply as edge lengths. The map stretches each edge onto some sequence of edges; this data is encoded by an incidence matrix. The stretched length is then some particular sum of original edge lengths, and one wishes to attribute all the stretching to a single scale factor. This, of course, is again an eigenvalue problem. \begin{figure} \begin{center} \includegraphics[scale=0.25]{TrackMod} \end{center} \caption{The modified track has just two classes of branches. The semicircular branches have been completely split, and each short branch has been reduced to a switch located at the edge-midpoint of a face. } \label{TrackMod} \end{figure} The full incidence matrix of a train track for ${\mathscr{H}}$ is rather large, but two easy simplifications make the problem tractable. First we modify the track as shown in Figure \ref{TrackMod}, so there are just two classes of branches. These are labeled ${\tilde{w}}$ and ${\tilde{z}}$. Then we replace the incidence matrix by a two-by-two matrix that imposes the same constraints on edge lengths that are implicit in the incidence matrix. Using the diagrams in Figures \ref{PointPush} through \ref{TrackMod} it is rather straightforward to trace out the image of a ${\tilde{w}}$ edge: it is stretched onto a sequence of edges of type ${\tilde{w}},{\tilde{z}},{\tilde{w}},{\tilde{z}},{\tilde{w}}$. Similarly, a ${\tilde{z}}$ edge is mapped onto ${\tilde{w}},{\tilde{z}},{\tilde{w}},{\tilde{z}},{\tilde{w}},{\tilde{z}},{\tilde{w}}$. Hence we have $$3{\tilde{w}} + 2{\tilde{z}} = \lambda{\tilde{w}} \quad\quad \textup{and}\quad\quad 4{\tilde{w}} + 3{\tilde{z}} = \lambda{\tilde{z}}.$$ The matrix for this linear system is just the transpose of the one that occurred earlier, so the eigenvalues are unchanged. The weights ${\tilde{w}}$ and ${\tilde{z}}$ for the tangential measure are the reciprocals (up to a scale factor) of those obtained earlier for the transverse measure. An overview of these concepts, placing them in the larger context of Thurston's work, can be found in the Epilogue of \cite{Penner:1992vn}. Yet another approach to analyzing ${\mathscr{H}}$ has been generously pointed out by an anonymous referee. Due to the large symmetry group $A(1,\textup{\sf{F}})$, the associated quotient space of $S$ is quite simple. A fundamental domain consists of two neighboring triangles in the barycentric subdivision of a face, and the induced edge identifications yield a topological sphere with three cone points, something like a triangular pillow or a turnover pastry. The punctures all get identified to a single point of the quotient; removing this point, along with the three cone points, produces a four-punctured sphere. This surface has a natural metric coming from its two-covering by a flat torus via the classical elliptic involution, with the four fixed points corresponding to the punctures. The image of ${\mathscr{H}}$ in this reduced setting can be analyzed explicitly using Dehn twists, and its lift to the torus is a genuine Anosov transformation having scale factors $3\pm2\sqrt{2}$. Details for these steps can be found in \cite{bestvina1995train}, \cite{thurston1988geometry}, and the primer \cite{farb2011primer} by Farb and Margalit. The details used in the above approaches (specifically, the diagrams in Figures \ref{Dilatation} and \ref{TrackMod}, and the nature of the quotient space) do not depend on the faces being squares. Thus the computations work out as shown not just for $n=5$, but for every prime-power value of $n$. Hence the same dilatation occurs in every case. \section{Further questions} \label{Conclusion} The constructions shown in Section \ref{Examples}, along with Kojima's method, suggest that 1-transitive manifolds may allow for quite a diversity of structures. It would be interesting to find a more systematic understanding of the big picture. For $k=2$, more examples can be produced by easy variations of the above construction based on the Biggs surfaces. Are there other 2-transitive manifolds having substantially different structure? Is every 2-transitive group action realized by some 2-transitive manifold? There are lots of 3-transitive manifolds having just three cusps, but this is not too surprising since a 3-transitive action on a set of three objects is not really very exotic. In particular, the three-component chain links described earlier all have obvious 3-transitive symmetry, and all but two of them are hyperbolic. The famous Borromean rings are another example. For more than three cusps, the situation appears much harder. The author is aware of one 3-transitive manifold with six cusps, and another with eight, but no others. For $k=4$, our only known example is the manifold described in Section \ref{Examples}, and easy variations of it, all having four cusps. \eat{ For $k=5$, not a single example is known to the author. It seems reasonable to conjecture that there is a largest $k$ for which $k$-transitive manifolds exist, and that for each $k\ge 3$ there is an upper bound on the possible number of cusps. In the original version of this paper we posed the following conjecture which has since been answered in .... We include the original statement of the conjecture to accurately reflect the history of the problem. " } In the original version of this paper we stated two conjectures: that there is a largest $k$ for which $k$-transitive manifolds exist, and that for each $k\ge 3$ there is an upper bound on the possible number of cusps. Both have since been proven, and sharp bounds provided, by Ratcliffe and Tschantz \cite{ratcliffe2019cusp}. \bibliographystyle{amsplain}	{ "redpajama_set_name": "RedPajamaArXiv" }	3,094
Donut is a dictionary and grammar toolkit that makes it easy to create and mantain an online dictionary and grammar for any language. It has purposes within descriptive linguistics and language construction. Please note that Donut is under heavy development, so its structure might change drastically. If you are eager to try out some of the features already, installation goes as follows. The example database is filled with example content of the Dutch language. Donut is licensed under MIT. ### Requirements * PHP 5.6+ (ideally PHP 7+), might work with PHP 5.4+ (not tested) * MySQL or MariaDB-server ### Installation * Clone the git repository to a web server (alternativly just download its contents) * Edit config.php to fit your configuaration (database usernames etc.) * Import `db.sql` to the database * It should work now. Note: for now `db.sql` is filled with Dutch example content. Please note that donut still lacks a lot of features. At this moment you should only install donut if you want to take a look at its progress. If your host does not allow for .htacces rewriting of urls, simply go to `config.php` and change `define('CONFIG_REWRITE', true);` to `define('CONFIG_REWRITE', false);`. #### Test account Username: donut Password: yeast	{ "redpajama_set_name": "RedPajamaGithub" }	7,923
«One for the Radio» —en español: «Una para la radio»— es el décimo cuarto single de la banda británica McFly, y primer sencillo perteneciente a su cuarto álbum de estudio, Radio:ACTIVE, publicado bajo su propio sello discográfico, Super Records, después de que la banda abandonase su antigua discográfica, Island Records. El 25 de junio de 2008, el single consiguió entrar como «A Listed» en la lista de la BBC Radio 1, objetivo que solo había conseguido con su primer sencillo, «5 colours in her hair». «One for the Radio» se convirtió en disco de platino gracias a vender más de 100.000 copias de descarga digital en Brasil. Descripción El mensaje de «One for the Radio» es descrito por la banda como la «lucha constante por la aceptación crítica. Vídeo musical El videoclip se estrenó el 29 de junio de 2008, filmado en Toronto bajo la dirección de Steve Jocz, batería de la banda punk Sum 41. La secuencia de apertura del vídeo es una recreación de una escena de la película Back to the Future, filme del cual McFly obtuvo su nombre. Al igual que Michael J. Fox interpretando a Marty McFly, el guitarrista de la banda, Danny Jones, eleva al máximo el volumen de un amplificador gigante con el objetivo de realizar un potente rasgueo con su guitarra. Lista de canciones Historial de lanzamientos Posicionamiento en las listas de ventas Certificaciones Personal Danny Jones - guitarra, voz principal, productor ejecutivo. Tom Fletcher - compositor, guitarra, voz principal, piano, teclado. Harry Judd - batería, percusión. Dougie Poynter - bajo, coros. Jason Perry - productor Julian Emery - productor adicional Tom Lord-Alge - mezcla Ted Jensen - masterización Véase también Radio:ACTIVE Lista de canciones de McFly Discografía de McFly Referencias Enlaces externos McFly.com (en inglés) (en inglés) (en inglés) (en inglés) (en inglés) Sencillos de McFly Sencillos de 2008 Canciones en inglés	{ "redpajama_set_name": "RedPajamaWikipedia" }	5,382
{"url":"https:\/\/havingareapgoodtime.travellerspoint.com\/archive\/122010\/","text":"# December 2010\n\n## Nha Trang\n\nOh I do like to be beside the seaside...except when it's cloudy and cold and too windy for swimming\n\n20 \u00b0C\n\nWe arrived at 8am, and were dropped off outside a $6 a night hotel. Score! It was fairly nice, if a little out of the centre, so we checked in. Then we headed straight out to get breakfast. We found somewhere that had a buffet breakfast, and for$3 each, we tucked into an eclectic mix of bread, cheese, dumplings, bacon, salad, fruit, rice, vegetables, soup, noodles, beef stew, sausages, eggs, and just about anything else that gets eaten (or the Vietnamese think gets eaten) anywhere in the world!!\n\nWe then walked along the seafront to the centre.\n\nWe got a tea, more because we wanted the free wi-fi than the tea too see whether our friend Flic from volunteering who was in Nha Trang had got back to us. She hadn't, so after another wander round, we headed back to our hotel to chill out for a while. After a bit we went out to try and find Flic. We didn't have any luck, so we went to a posh place called Louisiana Brewery. John tried all 4 of their beers for $4, and Susie had a VERY yummy chocolate cake for$2. Yummmm! We were going to have a swim in the pool that they have for free use, but it started to get a little rainy and it was very windy, so we decided against it in the end.\n\nWe set off to walk back to our hotel to see if there was any news from Flic, but on the way, who should we see but the lady herself, having a drink on the seafront with her friend Amanda.\n\nThey took us to the market, where they did some shopping, and we just window shopped, seeing as we had no money left after Hoi An! It was great to see Flic and have some other company! Then we went back to our hotel, chilled out and then headed out to meet Flic and Amanda for dinner.\n\nWe had a tasty tasty seafood hotpot for dinner, had a couple of drinks, and then went back and got a fairly early night, to recover from our overnight trip from the night before!\n\nThe next day we had noodle soup (called Pho, and it's the Vietnamese FAVOURITE THING EVER. WE just think it's OK, and are getting a little fed up of it to be honest!) for breakfast. We then walked out to a mud spa that Flic had recommended. It was further than we expected, at 6km, and down a rather muddy track. We definitely don't recommend walking it!\n\nAt the, rather posh, spa, we opted for the decadent 900,000 dong ($45) package for the two of us. In hindsight, it probably wasn't worth it, and the public mud\/hot baths would be good enough, but we decided that after our horrible long bus journeys we'd earnt some pampering! Our time included 20 minutes in a warm mud bath - rather satisfying but horrible, but left our skin feeling silky smooth - followed by 45 minutes in a secluded little bath of our own, where we got given water and fruit, and into which they put some bags of herbs, which smelt nice, but made us feel rather like we were being made into a cup of tea!! Then we had a 30 minute massage - John's first ever - that was lovely, and left us both feeling very pampered! Then we could have gone swimming afterwards, but were both feeling too nice and soft skinned to want to go in the water again! It was a lovely couple of hours! Then we went back to the city (getting a$3 taxi this time) to meet Flic and continue our extravagant day by having lobster on the beach for lunch! It was cooked by a lady who had a BBQ right on the beach, and we sat on a blue tarpaulin to enjoy it. It was slightly stressful, due to the wind and the waves that came right up to where we were sitting, but the food was delicious! We only paid $15 between us for 3 crabs, 3 lobsters and 3 shrimps! It was fantastic, and great eating right on the beach too, even if there were lots of people around trying to sell us stuff! We topped off our day of luxury by having cheesecake and beer at Louisiana Brewery again, and then having another massage in an open hut right next to the beach. Ahhhhh, bliss!! Our day had been rather extravagant and luxurious, but the whole thing only cost us about$35 each, which is only 22 pounds! Not bad, when you consider the massage alone would be more than that at home!!\n\nWe then headed back to our hotel, where John started to feel a bit ill, so Susie headed out alone to meet Flic for dinner. They had a good chat over dinner, but the Indian restaurant we went to was very disappointing. Boo! Susie then said goodbye to Flic, and we arranged to meet up again in Saigon, when we were all there in a few days.\n\nWe went to bed, ready for an early start the next day to head to Dalat.\n\nPosted by Susiep539 03:37 Archived in Vietnam Comments (0)\n\n## Hoi An\n\n27 \u00b0C\n\nWe woke up in Hoi An and took our time over getting out of bed. We felt we deserved it! The girl that had told us to come to her Uncle's hotel the night before had also recommended her clothes shop to us so we decided to head over there to see what they had to offer. When we arrived we were shown the dresses they tailor make and several English clothes catalogues. \"You chose, we make,\" they said....\n\nWe were measured, fitted, coloured and walked out with a new dress, some trousers and a suit with a rather swanky waistcoat and were booked in for a 5pm fitting. We left 'Su's' and had a coffee which sent John buzzing for the rest of the day. Vietnamese coffee is amazingly tasty but very strong! We walked around Hoi An some more afterwards and found ourselves in another shop where Susie bought a new red and white spotty jump suit. Very kitsch! Then we walked some more.....we seemed to do an awful lot of walking in Hoi An, but the streets just beg you to. As it's a world heritage town, all the buildings have received funding to be renovated. Also many of the streets are sort of pedestrianised (though nowhere in Vietnam is truly safe from motos!) which makes it much safer to walk about than anywhere else we've been!\n\nAfter a wander we used the first ticket from out Hoi An visitor ticket, which allows you to visit 5 attractions over 3 days, and in theory permits you to actually enter the old town, though noone seemed to be checking entry points anywhere, and to be honest I don't know how they ever could! Our first choice was a small museum about Hoi An's history. Although it contained one or two old photographs, and a rather nice old map of indochina from the 19th century, the museum itself didn't have alot to show. Ah well, back to the shops we headed! A pair of leather shoes and a coat followed. Sigh. Hard life. As it was approaching 5pm we returned to Su's for our first fitting. Everything was pretty much in order and Susie left with another dress on order.\n\nDay two!\n\nDay two was our 3 year anniversary so we decided to go out for a nice dinner in the evening. First off we had some more shops and attractions to visit though. To begin with we headed to a temple which was unremarkable, aside from the small carved giraffes which adorned their entrance, random even for Vietnam! Next we headed to a restaurant Susie had found in the guide book which was on an island across from to the majority of Hoi An. It was called the lighthouse and was run by a Dutch man and his Vietnamese wife. The setting was beautiful and sitting on the 3rd floor with Vietnamese wine, looking out on the town, we certainly felt that this was the life! We had a few more fittings after this and had probably our best indian yet for lunch! In the afternoon we headed to a cultural performance of music and drama which was surprisingly entertaining.\n\nMore shopping. Then, in the evening we found a rather tucked away restaurant down a back alley. In reality, there was nothing back alley about the \"Secret Garden\" and we had an absolutely delicious dinner, despite being told by our waitress (who wasn't in any sort of uniform, we assume that she did work there) we were eating most of our dishes incorrectly! Fortunately she corrected us, though rolling up a Vietnamese dumpling in a lettuce leaf, with chili, and dipping it into a sauce, and managing to put in into our mouths without spilling any, was a little beyond both of us! That said it really was delicious and the live music added to the evening (though it took Susie far too long to realise it was actually live!)\n\nThe next day we headed to the oldest original house in Hoi An. After being told, with no arguments, where we should sit to listen to the tour we were told about the Japanese and Chinese influences of the house and also that it had been in the same family for 7 generations. We were also shown the level where the waters flooded to in the rainy season, over 1.5m, during which time they move all the furniture upstairs. We also saw some beautiful wooden panels with chinese characters carved in mother of pearl. Even more amazing was that the characters were made up of tiny models of birds!\n\nAfter the house we visited the \"Japanese covered bridge,\" one of the most famous landmarks in Hoi An, but to us, pretty unremarkable. I mean, the name kinda describes it.\n\nNext on the tour was another original house, which was essentially identical to the first one, perhaps unsurprising given they were only built 20 years apart, but a little disappointing. With 4 hours to go until our bus, Susie's insistance that John should get a lumberjack shirt finally reached a head and it was added the the pile. More impressive than the tenacity of the credit line (thanks again Mum) was the fact that the shirt only took 2.5 hours from it's first try on to being completely made to measure and finished! Hoi An certainly don't want to stop you parting with your cash! 5pm eventually came and our time in Hoi An was at an end. Phew!\n\nOur tally was therefore one 3 piece suit, 2 pairs of shoes, 2 shirts, 2 dresses, a jump suit, 2 coats, one pair of trousers, some plates and some other things.......which cost.....ENOUGH!\n\nPosted by John_713 02:48 Archived in Vietnam Comments (0)\n\n## Hanoi (part 2), the overnight bus and onto Hoi An\n\nOh, and, unexpectedly, Hue. Stupid bus company.\n\n22 \u00b0C\n\nThe next day, after our return from Halong bay, we had a slice of leftover pizza for brekkie, before heading downstairs, where it transpired that we had breakfast included at our hotel. So, two breakfasts it was! Susie had a desert, by having a banana pancake, while John had an omelet.\n\nWe then set off, very full, on attempt 2 to see Uncle Ho! When we arrived this time, the presence of guards, scanners, hundreds of tour groups, etc, alerted us to the fact that HCM was available for viewing. Hurrah! After getting a little lost, and then being put through an airport style scanner, where you weren't allowed to take water through (more security than the land border we entered through, where a guard just had a little rifle around in our bags!), we had our camera taken off us, and then we joined a queue ready for our sighting! As we headed in in our line, past LOTS of armed security guards, we were told off for talking before we'd even entered the building! Then we thought we'd better be quiet! We were walked into the Mausoleum, where we walked past lots more security guards, in\\\\to the room where Uncle Ho himself is (except for the 3 months of the year when he goes to Russia for maintenance of course!). In the room there were 6 security guards around the sides where you can walk, and 4 more in the central bit, surrounding a glass coffin\/case with the big man himself in. He is is lying down, and looks rather fake and waxworky really, but would do you expect when he's been dead for 40 years??? Apparently, so we found out later, his head looks big, because of how many times they've had to re-embalm it, but because he's dressed it's not all that obvious. It was the most surreal experience, but a definite must do for anyone in Hanoi!!!!\n\nThe Mausoleum\n\nWe headed out, past all the horrible gift shops that would have HCM turning in his grave, if he was in one, and then went to the 'Hanoi Hilton', an old prison that is now a Museum. It was built by the French, when Vietnam was under their control, and has since been used by the Japanese, and by the Vietnamese against the Americans (when it held mostly American pilots, including John McCain), when it gained the nickname it now holds.\n\nThe Museum was interesting, but most of the prison has been knocked down now, and the Museum was so biased that it made for irritating, if funny reading. Lots of talk of the horrible oppression of the French and Japanese (which, don't get us wrong, we're sure was awful), but only a little bit of information about it during the Vietnam war, and that was highly complementary to the Vietnamese. The exhibits actually said that it gained it's nickname because of the good conditions...apparently the Vietnamese don't get sarcasm!!\n\nSome slightly scary models demonstrating conditions under French oppression\n\nAfter that, we headed back to the city centre. We went to try and find somewhere to exchange the books that we had finished reading, but despite finding two places were unsuccessful - one didn't seem to exist (it turned out it has moved recently) and the other one sneered at our books, since one was a hardback and one a photocopy, and refused to give us any money off the books he had to sell, despite having about 1,000,000, and pricing them waaaaay too high (even an old, tatty copy of Rebecca was $3, and most were$5 or more for second hand books), so we gave up. We then went and had lunch at a little cafe, which was boring and average, and then chilled out for the rest of the afternoon, reading, using the internet and just chilling by the lake.\n\nWe're not going to lie, it wasn't the best nights sleep either of us have ever had. But we did both sleep (yes, even Susie who never sleeps on transport), and probably just about got our 8 hours, during the 11 hours or so we tried to sleep! It was very bumpy, but our seatbelts held us in, and the choice of beds proved worthy, as the bed being flat made a lot of difference!\n\nWe arrived in Hue at 9am, feeling a little dazed and sleepy but not too bad considering, expecting to catch a connecting bus straightaway (that was what we'd been told!), but it turned out we had a 4 hour stopover. Grrrrrr.\n\nOh well, we decided to make the most of it and to explore Hue. We had tasty noodle soup for breakfast, then wandered over to the Citadel, which is where the capital of Vietnam was for a long time (don't ask me when or for how long, I don't remember!). We had a tea, and then walked all the way around. It was really impressive, but we decided not to go inside.\n\nInstead we wandered along the river to the local market, where we window shopped for a while, before going back to have lunch...a very Vietnamese caesar salad and chips. Yum!!\n\nWe then went back to get our bus...it turns out when you're told the bus will be there at 1, that's just accounting for Western stupidity, and so that actually means 2:10...Since we'd been there since 12:30, we were slightly annoyed, but we bought some oreos, and Susie made John play fun fun cards games (that he strangely didn't enjoy!), which kept us both entertained (if stressed on John's part) until the bus came.\n\nAnother four hour bus journey later (still on a sleeping bus...this is where we realised how good our choices had been - these beds only went down to a 45 degree angle, and we both struggled to sleep much. We arrived in Hoi An, finally, at 6pm, 25 hours after we started the journey. Pheeeeew!!!!\n\nThe hotel we were dropped off at wanted $18 a night...screw that, we started to walk down the street, when a lady on a moped called to us \"you come to my uncles Hotel, only$10\". Brilliant, we thought, only to have her drive off and leave us to guess the way, and keep driving past, shouting \"England\" at us. Very confusing, and then by chance we did end up in her Uncle's hotel! It was very nice, and they were all very friendly. The lady who'd taken us to the hotel (kind of) then came into our room and told us about her dress shop. We decided to go and see the next day, since Susie did want one dress. We then went and had a surprisingly tasty dinner at a restaurant a couple of doors down - Susie had very spicy but yummy chicken with chilli and lemongrass and John had some other chicken dish! It was the nicest Asian food we'd had since Cambodia! Hoi An was off to a good start! We then went and collapsed into bed, glad of a real bed!\n\nNB - Sorry for the lack of photos at the minute, we'll upload them soon. We're having camera-computer connectivity issues at the moment!\n\nPosted by Susiep539 04:19 Archived in Vietnam Comments (0)\n\n## Halong Bay\n\n14 \u00b0C\n\nHalong bay is one of those 'must see' things in SE asia, possibly even a must see in the world really. So we decided we must see it! Fortunately our lovely hotel booked tours, and despite them understandably trying to sell us the Deluxe, VIP, SUPER DUPER $70 tour, we decided to opt for$40, 2 days in the bay and one night on a boat, Susie's favourite!\n\nSimply enough we got picked up from our hotel and driven the 4 hours or so towards Halong City. One the way we stopped off at the mother of all tourist traps, a traditional arts shop, in the middle of nowhere, which probably knocked a few quid off the cost of our tour. Of course we didn't buy anything and to be honest everything there you could get cheaper in Hanoi, still they had clean toilets. Only 20 minutes out of our day and we headed off again.\n\nWe were greeted from the bus by tourists who had taken the tour the day before. They looked rather bedraggled, sleepy and fed up, but we didn't take too much notice. We were told to wait for a while by our guide, and meanwhile, we were overtaken by several very organised Japanese tours (who didn't have to wait, naturally)! Next, onto a boat which \"moored\" by constantly running it's engine and driving its bow into the pier, mmm eco! Fortunately, we only had to hang about long enough for a random member of staff to arrive with some food and we were off!\n\nSoon we arrived at our rather fancy \"Junk\".\n\n(Susie expects this luxury on Drommie from now on!)\n\nSeveral blogs and LP heavily criticise the unauthentic and touristic origins of the junks, but we found ours rather charming. It might have been contrived, but it had some charm and hey, Halong is a tourist spot, what youi gonna do?! At lunch we sat with 2 Aussies and two Scottish girls who were on a gap year teaching in Malaysia. In fact, they were on the same scheme, Project Trust, that Susie had turned down before going to York (John considers his options whether this had been for the best or not....:p)Lunch was a fairly ordinary affair but there were CHIPS! Although not nearly enough, but still.\n\nAfter lunch we arrived at a pier and were pointed towards a rather large and impressive (though no Kong Lor) cave. We had heard it was often dubbed the disco cave, and we could see why as the whole thing was lit up like a giant night club! Kind of beautiful, if somewhat ridiculous. Of course the Japanese were ahead of us, but they were being told, in intricate details, about the rock formations. We declined the explanation and continued out. We visited another smaller cave and then headed back to the boat.\n\nNext on our tour was a floating village, not unlike the ones we had seen on our Battambang - Siem Reap boat trip, only this time it was at sea! Our boat was also approached by \"floating coops\", ladies with rowing boats filled with crisps, drinks, fruit, you name it! Kinda cool really, too bad we weren't hungry. Our guide also pointed out that one of the rocks in this bay was on the back of a 200,000d ($10) note. After the village we continued on our cruise along the bay for what felt like years, and the whole time all we could see, from horizon to horizon, were limestone karsts. Endlessly. John kept exclaiming, \"there are too many rocks!\" it was insane how many there are and for how long they continue. It was incredible. Pictures say it all..... Eons later we moored up with every other boat in Halong bay (which is alot) and were told now was the time for swimming! By this point it was getting dark, and it was pretty cold, but John was keen (Susie less so) and an Irish guy and the Aussie from earlier were goading excessively. Of course John had to jump in off the top of the 3 storey boat.....while Susie could just about manage to slide herself in from about 1m up. Hehe it was fun, but freezing, and the water was full of oil (which John swallowed of course, as he couldn't keep his mouth shut during the drop. Tasty!) After we dried off it was time for dinner, another indifferent affair, and I'm afraid we had to concede to tiredness and headed off to bed at around 830! Ah well early day tomorrow, kayaking! Now this kayaking business was a bit of an enigma to us, because we'd never been told about it when we were sold the tour, but the Scottish girls had. Anyway, 6:30AM, bright and early we got up ready for a paddle. Annoyingly our boat seemed to arrive last and all the boats were already out, meaning we had to wait another 20 minutes. Not a long time, but a pain since we'd been told we had to get up early. Also it was only the company our boat had booked with that was out of canoes, there were plenty sitting around not being used, grrr. Anyway, after a while we headed off into the water, and, despite a little argument we managed to make it about as far as we could around the bay. It was really beautiful, shame about the rubbish in the water, but we did rescue a plastic bottle! After Kayaking we were taken to a small island which had a rather nice beach and a karst to climb. It was 50,000d ($2.50) each to visit but we decided the view would be worth it. It certainly was\u2026.\n\nAfterwards we slowly headed back to Halong city and joined a convoy of boats doing the same. It was strange because we hadn\u2019t seen any on our first day, despite reading it was a bit like a conveyor belt, but now we could see what they meant! Though it wasn\u2019t annoying at all, it\u2019s not like they can make Halong Bay bigger!\n\nOnce we\u2019d docked we found out why the tourists had been so aggravated the day before. Despite being ushered off the boat, we then had to wait 45 minutes for the bus, which would take us just 5 minutes down the road for lunch. Not cool. Lunch was pretty dire too. Meh. Finally we got on the road again (not before stopping at another tourist trap, whose saving grace was ice creams this time, which we recommended to 4 other people and saw about 10 with before we left, note to tourist trappers, ice creams, not giant statues of Buddha, no matter how happy he looks!!)\n\nAs we pulled away from the trap our tour guide got out of the bus and was replaced by another Vietnamese and an American who seemed a bit confused. A discussion followed with him being told he would be taken to the airport. Hmm\u2026we didn\u2019t want to go to the airport, and nor did anyone else, though he had only agreed to come on our bus because he\u2019d been told in advance that we were all going. This was a 1.5 hour detour for us and noone was very happy about it, oh except the Vietnamese and the driver, who pocketed an above market rate, $20 for the journey. Meh nothing we could do in the end but a shame. Eventually we got back to our lovely hotel to meet a shocked and upset looking receptionist who had, the day before, promised to save our room for us. Guess what, she\u2019d forgotten! She was quick to offer us an apology and a room in another hotel. Hmm we thought, how much is this going to cost us?$15 she said, the same as we\u2019d had before, and she\u2019d pay the difference. Well it was a shame, because our new hotel was technically nicer, but the staff weren\u2019t nearly as friendly and the room didn\u2019t have a view, but you can\u2019t beat that for customer service!\n\nFinally, to top off the day we\u2019d promised ourselves a little naughty treat, after a recommendation by one of the Scottish volunteers. PIZZA HUT! It was a long walk, to a suitably faceless mall, filled with rich Vietnamese, there to buy tvs and cars and things 90% of the population can\u2019t afford, and we did get two larges between us (which drew shocked looks from pretty much everyone) and we did take half of it home and have it for breakfast and lunch the next day, but DAMN WAS IT DELICIOUS!\n\nPosted by John_713 02:48 Archived in Vietnam Tagged halong halong_bay Comments (1)\n\n## Hanoi!\n\nThe arrival to real life!\n\n23 \u00b0C\n\nSo, there we were, somewhere in Hanoi, but luckily still alive despite the bus drivers best efforts. We walked into the bus station to try to find a map, or someone to ask. No go, it was all shut and dark. Fantastic. We decided to just start walking, and wandered around some fairly main, lit streets, but they were all very local, and there was no English anywhere. We walked past a couple of places that could\u2019ve been hotels, but we weren\u2019t sure and didn\u2019t dare go in and ask! 10 minutes and lots more maybe hotels\/maybe nots later, we braved it, and after one telling us they had no beds, and looking shocked at the very prospect of us checking in, another one scooped us up, and hurrah, we had a bed! Admittedly a rock solid bed, in what may or may not have been somewhere that people normally rent \u2018by the hour\u2019 (read, where to take your mistress\/prostitute...), but we decided to ignore that possible fact, and just went to sleep!\n\nThe next morning, first task, find out where on earth we were, and how to get to the city centre. After a little walk around, which stressed Susie out because she had no idea where anywhere was in relation to our hotel etc (John did though so it was OK), we found a coffee house with wi-fi. We eventually worked out where we were \u2013 about 6km south of the city centre. We decided in our infinite wisdom to walk it, and after getting some money out, checking out (where the woman charged us $3 less than the man had said, which made up for the fact he charged us 5 times more than he should have done for water. Haha. The walk was rather long, but straightforward, and we were both enjoying being somewhere with some life to it, after all of Laos (which although lovely is very quiet!). After about 90 minutes, we arrived at the hotel we\u2019d planning to stay in, Liberty Hotel, where we were greeted by a lovely, yet completely insane lady who asked us about 10 questions in quick succession, and then finally took us to a really nice room. It had a HOT SHOWER, CABLE TELEVISION, SOFT PILLOWS, and various other luxuries unknown to us for weeks! It was an extravagance at$15 a night, but soooo worth it. Ahhhhh.\n\nWe went out and got our bearings (well, John did anyway, Susie seems to have a mental block knowing her way round Hanoi). After a little wander, we went and got a very locals lunch of Bun Cha (grilled pork mince meat balls, with a tasty soup with more pork in it, that is served with a massive plate of lettuce\/other greens, loads of noodles, fish spring rolls and a beer), which was very tasty, but LOTS of food and far too much meat for people who\u2019ve basically been eating vegetarian for 2 weeks!\n\nWe then went back to the room, and proceeded to have a VERY lazy afternoon, which was much needed after the busy last week or so we\u2019d had! We spent almost the whole afternoon in our room, making the most of having cable tv in our room (first time since Siem Reap!), and watched \u2018America\u2019s Next Top Model\u2019 for about 5 hours. Disgraceful, yes, but definitely some much needed trash! Our brains hadn\u2019t chilled out that much for weeks!\n\nAfter America\u2019s Next Top Model finished, an episode of Masterchef USA gave us both a massive craving for ribs, so a short guide book flick later, we ended up at Al Fresco\u2019s for dinner. This is a small Australian run chain that does ribs, burgers, etc. Upon arrival, we deliberated for a while about whether to get a whole rack each, but descided against it, mainly because it was \\$20! In the end we shared one, and we were so glad we did. It was huuuuuuge!! With that and an extra potato wedges, we were both struggling to finish it, and we were really hungry before! We did finish though, because they were quite possible the best ribs we\u2019ve ever had - so meaty and delicious, and yummmmm!!!\n\nWhat made the whole experience even better was the fact that there was paper over the table, and crayons, for drawing on. WIN! We had great fun, and Susie drew an awesome map of our route so far!\n\nWe staggered back along the edge of the Hoan Kiem Lake, which was surrounded by couples, cuddling up on the benches! We declined to join in, and instead went back and went to bed!\n\nDid we mention that there's a LOT of motorbikes here???\n\nThe next day we woke up at 8am, which is fairly late for us, and set off with the intention to go and see Ho Chi Min\u2019s (or Uncle Ho as the Vietnamese fondly call him) dead, embalmed body. However, when we got there it turns out that it\u2019s shut on Mondays, we can only assume because he needs some down time! Undetered, we set off to find more about him, and went to see his house, a simple wooden building, and the palace next door, which was where the Royal family lived, and is supposed to contrast how wonderfully simply Uncle Ho lived his life!\n\nWe also went to the Ho Chi Min Museum, which tells you about his life and times in a stupidly abstract way!\n\nTHis tells you something about HCM, of course :s\n\nWe found it all rather amusing though, and the contrast between everything that Ho Chi Min and the Vietnamese communists stood for, compared to Vietnam today, and the stalls outside the museum selling tacky souvenirs, is funny but a little ridiculous and sad.\n\nAfter that, we went to the Temple of Literature, a Confucian temple, which was very pretty and peaceful.\n\nOur tummys finally started rumbling after last nights ribs, and so we headed to a little cafe. It provides jobs for locals from poor backgrounds, and so we felt very good about ourselves, both because our money was going to a good cause, and because we had yummy cakes and tea. Mmmm!\n\nIn the afternoon, we watched some more TV, and then went out to St. Joseph's Cathedral. This looks like a small version of the Notre Dame from the outside, and inside looked exactly like a church\/cathedral would at home. Despite not being in the least religious, it was really comforting, just because of how British it felt!!\n\nIn the evening, we went to a vegetarian restaurant, which specialising in making dishes that look and taste like meat, while still being suitable for veggies. This is fairly common in Vietnam, as traditionally hosts wanted to make food for their Buddhist guests that was the same as their other guests. It was OK, but we caught them at a bad time, as they were very busy, and so it wasn\u2019t as good as it could have been. It did look very like meat, and the taste was there, but the texture was missing!!\n\nWe then headed off to bed, ready for our early start to Halong Bay the next day.\n\nPosted by Susiep539 00:31 Archived in Vietnam Comments (0)\n\n(Entries 1 - 5 of 7) Page [1] 2 \u00bb Next","date":"2022-07-02 04:23:23","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.2575821876525879, \"perplexity\": 3695.648552651734}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-27\/segments\/1656103984681.57\/warc\/CC-MAIN-20220702040603-20220702070603-00526.warc.gz\"}"}	null	null
require 'gogokit/utils' require 'gogokit/resource/currency' module GogoKit class Client # {GogoKit::Client} methods for getting currencies module Currency include GogoKit::Utils # Retrieves a currency by currency code # # @param [String] code The currency code of the currency to be retrieved # @param [Hash] options Optional options # @return [GogoKit::Country] The requested currency def get_currency(code, options = {}) root = get_root object_from_response(GogoKit::Currency, GogoKit::CurrencyRepresenter, :get, "#{root.links['self'].href}/currencies/#{code}", options) end # Retrieves all currencies supported by viagogo # # @see http://viagogo.github.io/developer.viagogo.net/#viagogocurrencies # @param [Hash] options Optional options # @return [GogoKit::PagedResource] All currencies def get_currencies(options = {}) object_from_response(GogoKit::PagedResource, GogoKit::CurrenciesRepresenter, :get, get_root.links['viagogo:currencies'].href, options) end end end end	{ "redpajama_set_name": "RedPajamaGithub" }	5,026
Q: [OLVED. Error getting data from POST ajax petition Symfony2 It has been a rough night and morning today hahaha. I'm trying to get some data with symfony2 from an AJAX 'POST' petition. Actually I want to sent an array and get it in the controller but I'm receiving an error like this variable is null. I think I'm trying to get it in a right way but... Let's take a look! This is the JS AJAX petition, I'm getting the ul#sortable.children() order to update it on the dataBase, so I sent an array with the position and id. example: ["1", "3", "2"]. So the object with id=1 in the db is going to be in the position 1. The element with id=3 is going to be in the position 2 and the element with id=2 is going to be in the position 3. $('#ordenar').click(function(){ var $children = $('#sortable').children(); var numElementos = $children.length; var socialSorted = []; for(var i=0; i<numElementos; i++){ socialSorted.push($children[i].id); } $.ajax({ url: ' {{ path('admin_update_social_position') }} ', datos: socialSorted, method: 'POST' }).done(function (data) { if(data.type == 'OK'){ window.location.reload(); } if(data.type == 'ERROR'){ $('#error-message').slideDown(); } }); }); And here is the controller /** * @Route("/admin/update/order/social", name="admin_update_social_position") */ public function orderSocial(Request $request) { $em = $this->getDoctrine()->getManager(); $socialSorted = $request->request->get('socialSorted'); $numElementos = count($socialSorted); for($i=0; $i<$numElementos; $i++) { $social = $em->getRepository('AppBundle:Social')->findById($socialSorted[$i]); $social->setPosition($i+1); $em->persist($social); } if (empty($socialSorted)) { $this->sendResponseStatus('ERROR'); return new JSONResponse($this->getData()); } $em->flush(); $this->sendResponseStatus('OK'); // Generamos los datos para la respuesta ajax return new JSONResponse($this->getData()); } I tried many ways... sending the array, sending a JSON with an array in and also different ways to get the data from the controller... any advice/solution? Thanks you to all of you EDIT: The error was in the lines $social = $em->getRepository('AppBundle:Social')->findById($socialSorted[$i]); $social->setPosition($i+1); $em->persist($social); Becausee after findBy it returns you and arrayCollection and then I should do: $social = $em->getRepository('AppBundle:Social')->findById($socialSorted[$i]); $social[0]->setPosition($i+1); $em->persist($social[0]); A: Try this: $.ajax({ url: ' {{ path('admin_update_social_position') }} ', data: { socialSorted: socialSorted, }, method: 'POST' }).done(function (data) { if(data.type == 'OK'){ window.location.reload(); } if(data.type == 'ERROR'){ $('#error-message').slideDown(); } }); You need to send the data as an array. You ask for socialSorted key in request, but actually you don't send it A: The problem here lies in the fact that you are expecting a socialSorted variable from AJAX but never getting it: In controller: $socialSorted = $request->get('socialSorted'); But in AJAX call.. datos: socialSorted, In your controller, just make it read... $socialSorted = $request->get('datos'); or change the AJAX call to socialSorted: socialSorted	{ "redpajama_set_name": "RedPajamaStackExchange" }	586
Q: Not able to set data in guacamole clipboard I am using Apache Guacamole library in our project for rendering Windows VM in web browser. For Clipboard integration I need to transfer clipboard content from Local System to remote VM (guacamole Clipboard) and vice versa. I am able to get the clipboard content of remote VM using the guacamole onclipboard event. But I am unable to send Local System clipboard content to remote VM (Guacamole clipboard).I am using createClipboardStream() API for setting data to guacamole clipboard but I am not getting any data in remote VM clipboard. Please find the code snippet as below - Guacamole API reference - https://guacamole.apache.org/doc/0.9.2/guacamole-common-js/symbols/Guacamole.Client.html#createClipboardStream // sending Local System Clipboard content to Remote VM (Guacamole Clipboard) function setGuacamoleClipboard(data) { var stream = guac.createClipboardStream("text/plain"); var writer = new Guacamole.StringWriter(stream); for (var i=0; i<data.length; i += 4096){ writer.sendText(data.substring(i, i+4096)); } writer.sendEnd(); } I have also tried below Java code for setting guacamole clipboard using writeInstruction().This approach also did not work for me tunnel.getSocket().getWriter().writeInstruction(new GuacamoleInstruction("clipboard","text/plain","Welcome Guacamole clipboard")); Am I missing anything ?	{ "redpajama_set_name": "RedPajamaStackExchange" }	7,966
Exceptional Cuisine Ouverte Sur Sejour Petite Surface #10 - Maison Bois CARLA 100 Maison Bois GreenLife was uploaded in June 10, 2018 at 6:27 pm. If you want to apply this file as your PC background, you should tap the download link at the bottom or you can just right click on the image above and choose "Save Image As" to save the Exceptional Cuisine Ouverte Sur Sejour Petite Surface #10 - Maison Bois CARLA 100 Maison Bois GreenLife or by choose the "Set Desktop Background As" section if your internet browser has that option. If you were no able to grab the the most outstanding picture you are looking for, you need to go for "Search Column" at top right or browse other photo wallpapers whatever you want. This image has the image size is 235kB and the dimension of 840x630. Exceptional Cuisine Ouverte Sur Sejour Petite Surface #10 - Maison Bois CARLA 100 Maison Bois GreenLife has been seen by 27 users and it is a picture from Cuisine Ouverte Sur Sejour Petite Surface.	{ "redpajama_set_name": "RedPajamaC4" }	8,187
title: Microsoft-myanalytics inshort: määratlemata translator: Microsoft Cognitive Services ---	{ "redpajama_set_name": "RedPajamaGithub" }	6,072
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Pick you your copy of Cash Magnets here and qualify for instant access to all my bonuses.	{ "redpajama_set_name": "RedPajamaC4" }	106
We can't stress enough that wine is made in the vineyard, which is why our vineyards are so important to us. Domaine Berrien Cellars is an all estate winery. What does that mean? It means that all of our wines are made only from grapes grown in our vineyards and that all of our winemaking and bottling takes place right here on site as well. This gives us the control over the grapes and we make decisions all during the growing year that maximize the quality (not quantity) of our grapes. This gives us a higher probability of producing the most premium wines. Our unique site located on one of the highest points in Berrien County, within the Lake Michigan Shore AVA growing region, provides what can be the ideal climate for outstanding wine grapes. The extended growing season and gentle ripening contribute to the characteristics of quality and complexity in our wines. Located on southerly facing hillsides ranging from 900' to 800' of elevation, our vineyards are trellised in a north/south direction to provide even sunlight on both sides of the vines, and hold the sun's heat to allow better ripening of the grapes, especially for red wines. Spring in the Vineyard: Spring is a busy time in the vineyard – lots of pruning and clean up and renewal for the growing season ahead! Grapevines are similar to rose bushes, in that the vine (or bush) stays alive from year to year but last year's old growth up in the trellis needs to be pruned back each year in order to encourage new growth for the coming year. After we prune the vines, we collect the dead vine cuttings and remove them from the vineyard to avoid spreading any disease/mold spores that might be hiding there. Once the grapevines have started budding out, our greatest enemy in the vineyard is late spring freezes, which can kill or severely injure the new buds. This threat is usually past by mid-May.	{ "redpajama_set_name": "RedPajamaC4" }	6,922
I have a prediction: summer 2017 will be remembered as hot and hazy. Let's hope for long lazy days on the beach, backyard barbecues, fun and laughter with friends, warm starlit evenings, and dancing on the sand. May bank holiday weekend sees a new event at The Wyldes, the fabulous rural home of the Leopallooza Festival. Expect live music and DJs from 4pm until 1am each night. Camping available. 26 May ~ Double Brit award-winner Rag 'n' Bone Man. 27 May ~ Headline DJ set by Chase and Status. 28 May ~ Legendary 80's band The Human League. Tickets available online: £39.60 for each evening (£11 for children, under 5's free), £5.50 per person camping per night. VIP tickets (£71.50) give access to the VIP area with a relaxed lounge bar, gourmet food options and flushing toilets. VIP camping tickets (£22) give access to a separate camping area with flushing toilets and showers. A new event for 2017, The Great Estate Festival will be held in the grounds of Scorrier House. The line-up for the festival stage includes Echo and the Bunnymen, Hong Kong Ping Pong, The Showhawk Duo and Electric Swing Circus amongst others. Don't miss Craig Charles, who brings his Funk and Soul Show to Cornwall on the Sunday. Visit the website for full details of what's on, including hot air balloons, camel racing, a tattoo parlour, food and drink, hot tubs, and glamping. Tickets seem very reasonably priced: £75 for an adult weekend camping ticket, £22.50 for 10-18 year olds, under 10s are free. Day tickets also available. The Electric Beach Festival will be held on Great Western Beach in Newquay this year, with food and drink, SUP, yoga and a belly boarding competition all part of the weekend fun. Badly Drawn Boy headlines the Saturday night, along with Cuban Brothers, Backbeat Sound System, Wolfclub and Regime. After parties will continue into the night at the Koola Club and Chy Bar. Super Early Bird tickets available at the time of writing this, £30 for the weekend, £19 for each day. £14.50 for weekend tickets for 10 to 18 year olds, under 10s are free. Accommodation packages also available. The Eden Project always attracts big names, and this year's Eden Sessions are no exception. The atmosphere at the Eden Sessions is always fantastic, with great food and drink available, and ticket price includes admission to The Eden Project on the day of the gig, and the day after, so you can make the most of your time there. Accommodation available in the very cool Eden Project Youth Hostel – check out their "snoozeboxes". Tickets are available online, £45-£65 depending on the event. 2017 is the third Tunes in the Dunes and this year will be bigger than ever, with four stages between The Watering Hole and the end of Perranporth beach, each with its own identity. Headline acts include Reef, Xavier Rudd, Example, KT Tunstall, The Levellers, Billy Ocean, Backbeat Soundsystem, Land of the Giants and Izzy Bizu. See the full line-up here. Plus a giant water slide, yoga, great food and drink, and a secret beach party, if you can find it. Book online. £80 for an adult weekend camping ticket, £45 for under 15s, under 5s are free. Day tickets, after party tickets and VIP packages also available. Organised by the team behind Tunes in the Dunes, Bands in the Sands is a series of one-off gigs at Perranporth. Each event will be followed by an after party until 2am, free for ticket holders, at The Watering Hole. Tickets available online, prices vary (e.g. £20 for Feeder, £70 for Tom Jones) nearby campsites are listed on the website. So popular they've extended this year's festival to three nights, Leopallooza is a lot of fun in a field near Bude. Over 100 acts will appear on the seven stages (including the impressive permanent stage, pictured above); headlining are The Cribs and Gabrielle Aplin, with more to be announced soon. Leopallooza has a strong history of booking artists just before they break into the mainstream. Bastille played low on the bill in 2012, before the release of their debut Bad Blood, and returned as headliners in 2013. Rag'n'Bone Man played on the main stage in 2016, a full six months before releasing his bestselling debut album. So there is a good chance you'll see the next big thing, long before anyone else. See website for the full line-up and to book tickets. Weekend camping tickets are £110 for adults, family weekend tickets are £230, golden squirrel weekend tickets are £180 (includes access to the Golden Hollow, including gourmet food, luxury showers and toilets, and a separate camping area). Music forms just a small part of Port Eliot Festival. Originally a literary festival, this family-friendly festival now includes fashion, art, food and drink, comedy, adventure, science, film, gardening….and music. St Etienne headlines the Park Stage on the Saturday night, but wander the beautiful Port Eliot Estate to discover some hidden gems. Catch DJs by night at Caught by the River, and hear everything from synthpop to brass bands, classical groups to ceilidh bands, at venues such as The Ace of Clubs, The Walled Garden, The Orangery and The Black Cow Saloon. Day and camping tickets available online, prices vary. E.g. £64 for an adult day ticket, £172.50 for an adult weekend camping ticket, £455 for a family weekend camping ticket. Another incredible line-up for Cornwall's biggest music festival. You'll struggle to decide when, where and who to see. Star billing goes to Two Door Cinema Club, Jamiroquai and Alt-J. This huge event encompasses Fistral and Watergate, with WSL surf contests, BMX and skate ramps, shopping, food and drink, yoga, and more. Various ticket options are available, e.g. day tickets £59, weekend camping £169, VIP camping £259. This event at Healeys Cyder Farm is basically a big party in a field, with good music, a lively atmosphere, great food, and a lot of cider. So far acts confirmed are Electric Swing Circus, The Wurzels and Son of Dave. Keep an eye on their website for more details, and to book tickets. Weekend tickets £67.50 with camping, or £47.50 without. Under 14s are free.	{ "redpajama_set_name": "RedPajamaC4" }	9,954
All the texture and layers of your piece is just lovely! Now this totally made my day!!! Thanks for the love. Oh my goodness! This is so pretty. I really like the textures. Very pretty! The crackle is really great.	{ "redpajama_set_name": "RedPajamaC4" }	7,719
var module = angular.module("example", ["angularGrid"]); module.controller("exampleCtrl", function($scope, $http) { var columnDefs = [ {displayName: "Athlete", field: "athlete", width: 150, cellRenderer: athleteCellRendererFunc}, {displayName: "Age", field: "age", width: 90, cellRenderer: ageCellRendererFunc}, {displayName: "Country", field: "country", width: 120, cellRenderer: countryCellRendererFunc}, {displayName: "Year", field: "year", width: 90}, {displayName: "Date", field: "date", width: 110}, {displayName: "Sport", field: "sport", width: 110}, {displayName: "Gold", field: "gold", width: 100}, {displayName: "Silver", field: "silver", width: 100}, {displayName: "Bronze", field: "bronze", width: 100}, {displayName: "Total", field: "total", width: 100} ]; $scope.gridOptions = { columnDefs: columnDefs, rowData: null, angularCompileRows: true }; function ageClicked(age) { window.alert("Age clicked: " + age); } function athleteCellRendererFunc() { return '<span ng-bind="data.athlete"></span>'; } function ageCellRendererFunc(params) { params.$scope.ageClicked = ageClicked; return '<button ng-click="ageClicked(data.age)" ng-bind="data.age"></button>'; } function countryCellRendererFunc(params) { return '<country name="'+params.value+'"></country>'; } $http.get("../olympicWinners.json") .then(function(res){ $scope.gridOptions.rowData = res.data; $scope.gridOptions.api.onNewRows(); }); }); module.directive('country', function () { var FLAG_CODES = { 'Ireland': 'ie', 'United States': 'us', 'Russia': 'ru', 'Australia': 'au', 'Canada': 'ca', 'Norway': 'no', 'China': 'cn', 'Zimbabwe': 'zw', 'Netherlands': 'nl', 'South Korea': 'kr', 'Croatia': 'hr', 'France': 'fr' }; var flagHtml = '<img ng-show="flagCode" class="flag" border="0" width="20" height="15" src="http://flags.fmcdn.net/data/flags/mini/{{flagCode}}.png" />'; var nameHtml = '<span ng-bind="countryName" />'; return { scope: true, template: flagHtml + ' ' + nameHtml, link: function(scope, element, attrs) { var countryName = attrs.name; scope.countryName = countryName; scope.flagCode = FLAG_CODES[countryName]; } }; });	{ "redpajama_set_name": "RedPajamaGithub" }	9,197
Produced by Phil Schempf THE ODYSSEYS OF HOMER Together with the shorter poems Translated according to the Greek by George Chapman London: Published by George Newnes Limited Southhampton Street Strand W.C. New York: Published by Charles Scribner's Sons TO THE MOST WORTHILY HONOURED, MY SINGULAR GOOD LORD, ROBERT, EARL OF SOMERSET, LORD CHAMBERLAIN, ETC. I have adventured, right noble Earl, out of my utmost and ever-vowed service to your virtues, to entitle their merits to the patronage of Homer's English life, whose wished natural life the great Macedon would have protected as the spirit of his empire, That he to his unmeasur'd mighty acts Might add a fame as vast; and their extracts, In fires as bright and endless as the stars, His breast might breathe and thunder out his wars. But that great monarch's love of fame and praise Receives an envious cloud in our foul days; For since our great ones ceased themselves to do, Deeds worth their praise, they hold it folly too To feed their praise in others. But what can, Of all the gifts that are, be giv'n to man More precious than Eternity and Glory, Singing their praises in unsilenc'd story? Which no black day, no nation, nor no age, No change of time or fortune, force nor rage, Shall ever rase? All which the monarch knew, Where Homer liv'd entitled, would ensue: _Cujus de gurgite vivo Combibit arcanos vatum omnis turba furores, etc._ From whose deep fount of life the thirsty rout Of Thespian prophets have lien sucking out Their sacred rages. And as th' influent stone Of Father Jove's great and laborious son Lifts high the heavy iron, and far implies The wide orbs that the needle rectifies, In virtuous guide of ev'ry sea-driv'n course, To all aspiring his one boundless force; So from one Homer all the holy fire That ever did the hidden heat inspire In each true Muse came clearly sparkling down, And must for him compose one flaming crown. He, at Jove's table set, fills out to us Cups that repair age sad and ruinous, And gives it built of an eternal stand With his all-sinewy Odyssæan hand, Shifts time and fate, puts death in life's free state, And life doth into ages propagate. He doth in men the Gods' affects inflame, His fuel Virtue blown by Praise and Fame; And, with the high soul's first impression driv'n, Breaks through rude chaos, earth, the seas, and heav'n. The nerves of all things hid in nature lie Naked before him; all their harmony Tun'd to his accents, that in beasts breathe minds. What fowls, what floods, what earth, what air, what winds, What fires ethereal, what the Gods conclude In all their counsels, his Muse makes indued With varied voices that ev'n rocks have mov'd. And yet for all this, naked Virtue lov'd, Honours without her he as abject prizes, And foolish Fame, deriv'd from thence, despises. When from the vulgar taking glorious bound Up to the mountain where the Muse is crown'd, He sits and laughs to see the jaded rabble Toil to his hard heights, t' all access unable, etc. And that your Lordship may in his face take view of his mind, the first words of his Iliads is _μη̑νιν, wrath_; the first word of his Odysseys, _ἄνδρα man:_ contracting in either word his each work's proposition. In one _predominant perturbation;_ in the other _over-ruling wisdom._ In one the body's fervour and fashion of outward fortitude to all possible height of heroical action; in the other the mind's inward, constant, and unconquered empire, unbroken, unaltered, with any most insolent, and tyrannous infliction. To many most sovereign praises is this poem entitled; but to that grace, in chief, which sets on the crown both of poets and orators; _τὸ‭ τὰ μικρὰ μεγάλως, καὶ τὰ κοινὰ καιίνως:_ that is, ‭_Parva magnè dicere; pervulgata novè; jejuna plenè.--To speak ‭things little greatly; things common rarely; things barren and empty ‭fruitfully and fully._ The return of a man into his country is his ‭whole scope and object; which in itself, your Lordship may well ‭say, is jejune and fruitless enough, affording nothing feastful, ‭nothing magnificent. And yet even this doth the divine inspiration ‭render vast, illustrious, and of miraculous composure. And for ‭this, my Lord, is this poem preferred to his lliads; for therein much ‭magnificence, both of person and action, gives great aid to his ‭industry; but in this are these helps exceeding sparing, or nothing; ‭and yet is the structure so elaborate and pompous that the poor ‭plain ground-work, considered together, may seem the naturally ‭rich womb to it, and produce it needfully. Much wondered at, ‭therefore, is the censure of Dionysius Longinus, (a man otherwise ‭affirmed grave and of elegant judgment,) comparing Homer in his ‭Iliads to the Sun rising, in his Odysseys to his descent or setting, ‭or to the ocean robbed of his æsture, many tributary floods and ‭rivers of excellent ornament withheld from their observance. When ‭this his work so far exceeds the ocean, with all his court and ‭concourse, that all his sea is only a serviceable stream to it. ‭Nor can it be compared to any one power to be named in nature, ‭being an entirely well-sorted and digested confluence of all; ‭where the most solid and grave is made as nimble and fluent as the ‭most airy and fiery, the nimble and fluent as firm and ‭well-bounded as the most grave and solid. And, taking all ‭together, of so tender impression, and of such command to the ‭voice of the Muse, that they knock heaven with her breath, and ‭discover their foundations as low as hell. Nor is this ‭all-comprising Poesy fantastic or mere fictive; but the most ‭material and doctrinal illations of truth, both for all manly ‭information of manners in the young, all prescription of justice, ‭and even Christian piety, in the most grave and high governed. To ‭illustrate both which, in both kinds, with all heightof expression, ‭the Poet creates both a body and a soul in them. Wherein, if the ‭body (being the letter or history) seems fictive, and beyond ‭possibility to bring into act, the sense then and allegory, which ‭is the soul, is to be sought, which intends a more eminent ‭expressure of Virtue for her loveliness, and of Vice for her ‭ugliness, in their several effects; going beyond the life than any art ‭within life can possibly delineate. Why then is fiction to this end ‭so hateful to our true ignorants? Or why should a poor chronicler ‭of a Lord Mayor's naked truth (that peradventure will last his year) ‭include more worth with our modern wizards than Homer for his ‭naked Ulysses clad in eternal fiction? But this proser Dionysius, ‭and the rest of these grave and reputatively learned--that dare ‭undertake for their gravities the headstrong censure of all things, ‭and challenge the understanding of these toys in their childhoods; ‭when even these childish vanities retain deep and most necessary ‭learning enough in them to make them children in their ages, ‭and teach them while they live--are not in these absolute divine ‭infusions allowed either voice or relish: for, _Qui Poeticas ad fores ‭accedit, etc._ (says the divine philosopher) he that knocks at the ‭gates of the Muses, _sine Musarum furore,_ is neither to be ‭admitted entry, nor a touch at their thresholds; his opinion of entry ‭ridiculous, and his presumption impious. Nor must Poets ‭themselves (might I a little insist on these contempts, not tempting ‭too far your Lordship's Ulyssean patience) presume to these doors ‭without the truly genuine and peculiar induction. There being in ‭Poesy a twofold rapture,--or alienation of soul, as the abovesaid ‭teacher terms it,--one _insania,_ a disease of the mind, and a mere ‭madness, by which the infected is thrust beneath all the degrees of ‭humanity: _et ex homine, brutum quodammodò redditur:_--(for ‭which poor Poesy, in this diseased and impostorous age, is so ‭barbarously vilified;)--the other is, _divinus furor,_ by which the ‭sound and divinely healthful _suprà hominis naturam erigitur, et in ‭Deum transit._ One a perfection directly infused from God; ‭the other an infection obliquely and degenerately proceeding ‭from man. Of the divine fury, my Lord, your Homer hath ever ‭been both first and last instance; being pronounced absolutely, ‭_τὸν σοφώτατον, καὶ τὸν θειότατον ποιητήν,_ "THE MOST WISE ‭AND MOST DIVINE POET." Against whom whosoever shall ‭open his profane mouth may worthily receive answer with ‭this of his divine defender--Empedocles, Heraclitus, Protagoras, ‭Epicharmus, etc., being of Homer's part--_τίς οο͒ν,_ etc.; who ‭against such an army, and the general Homer, dares attempt the ‭assault, but he must be reputed ridiculous? And yet against this ‭host, and this invincible commander, shall we have every ‭_besogne_ and fool a leader. The common herd, I assure myself, ‭ready to receive it on their horns. Their infected leaders, ‭ Such men as sideling ride the ambling Muse, ‭ Whose saddle is as frequent as the stews. ‭ Whose raptures are in ev'ry pageant seen, ‭ In ev'ry wassail-rhyme and dancing-green; ‭ When he that writes by any beam of truth ‭ Must dive as deep as he, past shallow youth. ‭ Truth dwells in gulfs, whose deeps hide shades so rich ‭ That Night sits muffled there in clouds of pitch, ‭ More dark than Nature made her, and requires, ‭ To clear her tough mists, heav'n's great fire of fires, ‭ To whom the sun itself is but a beam. ‭ For sick souls then--but rapt in foolish dream-- ‭ To wrastle with these heav'n-strong mysteries, ‭ What madness is it? when their light serves eyes ‭ That are not worldly in their least aspect, ‭ But truly pure, and aim at heav'n direct. ‭ Yet these none like but what the brazen head ‭ Blatters abroad, no sooner born but dead. ‭Holding, then, in eternal contempt, my Lord, those short-lived ‭bubbles, eternize your virtue and judgment with the Grecian ‭monarch; esteeming, not as the least of your new-year's presents, ‭ Homer, three thousand years dead, now reviv'd, ‭ Ev'n from that dull death that in life he liv'd; ‭ When none conceited him, none understood ‭ That so much life in so much death as blood ‭ Conveys about it could mix. But when death ‭ Drunk up the bloody mist that human breath ‭ Pour'd round about him--poverty and spite. ‭ Thick'ning the hapless vapour--then truth's light ‭ Glimmer'd about his poem; the pinch'd soul ‭ (Amidst the mysteries it did enrol) ‭ Brake pow'rfully abroad. And as we see ‭ The sun all-hid in clouds, at length got free, ‭ Through some forc'd covert, over all the ways, ‭ Near and beneath him, shoots his vented rays ‭ Far off, and sticks them in some little glade, ‭ All woods, fields, rivers, left besides in shade; ‭ So your Apollo, from that world of light ‭ Clos'd in his poem's body, shot to sight ‭ Some few forc'd beams, which near him were not seen, ‭ (As in his life or country) Fate and spleen ‭ Clouding their radiance; which when Death had clear'd, ‭ To far-off regions his free beams appear'd; ‭ In which all stood and wonder'd, striving which ‭ His birth and rapture should in right enrich. ‭ Twelve labours of your Thespian Hercules ‭ I now present your Lordship; do but please ‭ To lend life means till th' other twelve receive ‭ Equal achievement; and let Death then reave ‭ My life now lost in our patrician loves, ‭ That knock heads with the herd; in whom there moves ‭ One blood, one soul, both drown'd in one set height ‭ Of stupid envy and mere popular spite. ‭ Whose loves with no good did my least vein fill; ‭ And from their hates I fear as little ill. ‭ Their bounties nourish not when most they feed, ‭ But, where there is no merit or no need, ‭ Rain into rivers still, and are such show'rs ‭ As bubbles spring and overflow the flow'rs. ‭ Their worse parts and worst men their best suborns, ‭ Like winter cows whose milk runs to their horns. ‭ And as litigious clients' books of law ‭ Cost infinitely; taste of all the awe ‭ Bench'd in our kingdom's policy, piety, state; ‭ Earn all their deep explorings; satiate ‭ All sorts there thrust together by the heart ‭ With thirst of wisdom spent on either part; ‭ Horrid examples made of Life and Death ‭ From their fine stuff wov'n; yet when once the breath ‭ Of sentence leaves them, all their worth is drawn ‭ As dry as dust, and wears like cobweb lawn: ‭ So these men set a price upon their worth, ‭ That no man gives but those that trot it forth ‭ Though Need's foul ways, feed Humours with all cost ‭ Though Judgment sterves in them; rout, State engrost ‭ (At all tobacco-benches, solemn tables, ‭ Where all that cross their envies are their fables) ‭ In their rank faction; shame and death approv'd ‭ Fit penance for their opposites; none lov'd ‭ But those that rub them; not a reason heard ‭ That doth not soothe and glorify their preferr'd ‭ Bitter opinions. When, would Truth resume ‭ The cause to his hands, all would fly in fume ‭ Before his sentence; since the innocent mind ‭ Just God makes good, to Whom their worst is wind. ‭ For, that I freely all my thoughts express, ‭ My conscience is my thousand witnesses; ‭ And to this stay my constant comforts vow, ‭ _You for the world I have, or God for you._ ‭ CERTAIN ANCIENT GREEK EPIGRAMS TRANSLATED ‭ All stars are drunk-up by the fiery sun, ‭ And in so much a flame lies shrunk the moon. ‭ Homer's all-liv'd name all names leaves in death, ‭ Whose splendour only Muses' bosoms breathe. ‭ ANOTHER ‭ Heav'n's fires shall first fall darken'd from his sphere, ‭ Grave Night the light weed of the Day shall wear, ‭ Fresh streams shall chase the sea, tough ploughs shall tear ‭ Her fishy bottoms, men in long date dead ‭ Shall rise and live, before Oblivion shed ‭ Those still-green leaves that crown great Homer's head. ‭ ANOTHER ‭ The great Mæonides doth only write, ‭ And to him dictates the great God of Light. ‭ ANOTHER ‭ Sev'n kingdoms strove in which should swell the womb ‭ That bore great Homer, whom Fame freed from tomb; ‭ Argos, Chios, Pylos, Smyrna, Colophone, ‭ The learn'd Athenian, and Ulyssean throne. ‭ ANOTHER ‭ Art thou of Chios? No. Of Salamine? ‭ As little. Was the Smyrnean country thine? ‭ Nor so. Which then? Was Cuma's? Colophone? ‭ Nor one nor other. Art thou, then, of none ‭ That fame proclaims thee? None. Thy reason call. ‭ If I confess of one I anger all. ‭ CONTENTS ‭ THE ODYSSEYS ‭ THE BATRACHOMYOMACHIA ‭ HYMNS-- ‭ To Apollo ‭ To Hermes ‭ To Venus (First Hymn) ‭ To Venus (Second Hymn) ‭ Bacchus, or the Pirates ‭ To Mars ‭ To Diana ‭ To Venus (Third Hymn) ‭ To Pallas ‭ To Juno ‭ To Ceres ‭ To Cybele ‭ To Hercules ‭ To Æsculapius ‭ To Castor and Pollux ‭ To Mercury ‭ To Pan ‭ To Vulcan ‭ To Phœbus ‭ To Neptune ‭ To Jove ‭ To Vesta ‭ To the Muses and Apollo ‭ To Bacchus ‭ To Diana ‭ To Pallas ‭ To Vesta and Mercury ‭ To Earth ‭ To the Sun ‭ To the Moon ‭ To Castor and Pollux ‭ To Men of Hospitality ‭ EPIGRAMS AND OTHER POEMS-- ‭ To Cuma ‭ In his Return to Cuma ‭ Upon the Sepulchre of Midus ‭ Cuma, refusing to eternize their State, etc. ‭ An Essay of his begun Iliads ‭ To Thestor's Son inquisitive about the Causes of Things ‭ To Neptune ‭ To the City of Erythræa ‭ To Mariners ‭ The Pine ‭ To Glaucus ‭ Against the Samian Ministress or Nun ‭ Written on the Council Chamber ‭ The Furnace called in to sing by Potters ‭ Eiresione, or the Olive Branch ‭ To certain Fisher-Boys pleasing him with Riddles ‭ _The Translator's Epilogue_ ‭ THE FIRST BOOK OF HOMER'S ODYSSEYS ‭ THE ARGUMENT ‭ The Gods in council sit, to call ‭ Ulysses from Calypso's thrall, ‭ And order their high pleasures thus: ‭ Grey Pallas to Telemachus ‭ (In Ithaca) her way addrest; ‭ And did her heav'nly limbs invest ‭ In Mentas' likeness, that did reign ‭ King of the Taphians, in the main ‭ Whose rough waves near Leucadia run. ‭ Advising wise Ulysses' son ‭ To seek his father, and address ‭ His course to young Tantalides, ‭ That govern'd Sparta. Thus much said, ‭ She shew'd she was Heav'n's martial Maid, ‭ And vanish'd from him. Next to this, ‭ The Banquet of the Wooers is. ‭ ANOTHER ARGUMENT ‭ _Ἂλφα._ ‭ The Deities sit; ‭ The Man retired; ‭ Th' Ulyssean wit ‭ By Pallas fired. ‭ The man, O Muse, inform, that many a way [1] ‭ Wound with his wisdom to his wished stay; ‭ That wander'd wondrous far, when he the town ‭ Of sacred Troy had sack'd and shiver'd down; ‭ The cities of a world of nations, ‭ With all their manners, minds, and fashions, ‭ He saw and knew; at sea felt many woes, ‭ Much care sustain'd, to save from overthrows ‭ Himself and friends in their retreat for home; ‭ But so their fates he could not overcome, ‭ Though much he thirsted it. O men unwise, ‭ They perish'd by their own impieties! ‭ That in their hunger's rapine would not shun ‭ The oxen of the lofty-going Sun, ‭ Who therefore from their eyes the day bereft ‭ Of safe return. These acts, in some part left, ‭ Tell us, as others, deified Seed of Jove. ‭ Now all the rest that austere death outstrove ‭ At Troy's long siege at home safe anchor'd are, ‭ Free from the malice both of sea and war; ‭ Only Ulysses is denied access ‭ To wife and home. The grace of Goddesses, ‭ The rev'rend nymph Calypso, did detain ‭ Him in her caves, past all the race of men ‭ Enflam'd to make him her lov'd lord and spouse. ‭ And when the Gods had destin'd that his house, ‭ Which Ithaca on her rough bosom bears, ‭ (The point of time wrought out by ambient years) ‭ Should be his haven, Contention still extends ‭ Her envy to him, ev'n amongst his friends. ‭ All Gods took pity on him; only he, ‭ That girds earth in the cincture of the sea, ‭ Divine Ulysses ever did envy, ‭ And made the fix'd port of his birth to fly. ‭ But he himself solemniz'd a retreat ‭ To th' Æthiops, far dissunder'd in their seat, ‭ (In two parts parted, at the sun's descent, ‭ And underneath his golden orient, ‭ The first and last of men) t' enjoy their feast ‭ Of bulls and lambs, in hecatombs addrest; [2] ‭ At which he sat, giv'n over to delight. ‭ The other Gods in heav'n's supremest height ‭ Were all in council met; to whom began ‭ The mighty Father both of God and man ‭ Discourse, inducing matter that inclin'd ‭ To wise Ulysses, calling to his mind ‭ Faultful Ægisthus, who to death was done [3] ‭ By young Orestes, Agamemnon's son. ‭ His memory to the Immortals then ‭ Mov'd Jove thus deeply: "O how falsely men ‭ Accuse us Gods as authors of their ill! ‭ When, by the bane their own bad lives instill, ‭ They suffer all the mis'ries of their states, ‭ Past our inflictions, and beyond their fates. ‭ As now Ægisthus, past his fate, did wed ‭ The wife of Agamemnon, and (in dread ‭ To suffer death himself) to shun his ill, ‭ Incurr'd it by the loose bent of his will, ‭ In slaughtering Atrides in retreat. ‭ Which we foretold him would so hardly set ‭ To his murd'rous purpose, sending Mercury ‭ That slaughter'd Argus, our consid'rate spy, ‭ To give him this charge: 'Do not wed his wife, ‭ Nor murder him; for thou shalt buy his life ‭ With ransom of thine own, impos'd on thee ‭ By his Orestes, when in him shall be ‭ Atrides'-self renew'd, and but the prime ‭ Of youth's spring put abroad, in thirst to climb ‭ His haughty father's throne by his high acts.' ‭ These words of Hermes wrought not into facts ‭ Ægisthus' powers; good counsel he despis'd, ‭ And to that good his ill is sacrific'd." ‭ Pallas, whose eyes did sparkle like the skies, ‭ Answer'd: "O Sire! Supreme of Deities, ‭ Ægisthus pass'd his fate, and had desert ‭ To warrant our infliction; and convert ‭ May all the pains such impious men inflict ‭ On innocent suff'rers to revenge as strict, ‭ Their own hearts eating. But, that Ithacus, ‭ Thus never meriting, should suffer thus, ‭ I deeply suffer. His more pious mind ‭ Divides him from these fortunes. Though unkind ‭ Is piety to him, giving him a fate ‭ More suff'ring than the most unfortunate, ‭ So long kept friendless in a sea-girt soil, ‭ Where the sea's navel is a sylvan isle, ‭ In which the Goddess dwells that doth derive ‭ Her birth from Atlas, who of all alive ‭ The motion and the fashion doth command ‭ With his wise mind, whose forces understand [4] ‭ The inmost deeps and gulfs of all the seas, ‭ Who (for his skill of things superior) stays ‭ The two steep columns that prop earth and heav'n. ‭ His daughter 'tis, who holds this homeless-driv'n [5] ‭ Still mourning with her; evermore profuse ‭ Of soft and winning speeches, that abuse ‭ And make so languishingly, and possest [6] ‭ With so remiss a mind her loved guest, ‭ Manage the action of his way for home. ‭ Where he, though in affection overcome, ‭ In judgment yet more longs to show his hopes ‭ His country's smoke leap from her chimney tops, ‭ And death asks in her arms. Yet never shall ‭ Thy lov'd heart be converted on his thrall, ‭ Austere Olympius. Did not ever he, ‭ In ample Troy, thy altars gratify, ‭ And Grecians' fleet make in thy off'rings swim? ‭ Jove, why still then burns thy wrath to him?" ‭ The Cloud-assembler answer'd: "What words fly, ‭ Bold daughter, from thy pale of ivory? [7] ‭ As if I ever could cast from my care ‭ Divine Ulysses, who exceeds so far ‭ All men in wisdom, and so oft hath giv'n ‭ To all th' Immortals thron'd in ample heav'n ‭ So great and sacred gifts? But his decrees, ‭ That holds the earth in with his nimble knees, ‭ Stand to Ulysses' longings so extreme, ‭ For taking from the God-foe Polypheme ‭ His only eye; a Cyclop, that excell'd ‭ All other Cyclops, with whose burden swell'd ‭ The nymph Thoosa, the divine increase ‭ Of Phorcys' seed, a great God of the seas. ‭ She mix'd with Neptune in his hollow caves, ‭ And bore this Cyclop to that God of waves. ‭ For whose lost eye, th' Earth-shaker did not kill ‭ Erring Ulysses, but reserves him still ‭ In life for more death. But use we our pow'rs, ‭ And round about us cast these cares of ours, ‭ All to discover how we may prefer ‭ His wish'd retreat, and Neptune make forbear ‭ His stern eye to him, since no one God can, ‭ In spite of all, prevail, but 'gainst a man." ‭ To this, this answer made the grey-eyed Maid: ‭ "Supreme of rulers, since so well apaid ‭ The blesséd Gods are all then, now, in thee, ‭ To limit wise Ulysses' misery, ‭ And that you speak as you referr'd to me ‭ Prescription for the means, in this sort be ‭ Their sacred order: Let us now address ‭ With utmost speed our swift Argicides, ‭ To tell the nymph that bears the golden tress ‭ In th' isle Ogygia, that 'tis our will ‭ She should not stay our lov'd Ulysses still, ‭ But suffer his return; and then will I ‭ To Ithaca, to make his son apply ‭ His sire's inquest the more; infusing force ‭ Into his soul, to summon the concourse ‭ Of curl'd-head Greeks to council, and deter ‭ Each wooer, that hath been the slaughterer ‭ Of his fat sheep and crooked-headed beeves. ‭ From more wrong to his mother, and their leaves ‭ Take in such terms as fit deserts so great. ‭ To Sparta then, and Pylos, where doth beat ‭ Bright Amathus, the flood, and epithet ‭ To all that kingdom, my advice shall send ‭ The spirit-advanc'd Prince, to the pious end ‭ Of seeking his lost father, if he may ‭ Receive report from Fame where rests his stay; ‭ And make, besides, his own successive worth ‭ Known to the world, and set in action forth." ‭ This said, her wing'd shoes to her feet she tied, ‭ Form'd all of gold, and all eternified, ‭ That on the round earth or the sea sustain'd ‭ Her ravish'd substance swift as gusts of wind. ‭ Then took she her strong lance with steel made keen, ‭ Great, massy, active, that whole hosts of men, ‭ Though all heroës, conquers, if her ire ‭ Their wrongs inflame, back'd by so great a Sire. ‭ Down from Olympus' tops she headlong <DW37>'d, ‭ And swift as thought in Ithaca arriv'd, ‭ Close at Ulysses' gates; in whose first court ‭ She made her stand, and, for her breast's support, ‭ Lean'd on her iron lance; her form imprest ‭ With Mentas' likeness, come as being a guest. ‭ There found she those proud wooers, that were then ‭ Set on those ox-hides that themselves had slain, ‭ Before the gates, and all at dice were playing. ‭ To them the heralds, and the rest obeying, ‭ Fill'd wine and water; some, still as they play'd, ‭ And some, for solemn supper's state, purvey'd, ‭ With porous sponges cleansing tables, serv'd ‭ With much rich feast; of which to all they kerv'd. ‭ God-like Telemachus amongst them sat, ‭ Griev'd much in mind; and in his heart begat ‭ All representment of his absent sire, ‭ How, come from far-off parts, his spirits would fire ‭ With those proud wooers' sight, with slaughter parting ‭ Their bold concourse, and to himself converting ‭ The honours they usurp'd, his own commanding. ‭ In this discourse, he first saw Pallas standing, ‭ Unbidden entry; up rose, and addrest ‭ His pace right to her, angry that a guest ‭ Should stand so long at gate; and, coming near, ‭ Her right hand took, took in his own her spear, ‭ And thus saluted: "Grace to your repair, ‭ Fair guest, your welcome shall be likewise fair. ‭ Enter, and, cheer'd with feast, disclose th' intent ‭ That caus'd your coming." This said, first he went, ‭ And Pallas follow'd. To a room they came, ‭ Steep, and of state; the jav'lin of the Dame ‭ He set against a pillar vast and high, ‭ Amidst a large and bright-kept armory, ‭ Which was, besides, with woods of lances grac'd ‭ Of his grave father's. In a throne he plac'd ‭ The man-turn'd Goddess, under which was spread ‭ A carpet, rich and of deviceful thread; ‭ A footstool staying her feet; and by her chair ‭ Another seat (all garnish'd wondrous fair, ‭ To rest or sleep on in the day) he set, ‭ Far from the prease of wooers, lest at meat ‭ The noise they still made might offend his guest, ‭ Disturbing him at banquet or at rest, ‭ Ev'n to his combat with that pride of theirs, ‭ That kept no noble form in their affairs. ‭ And these he set far from them, much the rather ‭ To question freely of his absent father. ‭ A table fairly-polish'd then was spread, ‭ On which a rev'rend officer set bread, ‭ And other servitors all sorts of meat ‭ (Salads, and flesh, such as their haste could get) ‭ Serv'd with observance in. And then the sewer ‭ Pour'd water from a great and golden ewer, ‭ That from their hands t' a silver caldron ran. ‭ Both wash'd, and seated close, the voiceful man ‭ Fetch'd cups of gold, and set by them, and round ‭ Those cups with wine with all endeavour crown'd. ‭ Then rush'd in the rude wooers, themselves plac'd; ‭ The heralds water gave; the maids in haste ‭ Serv'd bread from baskets. When, of all prepar'd ‭ And set before them, the bold wooers shar'd, ‭ Their pages plying their cups past the rest. ‭ But lusty wooers must do more than feast; ‭ For now, their hungers and their thirsts allay'd, ‭ They call'd for songs and dances; those, they said, ‭ Were th' ornaments of feast. The herald straight ‭ A harp, carv'd full of artificial sleight, ‭ Thrust into Phemius', a learn'd singer's, hand, ‭ Who, till he much was urg'd, on terms did stand, ‭ But, after, play'd and sung with all his art. ‭ Telemachus to Pallas then (apart, ‭ His ear inclining close, that none might hear) ‭ In this sort said: "My guest, exceeding dear, ‭ Will you not sit incens'd with what I say? ‭ These are the cares these men take; feast and play. ‭ Which eas'ly they may use, because they eat, ‭ Free and unpunish'd, of another's meat; ‭ And of a man's, whose white bones wasting lie ‭ In some far region; with th' incessancy ‭ Of show'rs pour'd down upon them, lying ashore, ‭ Or in the seas wash'd nak'd. Who, if he wore ‭ Those bones with flesh and life and industry, ‭ And these might here in Ithaca set eye ‭ On him return'd, they all would wish to be ‭ Either past other in celerity ‭ Of feet and knees, and not contend t' exceed ‭ In golden garments. But his virtues feed ‭ The fate of ill death; nor is left to me ‭ The least hope of his life's recovery, ‭ No, not if any of the mortal race ‭ Should tell me his return; the cheerful face ‭ Of his return'd day never will appear. ‭ But tell me, and let Truth your witness bear, ‭ Who, and from whence you are? What city's birth? ‭ What parents? In what vessel set you forth? ‭ And with what mariners arriv'd you here? ‭ I cannot think you a foot passenger. ‭ Recount then to me all, to teach me well ‭ Fit usage for your worth. And if it fell ‭ In chance now first that you thus see us here, ‭ Or that in former passages you were ‭ My father's guest? For many men have been ‭ Guests to my father. Studious of men ‭ His sociable nature ever was." ‭ On him again the grey-eyed Maid did pass ‭ This kind reply: "I'll answer passing true ‭ All thou hast ask'd: My birth his honour drew ‭ From wise Anchialus. The name I bear ‭ Is Mentas, the commanding islander ‭ Of all the Taphians studious in the art ‭ Of navigation; having touch'd this part ‭ With ship and men, of purpose to maintain ‭ Course through the dark seas t' other-languag'd men; ‭ And Temesis sustains the city's name ‭ For which my ship is bound, made known by fame ‭ For rich in brass, which my occasions need, ‭ And therefore bring I shining steel in stead, ‭ Which their use wants, yet makes my vessel's freight, ‭ That near a plough'd field rides at anchor's weight, ‭ Apart this city, in the harbour call'd ‭ Rhethrus, whose waves with Neius' woods are wall'd. ‭ Thy sire and I were ever mutual guests, ‭ At either's house still interchanging feasts. ‭ I glory in it. Ask, when thou shalt see ‭ Laertes, th' old heroë, these of me, ‭ From the beginning. He, men say, no more ‭ Visits the city, but will needs deplore ‭ His son's believ'd loss in a private field; ‭ One old maid only at his hands to yield ‭ Food to his life, as oft as labour makes ‭ His old limbs faint; which, though he creeps, he takes ‭ Along a fruitful plain, set all with vines, ‭ Which husbandman-like, though a king, he proins. ‭ But now I come to be thy father's guest; ‭ I hear he wanders, while these wooers feast. ‭ And (as th' Immortals prompt me at this hour) ‭ I'll tell thee, out of a prophetic pow'r, ‭ (Not as profess'd a prophet, nor clear seen ‭ At all times what shall after chance to men) ‭ What I conceive, for this time, will be true: ‭ The Gods' inflictions keep your sire from you. ‭ Divine Ulysses, yet, abides not dead ‭ Above earth, nor beneath, nor buried ‭ In any seas, as you did late conceive, ‭ But, with the broad sea sieg'd, is kept alive ‭ Within an isle by rude and upland men, ‭ That in his spite his passage home detain. ‭ Yet long it shall not be before he tread ‭ His country's dear earth, though solicited, ‭ And held from his return, with iron chains; ‭ For he hath wit to forge a world of trains, ‭ And will, of all, be sure to make good one ‭ For his return, so much relied upon. ‭ But tell me, and be true: Art thou indeed ‭ So much a son, as to be said the seed [8] ‭ Of Ithacus himself? Exceeding much ‭ Thy forehead and fair eyes at his form touch; ‭ For oftentimes we met, as you and I ‭ Meet at this hour, before he did apply ‭ His pow'rs for Troy, when other Grecian states ‭ In hollow ships were his associates. ‭ But, since that time, mine eyes could never see ‭ Renown'd Ulysses, nor met his with me." ‭ The wise Telemachus again replied: ‭ "You shall with all I know be satisfied. ‭ My mother certain says I am his son; ‭ I know not; nor was ever simply known ‭ By any child the sure truth of his sire. ‭ But would my veins had took in living fire ‭ From some man happy, rather than one wise, ‭ Whom age might see seis'd of what youth made prise. ‭ But he whoever of the mortal race ‭ Is most unblest, he holds my father's place. ‭ This, since you ask, I answer." She, again: ‭ "The Gods sure did not make the future strain ‭ Both of thy race and days obscure to thee, ‭ Since thou wert born so of Penelope. ‭ The style may by thy after acts be won, ‭ Of so great sire the high undoubted son. ‭ Say truth in this then: What's this feasting here? ‭ What all this rout? Is all this nuptial cheer? ‭ Or else some friendly banquet made by thee? ‭ For here no shots are, where all sharers be. ‭ Past measure contumeliously this crew ‭ Fare through thy house; which should th' ingenuous view ‭ Of any good or wise man come and find, ‭ (Impiety seeing play'd in ev'ry kind) ‭ He could not but through ev'ry vein be mov'd." ‭ Again Telemachus: "My guest much lov'd. ‭ Since you demand and sift these sights so far, ‭ I grant 'twere fit a house so regular, ‭ Rich, and so faultless once in government, ‭ Should still at all parts the same form present ‭ That gave it glory while her lord was here. ‭ But now the Gods, that us displeasure bear, ‭ Have otherwise appointed, and disgrace ‭ My father most of all the mortal race. ‭ For whom I could not mourn so were he dead, ‭ Amongst his fellow-captains slaughteréd ‭ By common enemies, or in the hands ‭ Of his kind friends had ended his commands, ‭ After he had egregiously bestow'd ‭ His pow'r and order in a war so vow'd, ‭ And to his tomb all Greeks their grace had done, ‭ That to all ages he might leave his son ‭ Immortal honour; but now Harpies have ‭ Digg'd in their gorges his abhorréd grave. ‭ Obscure, inglorious, death hath made his end, ‭ And me, for glories, to all griefs contend. ‭ Nor shall I any more mourn him alone, ‭ The Gods have giv'n me other cause of moan. ‭ For look how many optimates remain ‭ In Samos, or the shores Dulichian, ‭ Shady Zacynthus, or how many bear ‭ Rule in the rough brows of this island here; ‭ So many now my mother and this house ‭ At all parts make defam'd and ruinous; ‭ And she her hateful nuptials nor denies, ‭ Nor will despatch their importunities, ‭ Though she beholds them spoil still as they feast ‭ All my free house yields, and the little rest ‭ Of my dead sire in me perhaps intend ‭ To bring ere long to some untimely end." ‭ This Pallas sigh'd and answer'd: "O," said she, ‭ "Absent Ulysses is much miss'd by thee, ‭ That on these shameless suitors he might lay ‭ His wreakful hands. Should he now come, and stay ‭ In thy court's first gates, arm'd with helm and shield, ‭ And two such darts as I have seen him wield, ‭ When first I saw him in our Taphian court, ‭ Feasting, and doing his desert's disport; ‭ When from Ephyrus he return'd by us ‭ From Ilus, son to Centaur Mermerus, ‭ To whom he travell'd through the wat'ry dreads, ‭ For bane to poison his sharp arrows' heads, ‭ That death, but touch'd, caus'd; which he would not give, ‭ Because he fear'd the Gods that ever live ‭ Would plague such death with death; and yet their fear ‭ Was to my father's bosom not so dear ‭ As was thy father's love; (for what he sought ‭ My loving father found him to a thought.) ‭ If such as then Ulysses might but meet ‭ With these proud wooers, all were at his feet ‭ But instant dead men, and their nuptialls ‭ Would prove as bitter as their dying galls. ‭ But these things in the Gods' knees are repos'd, ‭ If his return shall see with wreak inclos'd, ‭ These in his house, or he return no more; ‭ And therefore I advise thee to explore ‭ All ways thyself, to set these wooers gone; ‭ To which end give me fit attentión: ‭ To-morrow into solemn council call ‭ The Greek heroës, and declare to all ‭ (The Gods being witness) what thy pleasure is. ‭ Command to towns of their nativity ‭ These frontless wooers. If thy mother's mind ‭ Stands to her second nuptials so inclin'd, ‭ Return she to her royal father's tow'rs, ‭ Where th' one of these may wed her, and her dow'rs ‭ Make rich, and such as may consort with grace ‭ So dear a daughter of so great a race ‭ And thee I warn as well (if thou as well ‭ Wilt hear and follow) take thy best-built sail, ‭ With twenty oars mann'd, and haste t' inquire ‭ Where the abode is of thy absent sire, ‭ If any can inform thee, or thine ear ‭ From Jove the fame of his retreat may hear, ‭ For chiefly Jove gives all that honours men. ‭ To Pylos first be thy addression then, ‭ To god-like Nestor; thence to Sparta haste, ‭ To gold-lock'd Menelaus, who was last ‭ Of all the brass-arm'd Greeks that sail'd from Troy; ‭ And try from both these, if thou canst enjoy ‭ News of thy sire's return'd life anywhere, ‭ Though sad thou suffer'st in his search a year. ‭ If of his death thou hear'st, return thou home, ‭ And to his memory erect a tomb, ‭ Performing parent-rites, of feast and game, ‭ Pompous, and such as best may fit his fame; ‭ And then thy mother a fit husband give. ‭ These past, consider how thou mayst deprive ‭ Of worthless life these wooers in thy house, ‭ By open force, or projects enginous. ‭ Things childish fit not thee; th' art so no more. ‭ Hast thou not heard, how all men did adore ‭ Divine Orestes, after he had slain ‭ Ægisthus murd'ring by a treach'rous train ‭ His famous father? Be then, my most lov'd, ‭ Valiant and manly, ev'ry way approv'd ‭ As great as he. I see thy person fit, ‭ Noble thy mind, and excellent thy wit, ‭ All giv'n thee so to use and manage here ‭ That ev'n past death they may their memories bear. ‭ In meantime I'll descend to ship and men, ‭ That much expect me. Be observant then ‭ Of my advice, and careful to maintain ‭ In equal acts thy royal father's reign." ‭ Telemachus replied: "You ope, fair guest, ‭ A friend's heart in your speech, as well exprest ‭ As might a father serve t' inform his son; ‭ All which sure place have in my memory won. ‭ Abide yet, though your voyage calls away, ‭ That, having bath'd, and dignified your stay ‭ With some more honour, you may yet beside ‭ Delight your mind by being gratified ‭ With some rich present taken in your way, ‭ That, as a jewel, your respect may lay ‭ Up in your treasury, bestow'd by me, ‭ As free friends use to guests of such degree." ‭ "Detain me not," said she, "so much inclin'd ‭ To haste my voyage. What thy loved mind ‭ Commands to give, at my return this way, ‭ Bestow on me, that I directly may ‭ Convey it home; which more of price to me ‭ The more it asks my recompense to thee." ‭ This said, away grey-eyed Minerva flew, ‭ Like to a mounting lark; and did endue ‭ His mind with strength and boldness, and much more ‭ Made him his father long for than before; ‭ And weighing better who his guest might be, ‭ He stood amaz'd, and thought a Deity ‭ Was there descended; to whose will he fram'd ‭ His pow'rs at all parts, and went so inflam'd ‭ Amongst the wooers, who were silent set, ‭ To hear a poet sing the sad retreat ‭ The Greeks perform'd from Troy; which was from thence ‭ Proclaim'd by Pallas, pain of her offence. ‭ When which divine song was perceiv'd to bear ‭ That mournful subject by the list'ning ear ‭ Of wise Penelope, Icarius' seed, ‭ Who from an upper room had giv'n it heed, ‭ Down she descended by a winding stair, ‭ Not solely, but the state in her repair ‭ Two maids of honour made. And when this queen ‭ Of women stoop'd so low, she might be seen ‭ By all her wooers. In the door, aloof, ‭ Ent'ring the hall grac'd with a goodly roof, ‭ She stood, in shade of graceful veils, implied ‭ About her beauties; on her either side, ‭ Her honour'd women. When, to tears mov'd, thus ‭ She chid the sacred singer: "Phemiüs, ‭ You know a number more of these great deeds ‭ Of Gods and men, that are the sacred seeds, ‭ And proper subjects, of a poet's song, ‭ And those due pleasures that to men belong, ‭ Besides these facts that furnish Troy's retreat, ‭ Sing one of those to these, that round your seat ‭ They may with silence sit, and taste their wine; ‭ But cease this song, that through these ears of mine ‭ Conveys deserv'd occasion to my heart ‭ Of endless sorrows, of which the desert ‭ In me unmeasur'd is past all these men, ‭ So endless is the memory I retain, ‭ And so desertful is that memory, ‭ Of such a man as hath a dignity ‭ So broad it spreads itself through all the pride ‭ Of Greece and Argos." To the queen replied ‭ Inspir'd Telemachus: "Why thus envies ‭ My mother him that fits societies [9] ‭ With so much harmony, to let him please ‭ His own mind in his will to honour these? ‭ For these ingenious and first sort of men, [10] ‭ That do immediately from Jove retain ‭ Their singing raptures, are by Jove as well ‭ Inspir'd with choice of what their songs impell, ‭ Jove's will is free in it, and therefore theirs. ‭ Nor is this man to blame, that the repairs ‭ The Greeks make homeward sings; for his fresh muse ‭ Men still most celebrate that sings most news. ‭ And therefore in his note your ears employ: ‭ For not Ulysses only lost in Troy ‭ The day of his return, but numbers more ‭ The deadly ruins of his fortunes bore. ‭ Go you then in, and take your work in hand, ‭ Your web, and distaff; and your maids command ‭ To ply their fit work. Words to men are due, ‭ And those reproving counsels you pursue, ‭ And most to me of all men, since I bear ‭ The rule of all things that are manag'd here." ‭ She went amaz'd away, and in her heart ‭ Laid up the wisdom Pallas did impart ‭ To her lov'd son so lately, turn'd again ‭ Up to her chamber, and no more would reign ‭ In manly counsels. To her women she ‭ Applied her sway; and to the wooers he ‭ Began new orders, other spirits bewray'd ‭ Than those in spite of which the wooers sway'd. ‭ And (whiles his mother's tears still wash'd her eyes, ‭ Till grey Minerva did those tears surprise ‭ With timely sleep, and that her wooers did rouse ‭ Rude tumult up through all the shady house, ‭ Dispos'd to sleep because their widow was) ‭ Telemachus this new-giv'n spirit did pass ‭ On their old insolence: "Ho! you that are, ‭ My mother's wooers! much too high ye bear ‭ Your petulant spirits; sit; and, while ye may ‭ Enjoy me in your banquets, see ye lay ‭ These loud notes down, nor do this man the wrong, ‭ Because my mother hath disliked his song, ‭ To grace her interruption. 'Tis a thing ‭ Honest, and honour'd too, to hear one sing ‭ Numbers so like the Gods in elegance, ‭ As this man flows in. By the morn's first light, [11] ‭ I'll call ye all before me in a Court, ‭ That I may clearly banish your resort, ‭ With all your rudeness, from these roofs of mine. ‭ Away; and elsewhere in your feasts combine. ‭ Consume your own goods, and make mutual feast ‭ At either's house. Or if ye still hold best, ‭ And for your humours' more sufficéd fill, ‭ To feed, to spoil, because unpunish'd still, ‭ On other findings, spoil; but here I call ‭ Th' Eternal Gods to witness, if it fall ‭ In my wish'd reach once to be dealing wreaks, ‭ By Jove's high bounty, these your present checks ‭ To what I give in charge shall add more reins ‭ To my revenge hereafter; and the pains ‭ Ye then must suffer shall pass all your pride ‭ Ever to see redress'd, or qualified." ‭ At this all bit their lips, and did admire ‭ His words sent from him with such phrase and fire; ‭ Which so much mov'd them that Antinous, ‭ Eupitheus' son, cried out: "Telemachus! ‭ The Gods, I think, have rapt thee to this height ‭ Of elocution, and this great conceit ‭ Of self-ability. We all may pray, ‭ That Jove invest not in this kingdom's sway ‭ Thy forward forces, which I see put forth ‭ A hot ambition in thee for thy birth." ‭ "Be not offended," he replied, "if I [12] ‭ Shall say, I would assume this empery, ‭ If Jove gave leave. You are not he that sings: ‭ _The rule of kingdoms is the worst of things._ ‭ Nor is it ill, at all, to sway a throne; ‭ A man may quickly gain possession ‭ Of mighty riches, make a wondrous prize ‭ Set of his virtues; but the dignities ‭ That deck a king, there are enough beside ‭ In this circumfluous isle that want no pride ‭ To think them worthy of, as young as I, ‭ And old as you are. An ascent so high ‭ My thoughts affect not. Dead is he that held ‭ Desert of virtue to have so excell'd. ‭ But of these turrets I will take on me ‭ To be the absolute king, and reign as free, ‭ As did my father, over all his hand ‭ Left here in this house slaves to my command." ‭ Eurymachus, the son of Polybus, ‭ To this made this reply: "Telemachus! ‭ The girlond of this kingdom let the knees ‭ Of Deity run for; but the faculties ‭ This house is seis'd of, and the turrets here, ‭ Thou shalt be lord of, nor shall any bear ‭ The least part off of all thou dost possess, ‭ As long as this land is no wilderness. ‭ Nor rul'd by out-laws. But give these their pass, ‭ And tell me, best of princes, who he was ‭ That guested here so late? From whence? And what ‭ In any region boasted he his state? ‭ His race? His country? Brought he any news ‭ Of thy returning father? Or for dues ‭ Of moneys to him made he fit repair? ‭ How suddenly he rush'd into the air, ‭ Nor would sustain to stay and make him known! ‭ His port show'd no debauch'd companion." ‭ He answer'd: "The return of my lov'd sire ‭ Is past all hope; and should rude Fame inspire ‭ From any place a flatt'ring messenger ‭ With news of his survival, he should bear ‭ No least belief off from my desp'rate love. ‭ Which if a sacred prophet should approve, ‭ Call'd by my mother for her care's unrest, ‭ It should not move me. For my late fair guest, ‭ He was of old my father's, touching here ‭ From sea-girt Taphos; and for name doth bear ‭ Mentas, the son of wise Anchialus; ‭ And governs all the Taphians studious ‭ Of navigation." This he said, but knew ‭ It was a Goddess. These again withdrew ‭ To dances and attraction of the song; ‭ And while their pleasures did the time prolong, ‭ The sable Even descended, and did steep ‭ The lids of all men in desire of sleep. ‭ Telemachus, into a room built high, ‭ Of his illustrious court, and to the eye ‭ Of circular prospect, to his bed ascended, ‭ And in his mind much weighty thought contended ‭ Before him Euryclea (that well knew ‭ All the observance of a handmaid's due, ‭ Daughter to Opis Pisenorides) ‭ Bore two bright torches; who did so much please ‭ Laërtes in her prime, that, for the price ‭ Of twenty oxen, he made merchandise ‭ Of her rare beauties; and love's equal flame, ‭ To her he felt, as to his nuptial dame, ‭ Yet never durst he mix with her in bed, ‭ So much the anger of his wife he fled. ‭ She, now grown old, to young Telemachus ‭ Two torches bore, and was obsequious ‭ Past all his other maids, and did apply ‭ Her service to him from his infancy. ‭ His well-built chamber reach'd, she op'd the door, ‭ He on his bed sat, the soft weeds he wore ‭ Put off, and to the diligent old maid ‭ Gave all; who fitly all in thick folds laid, ‭ And hung them on a beam-pin near the bed, ‭ That round about was rich embroidered. ‭ Then made she haste forth from him, and did bring ‭ The door together with a silver ring, ‭ And by a string a bar to it did pull. ‭ He, laid, and cover'd well with curled wool ‭ Wov'n in silk quilts, all night employ'd his mind ‭ About the task that Pallas had design'd. ‭ FINIS LIBRI PRIMI HOM. ODYSS. ‭[1] The information or fashion of an absolute man; and necessary (or ‭fatal) passage through many afflictions (according with the most ‭Sacred Letter) to his natural haven and country, is the whole ‭argument and scope of this inimitable and miraculous poem. And ‭therefore is the epithet _πολὐτροπον_ given him in the first verse: ‭_πολὐτροπος_ signifying, _Homo cujus ingenium velut per multas ‭et varias vias vertitur in verum._ ‭[2] These notes following I am forced to insert (since the words ‭they contain differ from all other translations) lest I be thought to ‭err out of that ignorance that may perhaps possess my depraver. ‭[3] _'Αμὑμονος_ translated in this place _inculpabilis,_ and made ‭the epithet of Ægisthus, is from the true sense of the word, as it is ‭here to be understood; which is quite contrary. As _ὰντίθεος_ is ‭to be expounded in some place _Divinus,_ or _Deo similis,_ but in ‭another (soon after) _contrarius Deo._ The person to whom the ‭epithet is given giving reason to distinguish it. And so ‭_ὀλοὁφρων,_ an epithet given to Atlas, instantly following, in one ‭place signifies _mente perniciosus,_ in the next, _qui universa ‭mente gerit._ ‭[4] In this place is Atlas given the epithet _ὀλοὁφρων,_ which ‭signifies _qui universa mente agitat,_ here given him for the power ‭the stars have in all things. Yet this receives other interpretation in ‭other places, as abovesaid. ‭[5] _Δὐστηνος_ is here turned by others, _infelix,_ in the general ‭collection; when it hath here a particular exposition, applied to ‭express Ulysses' desert errors, _'παρἁ τὁ στἣναι, ut sit, qui vix ‭locum invenire potest ubi consistat._ ‭[6] This is thus translated, the rather to express and approve the ‭allegory driven through the whole Odysseys. Deciphering the ‭intangling of the wisest in his affections; and the torments that ‭breed in every pious mind; to be thereby hindered to arrive so ‭directly as he desires, at the proper and only true natural country ‭of every worthy man, whose haven is heaven and the next life, to ‭which, this life is but a sea in continual æsture and vexation. The ‭words occasioning all this are _μαλακοἳς λὀλοις: μαλακὀς_ ‭signifying, _qui languide, et animo remisso rem aliquam gerit;_ ‭which being the effect of Calypso's sweet words in Ulysses, is here ‭applied passively to his own sufferance of their operation. ‭[7] _῞Ερκος ὀδὀντων,_ viz. _vallum_ or _clanstrum dentium,_ ‭which, for the better sound in our language, is here turned, Pale of ‭Ivory. The teeth being that rampire, or pale, given us by nature in ‭that part for restraint and compression of our speech, till the ‭imagination, appetite, and soul (that ought to rule in their ‭examination, before their delivery) have given worthy pass to ‭them. The most grave and divine poet, teaching therein, that not so ‭much for the necessary chewing of our sustenance our teeth are ‭given us, as for their stay of our words, lest we utter them rashly. ‭[8] _Τὀσος παîς, Tantus filius._ Pallas thus enforcing her question ‭to stir up the son the more to the father's worthiness. ‭[9] _'Ερἰηρος ἀοιδὀς. Cantor, cujus tam apta est societas ‭hominibus._ ‭[10] _'Ανδρἀσιν ἀλφηστᾔσιν. 'Αλφηστᾔσιν_ is an epithet proper to ‭poets for their first finding out of arts and documents tending to ‭elocution and government inspired only by Jove, and are here ‭called the first of men, since first they gave rules to manly life, and ‭have their information immediately from Jove (as Plato in Ione ‭witnesseth); the word deduced from _ἅλφα,_ which is taken for ‭him _qui primas teneat aliquâ in re,_ and will _ἀλφηστῃσιν_ then ‭be sufficiently expressed with _ingeniosis,_ than which no ‭exposition goes further. ‭[11] _'Ηωθεν, prima luce._ ‭[12] Upon this answer of Telemachus, because it hath so sudden a ‭change and is so far let down from his late height of heat, altering ‭and tempering so commandingly his affections I thought not amiss ‭to insert here Spondanus' further annotations, which is this: ‭_Prudenter Telemachus joco furorem Antinoi ac asperitatem ‭emolliit. Nam ita dictum illius interpretatur, ut existimetur censere ‭jocosè ilia etiam ab Antinoo adversum se pronunciata. Et primum ‭ironicè se Regem esse exoptat propter commoda quæ Reges solent ‭comitari. Ne tamen invidiam in se ambitionis concitet, testatur se ‭regnum, Ithacæ non ambire, mortuo Ulysse, cum id alii possidere ‭queant se longe præstantiores ac digniores: hoc unum ait se moliri, ‭ut propriarum ædium et bonorum solus sit dominus, iis exclusis, ac ‭ejectis, qui vi illa occupare ac disperdere conantur._ ‭ THE SECOND BOOK OF HOMER'S ODYSSEYS ‭ THE ARGUMENT ‭ Telemachus to court doth call ‭ The Wooers, and commands them all ‭ To leave his house; and taking then ‭ From wise Minerva ship and men, ‭ And all things fit for him beside, ‭ That Euryclea could provide ‭ For sea-rites till he found his sire, ‭ He hoists sail; when Heav'n stoops his fire. ‭ ANOTHER ARGUMENT ‭ _βητα._ ‭ The old Maid's store ‭ The voyage cheers. ‭ The ship leaves shore, ‭ Minerva steers. ‭ Now when with rosy fingers, th' early born ‭ And thrown through all the air, appear'd the Morn, ‭ Ulysses' lov'd son from his bed appear'd, ‭ His weeds put on, and did about him gird ‭ His sword that thwart his shoulders hung, and tied ‭ To his fair feet fair shoes, and all parts plied ‭ For speedy readiness: who, when he trod ‭ The open earth, to men show'd like a God. ‭ The heralds then he straight charg'd to consort ‭ The curl'd-head Greeks, with loud calls, to a Court. ‭ They summon'd; th' other came in utmost haste. ‭ Who all assembled, and in one heap plac'd ‭ He likewise came to council, and did bear ‭ In his fair hand his iron-headed spear. ‭ Nor came alone, nor with men-troops prepar'd, ‭ But two fleet dogs made both his train and guard. ‭ Pallas supplied with her high wisdom's grace, ‭ That all men's wants supplies, State's painted face. ‭ His ent'ring presence all men did admire; ‭ Who took seat in the high throne of his sire, ‭ To which the grave peers gave him rev'rend way. ‭ Amongst whom, an Egyptian heroë ‭ (Crookéd with age, and full of skill) begun ‭ The speech to all; who had a loved son ‭ That with divine Ulysses did ascend ‭ His hollow fleet to Troy; to serve which end, ‭ He kept fair horse, and was a man-at-arms, ‭ And in the cruel Cyclop's stern alarms ‭ His life lost by him in his hollow cave, ‭ Whose entrails open'd his abhorréd grave, ‭ And made of him, of all Ulysses' train, ‭ His latest supper, being latest slain; ‭ His name was Antiphus, And this old man, ‭ This crookéd-grown, this wise Egyptian, ‭ Had three sons more; of which one riotous ‭ A wooer was, and call'd Eurynomus; ‭ The other two took both his own wish'd course. ‭ Yet both the best fates weigh'd not down the worse, ‭ But left the old man mindful still of moan; ‭ Who, weeping, thus bespake the Session: ‭ "Hear, Ithacensians, all I fitly say: ‭ Since our divine Ulysses' parting day ‭ Never was council call'd, nor session, ‭ And now by whom is this thus undergone? ‭ Whom did necessity so much compell, ‭ Of young or old? Hath anyone heard tell ‭ Of any coming army, that he thus now ‭ May openly take boldness to avow, ‭ First having heard it? Or will any here ‭ Some motion for the public good prefer? ‭ Some worth of note there is in this command; ‭ And, methinks, it must be some good man's hand ‭ That's put to it, that either hath direct ‭ Means to assist, or, for his good affect, ‭ Hopes to be happy in the proof he makes; ‭ And that Jove grant, whate'er he undertakes." ‭ Telemachus (rejoicing much to hear ‭ The good hope and opinion men did bear ‭ Of his young actions) no longer sat, ‭ But long'd t' approve what this man pointed at, ‭ And make his first proof in a cause so good; ‭ And in the council's chief place up he stood; ‭ When straight Pisenor (herald to his sire, ‭ And learn'd in counsels) felt his heart on fire ‭ To hear him speak, and put into his hand ‭ The sceptre that his father did command; ‭ Then, to the old Egyptian turn'd, he spoke: ‭ "Father, not far he is that undertook ‭ To call this Council; whom you soon shall know. ‭ Myself, whose wrongs my griefs will make me show, ‭ Am he that author'd this assembly here. ‭ Nor have I heard of any army near, ‭ Of which, being first told, I might iterate, ‭ Nor for the public good can aught relate, ‭ Only mine own affairs all this procure, ‭ That in my house a double ill endure; ‭ One, having lost a father so renown'd, ‭ Whose kind rule once with' your command was crown'd; ‭ The other is, what much more doth augment ‭ His weighty loss, the ruin imminent ‭ Of all my house by it, my goods all spent. ‭ And of all this the wooers, that are sons ‭ To our chief peers, are the confusións, ‭ Importuning my mother's marriáge ‭ Against her will; nor dares their blood's bold rage ‭ Go to Icarius', her father's, court, ‭ That, his will ask'd in kind and comely sort, ‭ He may endow his daughter with a dow'r, ‭ And, she consenting, at his pleasure's pow'r ‭ Dispose her to a man, that, thus behav'd, ‭ May have fit grace, and see her honour sav'd. ‭ But these, in none but my house, all their lives ‭ Resolve to spend; slaught'ring my sheep and beeves, ‭ And with my fattest goats lay feast on feast, ‭ My gen'rous wine consuming as they list. ‭ A world of things they spoil, here wanting one, ‭ That, like Ulysses, quickly could set gone ‭ These peace-plagues from his house, that spoil like war; ‭ Whom my pow'rs are unfit to urge so far, ‭ Myself immartial. But, had I the pow'r, ‭ My will should serve me to exempt this hour ‭ From out my life-time. For, past patience, ‭ Base deeds are done here, that exceed defence ‭ Of any honour. Falling is my house, ‭ Which you should shame to see so ruinous. ‭ Rev'rence the censures that all good men give, ‭ That dwell about you; and for fear to live ‭ Expos'd to heav'n's wrath (that doth ever pay ‭ Pains for joys forfeit) even by Jove I pray, ‭ Or Themis, both which pow'rs have to restrain, ‭ Or gather, councils, that ye will abstain ‭ From further spoil, and let me only waste ‭ In that most wretched grief I have embrac'd ‭ For my lost father. And though I am free ‭ From meriting your outrage, yet, if he, ‭ Good man, hath ever with a hostile heart ‭ Done ill to any Greek, on me convert ‭ Your like hostility, and vengeance take ‭ Of his ill on my life, and all these make ‭ Join in that justice; but, to see abus'd ‭ Those goods that do none ill but being ill-us'd, ‭ Exceeds all right. Yet better 'tis for me, ‭ My whole possessions and my rents to see ‭ Consum'd by you, than lose my life and all; ‭ For on your rapine a revenge may fall, ‭ While I live; and so long I may complain ‭ About the city, till my goods again, ‭ Oft ask'd, may be with all amends repaid. ‭ But in the mean space your misrule hath laid ‭ Griefs on my bosom, that can only speak, ‭ And are denied the instant pow'r of wreak." ‭ This said, his sceptre 'gainst the ground he threw, ‭ And tears still'd from him; which mov'd all the crew, ‭ The court struck silent, not a man did dare ‭ To give a word that might offend his ear. ‭ Antinous only in this sort replied: ‭ "High spoken, and of spirit unpacified, ‭ How have you sham'd us in this speech of yours! ‭ Will you brand us for an offence not ours? ‭ Your mother, first in craft, is first in cause. ‭ Three years are past, and near the fourth now draws, ‭ Since first she mock'd the peers Achaian. ‭ All she made hope, and promis'd ev'ry man, ‭ Sent for us ever, left love's show in nought, ‭ But in her heart conceal'd another thought. ‭ Besides, as curious in her craft, her loom ‭ She with a web charg'd, hard to overcome, ‭ And thus bespake us: 'Youths, that seek my bed, ‭ Since my divine spouse rests amongst the dead, ‭ Hold on your suits but till I end, at most, ‭ This funeral weed, lest what is done be lost. ‭ Besides, I purpose, that when th' austere fate ‭ Of bitter death shall take into his state ‭ Laertes the heroë, it shall deck ‭ His royal corse, since I should suffer check ‭ In ill report of ev'ry common dame, ‭ If one so rich should show in death his shame.' ‭ This speech she us'd; and this did soon persuade ‭ Our gentle minds. But this a work she made ‭ So hugely long, undoing still in night, ‭ By torches, all she did by day's broad light, ‭ That three years her deceit <DW37>'d past our view, ‭ And made us think that all she feign'd was true. ‭ But when the fourth year came, and those sly hours ‭ That still surprise at length dames' craftiest powers, ‭ One of her women, that knew all, disclos'd ‭ The secret to us, that she still unloos'd ‭ Her whole day's fair affair in depth of night. ‭ And then no further she could force her sleight, ‭ But, of necessity, her work gave end. ‭ And thus, by me, doth ev'ry other friend, ‭ Professing love to her, reply to thee; ‭ That ev'n thyself, and all Greeks else, may see, ‭ That we offend not in our stay, but she. ‭ To free thy house then, send her to her sire, ‭ Commanding that her choice be left entire ‭ To his election, and one settled will. ‭ Nor let her vex with her illusions still ‭ Her friends that woo her, standing on her wit, ‭ Because wise Pallas hath giv'n wills to it ‭ So full of art, and made her understand ‭ All works in fair skill of a lady's hand. ‭ But (for her working mind) we read of none ‭ Of all the old world, in which Greece hath shown ‭ Her rarest pieces, that could equal her: ‭ Tyro, Alcmena, and Mycena were ‭ To hold comparison in no degree, ‭ For solid brain, with wise Penelope. ‭ And yet, in her delays of us, she shows ‭ No prophet's skill with all the wit she owes; ‭ For all this time thy goods and victuals go ‭ To utter ruin; and shall ever so, ‭ While thus the Gods her glorious mind dispose. ‭ Glory herself may gain, but thou shalt lose ‭ Thy longings ev'n for necessary food, ‭ For we will never go where lies our good, ‭ Nor any other where, till this delay ‭ She puts on all she quits with th' endless stay ‭ Of some one of us, that to all the rest ‭ May give free farewell with his nuptial feast." ‭ The wise young prince replied: "Antinous! ‭ I may by no means turn out of my house ‭ Her that hath brought me forth and nourish'd me. ‭ Besides, if quick or dead my father be ‭ In any region, yet abides in doubt; ‭ And 'twill go hard, my means being so run out, ‭ To tender to Icarius again, ‭ If he again my mother must maintain ‭ In her retreat, the dow'r she brought with her. ‭ And then a double ill it will confer, ‭ Both from my father and from God on me, ‭ When, thrust out of her house, on her bent knee, ‭ My mother shall the horrid Furies raise ‭ With imprecations, and all men dispraise ‭ My part in her exposure. Never then ‭ Will I perform this counsel. If your spleen ‭ Swell at my courses, once more I command ‭ Your absence from my house; some other's hand ‭ Charge with your banquets; on your own goods eat, ‭ And either other mutually in treat, ‭ At either of your houses, with your feast. ‭ But if ye still esteem more sweet and best ‭ Another's spoil, so you still wreakless live, ‭ Gnaw, vermin-like, things sacred, no laws give [1] ‭ To your devouring; it remains that I ‭ Invoke each Ever-living Deity, ‭ And vow, if Jove shall deign in any date ‭ Pow'r of like pains for pleasure so past rate, ‭ From thenceforth look, where ye have revell'd so ‭ Unwreak'd, your ruins all shall undergo." ‭ Thus spake Telemachus; t' assure whose threat, ‭ Far-seeing Jove upon their pinions set ‭ Two eagles from the high brows of a hill, ‭ That, mounted on the Winds, together still ‭ Their strokes extended; but arriving now ‭ Amidst the Council, over ev'ry brow ‭ Shook their thick wings and, threat'ning death's cold fears, ‭ Their necks and cheeks tore with their eager seres; ‭ Then, on the court's right hand away they flew, ‭ Above both court and city. With whose view, ‭ And study what events they might foretell ‭ The Council into admiration fell. ‭ The old heroë, Halitherses, then, ‭ The son of Nestor, that of all old men, ‭ His peers in that court, only could foresee ‭ By flight of fowls man's fixed destiny, ‭ 'Twixt them and their amaze, this interpos'd: ‭ "Hear, Ithacensians, all your doubts disclos'd. ‭ The Wooers most are touch'd in this ostent, ‭ To whom are dangers great and imminent; ‭ For now not long more shall Ulysses bear ‭ Lack of his most lov'd, but fills some place near, ‭ Addressing to these Wooers fate and death. ‭ And many more this mischief menaceth ‭ Of us inhabiting this famous isle. ‭ Let us consult yet, in this long forewhile, ‭ How to ourselves we may prevent this ill. ‭ Let these men rest secure, and revel still; ‭ Though they might find it safer, if with us ‭ They would in time prevent what threats them thus; ‭ Since not without sure trial I foretell ‭ These coming storms, but know their issue well. ‭ For to Ulysses all things have event, ‭ As I foretold him, when for Ilion went ‭ The whole Greek fleet together, and with them ‭ Th' abundant-in-all-counsels took the stream. ‭ I told him, that, when much ill he had past, ‭ And all his men were lost, he should at last, ‭ The twentieth year, turn home, to all unknown; ‭ All which effects are to perfection grown." ‭ Eurymachus, the son of Polybus, ‭ Oppos'd this man's presage, and answer'd thus: ‭ "Hence, great in years, go, prophesy at home, ‭ Thy children teach to shun their ills to come. ‭ In these superior far to thee am I. ‭ A world of fowls beneath the sun-beams fly ‭ That are not fit t' inform a prophecy. ‭ Besides, Ulysses perish'd long ago; ‭ And would thy fates to thee had destin'd so, ‭ Since so thy so much prophecy had spar'd ‭ Thy wronging of our rights, which, for reward ‭ Expected home with thee, hath summon'd us ‭ Within the anger of Telemachus. ‭ But this I will presage, which shall be true: ‭ If any spark of anger chance t' ensue ‭ Thy much old art in these deep auguries, ‭ In this young man incenséd by thy lies, ‭ Ev'n to himself his anger shall confer ‭ The greater anguish, and thine own ends err ‭ From all their objects; and, besides, thine age ‭ Shall feel a pain, to make thee curse presage ‭ With worthy cause, for it shall touch thee near. ‭ But I will soon give end to all our fear, ‭ Preventing whatsoever chance can fall, ‭ In my suit to the young prince for us all, ‭ To send his mother to her father's house, ‭ That he may sort her out a worthy spouse, ‭ And such a dow'r bestow, as may befit ‭ One lov'd, to leave her friends and follow it. ‭ Before which course be, I believe that none ‭ Of all the Greeks will cease th' ambitión ‭ Of such a match. For, chance what can to us, ‭ We no man fear, no not Telemachus, ‭ Though ne'er so greatly spoken. Nor care we ‭ For any threats of austere prophecy, ‭ Which thou, old dotard, vaunt'st of so in vain. ‭ And thus shalt thou in much more hate remain; ‭ For still the Gods shall bear their ill expense, ‭ Nor ever be dispos'd by competence, ‭ Till with her nuptials she dismiss our suits, ‭ Our whole lives' days shall sow hopes for such fruits. ‭ Her virtues we contend to, nor will go ‭ To any other, be she never so ‭ Worthy of us, and all the worth we owe." ‭ He answer'd him: "Eurymachus, and all ‭ Ye gen'rous Wooers, now, in general, ‭ I see your brave resolves, and will no more ‭ Make speech of these points, and, much less, implore. ‭ It is enough, that all the Grecians here, ‭ And all the Gods besides, just witness bear, ‭ What friendly premonitions have been spent ‭ On your forbearance, and their vain event. ‭ Yet, with my other friends, let love prevail ‭ To fit me with a vessel free of sail, ‭ And twenty men, that may divide to me ‭ My ready passage through the yielding sea ‭ For Sparta, and Amathoan Pylos' shore, ‭ I now am bound, in purpose to explore ‭ My long-lack'd father, and to try if fame ‭ Or Jove, most author of man's honour'd name, ‭ With his return and life may glad mine ear, ‭ Though toil'd in that proof I sustain a year. ‭ If dead I hear him, nor of more state, here ‭ Retir'd to my lov'd country, I will rear ‭ A sepulchre to him, and celebrate ‭ Such royal parent-rites, as fits his state; ‭ And then my mother to a spouse dispose." ‭ This said, he sat; and to the rest arose ‭ Mentor, that was Ulysses' chosen friend, ‭ To whom, when he set forth, he did commend ‭ His cómplete family, and whom he will'd ‭ To see the mind of his old sire fulfill'd, ‭ All things conserving safe, till his retreat. ‭ Who, tender of his charge, and seeing so set ‭ In slight care of their king his subjects there, ‭ Suff'ring his son so much contempt to bear, ‭ Thus gravely, and with zeal, to him began: ‭ "No more let any sceptre-bearing man, ‭ Benevolent, or mild, or human be, ‭ Nor in his mind form acts of piety, ‭ But ever feed on blood, and facts unjust ‭ Commit, ev'n to the full swing of his lust, ‭ Since of divine Ulysses no man now, ‭ Of all his subjects, any thought doth show. ‭ All whom he govern'd, and became to them, ‭ Rather than one that wore a diadem, ‭ A most indulgent father. But, for all ‭ That can touch me, within no envy fall ‭ These insolent Wooers, that in violent kind ‭ Commit things foul by th' ill wit of the mind, ‭ And with the hazard of their heads devour ‭ Ulysses' house, since his returning hour ‭ They hold past hope. But it affects me much, ‭ Ye dull plebeians, that all this doth touch ‭ Your free states nothing; who, struck dumb, afford ‭ These Wooers not so much wreak as a word, ‭ Though few, and you with only number might ‭ Extinguish to them the profaned light." ‭ Evenor's son, Leocritus, replied: ‭ "Mentor! the railer, made a fool with pride, ‭ What language giv'st thou that would quiet us ‭ With putting us in storm, exciting thus ‭ The rout against us? Who, though more than we, ‭ Should find it is no easy victory ‭ To drive men, habited in feast, from feasts, ‭ No not if Ithacus himself such guests ‭ Should come and find so furnishing his Court, ‭ And hope to force them from so sweet a fort. ‭ His wife should little joy in his arrive, ‭ Though much she wants him; for, where she alive ‭ Would her's enjoy, there death should claim his rights. ‭ _He must be conquer'd that with many fights._ ‭ Thou speak'st unfit things. To their labours then ‭ Disperse these people; and let these two men, ‭ Mentor and Halitherses, that so boast ‭ From the beginning to have govern'd most ‭ In friendship of the father, to the son ‭ Confirm the course he now affects to run. ‭ But my mind says, that, if he would but use ‭ A little patience, he should here hear news ‭ Of all things that his wish would understand, ‭ But no good hope for of the course in hand." ‭ This said, the Council rose; when ev'ry peer ‭ And all the people in dispersion were ‭ To houses of their own; the Wooers yet ‭ Made to Ulysses' house their old retreat. ‭ Telemachus, apart from all the prease, ‭ Prepar'd to shore, and, in the aged seas ‭ His fair hands wash'd, did thus to Pallas pray: ‭ "Hear me, O Goddess, that but yesterday ‭ Didst deign access to me at home, and lay ‭ Grave charge on me to take ship, and inquire ‭ Along the dark seas for mine absent sire! ‭ Which all the Greeks oppose; amongst whom most ‭ Those that are proud still at another's cost, ‭ Past measure, and the civil rights of men, ‭ My mother's Wooers, my repulse maintain." ‭ Thus spake he praying; when close to him came ‭ Pallas, resembling Mentor both in frame ‭ Of voice and person, and advis'd him thus: ‭ "Those Wooers well might know, Telemachus, ‭ Thou wilt not ever weak and childish be, ‭ If to thee be instill'd the faculty ‭ Of mind and body that thy father grac'd; ‭ And if, like him, there be in thee enchac'd ‭ Virtue to give words works, and works their end. ‭ This voyage, that to them thou didst commend, ‭ Shall not so quickly, as they idly ween, ‭ Be vain, or giv'n up, for their opposite spleen. ‭ But, if Ulysses nor Penelope ‭ Were thy true parents, I then hope in thee ‭ Of no more urging thy attempt in hand; ‭ For few, that rightly bred on both sides stand, ‭ Are like their parents, many that are worse, ‭ And most few better. Those then that the nurse ‭ Or mother call true-born yet are not so, ‭ Like worthy sires much less are like to grow. ‭ But thou show'st now that in thee fades not quite ‭ Thy father's wisdom; and that future light ‭ Shall therefore show thee far from being unwise, ‭ Or touch'd with stain of bastard cowardice. ‭ Hope therefore says, that thou wilt to the end ‭ Pursue the brave act thou didst erst intend. ‭ But for the foolish Wooers, they bewray ‭ They neither counsel have nor soul, since they ‭ Are neither wise nor just, and so must needs ‭ Rest ignorant how black above their heads ‭ Fate hovers holding Death, that one sole day ‭ Will make enough to make them all away. ‭ For thee, the way thou wishest shall no more ‭ Fly thee a step; I, that have been before ‭ Thy father's friend, thine likewise now will be, ‭ Provide thy ship myself, and follow thee. ‭ Go thou then home, and sooth each Wooer's vein, ‭ But under hand fit all things for the main; ‭ Wine in as strong and sweet casks as you can, ‭ And meal, the very marrow of a man, ‭ Which put in good sure leather sacks, and see ‭ That with sweet food sweet vessels still agree. ‭ I from the people straight will press for you ‭ Free voluntaries; and, for ships, enow ‭ Sea-circled Ithaca contains, both new ‭ And old-built; all which I'll exactly view, ‭ And choose what one soever most doth please; ‭ Which rigg'd, we'll straight launch, and assay the seas." ‭ This spake Jove's daughter, Pallas; whose voice heard, ‭ No more Telemachus her charge deferr'd, ‭ But hasted home, and, sad at heart, did see ‭ Amidst his hall th' insulting Wooers flea ‭ Goats, and roast swine. 'Mongst whom, Antinous ‭ Careless, discov'ring in Telemachus ‭ His grudge to see them, laugh'd, met, took his hand, ‭ And said: "High-spoken, with the mind so mann'd! ‭ Come, do as we do, put not up your spirits ‭ With these low trifles, nor our loving merits ‭ In gall of any hateful purpose steep, ‭ But eat egregiously, and drink as deep. ‭ The things thou think'st on, all at full shall be ‭ By th' Achives thought on, and perform'd to thee; ‭ Ship, and choice oars, that in a trice will land ‭ Thy hasty fleet on heav'nly Pylos' sand, ‭ And at the fame of thy illustrious sire." ‭ He answer'd: "Men, whom pride did so inspire, ‭ Are not fit consorts for an humble guest; ‭ Nor are constrain'd men merry at their feast. ‭ Is 't not enough, that all this time ye have ‭ Op'd in your entrails my chief goods a grave, ‭ And, while I was a child, made me partake? ‭ My now more growth more grown my mind doth make, ‭ And, hearing speak more judging men than you, ‭ Perceive how much I was misgovern'd now. ‭ I now will try if I can bring ye home ‭ An ill Fate to consort you; if it come ‭ From Pylos, or amongst the people here. ‭ But thither I resolve, and know that there ‭ I shall not touch in vain. Nor will I stay, ‭ Though in a merchant's ship I steer my way; ‭ Which shows in your sights best; since me ye know ‭ Incapable of ship, or men to row." ‭ This said, his hand he coyly snatch'd away ‭ From forth Antinous' hand. The rest the day ‭ Spent through the house with banquets; some with jests, ‭ And some with railings, dignifying their feasts. ‭ To whom a jest-proud youth the wit began: ‭ "Telemachus will kill us ev'ry man. ‭ From Sparta, to the very Pylian sand, ‭ He will raise aids to his impetuous hand. ‭ O he affects it strangely! Or he means ‭ To search Ephyra's fat shores, and from thence ‭ Bring deathful poisons, which amongst our bowls ‭ Will make a general shipwrack of our souls." ‭ Another said: "Alas, who knows but he ‭ Once gone, and erring like his sire at sea, ‭ May perish like him, far from aid of friends, ‭ And so he makes us work? For all the ends ‭ Left of his goods here we shall share, the house ‭ Left to his mother and her chosen spouse." ‭ Thus they; while he a room ascended, high ‭ And large, built by his father, where did lie ‭ Gold and brass heap'd up, and in coffers were ‭ Rich robes, great store of odorous oils, and there ‭ Stood tuns of sweet old wines along the wall, ‭ Neat and divine drink, kept to cheer with all ‭ Ulysses' old heart, if he turn'd again ‭ From labours fatal to him to sustain. ‭ The doors of plank were, their close exquisite, ‭ Kept with a double key, and day and night ‭ A woman lock'd within; and that was she ‭ Who all trust had for her sufficiency, ‭ Old Euryclea, one of Opis' race, ‭ Son to Pisenor, and in passing grace ‭ With grey Minerva; her the prince did call, ‭ And said: "Nurse! Draw me the most sweet of all ‭ The wine thou keep'st; next that which for my sire ‭ Thy care reserves, in hope he shall retire. ‭ Twelve vessels fill me forth, and stop them well. ‭ Then into well-sew'd sacks of fine ground meal ‭ Pour twenty measures. Nor, to anyone ‭ But thee thyself, let this design be known. ‭ All this see got together; I it all ‭ In night will fetch off, when my mother shall ‭ Ascend her high room, and for sleep prepare. ‭ Sparta and Pylos I must see, in care ‭ To find my father." Out Euryclea cried, ‭ And ask'd with tears: "Why is your mind applied. ‭ Dear son, to this course? Whither will you go? ‭ So far off leave us, and belovéd so, ‭ So only? And the sole hope of your race? ‭ Royal Ulysses, far from the embrace ‭ Of his kind country, in a land unknown ‭ Is dead; and, you from your lov'd country gone, ‭ The Wooers will with some deceit assay ‭ To your destruction, making then their prey ‭ Of all your goods. Where, in your own y'are strong, ‭ Make sure abode. It fits not you so young ‭ To suffer so much by the aged seas, ‭ And err in such a wayless wilderness." ‭ "Be cheer'd, lov'd nurse," said he, "for, not without ‭ The will of God, go my attempts about. ‭ Swear therefore, not to wound my mother's ears ‭ With word of this, before from heav'n appears ‭ Th' elev'nth or twelfth light, or herself shall please ‭ To ask of me, or hears me put to seas, ‭ Lest her fair body with her woe be wore." ‭ To this the great oath of the Gods she swore; ‭ Which having sworn, and of it every due ‭ Perform'd to full, to vessels wine she drew, ‭ And into well-sew'd sacks pour'd foody meal. ‭ In mean time he, with cunning to conceal ‭ All thought of this from others, himself bore ‭ In broad house, with the Wooers, as before. ‭ Then grey-eyed Pallas other thoughts did own, ‭ And like Telemachus trod through the town, ‭ Commanding all his men in th' even to be ‭ Aboard his ship. Again then question'd she ‭ Noënon, fam'd for aged Phronius' son, ‭ About his ship; who all things to be done ‭ Assur'd her freely should. The sun then set, ‭ And sable shadows slid through ev'ry street, ‭ When forth they launch'd, and soon aboard did bring ‭ All arms, and choice of ev'ry needful thing ‭ That fits a well-rigg'd ship. The Goddess then ‭ Stood in the port's extreme part, where her men, ‭ Nobly appointed, thick about her came, ‭ Whose ev'ry breast she did with spirit enflame. ‭ Yet still fresh projects laid the grey-eyed Dame. ‭ Straight to the house she hasted, and sweet sleep ‭ Pour'd on each Wooer; which so laid in steep ‭ Their drowsy temples, that each brow did nod, ‭ As all were drinking, and each hand his load, ‭ The cup, let fall. All start up, and to bed, ‭ Nor more would watch, when sleep so surfeited ‭ Their leaden eye-lids. Then did Pallas call ‭ Telemachus, in body, voice, and all, ‭ Resembling Mentor, from his native nest, ‭ And said, that all his arm'd men were addrest ‭ To use their oars, and all expected now ‭ He should the spirit of a soldier show. ‭ "Come then," said she, "no more let us defer ‭ Our honour'd action." Then she took on her ‭ A ravish'd spirit, and led as she did leap; ‭ And he her most haste took out step by step. ‭ Arrived at sea and ship, they found ashore ‭ The soldiers that their fashion'd-long hair wore; ‭ To whom the prince said: "Come, my friends, let's bring ‭ Our voyage's provision; ev'ry thing ‭ Is heap'd together in our court; and none, ‭ No not my mother, nor her maids, but one ‭ Knows our intention." This express'd, he led, ‭ The soldiers close together followed; ‭ And all together brought aboard their store. ‭ Aboard the prince went; Pallas still before ‭ Sat at the stern, he close to her, the men ‭ Up hasted after. He and Pallas then ‭ Put from the shore. His soldiers then he bad ‭ See all their arms fit; which they heard, and had. ‭ A beechen mast, then, in the hollow base ‭ They put, and hoisted, fix'd it in its place ‭ With cables; and with well-wreath'd halsers hoise ‭ Their white sails, which grey Pallas now employs ‭ With full and fore-gales through the dark deep main. ‭ The purple waves, so swift cut, roar'd again ‭ Against the ship sides, that now ran and plow'd ‭ The rugged seas up. Then the men bestow'd ‭ Their arms about the ship, and sacrifice ‭ With crown'd wine-cups to th' endless Deities ‭ They offer'd up. Of all yet thron'd above, ‭ They most observ'd the grey-eyed seed of Jove; ‭ Who, from the evening till the morning rose, ‭ And all day long their voyage did dispose. ‭ FINIS LIBRI SECUNDI HOM. ODYSS. ‭[1] The word is _κεἰρετε, κεἰρω_ signifying _insatiabili, quddâm ‭edacitate voro._ ‭ THE THIRD BOOK OF HOMER'S ODYSSEYS ‭ THE ARGUMENT ‭ Telemachus, and Heav'n's wise Dame ‭ That never husband had, now came ‭ To Nestor; who his either guest ‭ Receiv'd at the religious feast ‭ He made to Neptune, on his shore; ‭ And there told what was done before ‭ The Trojan turrets, and the state ‭ Of all the Greeks since Ilion's fate. ‭ This book these three of greatest place ‭ Doth serve with many a varied grace. ‭ Which past, Minerva takes her leave. ‭ Whose state when Nestor doth perceive, ‭ With sacrifice he makes it known, ‭ Where many a pleasing rite is shown. ‭ Which done, Telemachus hath gain'd ‭ A chariot of him; who ordain'd ‭ Pisistratus, his son, his guide ‭ To Sparta; and when starry eyed ‭ The ample heav'n began to be, ‭ All house-rites to afford them free, ‭ In Pheris, Diocles did please, ‭ His surname Ortilochides. ‭ ANOTHER ARGUMENT ‭ _Γἀμμα._ ‭ Ulysses' son ‭ With Nestor lies, ‭ To Sparta gone; ‭ Thence Pallas flies. ‭ The sun now left the great and goodly lake, ‭ And to the firm heav'n bright ascent did make, ‭ To shine as well upon the mortal birth, ‭ Inhabiting the plow'd life-giving earth, ‭ As on the ever-treaders upon death. ‭ And now to Pylos, that so garnisheth ‭ Herself with buildings, old Neleus' town, ‭ The prince and Goddess come had strange sights shown, ‭ For, on the marine shore, the people there ‭ To Neptune, that the azure locks doth wear, ‭ Beeves that were wholly black gave holy flame. ‭ Nine seats of state they made to his high name; ‭ And ev'ry seat set with five hundred men, ‭ And each five hundred was to furnish then ‭ With nine black oxen ev'ry sacred seat. ‭ These of the entrails only pleas'd to eat, ‭ And to the God enflam'd the fleshy thighs. ‭ By this time Pallas with the sparkling eyes, ‭ And he she led, within the haven bore, ‭ Struck sail, cast anchor, and trod both the shore, ‭ She first, he after. Then said Pallas: "Now ‭ No more befits thee the least bashful brow; ‭ T' embolden which this act is put on thee, ‭ To seek thy father both at shore and sea, ‭ And learn in what clime he abides so close, ‭ Or in the pow'r of what Fate doth repose. ‭ Come then, go right to Nestor; let us see, ‭ If in his bosom any counsel be, ‭ That may inform us. Pray him not to trace ‭ The common courtship, and to speak in grace ‭ Of the demander, but to tell the truth; ‭ Which will delight him, and commend thy youth ‭ For such prevention; for he loves no lies, ‭ Nor will report them, being truly wise." ‭ He answer'd: "Mentor! how, alas! shall I ‭ Present myself? How greet his gravity? ‭ My youth by no means that ripe form affords, ‭ That can digest my mind's instinct in words ‭ Wise, and beseeming th' ears of one so sage. ‭ Youth of most hope blush to use words with age." ‭ She said: "Thy mind will some conceit impress, ‭ And something God will prompt thy towardness; ‭ For, I suppose, thy birth, and breeding too, ‭ Were not in spite of what the Gods could do." ‭ This said, she swiftly went before, and he ‭ Her steps made guides, and follow'd instantly. ‭ When soon they reach'd the Pylian throngs and seats, ‭ Where Nestor with his sons sat; and the meats, ‭ That for the feast serv'd, round about them were ‭ Adherents dressing, all their sacred cheer, ‭ Being roast and boil'd meats. When the Pylians saw ‭ These strangers come, in thrust did all men draw ‭ About their entry, took their hands, and pray'd ‭ They both would sit; their entry first assay'd ‭ By Nestor's son, Pisistratus. In grace ‭ Of whose repair, he gave them honour'd place ‭ Betwixt his sire and brother Thrasymed, ‭ Who sat at feast on soft fells that were spread ‭ Along the sea sands, kerv'd, and reach'd to them ‭ Parts of the inwards, and did make a stream ‭ Of spritely wine into a golden bowl; ‭ Which to Minerva with a gentle soul ‭ He gave, and thus spake: "Ere you eat, fair guest, ‭ Invoke the Seas' King, of whose sacred feast ‭ Your travel hither makes ye partners now; ‭ When, sacrificing as becomes, bestow ‭ This bowl of sweet wine on your friend, that he ‭ May likewise use these rites of piety; ‭ For I suppose his youth doth prayers use, ‭ Since all men need the Gods. But you I choose ‭ First in this cup's disposure, since his years ‭ Seem short of yours, who more like me appears." ‭ Thus gave he her the cup of pleasant wine; ‭ And since a wise and just man did design ‭ The golden bowl first to her free receit, ‭ Ev'n to the Goddess it did add delight, ‭ Who thus invok'd: "Hear thou, whose vast embrace ‭ Enspheres the whole earth, nor disdain thy grace ‭ To us that ask it in performing this: ‭ To Nestor first, and these fair sons of his, ‭ Vouchsafe all honour; and, next them, bestow ‭ On all these Pylians, that have offer'd now ‭ This most renowned hecatomb to thee, ‭ Remuneration fit for them, and free; ‭ And lastly deign Telemachus and me, ‭ The work perform'd for whose effect we came, ‭ Our safe return, both with our ship and fame." ‭ Thus pray'd she; and herself herself obey'd, ‭ In th' end performing all for which she pray'd. ‭ And now, to pray, and do as she had done, ‭ She gave the fair round bowl t' Ulysses' son. ‭ The meat then dress'd, and drawn, and serv'd t' each guest, ‭ They celebrated a most sumptuous feast. ‭ When appetite to wine and food allay'd, ‭ Horse-taming Nestor then began, and said: ‭ "Now life's desire is serv'd, as far as fare, ‭ Time fits me to enquire what guests these are. ‭ Fair guests, what are ye? And for what coast tries ‭ Your ship the moist deeps? For fit merchandise? ‭ Or rudely coast ye, like our men of prise, ‭ The rough seas tempting, desperately erring, ‭ The ill of others in their good conferring?" ‭ The wise prince now his boldness did begin, ‭ For Pallas' self had harden'd him within, ‭ By this device of travel to explore ‭ His absent father; which two girlonds wore; ‭ His good by manage of his spirits; and then ‭ To gain him high grace in th' accounts of men. ‭ "O Nestor! still in whom Nelëus lives! ‭ And all the glory of the Greeks survives, ‭ You ask from whence we are, and I relate: ‭ From Ithaca (whose seat is situate ‭ Where Neius, the renownéd mountain, rears ‭ His haughty forehead, and the honour bears ‭ To be our sea-mark) we assay'd the waves. ‭ The business, I must tell, our own good craves, ‭ And not the public. I am come t' enquire, ‭ If, in the fame that best men doth inspire ‭ Of my most-suff'ring father, I may hear ‭ Some truth of his estate now, who did bear ‭ The name, being join'd in fight with you alone, ‭ To even with earth the height of Ilion. ‭ Of all men else, that any name did bear, ‭ And fought for Troy, the sev'ral ends we hear; ‭ But his death Jove keeps from the world unknown, ‭ The certain fame thereof being told by none; ‭ If on the continent by enemies slain, ‭ Or with the waves eat of the ravenous main. ‭ For his love 'tis that to your knees I sue, ‭ That you would please, out of your own clear view, ‭ T' assure his sad end; or say, if your ear ‭ Hath heard of the unhappy wanderer, ‭ To too much sorrow whom his mother bore. ‭ You then by all your bounties I implore, ‭ (If ever to you deed or word hath stood, ‭ By my good father promis'd, render'd good ‭ Amongst the Trojans, where ye both have tried ‭ The Grecian suff'rance) that in nought applied ‭ To my respect or pity you will glose, ‭ But uncloth'd truth to my desires disclose." ‭ "O my much-lov'd," said he, "since you renew ‭ Remembrance of the miseries that grew ‭ Upon our still-in-strength-opposing Greece ‭ Amongst Troy's people, I must touch a piece ‭ Of all our woes there, either in the men ‭ Achilles brought by sea and led to gain ‭ About the country, or in us that fought ‭ About the city, where to death were brought ‭ All our chief men, as many as were there. ‭ There Mars-like Ajax lies; Achilles there; ‭ There the in-counsel-like-the-Gods, his friend; ‭ There my dear son Antilochus took end, ‭ Past measure swift of foot, and staid in fight. ‭ A number more that ills felt infinite; ‭ Of which to reckon all, what mortal man, ‭ If five or six years you should stay here, can ‭ Serve such enquiry? You would back again, ‭ Affected with unsufferable pain, ‭ Before you heard it. Nine years sieg'd we them, ‭ With all the depth and sleight of stratagem ‭ That could be thought. Ill knit to ill past end. ‭ Yet still they toil'd us; nor would yet Jove send ‭ Rest to our labours, nor will scarcely yet. ‭ But no man liv'd, that would in public set ‭ His wisdom by Ulysses' policy, ‭ As thought his equal; so excessively ‭ He stood superior all ways. If you be ‭ His son indeed, mine eyes ev'n ravish me ‭ To admiration. And in all consent ‭ Your speech puts on his speech's ornament. ‭ Nor would one say, that one so young could use, ‭ Unless his son, a rhetoric so profuse. ‭ And while we liv'd together, he and I ‭ Never in speech maintain'd diversity; ‭ Nor sat in council but, by one soul led, ‭ With spirit and prudent counsel furnishéd ‭ The Greeks at all hours, that, with fairest course, ‭ What best became them, they might put in force. ‭ But when Troy's' high tow'rs we had levell'd thus, ‭ We put to sea, and God divided us. ‭ And then did Jove our sad retreat devise; ‭ For all the Greeks were neither just nor wise, ‭ And therefore many felt so sharp a fate, ‭ Sent from Minerva's most pernicious hate; ‭ Whose mighty Father can do fearful things. ‭ By whose help she betwixt the brother kings ‭ Let fall contention; who in council met ‭ In vain, and timeless, when the sun was set, ‭ And all the Greeks call'd, that came charg'd with wine. ‭ Yet then the kings would utter their design, ‭ And why they summon'd. Menelaus, he ‭ Put all in mind of home, and cried, To sea. ‭ But Agamemnon stood on contraries, ‭ Whose will was, they should stay and sacrifice ‭ Whole hecatombs to Pallas, to forego ‭ Her high wrath to them. Fool! that did not know ‭ She would not so be won; for not with ease ‭ Th' Eternal Gods are turn'd from what they please. ‭ So they, divided, on foul language stood. ‭ The Greeks in huge rout rose, their wine-heat blood ‭ Two ways affecting. And, that night's sleep too, ‭ We turn'd to studying either other's woe; ‭ When Jove besides made ready woes enow. ‭ Morn came, we launch'd, and in our ships did stow ‭ Our goods, and fair-girt women. Half our men ‭ The people's guide, Atrides, did contain, ‭ And half, being now aboard, put forth to sea. ‭ A most free gale gave all ships prosp'rous way. ‭ God settled then the huge whale-bearing lake, ‭ And Tenedos we reach'd; where, for time's sake, ‭ We did divine rites to the Gods. But Jove, ‭ Inexorable still, bore yet no love ‭ To our return, but did again excite ‭ A second sad contention, that turn'd quite ‭ A great part of us back to sea again; ‭ Which were th' abundant-in-all-counsels man, ‭ Your matchless father, who, to gratify ‭ The great Atrides, back to him did fly. ‭ But I fled all, with all that follow'd me, ‭ Because I knew God studied misery, ‭ To hurl amongst us. With me likewise fled ‭ Martial Tydides. I the men he led ‭ Gat to go with him. Winds our fleet did bring ‭ To <DW26>s, where the yellow-headed king, ‭ Though late, yet found us, as we put to choice ‭ A tedious voyage; if we sail should hoise ‭ Above rough Chius, left on our left hand, ‭ To th' isle of Psyria, or that rugged land ‭ Sail under, and for windy Mimas steer. ‭ We ask'd of God that some ostent might clear ‭ Our cloudy business, who gave us sign, ‭ And charge, that all should, in a middle line, ‭ The sea cut for Eubœa, that with speed ‭ Our long-sustain'd infortune might be freed. ‭ Then did a whistling wind begin to rise, ‭ And swiftly flew we through the fishy skies, ‭ Till to Geræstus we in night were brought; ‭ Where, through the broad sea since we safe had wrought, ‭ At Neptune's altars many solid thighs ‭ Of slaughter'd bulls we burn'd for sacrifice. ‭ The fourth day came, when Tydeus' son did greet ‭ The haven of Argos with his cómplete fleet. ‭ But I for Pylos straight steer'd on my course; ‭ Nor ever left the wind his foreright force, ‭ Since God fore-sent it first. And thus I came, ‭ Dear son, to Pylos, uninform'd by fame, ‭ Nor know one sav'd by Fate, or overcome. ‭ Whom I have heard of since, set here at home, ‭ As fits, thou shalt be taught, nought left unshown. ‭ The expert spear-men, ev'ry Myrmidon, ‭ Led by the brave heir of the mighty-soul'd ‭ Unpeer'd Achilles, safe of home got hold; ‭ Safe Philoctetes, Pœan's famous seed; ‭ And safe Idomenæus his men led ‭ To his home, Crete, who fled the arméd field, ‭ Of whom yet none the sea from him withheld. ‭ Atrides, you have both heard, though ye be ‭ His far-off dwellers, what an end had he, ‭ Done by Ægisthus to a bitter death; ‭ Who miserably paid for forcéd breath, ‭ Atrides leaving a good son, that dyed, ‭ In blood of that deceitful parricide, ‭ His wreakful sword. And thou my friend, as he ‭ For this hath his fame, the like spirit in thee ‭ Assume at all parts. Fair and great, I see, ‭ Thou art in all hope, make it good to th' end, ‭ That after-times as much may thee commend." ‭ He answer'd: "O thou greatest grace of Greece, ‭ Orestes made that wreak his master-piece, ‭ And him the Greeks will give a master-praise, ‭ Verse finding him to last all after-days. ‭ And would to God the Gods would favour me ‭ With his performance, that my injury, ‭ Done by my mother's Wooers, being so foul, ‭ I might revenge upon their ev'ry soul; ‭ Who, pressing me with contumelies, dare ‭ Such things as past the pow'r of utt'rance are. ‭ But Heav'n's great Pow'rs have grac'd my destiny ‭ With no such honour. Both my sire and I ‭ Are born to suffer everlastingly." ‭ "Because you name those Wooers, friend," said he, ‭ "Report says, many such, in spite of thee, ‭ Wooing thy mother, in thy house commit ‭ The ills thou nam'st. But say: Proceedeth it ‭ From will in thee to bear so foul a foil? ‭ Or from thy subjects' hate, that wish thy spoil, ‭ And will not aid thee, since their spirits rely, ‭ Against thy rule, on some grave augury? ‭ What know they, but at length thy father may ‭ Come, and with violence their violence pay; ‭ Or he alone, or all the Greeks with him? ‭ But if Minerva now did so esteem ‭ Thee, as thy father in times past; whom, past ‭ All measure, she with glorious favours grac't ‭ Amongst the Trojans, where we suffer'd so; ‭ (O! I did never see, in such clear show, ‭ The Gods so grace a man, as she to him, ‭ To all our eyes, appear'd in all her trim) ‭ If so, I say, she would be pleas'd to love, ‭ And that her mind's care thou so much couldst move, ‭ As did thy father, ev'ry man of these ‭ Would lose in death their seeking marriages." ‭ "O father," answer'd he, "you make amaze ‭ Seize me throughout. Beyond the height of phrase ‭ You raise expression; but 'twill never be, ‭ That I shall move in any Deity ‭ So blest an honour. Not by any means, ‭ If Hope should prompt me, or blind Confidence, ‭ (The Gods of Fools) or ev'ry Deity ‭ Should will it; for 'tis past my destiny." ‭ The burning-eyed Dame answer'd: "What a speech ‭ Hath past the teeth-guard Nature gave to teach ‭ Fit question of thy words before they fly! ‭ God easily can [1] (when to mortal eye ‭ He's furthest off) a mortal satisfy; ‭ And does the more still. For thy car'd-for sire, ‭ I rather wish, that I might home retire, ‭ After my suff'rance of a world of woes, ‭ Far off, and then my glad eyes might disclose ‭ The day of my return, then straight retire, ‭ And perish standing by my household fire; ‭ As Agamemnon did, that lost his life ‭ By false Ægisthus, and his falser wife. ‭ For Death to come at length, 'tis due to all; ‭ Nor can the Gods themselves, when Fate shall call ‭ Their most-lov'd man, extend his vital breath ‭ Beyond the fix'd bounds of abhorréd Death." ‭ "Mentor!" said he, "let's dwell no more on this, ‭ Although in us the sorrow pious is. ‭ No such return, as we wish, Fates bequeath ‭ My erring father; whom a present death ‭ The Deathless have decreed. I'll now use speech ‭ That tends to other purpose; and beseech ‭ Instruction of grave Nestor, since he flows ‭ Past shore in all experience, and knows ‭ The sleights and wisdoms, and whose heights aspire ‭ Others, as well as my commended sire, ‭ Whom Fame reports to have commanded three ‭ Ages of men, and doth in sight to me ‭ Show like th' Immortals. Nestor! the renown ‭ Of old Neleius, make the clear truth known, ‭ How the most-great-in-empire, Atreus' son, ‭ Sustain'd the act of his destruction, ‭ Where then was Menelaus? How was it ‭ That false Ægisthus, being so far unfit ‭ A match for him, could his death so enforce? ‭ Was he not then in Argos? or his course ‭ With men so left, to let a coward breathe ‭ Spirit enough to dare his brother's death?" ‭ "I'll tell thee truth in all, fair son," said he: ‭ "Right well was this event conceiv'd by thee. ‭ If Menelaus in his brother's house ‭ Had found the idle liver with his spouse, ‭ Arriv'd from Troy, he had not liv'd, nor dead ‭ Had the digg'd heap pour'd on his lustful head, ‭ But fowls and dogs had torn him in the fields, ‭ Far off of Argos; not a dame it yields ‭ Had giv'n him any tear, so foul his fact ‭ Show'd ev'n to women. Us Troy's wars had rack'd ‭ To ev'ry sinew's sufferance, while he ‭ In Argos' uplands liv'd, from those works free, ‭ And Agamemnon's wife with force of word ‭ Flatter'd and soften'd, who, at first, abhorr'd ‭ A fact so infamous. The heav'nly dame ‭ A good mind had, but was in blood to blame. ‭ There was a poet, to whose care the king ‭ His queen committed, and in ev'ry thing, ‭ When he from Troy went, charg'd him to apply ‭ Himself in all guard to her dignity. ‭ But when strong Fate so wrapt-in her effects, ‭ That she resolv'd to leave her fit respects, ‭ Into a desert isle her guardian led, ‭ There left, the rapine of the vultures fed. ‭ Then brought he willing home his will's won prize, ‭ On sacred altars offer'd many thighs, ‭ Hung in the God's fanes many ornaments, ‭ Garments and gold, that he the vast events ‭ Of such a labour to his wish had brought, ‭ As neither fell into his hope nor thought. ‭ At last, from Troy sail'd Sparta's king and I, ‭ Both holding her untouch'd. And, that his eye ‭ Might see no worse of her, when both were blown ‭ To sacred Sunium, of Minerva's town ‭ The goodly promontory, with his shafts severe ‭ Augur Apollo slew him that did steer ‭ Atrides' ship, as he the stern did guide, ‭ And she the full speed of her sail applied. ‭ He was a man that natións of men ‭ Excell'd in safe guide of a vessel, when ‭ A tempest rush'd in on the ruffled seas; ‭ His name was Phrontis Onetorides. ‭ And thus was Menelaus held from home, ‭ Whose way he thirsted so to overcome, ‭ To give his friend the earth, being his pursuit, ‭ And all his exequies to execute. ‭ But sailing still the wine-hued seas, [2] to reach ‭ Some shore for fit performance, he did fetch ‭ The steep mount of the Malians, and there, ‭ With open voice, offended Jupiter ‭ Proclaim'd the voyage his repugnant mind, ‭ And pour'd the puffs out of a shrieking wind, ‭ That nourish'd billows heighten'd like to hills; ‭ And with the fleet's division fulfills ‭ His hate proclaim'd; upon a part of Crete ‭ Casting the navy, where the sea-waves meet ‭ Rough Jardanus, and where the Cydons live. ‭ There is a rock, on which the sea doth drive, ‭ Bare, and all broken, on the confines set ‭ Of Gortys, that the dark seas likewise fret; ‭ And hither sent the South a horrid drift ‭ Of waves against the top, that was the left ‭ Of that torn cliff as far as Phæstus' strand. ‭ A little stone the great sea's rage did stand. ‭ The men here driv'n 'scap'd hard the ship's sore shocks, ‭ The ships themselves being wrack'd against the rocks, ‭ Save only five, that blue fore-castles bore, ‭ Which wind and water cast on Egypt's shore. ‭ When he (there victling well, and store of gold ‭ Aboard his ships brought) his wild way did hold, ‭ And t' other languag'd men was forc'd to roam. ‭ Mean space Ægisthus made sad work at home, ‭ And slew his brother, forcing to his sway ‭ Atrides' subjects, and did sev'n years lay ‭ His yoke upon the rich Mycenian state. ‭ But in the eighth, to his affrighting fate, ‭ Divine Orestes home from Athens came, ‭ And what his royal father felt, the same ‭ He made the false Ægisthus groan beneath. ‭ _Death evermore is the reward of death._ ‭ Thus having slain him, a sepulchral feast ‭ He made the Argives for his lustful guest, ‭ And for his mother whom he did detest. ‭ The self-same day upon him stole the king ‭ Good-at-a-martial-shout, and goods did bring, ‭ As many as his freighted fleet could bear. ‭ But thou, my son, too long by no means err, ‭ Thy goods left free for many a spoilful guest, ‭ Lest they consume some, and divide the rest, ‭ And thou, perhaps, besides, thy voyage lose. ‭ To Menelaus yet thy course dispose ‭ I wish and charge thee; who but late arriv'd ‭ From such a shore and men, as to have liv'd ‭ In a return from them he never thought, ‭ And whom black whirlwinds violently brought ‭ Within a sea so vast, that in a year ‭ Not any fowl could pass it anywhere, ‭ So huge and horrid was it. But go thou ‭ With ship and men (or, if thou pleasest now ‭ To pass by land, there shall be brought for thee ‭ Both horse and chariot, and thy guides shall be ‭ My sons themselves) to Sparta the divine, ‭ And to the king whose locks like amber shine. ‭ Intreat the truth of him, nor loves he lies, ‭ Wisdom in truth is, and he's passing wise." ‭ This said, the Sun went down, and up rose Night, ‭ When Pallas spake: "O father, all good right ‭ Bear thy directions. But divide we now ‭ The sacrifices' tongues, mix wines, and vow ‭ To Neptune, and the other Ever-Blest, ‭ That, having sacrific'd, we may to rest. ‭ The fit hour runs now, light dives out of date, ‭ At sacred feasts we must not sit too late." ‭ She said; they heard; the heralds water gave; ‭ The youths crown'd cups with wine, and let all have ‭ Their equal shares, beginning from the cup ‭ Their parting banquet. All the tongues cut up, ‭ The fire they gave them, sacrific'd, and rose, ‭ Wine, and divine rites us'd, to each dispose; ‭ Minerva and Telemachus desir'd ‭ They might to ship be, with his leave, retir'd. ‭ He, mov'd with that, provok'd thus their abodes: ‭ "Now Jove forbid, and all the long-liv'd Gods, ‭ Your leaving me, to sleep aboard a ship; ‭ As I had drunk of poor Penia's whip, ‭ Even to my nakedness, and had nor sheet ‭ Nor cov'ring in my house; that warm nor sweet ‭ A guest, nor I myself, had means to sleep; ‭ Where I, both weeds and wealthy cov'rings keep ‭ For all my guests. Nor shall Fame ever say, ‭ The dear son of the man Ulysses lay ‭ All night a-ship-board here while my days shine, ‭ Or in my court whiles any son of mine ‭ Enjoys survival, who shall guests receive, ‭ Whomever my house hath a nook to leave." ‭ "My much-lov'd father," said Minerva, "well ‭ All this becomes thee. But persuade to dwell ‭ This night with thee thy son Telemachus, ‭ For more convenient is the course for us, ‭ That he may follow to thy house and rest, ‭ And I may board our black-sail, that addrest ‭ At all parts I may make our men, and cheer ‭ All with my presence, since of all men there ‭ I boast myself the senior, th' others are ‭ Youths, that attend in free and friendly care ‭ Great-soul'd Telemachus, and are his peers ‭ In fresh similitude of form and years. ‭ For their confirmance, I will therefore now ‭ Sleep in our black bark. But, when light shall show ‭ Her silver forehead, I intend my way ‭ Amongst the Caucons, men that are to pay ‭ A debt to me, nor small, nor new. For this, ‭ Take you him home; whom in the morn dismiss, ‭ With chariot and your sons, and give him horse ‭ Ablest in strength, and of the speediest course" ‭ This said, away she flew, form'd like the fowl ‭ Men call the ossifrage; when ev'ry soul ‭ Amaze invaded; even th' old man admir'd, ‭ The youth's hand took, and said: "O most desir'd, ‭ My hope says thy proof will no coward show, ‭ Nor one unskill'd in war, when Deities now ‭ So young attend thee, and become thy guides; ‭ Nor any of the heav'n-hous'd States besides, ‭ But Tritogenia's self, the Seed of Jove, ‭ The great-in-prey, that did in honour move ‭ So much about thy father, amongst all ‭ The Grecian army. Fairest queen, let fall ‭ On me like favours! Give me good renown! ‭ Which, as on me, on my lov'd wife let down, ‭ And all my children. I will burn to thee ‭ An ox right bred, broad-headed, and yoke-free, ‭ To no man's hand yet humbled. Him will I, ‭ His horns in gold hid, give thy Deity." ‭ Thus pray'd he, and she heard; and home he led ‭ His sons, and all his heaps of kindered. ‭ Who ent'ring his court royal, ev'ry one ‭ He marshall'd in his sev'ral seat and throne; ‭ And ev'ry one, so kindly come, he gave ‭ His sweet-wine cup; which none was let to have ‭ Before his 'leventh year landed him from Troy; ‭ Which now the butleress had leave t' employ, ‭ Who therefore pierc'd it, and did give it vent. ‭ Of this the old duke did a cup present ‭ To ev'ry guest; made his Maid many a pray'r ‭ That wears the shield fring'd with his nurse's hair, ‭ And gave her sacrifice. With this rich wine ‭ And food suffic'd, sleep all eyes did decline, ‭ And all for home went; but his court alone ‭ Telemachus, divine Ulysses' son, ‭ Must make his lodging, or not please his heart. ‭ A bed, all chequer'd with elaborate art, ‭ Within a portico that rung like brass, ‭ He brought his guest to; and his bedfere was ‭ Pisistratus, the martial guide of men, ‭ That liv'd, of all his sons, unwed till then. ‭ Himself lay in a by-room, far above, ‭ His bed made by his barren wife, his love. ‭ The rosy-finger'd Morn no sooner shone, ‭ But up he rose, took air, and sat upon ‭ A seat of white and goodly polish'd stone, ‭ That such a gloss as richest ointments wore, ‭ Before his high gates; where the counsellor ‭ That match'd the Gods (his father) us'd to sit, ‭ Who now, by fate forc'd, stoop'd as low as it. ‭ And here sat Nestor, holding in his hand ‭ A sceptre; and about him round did stand, ‭ As early up, his sons' troop; Perseus, ‭ The god-like Thrasymed, and Aretus, ‭ Echephron, Stratius, and sixth and last ‭ Pisistratus, and by him (half embrac'd ‭ Still as they came) divine Telemachus; ‭ To these spake Nestor, old Gerenius: ‭ "Haste, lovéd sons, and do me a desire, ‭ That, first of all the Gods, I may aspire ‭ To Pallas' favour, who vouchsaf'd to me ‭ At Neptune's feast her sight so openly. ‭ Let one to field go, and an ox with speed ‭ Cause hither brought, which let the herdsman lead; ‭ Another to my dear guest's vessel go, ‭ And all his soldiers bring, save only two; ‭ A third the smith that works in gold command ‭ (Laertius) to attend, and lend his hand, ‭ To plate the both horns round about with gold; ‭ The rest remain here close. But first, see told ‭ The maids within, that they prepare a feast, ‭ Set seats through all the court, see straight addrest ‭ The purest water, and get fuel fell'd." ‭ This said, not one but in the service held ‭ Officious hand. The ox came led from field; ‭ The soldiers troop'd from ship; the smith he came, ‭ And those tools brought that serv'd the actual frame ‭ His art conceiv'd, brought anvil, hammers brought, ‭ Fair tongs, and all, with which the gold was wrought. ‭ Minerva likewise came, to set the crown ‭ On that kind sacrifice, and make 't her own. ‭ Then th' old knight Nestor gave the smith the gold, ‭ With which he straight did both the horns infold, ‭ And trimm'd the off'ring so, the Goddess joy'd. ‭ About which thus were Nestor's sons employ'd: ‭ Divine Echephron, and fair Stratius, ‭ Held both the horns. The water odorous, ‭ In which they wash'd, what to the rites was vow'd, ‭ Aretus, in a caldron all bestrow'd ‭ With herbs and flowers, serv'd in from th' holy room ‭ Where all were drest, and whence the rites must come. ‭ And after him a hallow'd virgin came, ‭ That brought the barley-cake, and blew the flame. ‭ The axe, with which the ox should both be fell'd ‭ And cut forth, Thrasymed stood by and held. ‭ Perseus the vessel held that should retain ‭ The purple liquor of the off'ring slain. ‭ Then wash'd the pious father, then the cake ‭ (Of barley, salt, and oil, made) took, and brake, ‭ Ask'd many a boon of Pallas, and the state ‭ Of all the off'ring did initiate, ‭ In three parts cutting off the hair, and cast ‭ Amidst the flame. All th' invocation past, ‭ And all the cake broke, manly Thrasymed ‭ Stood near, and sure, and such a blow he laid ‭ Aloft the off'ring, that to earth he sunk, ‭ His neck-nerves sunder'd, and his spirits shrunk. ‭ Out shriek'd the daughters, daughter-in-laws, and wife ‭ Of three-ag'd Nestor, who had eldest life ‭ Of Clymen's daughters, chaste Eurydice. ‭ The ox on broad earth then laid laterally ‭ They held, while duke Pisistratus the throat ‭ Dissolv'd, and set the sable blood afloat, ‭ And then the life the bones left. Instantly ‭ They cut him up; apart flew either thigh, ‭ That with the fat they dubb'd, with art alone, ‭ The throat-brisk, and the sweet-bread pricking on. ‭ Then Nestor broil'd them on the coal-turn'd wood, ‭ Pour'd black wine on; and by him young men stood, ‭ That spits fine-pointed held, on which, when burn'd ‭ The solid thighs were, they transfix'd, and turn'd ‭ The inwards, cut in cantles; which, the meat ‭ Vow'd to the Gods consum'd, they roast and eat. ‭ In mean space, Polycasté (call'd the fair, ‭ Nestor's young'st daughter) bath'd Ulysses' heir; ‭ Whom having cleans'd, and with rich balms bespread, ‭ She cast a white shirt quickly o'er his head, ‭ And then his weeds put on; when forth he went, ‭ And did the person of a God present, ‭ Came, and by Nestor took his honour'd seat, ‭ This pastor of the people. Then, the meat ‭ Of all the spare parts roasted, off they drew, ‭ Sat, and fell to. But soon the temp'rate few ‭ Rose, and in golden bowls fill'd others wine. ‭ Till, when the rest felt thirst of feast decline, ‭ Nestor his sons bad fetch his high-man'd horse, ‭ And them in chariot join, to run the course ‭ The prince resolv'd. Obey'd, as soon as heard, ‭ Was Nestor by his sons, who straight prepar'd ‭ Both horse and chariot. She that kept the store, ‭ Both bread and wine, and all such viands more, ‭ As should the feast of Jove-fed kings compose, ‭ Purvey'd the voyage. To the rich coach rose ‭ Ulysses' son, and close to him ascended ‭ The duke Pisistratus, the reins intended, ‭ And scourg'd, to force to field, who freely flew; ‭ And left the town that far her splendour threw, ‭ Both holding yoke, and shook it all the day. ‭ But now the sun set, dark'ning ev'ry way, ‭ When they to Pheris came; and in the house ‭ Of Diocles (the son t' Orsilochus, ‭ Whom flood Alphëus got) slept all that night; ‭ Who gave them each due hospitable rite. ‭ But when the rosy-finger'd Morn arose, ‭ They went to coach, and did their horse inclose, ‭ Drave forth the fore-court, and the porch that yields ‭ Each breath a sound, and to the fruitful fields ‭ Rode scourging still their willing flying steeds, ‭ Who strenuously perform'd their wonted speeds. ‭ Their journey ending just when sun went down, ‭ And shadows all ways through the earth were thrown. ‭ FINIS LIBRI TERTII HOM. ODYSS. ‭[1] _Volente Deo, nihil est difficile._ ‭[2] _Οἲνοπα πὀντον: οἲνοψ cujus facies vinum repræsentat._ ‭ THE FOURTH BOOK OF HOMER'S ODYSSEYS ‭ THE ARGUMENT ‭ Receiv'd now in the Spartan court, ‭ Telemachus prefers report ‭ To Menelaus of the throng ‭ Of Wooers with him, and their wrong. ‭ Atrides tells the Greeks' retreat, ‭ And doth a prophecy repeat ‭ That Proteus made, by which he knew ‭ His brother's death; and then doth show ‭ How with Calypso liv'd the sire ‭ Of his young guest. The Wooers conspire ‭ Their prince's death. Whose treach'ry known, ‭ Penelope in tears doth drown. ‭ Whom Pallas by a dream doth cheer, ‭ And in similitude appear ‭ Of fair Iphthima, known to be ‭ The sister of Penelope. ‭ ANOTHER ARGUMENT ‭ _Δἐλτα._ ‭ Here of the sire ‭ The son doth hear. ‭ The Wooers conspire. ‭ The Mother's fear. ‭ In Lacedæmon now, the nurse of whales, [1] ‭ These two arriv'd, and found at festivals, ‭ With mighty concourse, the renownéd king, ‭ His son and daughter jointly marrying. ‭ Alector's daughter he did give his son, ‭ Strong Megapenthes, who his life begun ‭ By Menelaus' bondmaid; whom he knew ‭ In years when Helen could no more renew ‭ In issue like divine Hermione, ‭ Who held in all fair form as high degree ‭ As golden Venus. Her he married now ‭ To great Achilles' son, who was by vow ‭ Betroth'd to her at Troy, And thus the Gods ‭ To constant loves give nuptial periods. ‭ Whose state here past, the Myrmidons' rich town ‭ (Of which she shar'd in the imperial crown) ‭ With horse and chariots he resign'd her to. ‭ Mean space, the high huge house with feast did flow ‭ Of friends and neighbours, joying with the king. ‭ Amongst whom did a heav'nly poet sing, ‭ And touch his harp. Amongst whom likewise danc'd ‭ Two, who in that dumb motion advanc'd, ‭ Would prompt the singer what to sing and play. [2] ‭ All this time in the utter court did stay, ‭ With horse and chariot, Telemachus, ‭ And Nestor's noble son Pisistratus. ‭ Whom Eteoneus, coming forth, descried, ‭ And, being a servant to the king, most tried ‭ In care and his respect, he ran and cried: ‭ "Guests, Jove-kept Menelaus, two such men ‭ As are for form of high Saturnius' strain. ‭ Inform your pleasure, if we shall unclose ‭ Their horse from coach, or say they must dispose ‭ Their way to some such house, as may embrace ‭ Their known arrival with more welcome grace?" ‭ He, angry, answer'd: "Thou didst never show ‭ Thyself a fool, Boethides, till now; ‭ But now, as if turn'd child, a childish speech ‭ Vents thy vain spirits. We ourselves now reach ‭ Our home by much spent hospitality ‭ Of other men; nor know if Jove will try ‭ With other after-wants our state again; ‭ And therefore from our feast no more detain ‭ Those welcome guests, but take their steeds from coach, ‭ And with attendance guide in their approach." ‭ This said, he rush'd abroad, and call'd some more ‭ Tried in such service, that together bore ‭ Up to the guests, and took their steeds that swet ‭ Beneath their yokes from coach; at mangers set, ‭ Wheat and white barley gave them mix'd; and plac'd ‭ Their chariot by a wall so clear, it cast ‭ A light quite through it. And then they led ‭ Their guests to the divine house; which so fed ‭ Their eyes at all parts with illustrious sights, ‭ That admiration seiz'd them. Like the lights ‭ The sun and moon gave, all the palace threw ‭ A lustre through it. Satiate with whose view, ‭ Down to the king's most bright-kept baths they went, ‭ Where handmaids did their services present, ‭ Bath'd, balm'd them, shirts and well-napt weeds put on, ‭ And by Atrides' side set each his throne. ‭ Then did the handmaid-royal water bring, ‭ And to a laver, rich and glittering, ‭ Of massy gold, pour'd; which she plac'd upon ‭ A silver caldron, into which might run ‭ The water as they wash'd. Then set she near ‭ A polish'd table, on which all the cheer ‭ The present could afford a rev'rend dame, ‭ That kept the larder, set. A cook then came, ‭ And divers dishes, borne thence, serv'd again; ‭ Furnish'd the board with bowls of gold. And then, ‭ His right hand giv'n the guests, Atrides said: ‭ "Eat, and be cheerful. Appetite allay'd, ‭ I long to ask, of what stock ye descend; ‭ For not from parents whose race nameless end ‭ We must derive your offspring. Men obscure ‭ Could get none such as you. The portraiture ‭ Of Jove-sustain'd and sceptre-bearing kings ‭ Your either person in his presence brings." ‭ An ox's fat chine then they up did lift, ‭ And set before the guests; which was a gift, ‭ Sent as an honour to the king's own taste. ‭ They saw yet 'twas but to be eaten plac'd, ‭ And fell to it. But food and wine's care past, ‭ Telemachus thus prompted Nestor's son, ‭ (His ear close laying, to be heard of none): [3] ‭ "Consider, thou whom most of my mind esteems, ‭ The brass-work here, how rich it is in beams, ‭ And how, besides, it makes the whole house sound; ‭ What gold, and amber, silver, ivory, round ‭ Is wrought about it. Out of doubt, the hall ‭ Of Jupiter Olympius hath of all ‭ This state the like. How many infinites ‭ Take up to admiration all men's sights!" ‭ Atrides over-heard, and said: "Lov'd son, ‭ No mortal must affect contentión ‭ With Jove, whose dwellings are of endless date. ‭ Perhaps of men some one may emulate, ‭ Or none, my house, or me; for I am one ‭ That many a grave extreme have undergone, ‭ Much error felt by sea, and till th' eighth year, ‭ Had never stay, but wander'd far and near, ‭ Cyprus, Phœnicia, and Sidonia, ‭ And fetch'd the far-off Æthiopia, ‭ Reach'd the Erembi of Arabia, ‭ And Lybia, where with horns ewes yean their lambs, ‭ Which ev'ry full year ewes are three times dams, ‭ Where neither king, nor shepherd, want comes near ‭ Of cheese, or flesh, or sweet milk; all the year ‭ They ever milk their ewes. And here while I ‭ Err'd, gath'ring means to live, one, murd'rously, ‭ Unwares, unseen, bereft my brother's life, ‭ Chiefly betray'd by his abhorréd wife. ‭ So hold I, not enjoying, what you see. ‭ And of your fathers, if they living be, ‭ You must have heard this, since my suff'rings were ‭ So great and famous; from this palace here ‭ (So rarely-well-built, furnishéd so well, ‭ And substancéd with such a precious deal ‭ Of well-got treasure) banish'd by the doom ‭ Of Fate, and erring as I had no home. ‭ And now I have, and use it, not to take ‭ Th' entire delight it offers, but to make ‭ Continual wishes, that a triple part ‭ Of all it holds were wanting, so my heart ‭ Were eas'd of sorrows, taken for their deaths ‭ That fell at Troy, by their revivéd breaths. ‭ And thus sit I here weeping, mourning still ‭ Each least man lost; and sometimes make mine ill, ‭ In paying just tears for their loss, my joy. ‭ Sometimes I breathe my woes, for in annoy ‭ The pleasure soon admits satiety. ‭ But all these men's wants wet not so mine eye, ‭ Though much they move me, as one sole man's miss, ‭ For which my sleep and meat ev'n loathsome is ‭ In his renew'd thought, since no Greek hath won ‭ Grace for such labours as Laërtes' son ‭ Hath wrought and suffer'd, to himself nought else ‭ But future sorrows forging, to me hells ‭ For his long absence, since I cannot know ‭ If life or death detain him; since such woe ‭ For his love, old Laërtes, his wise wife, ‭ And poor young son sustains, whom new with life ‭ He left as sireless." This speech grief to tears ‭ (Pour'd from the son's lids on the earth) his ears, ‭ Told of the father, did excite; who kept ‭ His cheeks dry with his red weed as he wept, ‭ His both hands us'd therein. Atrides then ‭ Began to know him, and did strife retain, ‭ If he should let himself confess his sire, ‭ Or with all fitting circumstance enquire. ‭ While this his thoughts disputed, forth did shine, ‭ Like to the golden distaff-deck'd Divine, ‭ From her bed's high and odoriferous room, ‭ Helen. To whom, of an elaborate loom, ‭ Adresta set a chair; Alcippe brought ‭ A piece of tapestry of fine wool wrought; ‭ Phylo a silver cabinet conferr'd, ‭ Giv'n by Alcandra, nuptially endear'd ‭ To lord Polybius, whose abode in Thebes ‭ Th' Ægyptian city was, where wealth in heaps ‭ His famous house held, out of which did go, ‭ In gift t' Atrides, silver bath-tubs two, ‭ Two tripods, and of fine gold talents ten. ‭ His wife did likewise send to Helen then ‭ Fair gifts, a distaff that of gold was wrought, ‭ And that rich cabinet that Phylo brought, ‭ Round, and with gold ribb'd, now of fine thread full; ‭ On which extended (crown'd with finest wool, ‭ Of violet gloss) the golden distaff-lay. ‭ She took her state-chair, and a foot-stool's stay ‭ Had for her feet; and of her husband thus ‭ Ask'd to know all things: "Is it known to us, ‭ King Menelaus, whom these men commend ‭ Themselves for, that our court now takes to friend? ‭ I must affirm, be I deceiv'd or no, ‭ I never yet saw man nor woman so ‭ Like one another, as this man is like ‭ Ulysses' son. With admiration strike ‭ His looks my thoughts, that they should carry now ‭ Pow'r to persuade me thus, who did but know, ‭ When newly he was born, the form they bore. ‭ But 'tis his father's grace, whom more and more ‭ His grace resembles, that makes me retain ‭ Thought that he now is like Telemachus, then ‭ Left by his sire, when Greece did undertake ‭ Troy's bold war for my impudency's sake." ‭ He answer'd: "Now wife, what you think I know, ‭ The true cast of his father's eye doth show ‭ In his eyes' order. Both his head and hair, ‭ His hands and feet, his very father's are. ‭ Of whom, so well remember'd, I should now ‭ Acknowledge for me his continual flow ‭ Of cares and perils, yet still patient. ‭ But I should too much move him, that doth vent ‭ Such bitter tears for that which hath been spoke, ‭ Which, shunning soft show, see how he would cloak, ‭ And with his purple weed his weepings hide." ‭ Then Nestor's son, Pisistratus, replied: ‭ "Great pastor of the people, kept of God! ‭ He is Ulysses' son, but his abode ‭ Not made before here, and he modest too, ‭ He holds it an indignity to do ‭ A deed so vain, to use the boast of words, ‭ Where your words are on wing; whose voice affords ‭ Delight to us as if a God did break ‭ The air amongst us, and vouchsafe to speak. ‭ But me my father, old duke Nestor, sent ‭ To be his consort hither; his content ‭ Not to be heighten'd so as with your sight, ‭ In hope that therewith words and actions might ‭ Inform his comforts from you, since he is ‭ Extremely griev'd and injur'd by the miss ‭ Of his great father; suff'ring ev'n at home, ‭ And few friends found to help him overcome ‭ His too weak suff'rance, now his sire is gone; ‭ Amongst the people, not afforded one ‭ To check the miseries that mate him thus. ‭ And this the state is of Telemachus." ‭ "O Gods," said he, "how certain, now, I see ‭ My house enjoys that friend's son, that for me ‭ Hath undergone so many willing fights! ‭ Whom I resolv'd, past all the Grecian knights, ‭ To hold in love, if our return by seas ‭ The far-off Thunderer did ever please ‭ To grant our wishes. And to his respect ‭ A palace and a city to erect, ‭ My vow had bound me; whither bringing then ‭ His riches, and his son, and all his men, ‭ From barren Ithaca, (some one sole town ‭ Inhabited about him batter'd down) ‭ All should in Argos live. And there would I ‭ Ease him of rule, and take the empery ‭ Of all on me. And often here would we, ‭ Delighting, loving either's company, ‭ Meet and converse; whom nothing should divide, ‭ Till death's black veil did each all over hide. ‭ But this perhaps hath been a mean to take ‭ Ev'n God himself with envy; who did make ‭ Ulysses therefore only the unblest, ‭ That should not reach his loved country's rest." ‭ These woes made ev'ry one with woe in love; ‭ Ev'n Argive Helen wept, the Seed of Jove; ‭ Ulysses' son wept; Atreus' son did weep; ‭ And Nestor's son his eyes in tears did steep, ‭ But his tears fell not from the present cloud ‭ That from Ulysses was exhal'd, but flow'd ‭ From brave Antilochus' remember'd due, ‭ Whom the renown'd Son of the Morning slew, ‭ Which yet he thus excus'd: "O Atreus' son! ‭ Old Nestor says, there lives not such a one ‭ Amongst all mortals as Atrides is ‭ For deathless wisdom. 'Tis a praise of his, ‭ Still giv'n in your remembrance, when at home ‭ Our speech concerns you. Since then overcome ‭ You please to be with sorrow, ev'n to tears, ‭ That are in wisdom so exempt from peers, ‭ Vouchsafe the like effect in me excuse, ‭ If it be lawful, I affect no use ‭ Of tears thus after meals; at least, at night; ‭ But when the morn brings forth, with tears, her light, ‭ It shall not then impair me to bestow ‭ My tears on any worthy's overthrow. ‭ It is the only rite that wretched men ‭ Can do dead friends, to cut hair, and complain. ‭ But Death my brother took, whom none could call ‭ The Grecian coward, you best knew of all. ‭ I was not there, nor saw, but men report ‭ Antilochus excell'd the common sort ‭ For footmanship, or for the chariot race, ‭ Or in the fight for hardy hold of place." ‭ "O friend," said he, "since thou hast spoken so, ‭ At all parts as one wise should say and do, ‭ And like one far beyond thyself in years, ‭ Thy words shall bounds be to our former tears. ‭ O he is questionless a right-born son, ‭ That of his father hath not only won ‭ The person but the wisdom; and that sire ‭ Complete himself that hath a son entire, ‭ Jove did not only his full fate adorn, ‭ When he was wedded, but when he was born. ‭ As now Saturnius, through his life's whole date, ‭ Hath Nestor's bliss rais'd to as steep a state, ‭ Both in his age to keep in peace his house, ‭ And to have children wise and valorous. ‭ But let us not forget our rear feast thus. ‭ Let some give water here. Telemachus! ‭ The morning shall yield time to you and me ‭ To do what fits, and reason mutually." ‭ This said, the careful servant of the king, ‭ Asphalion, pour'd on th' issue of the spring; ‭ And all to ready feast set ready hand. ‭ But Helen now on new device did stand, ‭ Infusing straight a medicine to their wine, ‭ That, drowning care and angers; did decline ‭ All thought of ill. Who drunk her cup could shed ‭ All that day not a tear, no not if dead ‭ That day his father or his mother were, ‭ Not if his brother, child, or chiefest dear, ‭ He should see murder'd then before his face. ‭ Such useful medicines, only borne in grace ‭ Of what was good, would Helen ever have. ‭ And this juice to her Polydamna gave ‭ The wife of Thoon, an Ægyptian born, ‭ Whose rich earth herbs of medicine do adorn ‭ In great abundance. Many healthful are, ‭ And many baneful. Ev'ry man is there ‭ A good physician out of Nature's grace, ‭ For all the nation sprung of Pæon's race. ‭ When Helen then her medicine had infus'd, ‭ She bad pour wine to it, and this speech us'd: ‭ "Atrides, and these good men's sons, great Jove ‭ Makes good and ill one after other move, ‭ In all things earthly; for he can do all. ‭ The woes past, therefore, he so late let fall, ‭ The comforts he affords us let us take; ‭ Feast, and, with fit discourses, merry make. ‭ Nor will I other use. As then our blood ‭ Griev'd for Ulysses, since he was so good, ‭ Since he was good, let us delight to hear ‭ How good he was, and what his suff'rings were; ‭ Though ev'ry fight, and ev'ry suff'ring deed, ‭ Patient Ulysses underwent, exceed ‭ My woman's pow'r to number, or to name. ‭ But what he did, and suffer'd, when he came ‭ Amongst the Trojans, where ye Grecians all ‭ Took part with suff'rance, I in part can call ‭ To your kind memories. How with ghastly wounds ‭ Himself he mangled, and the Trojan bounds, ‭ Thrust thick with enemies, adventur'd on, ‭ His royal shoulders having cast upon ‭ Base abject weeds, and enter'd like a slave. ‭ Then, beggar-like, he did of all men crave, ‭ And such a wretch was, as the whole Greek fleet ‭ Brought not besides. And thus through ev'ry street ‭ He crept discov'ring, of no one man known. ‭ And yet through all this diff'rence, I alone ‭ Smoked his true person, talk'd with him; but he ‭ Fled me with wiles still. Nor could we agree, ‭ Till I disclaim'd him quite; and so (as mov'd ‭ With womanly remorse of one that prov'd ‭ So wretched an estate, whate'er he were) ‭ Won him to take my house. And yet ev'n there, ‭ Till freely I, to make him doubtless, swore ‭ A pow'rful oath, to let him reach the shore ‭ Of ships and tents before Troy understood, ‭ I could not force on him his proper good. ‭ But then I bath'd and sooth'd him, and he then ‭ Confess'd, and told me all; and, having slain ‭ A number of the Trojan guards, retir'd, ‭ And reach'd the fleet, for sleight and force admir'd. ‭ Their husbands' deaths by him the Trojan wives ‭ Shriek'd for; but I made triumphs for their lives, ‭ For then my heart conceiv'd, that once again ‭ I should reach home; and yet did still retain ‭ Woe for the slaughters Venus made for me, ‭ When both my husband, my Hermione, ‭ And bridal room, she robb'd of so much right, ‭ And drew me from my country with her sleight, ‭ Though nothing under heaven I here did need, ‭ That could my fancy or my beauty feed." ‭ Her husband said: "Wife! what you please to tell ‭ Is true at all parts, and becomes you well; ‭ And I myself, that now may say have seen ‭ The minds and manners of a world of men, ‭ And great heroes, measuring many a ground, ‭ Have never, by these eyes that light me, found ‭ One with a bosom so to be belov'd, ‭ As that in which th' accomplish'd spirit mov'd ‭ Of patient Ulysses. What, brave man, ‭ He both did act, and suffer, when he wan ‭ The town of Ilion, in the brave-built horse, ‭ When all we chief states of the Grecian force ‭ Were hous'd together, bringing death and Fate ‭ Amongst the Trojans, you, wife, may relate; ‭ For you, at last, came to us; God, that would ‭ The Trojans' glory give, gave charge you should ‭ Approach the engine; and Deiphobus, ‭ The god-like, follow'd. Thrice ye circled us ‭ With full survey of it; and often tried ‭ The hollow crafts that in it were implied. [4] ‭ When all the voices of their wives in it ‭ You took on you with voice so like and fit, ‭ And ev'ry man by name so visited, ‭ That I, Ulysses, the king Diomed, ‭ (Set in the midst, and hearing how you call'd) ‭ Tydides, and myself (as half appall'd ‭ With your remorseful plaints) would passing fain ‭ Have broke our silence, rather than again ‭ Endure, respectless, their so moving cries. ‭ But Ithacus our strongest phantasies ‭ Contain'd within us from the slenderest noise, ‭ And ev'ry man there sat without a voice. ‭ Anticlus only would have answer'd thee, ‭ But his speech Ithacus incessantly ‭ With strong hand held in, till, Minerva's call ‭ Charging thee off, Ulysses sav'd us all." ‭ Telemachus replied: "Much greater is ‭ My grief, for hearing this high praise of his. ‭ For all this doth not his sad death divert, ‭ Nor can, though in him swell'd an iron heart. ‭ Prepare, and lead then, if you please, to rest: ‭ Sleep, that we hear not, will content us best." ‭ Then Argive Helen made her handmaid go, ‭ And put fair bedding in the portico, ‭ Lay purple blankets on, rugs warm and soft, ‭ And cast an arras coverlet aloft. ‭ They torches took, made haste, and made the bed; ‭ When both the guests were to their lodgings led ‭ Within a portico without the house. ‭ Atrides, and his large-train-wearing spouse, ‭ The excellent of women, for the way, ‭ In a retir'd receit, together lay. ‭ The Morn arose; the king rose, and put on ‭ His royal weeds, his sharp sword hung upon ‭ His ample shoulders, forth his chamber went, ‭ And did the person of a God present. ‭ Telemachus accosts him, who begun ‭ Speech of his journey's proposition: ‭ "And what, my young Ulyssean heroë, ‭ Provok'd thee on the broad back of the sea, ‭ To visit Lacedæmon the divine? ‭ Speak truth, some public [good] or only thine?" ‭ "I come," said he, "to hear, if any fame ‭ Breath'd of my father to thy notice came. ‭ My house is sack'd, my fat works of the field ‭ Are all destroy'd; my house doth nothing yield ‭ But enemies, that kill my harmless sheep, ‭ And sinewy oxen, nor will ever keep ‭ Their steels without them. And these men are they ‭ That woo my mother, most inhumanly ‭ Committing injury on injury. ‭ To thy knees therefore I am come, t' attend ‭ Relation of the sad and wretched end ‭ My erring father felt, if witness'd by ‭ Your own eyes, or the certain news that fly ‭ From others' knowledges. For, more than is ‭ The usual heap of human miseries, ‭ His mother bore him to. Vouchsafe me then, ‭ Without all ruth of what I can sustain, ‭ The plain and simple truth of all you know. ‭ Let me beseech so much, if ever vow ‭ Was made, and put in good effect to you, ‭ At Troy, where suff'rance bred you so much smart, ‭ Upon my father good Ulysses' part, ‭ And quit it now to me (himself in youth) ‭ Unfolding only the uncloséd truth." ‭ He, deeply sighing, answer'd him: "O shame, ‭ That such poor vassals should affect the fame ‭ To share the joys of such a worthy's bed! ‭ As when a hind, her calves late farrowéd, ‭ To give suck, enters the bold lion's den, ‭ He roots of hills and herby vallies then ‭ For food (there feeding) hunting; but at length ‭ Returning to his cavern, gives his strength ‭ The lives of both the mother and her brood ‭ In deaths indecent; so the Wooers' blood ‭ Must pay Ulysses' pow'rs as sharp an end. ‭ O would to Jove, Apollo, and thy friend ‭ The wise Minerva, that thy father were ‭ As once he was, when he his spirits did rear ‭ Against Philomelides, in a fight ‭ Perform'd in well-built <DW26>s, where, down-right ‭ He strook the earth with him, and gat a shout ‭ Of all the Grecians! O, if now full out ‭ He were as then, and with the Wooers coped, ‭ Short-liv'd they all were, and their nuptials hoped ‭ Would prove as desp'rate. But, for thy demand ‭ Enforc'd with pray'rs, I'll let thee understand ‭ The truth directly, nor decline a thought, ‭ Much less deceive, or sooth thy search in ought; ‭ But what the old and still-true-spoken God, ‭ That from the sea breathes oracles abroad, ‭ Disclos'd to me, to thee I'll all impart, ‭ Nor hide one word from thy sollicitous heart. ‭ I was in Ægypt, where a mighty time ‭ The Gods detain'd me, though my natural clime ‭ I never so desir'd, because their homes ‭ I did not greet with perfect hecatombs. ‭ For they will put men evermore in mind, ‭ How much their masterly commandments bind. ‭ There is, besides, a certain island, call'd ‭ Pharos, that with the high-wav'd sea is wall'd, ‭ Just against Ægypt, and so much remote, ‭ As in a whole day, with a fore-gale smote, ‭ A hollow ship can sail. And this isle bears ‭ A port most portly, where sea-passengers ‭ Put in still for fresh water, and away ‭ To sea again. Yet here the Gods did stay ‭ My fleet full twenty days; the winds, that are ‭ Masters at sea, no prosp'rous puff would spare ‭ To put us off; and all my victuals here ‭ Had quite corrupted, as my men's minds were, ‭ Had not a certain Goddess giv'n regard, ‭ And pitied me in an estate so hard; ‭ And 'twas Idothea, honour'd Proteus' seed, ‭ That old sea-farer. Her mind I make bleed ‭ With my compassion, when (walk'd all alone, ‭ From all my soldiers, that were ever gone ‭ About the isle on fishing with hooks bent; ‭ Hunger their bellies on her errand sent) ‭ She came close to me, spake, and thus began: ‭ 'Of all men thou art the most foolish man! ‭ Or slack in business, or stay'st here of choice, ‭ And dost in all thy suff'rances rejoice, ‭ That thus long liv'st detain'd here, and no end ‭ Canst give thy tarriance? Thou dost much offend ‭ The minds of all thy fellows.' I replied: ‭ 'Whoever thou art of the Deified, ‭ I must affirm, that no way with my will ‭ I make abode here; but, it seems, some ill ‭ The Gods, inhabiting broad heav'n, sustain ‭ Against my getting off. Inform me then, ‭ For Godheads all things know, what God is he ‭ That stays my passage from the fishy sea?' ‭ 'Stranger,' said she, 'I'll tell thee true: There lives ‭ An old sea-farer in these seas, that gives ‭ A true solution of all secrets here, ‭ Who deathless Proteus is, th' Ægyptian peer, ‭ Who can the deeps of all the seas exquire, ‭ Who Neptune's priest is, and, they say, the sire ‭ That did beget me. Him, if any way ‭ Thou couldst inveigle, he would clear display ‭ Thy course from hence, and how far off doth lie ‭ Thy voyage's whole scope through Neptune's sky. ‭ Informing thee, O God-preserv'd, beside, ‭ If thy desires would so be satisfied, ‭ Whatever good or ill hath got event, ‭ In all the time thy long and hard course spent, ‭ Since thy departure from thy house.' This said; ‭ Again I answer'd: 'Make the sleights display'd ‭ Thy father useth, lest his foresight see, ‭ Or his foreknowledge taking note of me, ‭ He flies the fixt place of his us'd abode. ‭ 'Tis hard for man to countermine with God.' ‭ She straight replied: 'I'll utter truth in all: ‭ When heav'n's supremest height the sun doth skall, ‭ The old Sea-tell-truth leaves the deeps, and hides ‭ Amidst a black storm, when the West Wind chides, ‭ In caves still sleeping. Round about him sleep ‭ (With short feet swimming forth the foamy deep) ‭ The sea-calves, lovely Halosydnes call'd, ‭ From whom a noisome odour is exhal'd, ‭ Got from the whirl-pools, on whose earth they lie. ‭ Here, when the morn illustrates all the sky, ‭ I'll guide, and seat thee in the fittest place ‭ For the performance thou hast now in chace. ‭ In mean time, reach thy fleet, and choose out three ‭ Of best exploit, to go as aids to thee. ‭ But now I'll show thee all the old God's sleights: ‭ He first will number, and take all the sights ‭ Of those his guard, that on the shore arrives. ‭ When having view'd, and told them forth by fives, ‭ He takes place in their midst, and there doth sleep, ‭ Like to a shepherd midst his flock of sheep. ‭ In his first sleep, call up your hardiest cheer, ‭ Vigour and violence, and hold him there, ‭ In spite of all his strivings to be gone. ‭ He then will turn himself to ev'ry one ‭ Of all things that in earth creep and respire, ‭ In water swim, or shine in heav'nly fire. ‭ Yet still hold you him firm, and much the more ‭ Press him from passing. But when, as before, ‭ When sleep first bound his pow'rs, his form ye see, ‭ Then cease your force, and th' old heroë free, ‭ And then demand, which heav'n-born it may be ‭ That so afflicts you, hind'ring your retreat, ‭ And free sea-passage to your native seat.' ‭ This said, she <DW37>'d into the wavy seas, ‭ And I my course did to my ships address, ‭ That on the sands stuck; where arriv'd, we made ‭ Our supper ready. Then th' ambrosian shade ‭ Of night fell on us, and to sleep we fell. ‭ Rosy Aurora rose; we rose as well, ‭ And three of them on whom I most relied, ‭ For firm at ev'ry force, I choos'd, and hied ‭ Straight to the many-river-servéd seas; ‭ And all assistance ask'd the Deities. ‭ Mean time Idothea the sea's broad breast ‭ Embrac'd, and brought for me, and all my rest, ‭ Four of the sea-calves' skins but newly flay'd, ‭ To work a wile which she had fashionéd ‭ Upon her father. Then, within the sand ‭ A covert digging, when these calves should land, ‭ She sat expecting. We came close to her; ‭ She plac'd us orderly, and made us wear ‭ Each one his calf's skin. But we then must pass ‭ A huge exploit. The sea-calves' savour was ‭ So passing sour, they still being bred at seas, ‭ It much afflicted us; for who can please ‭ To lie by one of these same sea-bred whales? ‭ But she preserves us, and to memory calls ‭ A rare commodity; she fetch'd to us ‭ Ambrosia, that an air most odorous ‭ Bears still about it, which she 'nointed round ‭ Our either nosthrils, and in it quite drown'd ‭ The nasty whale-smell. Then the great event ‭ The whole morn's date, with spirits patient, ‭ We lay expecting. When bright noon did flame, ‭ Forth from the sea in shoals the sea-calves came, ‭ And orderly, at last lay down and slept ‭ Along the sands. And then th' old Sea-God crept ‭ From forth the deeps, and found his fat calves there, ‭ Survey'd, and number'd, and came never near ‭ The craft we us'd, but told us five for calves. ‭ His temples then dis-eas'd with sleep he salves; ‭ And in rush'd we, with an abhorréd cry, ‭ Cast all our hands about him manfully; ‭ And then th' old Forger all his forms began: ‭ First was a lion with a mighty mane, ‭ Then next a dragon, a pied panther then, ‭ A vast boar next, and suddenly did strain ‭ All into water. Last he was a tree, ‭ Curl'd all at top, and shot up to the sky. ‭ We, with resolv'd hearts, held him firmly still, ‭ When th' old one (held too strait for all his skill ‭ To extricate) gave words, and question'd me: ‭ "Which of the Gods, O Atreus' son,' said he, ‭ 'Advis'd and taught thy fortitude this sleight, ‭ To take and hold me thus in my despite?' ‭ 'What asks thy wish now?' I replied. 'Thou know'st. ‭ Why dost thou ask? What wiles are these thou show'st? ‭ I have within this isle been held for wind ‭ A wondrous time, and can by no means find ‭ An end to my retention. It hath spent ‭ The very heart in me. Give thou then vent ‭ To doubts thus bound in me, ye Gods know all, ‭ Which of the Godheads doth so foully fall ‭ On my addression home, to stay me here, ‭ Avert me from my way, the fishy clear ‭ Barr'd to my passage?' He replied: 'Of force, ‭ If to thy home thou wishest free recourse, ‭ To Jove, and all the other Deities, ‭ Thou must exhibit solemn sacrifice; ‭ And then the black sea for thee shall be clear, ‭ Till thy lov'd country's settled reach. But where ‭ Ask these rites thy performance? 'Tis a fate ‭ To thee and thy affairs appropriate, ‭ That thou shalt never see thy friends, nor tread ‭ Thy country's earth, nor see inhabited ‭ Thy so magnificent house, till thou make good ‭ Thy voyage back to the Ægyptian flood, ‭ Whose waters fell from Jove, and there hast giv'n ‭ To Jove, and all Gods housed in ample heav'n, ‭ Devoted hecatombs, and then free ways ‭ Shall open to thee, clear'd of all delays.' ‭ This told he; and, methought, he brake my heart, ‭ In such a long and hard course to divert ‭ My hope for home, and charge my back retreat ‭ As far as Ægypt. I made answer yet: ‭ 'Father, thy charge I'll perfect; but before ‭ Resolve me truly, if their natural shore ‭ All those Greeks, and their ships, do safe enjoy, ‭ That Nestor and myself left, when from Troy ‭ We first rais'd sail? Or whether any died ‭ At sea a death unwish'd? Or, satisfied, ‭ When war was past, by friends embrac'd, in peace ‭ Resign'd their spirits? He made answer: 'Cease ‭ To ask so far. It fits thee not to be ‭ So cunning in thine own calamity. ‭ Nor seek to learn what learn'd thou shouldst forget. ‭ Men's knowledges have proper limits set, ‭ And should not prease into the mind of God. ‭ But 'twill not long be, as my thoughts abode, ‭ Before thou buy this curious skill with tears. ‭ Many of those, whose states so tempt thine ears, ‭ Are stoop'd by death, and many left alive, ‭ One chief of which in strong hold doth survive, ‭ Amidst the broad sea. Two, in their retreat, ‭ Are done to death. I list not to repeat ‭ Who fell at Troy, thyself was there in fight, ‭ But in return swift Ajax lost the light, ‭ In his long-oar'd ship. Neptune, yet, awhile ‭ Saft him unwrack'd, to the Gyræan isle, ‭ A mighty-rock removing from his way. ‭ And surely he had 'scap'd the fatal day, ‭ In spite of Pallas, if to that foul deed ‭ He in her fane did, (when he ravishéd ‭ The Trojan prophetess) he had not here ‭ Adjoin'd an impious boast, that he would bear, ‭ Despite the Gods, his ship safe through the waves ‭ Then rais'd against him. These his impious braves ‭ When Neptune heard, in his strong hand he took ‭ His massy trident, and so soundly strook ‭ The rock Gyræan, that in two it cleft; ‭ Of which one fragment on the land he left, ‭ The other fell into the troubled seas; ‭ At which first rush'd Ajax Oïliades, ‭ And split his ship, and then himself afloat ‭ Swum on the rough waves of the world's vast mote, ‭ Till having drunk a salt cup for his sin, ‭ There perish'd he. Thy brother yet did win ‭ The wreath from death, while in the waves they strove, ‭ Afflicted by the rev'rend wife of Jove. ‭ But when the steep mount of the Malian shore ‭ He seem'd to reach, a most tempestuous blore, ‭ Far to the fishy world that sighs so sore, ‭ Straight ravish'd him again as far away, ‭ As to th' extreme bounds where the Agrians stay, ‭ Where first Thyestes dwelt, but then his son ‭ Ægisthus Thyestiades liv'd. This done, ‭ When his return untouch'd appear'd again, ‭ Back turn'd the Gods the wind, and set him then ‭ Hard by his house. Then, full of joy, he left ‭ His ship, and close t' his country earth he cleft, ‭ Kiss'd it, and wept for joy, pour'd tear on tear, ‭ To set so wishedly his footing there. ‭ But see, a sentinel that all the year ‭ Crafty Ægisthus in a watchtow'r set ‭ To spy his landing, for reward as great ‭ As two gold talents, all his pow'rs did call ‭ To strict remembrance of his charge, and all ‭ Discharg'd at first sight, which at first he cast ‭ On Agamemnon, and with all his haste ‭ Inform'd Ægisthus. He an instant train ‭ Laid for his slaughter: Twenty chosen men ‭ Of his plebeians he in ambush laid; ‭ His other men he charg'd to see purvey'd ‭ A feast; and forth, with horse and chariots grac'd, ‭ He rode t' invite him, but in heart embrac'd ‭ Horrible welcomes, and to death did bring, ‭ With treach'rous slaughter, the unwary king, ‭ Receiv'd him at a feast, and, like an ox ‭ Slain at his manger, gave him bits and knocks. ‭ No one left of Atrides' train, nor one ‭ Sav'd to Ægisthus, but himself alone, ‭ All strew'd together there the bloody court.' ‭ This said, my soul he sunk with his report, ‭ Flat on the sands I fell, tears spent their store, ‭ I light abhorr'd, my heart would live no more. ‭ When dry of tears, and tir'd of tumbling there, ‭ Th' old Tell-truth thus my daunted spirits did cheer: ‭ 'No more spend tears nor time, O Atreus' son, ‭ With ceaseless weeping never wish was won, ‭ Use uttermost assay to reach thy home, ‭ And all unwares upon the murderer come, ‭ For torture, taking him thyself alive; ‭ Or let Orestes, that should far out-strive ‭ Thee in fit vengeance, quickly quit the light ‭ Of such a dark soul, and do thou the rite ‭ Of burial to him with a funeral feast.' ‭ With these last words I fortified my breast, ‭ In which again a gen'rous spring began ‭ Of fitting comfort, as I was a man; ‭ But, as a brother, I must ever mourn. ‭ Yet forth I went, and told him the return ‭ Of these I knew; but he had nam'd a third, ‭ Held on the broad sea, still with life inspir'd, ‭ Whom I besought to know, though likewise dead, ‭ And I must mourn alike. He answeréd: ‭ 'He is Laertes' son; whom I beheld ‭ In nymph Calypso's palace, who compell'd ‭ His stay with her, and, since he could not see ‭ His country earth, he mourn'd incessantly. ‭ For he had neither ship instruct with oars, ‭ Nor men to fetch him from those stranger shores. ‭ Where leave we him, and to thy self descend, ‭ Whom not in Argos Fate nor Death shall end, ‭ But the immortal ends of all the earth, ‭ So rul'd by them that order death by birth, ‭ The fields Elysian, Fate to thee will give; ‭ Where Rhadamanthus rules, and where men live ‭ A never-troubled life, where snow, nor show'rs, ‭ Nor irksome Winter spends his fruitless pow'rs, ‭ But from the ocean Zephyr still resumes ‭ A constant breath, that all the fields perfumes. ‭ Which, since thou marriedst Helen, are thy hire, ‭ And Jove himself is by her side thy sire.' ‭ This said; he <DW37>'d the deepsome wat'ry heaps; ‭ I and my tried men took us to our ships, ‭ And worlds of thoughts I varied with my steps. ‭ Arriv'd and shipp'd, the silent solemn night ‭ And sleep bereft us of our visual light. ‭ At morn, masts, sails, rear'd, we sat, left the shores, ‭ And beat the foamy ocean with our oars. ‭ Again then we the Jove-fall'n flood did fetch, ‭ As far as Ægypt; where we did beseech ‭ The Gods with hecatombs; whose angers ceast, ‭ I tomb'd my brother that I might be blest. ‭ All rites perform'd, all haste I made for home, ‭ And all the prosp'rous winds about were come, ‭ I had the passport now of ev'ry God, ‭ And here clos'd all these labours' period. ‭ Here stay then till th' eleventh or twelfth day's light, ‭ And I'll dismiss thee well, gifts exquisite ‭ Preparing for thee, chariot, horses three, ‭ A cup of curious frame to serve for thee ‭ To serve th' immortal Gods with sacrifice, ‭ Mindful of me while all suns light thy skies." ‭ He answer'd: "Stay me not too long time here, ‭ Though I could sit attending all the year. ‭ Nor should my house, nor parents, with desire, ‭ Take my affections from you, so on fire ‭ With love to hear you are my thoughts; but so ‭ My Pylian friends I shall afflict with woe ‭ Who mourn ev'n this stay. Whatsoever be ‭ The gifts your grace is to bestow on me, ‭ Vouchsafe them such as I may bear and save ‭ For your sake ever. Horse, I list not have, ‭ To keep in Ithaca, but leave them here, ‭ To your soil's dainties, where the broad fields bear ‭ Sweet cypers grass, where men-fed lote doth flow, ‭ Where wheat-like spelt, and wheat itself, doth grow, ‭ Where barley, white, and spreading like a tree; ‭ But Ithaca hath neither ground to be, ‭ For any length it comprehends, a race ‭ To try a horse's speed, nor any place ‭ To make him fat in; fitter far to feed ‭ A cliff-bred goat, than raise or please a steed. ‭ Of all isles, Ithaca doth least provide ‭ Or meads to feed a horse, or ways to ride." ‭ He, smiling, said: "Of good blood art thou, son. ‭ What speech, so young! What observatión ‭ Hast thou made of the world! I well am pleas'd ‭ To change my gifts to thee, as being confess'd ‭ Unfit indeed, my store is such I may. ‭ Of all my house-gifts then, that up I lay ‭ For treasure there, I will bestow on thee ‭ The fairest, and of greatest price to me. ‭ I will bestow on thee a rich carv'd cup, ‭ Of silver all, but all the brims wrought up ‭ With finest gold; it was the only thing ‭ That the heroical Sidonian king ‭ Presented to me, when we were to part ‭ At his receipt of me, and 'twas the art ‭ Of that great Artist that of heav'n is free; ‭ And yet ev'n this will I bestow on thee." ‭ This speech thus ended, guests came, and did bring ‭ Muttons, for presents, to the God-like king, ‭ And spirit-prompting wine, that strenuous makes. ‭ Their riband-wreathed wives brought fruit and cakes. ‭ Thus in this house did these their feast apply; ‭ And in Ulysses' house activity ‭ The Wooers practis'd; tossing of the spear, ‭ The stone, and hurling; thus delighted, where ‭ They exercis'd such insolence before, ‭ Ev'n in the court that wealthy pavements wore ‭ Antinous did still their strifes decide, ‭ And he that was in person deified ‭ Eurymachus; both ring-leaders of all, ‭ For in their virtues they were principal. ‭ These by Noëmon, son to Phronius, ‭ Were sided now, who made the question thus: ‭ "Antinous! Does any friend here know, ‭ When this Telemachus returns, or no, ‭ From sandy Pylos? He made bold to take ‭ My ship with him; of which, I now should make ‭ Fit use myself, and sail in her as far ‭ As spacious Elis, where of mine there are ‭ Twelve delicate mares, and under their sides go ‭ Laborious mules, that yet did never know ‭ The yoke, nor labour; some of which should bear ‭ The taming now, if I could fetch them there." ‭ This speech the rest admir'd, nor dream'd that he ‭ Neleïan Pylos ever thought to see, ‭ But was at field about his flocks' survey, ‭ Or thought his herdsmen held him so away. ‭ Eupitheus son, Antinous, then replied: ‭ "When went he, or with what train dignified? ‭ Of his selected Ithacensian youth? ‭ Prest men, or bond men, were they? Tell the truth. ‭ Could he effect this? Let me truly know. ‭ To gain thy vessel did he violence show, ‭ And us'd her 'gainst thy will? or had her free, ‭ When fitting question he had made with thee?" ‭ Noëmon answer'd: "I did freely give ‭ My vessel to him. Who deserves to live ‭ That would do other, when such men as he ‭ Did in distress ask? He should churlish be ‭ That would deny him. Of our youth the best ‭ Amongst the people, to the interest ‭ His charge did challenge in them, giving way, ‭ With all the tribute all their pow'rs could pay. ‭ Their captain, as he took the ship, I knew, ‭ Who Mentor was, or God. A Deity's shew ‭ Mask'd in his likeness. But, to think 'twas he, ‭ I much admire, for I did clearly see, ‭ But yester-morning, God-like Mentor here; ‭ Yet th' other ev'ning he took shipping there, ‭ And went for Pylos." Thus went he for home, ‭ And left the rest with envy overcome; ‭ Who sat, and pastime left. Eupitheus son, ‭ Sad, and with rage his entrails overrun, ‭ His eyes like flames, thus interpos'd his speech: ‭ "Strange thing! An action of how proud a reach ‭ Is here committed by Telemachus! ‭ A boy, a child, and we, a sort of us, ‭ Vow'd 'gainst his voyage, yet admit it thus! ‭ With ship and choice youth of our people too! ‭ But let him on, and all his mischief do, ‭ Jove shall convert upon himself his pow'rs, ‭ Before their ill presum'd he brings on ours. ‭ Provide me then a ship, and twenty men ‭ To give her manage, that, against again ‭ He turns for home, on th' Ithacensian seas, ‭ Or cliffy Samian, I may interprease, ‭ Way-lay, and take him, and make all his craft ‭ Sail with his ruin for his father saft." ‭ This all applauded, and gave charge to do, ‭ Rose, and to greet Ulysses' house did go. ‭ But long time past not, ere Penelope ‭ Had notice of their far-fetch'd treachery. ‭ Medon the herald told her, who had heard ‭ Without the hall how they within conferr'd, ‭ And hasted straight to tell it to the queen, ‭ Who, from the entry having Medon seen, ‭ Prevents him thus: "Now herald, what affair ‭ Intend the famous Wooers, in your repair? ‭ To tell Ulysses' maids that they must cease ‭ From doing our work, and their banquets dress? ‭ I would to heav'n, that, leaving wooing me, ‭ Nor ever troubling other company, ‭ Here might the last feast be, and most extreme, ‭ That ever any shall address for them. ‭ They never meet but to consent in spoil, ‭ And reap the free fruits of another's toil. ‭ O did they never, when they children were, ‭ What to their fathers was Ulysses, hear? ‭ Who never did 'gainst anyone proceed ‭ With unjust usage, or in word or deed? ‭ 'Tis yet with other kings another right, ‭ One to pursue with love, another spite; ‭ He still yet just, nor would, though might, devour, ‭ Nor to the worst did ever taste of pow'r. ‭ But their unrul'd acts show their minds' estate. ‭ Good turns receiv'd once, thanks grow out of date." ‭ Medon, the learn'd in wisdom, answer'd her: ‭ "I wish, O queen, that their ingratitudes were ‭ Their worst ill towards you; but worse by far, ‭ And much more deadly, their endeavours are, ‭ Which Jove will fail them in. Telemachus ‭ Their purpose is, as he returns to us, ‭ To give their sharp steels in a cruel death; ‭ Who now is gone to learn, if fame can breathe ‭ News of his sire, and will the Pylian shore, ‭ And sacred Sparta, in his search explore." ‭ This news dissolv'd to her both knees and heart, ‭ Long silence held her ere one word would part, ‭ Her eyes stood full of tears, her small soft voice ‭ All late use lost; that yet at last had choice ‭ Of wonted words, which briefly thus she us'd: ‭ "Why left my son his mother? Why refus'd ‭ His wit the solid shore, to try the seas, ‭ And put in ships the trust of his distress, ‭ That are at sea to men unbridled horse, ‭ And run, past rule, their far-engagéd course, ‭ Amidst a moisture past all mean unstaid? ‭ No need compell'd this. Did he it, afraid ‭ To live and leave posterity his name?" ‭ "I know not," he replied, "if th' humour came ‭ From current of his own instinct, or flow'd ‭ From others' instigations; but he vow'd ‭ Attempt to Pylos, or to see descried ‭ His sire's return, or know what death he died." ‭ This said, he took him to Ulysses' house ‭ After the Wooers; the Ulyssean spouse, ‭ Run through with woes, let Torture seize her mind, ‭ Nor in her choice of state chairs stood inclin'd ‭ To take her seat, but th' abject threshold chose ‭ Of her fair chamber for her loath'd repose, ‭ And mourn'd most wretch-like. Round about her fell ‭ Her handmaids, join'd in a continuate yell. ‭ From ev'ry corner of the palace, all ‭ Of all degrees tun'd to her comfort's fall ‭ Their own dejections; to whom her complaint ‭ She thus enforc'd: "The Gods, beyond constraint ‭ Of any measure, urge these tears on me; ‭ Nor was there ever dame of my degree ‭ So past degree griev'd. First, a lord so good, ‭ That had such hardy spirits in his blood, ‭ That all the virtues was adorn'd withall, ‭ That all the Greeks did their superior call, ‭ To part with thus, and lose! And now a son, ‭ So worthily belov'd, a course to run ‭ Beyond my knowledge; whom rude tempests have ‭ Made far from home his most inglorious grave! ‭ Unhappy wenches, that no one of all ‭ (Though in the reach of ev'ry one must fall ‭ His taking ship) sustain'd the careful mind, ‭ To call me from my bed, who this design'd ‭ And most vow'd course in him had either stay'd, ‭ How much soever hasted, or dead laid ‭ He should have left me. Many a man I have, ‭ That would have call'd old Dolius my slave, ‭ (That keeps my orchard, whom my father gave ‭ At my departure) to have run, and told ‭ Laertes this; to try if he could hold ‭ From running through the people, and from tears, ‭ In telling them of these vow'd murderers; ‭ That both divine Ulysses' hope, and his, ‭ Resolv'd to end in their conspiracies." ‭ His nurse then, Euryclea, made reply: ‭ "Dear sov'reign, let me with your own hands die, ‭ Or cast me off here, I'll not keep from thee ‭ One word of what I know. He trusted me ‭ With all his purpose, and I gave him all ‭ The bread and wine for which he pleas'd to call. ‭ But then a mighty oath he made me swear, ‭ Not to report it to your royal ear ‭ Before the twelfth day either should appear, ‭ Or you should ask me when you heard him gone. ‭ Impair not then your beauties with your moan, ‭ But wash, and put untear-stain'd garments on, ‭ Ascend your chamber with your ladies here, ‭ And pray the seed of goat-nurs'd Jupiter, ‭ Divine Athenia, to preserve your son, ‭ And she will save him from confusión, ‭ Th' old king, to whom your hopes stand so inclin'd ‭ For his grave counsels, you perhaps may find ‭ Unfit affected, for his age's sake. ‭ But heav'n-kings wax not old, and therefore make ‭ Fit pray'rs to them; for my thoughts never will ‭ Believe the heav'nly Pow'rs conceit so ill ‭ The seed of righteous Arcesiades, ‭ To end it utterly, but still will please ‭ In some place evermore some one of them ‭ To save, and deck him with a diadem, ‭ Give him possession of erected tow'rs, ‭ And far-stretch'd fields, crown'd all of fruits and flowr's." ‭ This eas'd her heart, and dried her humorous eyes, ‭ When having wash'd, and weeds of sacrifice ‭ Pure, and unstain'd with her distrustful tears, ‭ Put on, with all her women-ministers ‭ Up to a chamber of most height she rose, ‭ And cakes of salt and barley did impose ‭ Within a wicker basket; all which broke ‭ In decent order, thus she did invoke: ‭ "Great Virgin of the goat-preservéd God, ‭ If ever the inhabited abode ‭ Of wise Ulysses held the fatted thighs ‭ Of sheep and oxen, made thy sacrifice ‭ By his devotion, hear me, nor forget ‭ His pious services, but safe see set ‭ His dear son on these shores, and banish hence ‭ These Wooers past all mean in insolence." ‭ This said, she shriek'd, and Pallas heard her pray'r. ‭ The Wooers broke with tumult all the air ‭ About the shady house; and one of them, ‭ Whose pride his youth had made the more extreme, ‭ Said: "Now the many-wooer-honour'd queen ‭ Will surely satiate her delayful spleen, ‭ And one of us in instant nuptials take. ‭ Poor dame, she dreams not, what design we make ‭ Upon the life and slaughter of her son." ‭ So said he; but so said was not so done; ‭ Whose arrogant spirit in a vaunt so vain ‭ Antinous chid, and said: "For shame, contain ‭ These braving speeches. Who can tell who hears? ‭ Are we not now in reach of others' ears? ‭ If our intentions please us, let us call ‭ Our spirits up to them, and let speeches fall. ‭ By watchful danger men must silent go. ‭ What we resolve on, let's not say, but do." ‭ This said, he choos'd out twenty men, that bore ‭ Best reckoning with him, and to ship and shore ‭ All hasted, reach'd the ship, launch'd, rais'd the mast, ‭ Put sails in, and with leather loops made fast ‭ The oars; sails hoisted, arms their men did bring, ‭ All giving speed and form to ev'rything. ‭ Then to the high deeps their rigg'd vessel driven, ‭ They supp'd, expecting the approaching even. ‭ Mean space, Penelope her chamber kept ‭ And bed, and neither eat, nor drank, nor slept, ‭ Her strong thoughts wrought so on her blameless son, ‭ Still in contention, if he should be done ‭ To death, or 'scape the impious Wooers' design. ‭ Look how a lion, whom men-troops combine ‭ To hunt, and close him in a crafty ring, ‭ Much varied thought conceives, and fear doth sting ‭ For urgent danger; so far'd she, till sleep ‭ All juncture of her joints and nerves did steep ‭ In his dissolving humour. When, at rest, ‭ Pallas her favours varied, when addrest ‭ An idol, that Iphthima did present ‭ In structure of her ev'ry lineament, [5] ‭ Great-soul'd Icarius' daughter, whom for spouse ‭ Eumelus took, that kept in Pheris' house. ‭ This to divine Ulysses' house she sent, ‭ To try her best mean how she might content ‭ Mournful Penelope, and make relent ‭ The strict addiction in her to deplore. ‭ This idol, like a worm, that less or more [6] ‭ Contracts or strains her, did itself convey, ‭ Beyond the wards or windings of the key, ‭ Into the chamber, and, above her head ‭ Her seat assuming, thus she comforted ‭ Distress'd Penelope: "Doth sleep thus seize ‭ Thy pow'rs, affected with so much dis-ease? ‭ The Gods, that nothing troubles, will not see ‭ Thy tears nor griefs, in any least degree, ‭ Sustain'd with cause, for they will guard thy son ‭ Safe to his wish'd and native mansión. ‭ Since he is no offender of their states, ‭ And they to such are firmer than their fates." ‭ The wise Penelope receiv'd her thus, ‭ Bound with a slumber most delicious, ‭ And in the port of dreams: "O sister, why ‭ Repair you hither, since so far off lie ‭ Your house and household? You were never here ‭ Before this hour, and would you now give cheer ‭ To my so many woes and miseries, ‭ Affecting fitly all the faculties ‭ My soul and mind hold, having lost before ‭ A husband, that of all the virtues bore ‭ The palm amongst the Greeks, and whose renown ‭ So ample was that Fame the sound hath blown ‭ Through Greece and Argos to her very heart? ‭ And now again, a son, that did convert ‭ My whole pow'rs to his love, by ship is gone; ‭ A tender plant, that yet was never grown ‭ To labour's taste, nor the commerce of men; ‭ For whom more than my husband I complain, ‭ And lest he should at any suff'rance touch ‭ (Or in the sea, or by the men so much ‭ Estrang'd to him that must his consorts be) ‭ Fear and chill tremblings shake each joint of me. ‭ Besides, his danger sets on foes profess'd ‭ To way-lay his return, that have address'd ‭ Plots for his death." The scarce-discernéd Dream, ‭ Said: "Be of comfort, nor fears so extreme ‭ Let thus dismay thee; thou hast such a mate ‭ Attending thee, as some at any rate ‭ Would wish to purchase, for her pow'r is great; ‭ Minerva pities thy delights' defeat, ‭ Whose grace hath sent me to foretell thee these." ‭ "If thou," said she, "be of the Goddesses, ‭ And heardst her tell thee these, thou mayst as well ‭ From her tell all things else. Deign then to tell, ‭ If yet the man to all misfortunes born, ‭ My husband, lives, and sees the sun adorn ‭ The darksome earth, or hides his wretched head ‭ In Pluto's house, and lives amongst the dead?" ‭ "I will not," she replied, "my breath exhale ‭ In one continued and perpetual tale, ‭ Lives he or dies he. 'Tis a filthy use, ‭ To be in vain and idle speech profuse." ‭ This said, she, through the key-hole of the door, ‭ Vanish'd again into the open blore. ‭ Icarius' daughter started from her sleep, ‭ And Joy's fresh humour her lov'd breast did steep, ‭ When now so clear, in that first watch of night, ‭ She saw the seen Dream vanish from her sight. ‭ The Wooers' ship the sea's moist waves did ply, ‭ And thought the prince a haughty death should die. ‭ There lies a certain island in the sea, ‭ Twixt rocky Samos and rough Ithaca, ‭ That cliffy is itself, and nothing great, ‭ Yet holds convenient havens that two ways let ‭ Ships in and out, call'd Asteris; and there ‭ The Wooers hop'd to make their massacre. ‭ FINIS LIBRI QUARTI HOM. ODYSS. ‭[1] _Αακεδαἰμονα κητὠσσαν_ which is expounded _Spartam ‭amplam,_ or _πεγἀλην magnam;_ where _κητὠεσσαν_ signifies ‭properly _plurima cete nutrientem._ ‭[2] _Μολπης ἐ ἄρχοντες Cantum auspicantes:_ of which place, the ‭critics affirm that _saltatores motu suo indicant cantori quo genere ‭cantus saltaturi forent._ The rapture of Eteoneus at sight of ‭Telemachus and Pisistratus. ‭[3] Telemachus to Pisistratus, in observation of the house, not so ‭much that he heartily admired it, as to please Menelaus, who he ‭knew heard, though he seemed desirous he should not hear. ‭[4] Helen counterfeited the wives' voices of those kings of Greece ‭that were in the wooden horse, and calls their husbands. ‭[5] _Δἐμας, membrorum structura._ ‭[6] _Παρἁ κληîδος ἱμἀντα. Ιμἀς, affectus curculionis significat ‭quod longior et gracilior evaserit._ ‭ THE FIFTH BOOK OF HOMER'S ODYSSEYS ‭ THE ARGUMENT ‭ A second Court on Jove attends; ‭ Who Hermes to Calypso sends, ‭ Commanding her to clear the ways ‭ Ulysses sought; and she obeys. ‭ When Neptune saw Ulysses free, ‭ And so in safety plough the sea, ‭ Enrag'd, he ruffles up the waves, ‭ And splits his ship. Leucothea saves ‭ His person yet, as being a Dame ‭ Whose Godhead govern'd in the frame ‭ Of those seas' tempers. But the mean, ‭ By which she curbs dread Neptune's spleen, ‭ Is made a jewel, which she takes ‭ From off her head, and that she makes ‭ Ulysses on his bosom wear, ‭ About his neck, she ties it there, ‭ And, when he is with waves beset, ‭ Bids wear it as an amulet, ‭ Commanding him, that not before ‭ He touch'd upon Phæacia's shore, ‭ He should not part with it, but then ‭ Return it to the sea again, ‭ And cast it from him. He performs; ‭ Yet, after this, bides bitter storms, ‭ And in the rocks sees death engrav'd, ‭ But on Phæacia's shore is sav'd. ‭ ANOTHER ARGUMENT ‭ E. ‭ Ulysses builds ‭ A ship; and gains ‭ The glassy fields; ‭ Pays Neptune pains. ‭ Aurora rose from high-born Tithon's bed, ‭ That men and Gods might be illustrated, ‭ And then the Deities sat. Imperial Jove, ‭ That makes the horrid murmur beat above, ‭ Took place past all, whose height for ever springs, ‭ And from whom flowers th' eternal pow'r of things. ‭ Then Pallas, mindful of Ulysses, told ‭ The many cares that in Calypso's hold ‭ He still sustain'd, when he had felt before ‭ So much affliction, and such dangers more. ‭ "O Father," said she, "and ye Ever-blest, ‭ Give never king hereafter interest ‭ In any aid of yours, by serving you, ‭ By being gentle, human, just, but grow ‭ Rude, and for ever scornful of your rights, ‭ All justice ord'ring by their appetites, ‭ Since he, that rul'd as it in right behov'd, ‭ That all his subjects as his children lov'd, ‭ Finds you so thoughtless of him and his birth. ‭ Thus men begin to say, ye rule in earth, ‭ And grudge at what ye let him undergo, ‭ Who yet the least part of his suff'rance know: ‭ Thrall'd in an island, shipwrack'd in his tears, ‭ And, in the fancies that Calypso bears, ‭ Bound from his birthright, all his shipping gone, ‭ And of his soldiers not retaining one. ‭ And now his most-lov'd son's life doth inflame ‭ Their slaught'rous envies; since his father's fame ‭ He puts in pursuit, and is gone as far ‭ As sacred Pylos, and the singular ‭ Dame-breeding Sparta." This, with this reply, ‭ The Cloud-assembler answer'd: "What words fly ‭ Thine own remembrance, daughter? Hast not thou ‭ The counsel giv'n thyself, that told thee how ‭ Ulysses shall with his return address ‭ His Wooers wrong? And, for the safe access ‭ His son shall make to his innative port, ‭ Do thou direct it, in as curious sort ‭ As thy wit serves thee; it obeys thy pow'rs; ‭ And in their ship return the speedless Wooers." ‭ Then turn'd he to his issue Mercury, ‭ And said: "Thou hast made good our ambassy ‭ To th' other Statists, to the Nymph then now, ‭ On whose fair head a tuft of gold doth grow, ‭ Bear our true-spoken counsel, for retreat ‭ Of patient Ulysses; who shall get ‭ No aid from us, nor any mortal man, ‭ But in a patch'd-up skiff (built as he can, [1] ‭ And suff'ring woes enough) the twentieth day ‭ At fruitful Scheria let him breathe his way, ‭ With the Phæacians, that half Deities live, ‭ Who like a God will honour him, and give ‭ His wisdom clothes, and ship, and brass, and gold, ‭ More than for gain of Troy he ever told; ‭ Where, at the whole division of the prey, ‭ If he a saver were, or got away ‭ Without a wound, if he should grudge, 'twas well. ‭ But th' end shall crown all; therefore Fate will deal ‭ So well with him, to let him land, and see ‭ His native earth, friends, house, and family." ‭ Thus charg'd he; nor Argicides denied, ‭ But to his feet his fair wing'd shoes he tied, ‭ Ambrosian, golden, that in his command ‭ Put either sea, or the unmeasur'd land, ‭ With pace as speedy as a puft of wind. ‭ Then up his rod went, with which he declin'd ‭ The eyes of any waker, when he pleas'd, ‭ And any sleeper, when he wish'd, diseas'd. ‭ This took; he stoop'd Pieria, and thence ‭ Glid through the air, and Neptune's confluence ‭ Kiss'd as he flew, and check'd the waves as light ‭ As any sea-mew in her fishing flight, ‭ Her thick wings sousing in the savory seas. ‭ Like her, he pass'd a world of wilderness; ‭ But when the far-off isle he touch'd, he went ‭ Up from the blue sea to the continent, ‭ And reach'd the ample cavern of the Queen, ‭ Whom he within found, without seldom seen. ‭ A sun-like fire upon the hearth did flame, ‭ The matter precious, and divine the frame, ‭ Of cedar cleft and incense was the pile, ‭ That breath'd an odour round about the isle. ‭ Herself was seated in an inner room, ‭ Whom sweetly sing he heard, and at her loom, ‭ About a curious web, whose yarn she threw ‭ In with a golden shittle. A grove grew ‭ In endless spring about her cavern round, ‭ With odorous cypress, pines, and poplars, crown'd, ‭ Where hawks, sea-owls, and long-tongued bittours bred, ‭ And other birds their shady pinions spread; ‭ All fowls maritimal; none roosted there, ‭ But those whose labours in the waters were. ‭ A vine did all the hollow cave embrace, ‭ Still green, yet still ripe bunches gave it grace. ‭ Four fountains, one against another, pour'd ‭ Their silver streams; and meadows all enflower'd ‭ With sweet balm-gentle, and blue-violets hid, ‭ That deck'd the soft breasts of each fragrant mead. ‭ Should anyone, though he immortal were, ‭ Arrive and see the sacred objects there, ‭ He would admire them, and be over-joy'd; ‭ And so stood Hermes' ravish'd pow'rs employ'd, ‭ But having all admir'd, he enter'd on ‭ The ample cave, nor could be seen unknown ‭ Of great Calypso (for all Deities are ‭ Prompt in each other's knowledge, though so far ‭ Sever'd in dwellings) but he could not see ‭ Ulysses there within; without was he, ‭ Set sad ashore, where 'twas his use to view ‭ Th' unquiet sea, sigh'd, wept, and empty drew ‭ His heart of comfort. Plac'd here in her throne, ‭ That beams cast up to admiratión, ‭ Divine Calypso question'd Hermes thus: ‭ "For what cause, dear, and much-esteem'd by us, ‭ Thou golden-rod-adorned Mercury, ‭ Arriv'st thou here? Thou hast not us'd t' apply ‭ Thy passage this way. Say, whatever be ‭ Thy heart's desire, my mind commands it thee, ‭ If in my means it lie, or pow'r of fact. ‭ But first, what hospitable rites exact, ‭ Come yet more near, and take." This said, she set ‭ A table forth, and furnish'd it with meat, ‭ Such as the Gods taste; and serv'd in with it ‭ Vermilion nectar. When with banquet fit ‭ He had confirm'd his spirits, he thus exprest ‭ His cause of coming: "Thou hast made request, ‭ Goddess of Goddesses, to understand ‭ My cause of touch here; which thou shalt command, ‭ And know with truth: Jove caus'd my course to thee ‭ Against my will, for who would willingly ‭ Lackey along so vast a lake of brine, ‭ Near to no city that the Pow'rs divine ‭ Receives with solemn rites and hecatombs? ‭ But Jove's will ever all law overcomes, ‭ No other God can cross or make it void; ‭ And he affirms, that one the most annoy'd ‭ With woes and toils of all those men that fought ‭ For Priam's city, and to end hath brought ‭ Nine years in the contention, is with thee. ‭ For in the tenth year, when roy victory ‭ Was won to give the Greeks the spoil of Troy, ‭ Return they did profess, but not enjoy, ‭ Since Pallas they incens'd, and she the waves ‭ By all the winds' pow'r, that blew ope their graves. ‭ And there they rested. Only this poor one ‭ This coast both winds and waves have cast upon; ‭ Whom now forthwith he wills thee to dismiss, ‭ Affirming that th' unalter'd Destinies ‭ Not only have decreed he shall not die ‭ Apart his friends, but of necessity ‭ Enjoy their sights before those fatal hours, ‭ His country earth reach, and erected tow'rs." ‭ This struck a love-check'd horror through her pow'rs, ‭ When, naming him, she this reply did give: ‭ "Insatiate are ye Gods, past all that live, ‭ In all things you affect; which still converts ‭ Your pow'rs to envies. It afflicts your hearts, ‭ That any Goddess should, as you obtain ‭ The use of earthly dames, enjoy the men, ‭ And most in open marriage. So ye far'd, ‭ When the delicious-finger'd Morning shar'd ‭ Orion's bed; you easy-living States ‭ Could never satisfy your emulous hates, ‭ Till in Ortygia the precise-liv'd Dame, ‭ Gold-thron'd Diana, on him rudely came, ‭ And with her swift shafts slew him. And such pains, ‭ When rich-hair'd Ceres pleas'd to give the reins ‭ To her affections, and the grace did yield ‭ Of love and bed, amidst a three-cropp'd field, ‭ To her Iasion, he paid angry Jove, ‭ Who lost no long time notice of their love, ‭ But with a glowing lightning was his death. ‭ And now your envies labour underneath ‭ A mortal's choice of mine; whose life I took ‭ To lib'ral safety, when his ship Jove strook, ‭ With red-hot flashes, piece-meal in the seas, ‭ And all his friends and soldiers succourless ‭ Perish'd but he. Him, cast upon this coast ‭ With blasts and billows, I, in life giv'n lost, ‭ Preserv'd alone, lov'd, nourish'd, and did vow ‭ To make him deathless, and yet never grow ‭ Crooked, or worn with age, his whole life long. ‭ But since no reason may be made so strong ‭ To strive with Jove's will, or to make it vain, ‭ No not if all the other Gods should strain ‭ Their pow'rs against it, let his will be law, ‭ So he afford him fit means to withdraw, ‭ As he commands him, to the raging main. ‭ But means from me he never shall obtain, ‭ For my means yield nor men, nor ship, nor oars, ‭ To set him off from my so envied shores. ‭ But if my counsel and good will can aid ‭ His safe pass home, my best shall be assay'd." ‭ "Vouchsafe it so," said heav'n's ambassador, ‭ "And deign it quickly. By all means abhor ‭ T' incense Jove's wrath against thee, that with grace ‭ He may hereafter all thy wish embrace." ‭ Thus took the Argus-killing God his wings. ‭ And since the rev'rend Nymph these awful things ‭ Receiv'd from Jove, she to Ulysses went; ‭ Whom she ashore found, drown'd in discontent, ‭ His eyes kept never dry he did so mourn, ‭ And waste his dear age for his wish'd return; ‭ Which still without the cave he us'd to do, ‭ Because he could not please the Goddess so, ‭ At night yet, forc'd, together took their rest, ‭ The willing Goddess and th' unwilling Guest; ‭ But he all day in rocks, and on the shore, ‭ The vex'd sea view'd, and did his fate deplore. ‭ Him, now, the Goddess coming near bespake: ‭ "Unhappy man, no more discomfort take ‭ For my constraint of thee, nor waste thine age, ‭ I now will passing freely disengage ‭ Thy irksome stay here. Come then, fell thee wood, ‭ And build a ship, to save thee from the flood. ‭ I'll furnish thee with fresh wave, bread, and wine ‭ Ruddy and sweet, that will the piner pine, [2] ‭ Put garments on thee, give the winds foreright, ‭ That ev'ry way thy home-bent appetite ‭ May safe attain to it; if so it please ‭ At all parts all the heav'n-hous'd Deities, ‭ That more in pow'r are, more in skill, than I, ‭ And more can judge what fits humanity." ‭ He stood amaz'd at this strange change in her, ‭ And said: "O Goddess! Thy intents prefer ‭ Some other project than my parting hence, ‭ Commanding things of too high consequence ‭ For my performance, that myself should build ‭ A ship of pow'r, my home-assays to shield ‭ Against the great sea of such dread to pass; ‭ Which not the best-built ship that ever was ‭ Will pass exulting, when such winds, as Jove ‭ Can thunder up, their trims and tacklings prove. ‭ But could I build one, I would ne'er aboard, ‭ Thy will oppos'd, nor, won, without thy word, ‭ Giv'n in the great oath of the Gods to me, ‭ Not to beguile me in the least degree." ‭ The Goddess smil'd, held hard his hand, and said: ‭ "O y' are a shrewd one, and so habited ‭ In taking heed thou know'st not what it is ‭ To be unwary, nor use words amiss. ‭ How hast thou charm'd me, were I ne'er so sly! ‭ Let earth know then, and heav'n, so broad, so high, ‭ And th' under-sunk waves of th' infernal stream, ‭ (Which is an oath, as terribly supreme, ‭ As any God swears) that I had no thought ‭ But stood with what I spake, nor would have wrought, ‭ Nor counsell'd, any act against thy good; ‭ But ever diligently weigh'd, and stood ‭ On those points in persuading thee, that I ‭ Would use myself in such extremity. ‭ For my mind simple is, and innocent, ‭ Not giv'n by cruel sleights to circumvent, ‭ Nor bear I in my breast a heart of steel, ‭ But with the suff'rer willing suff'rance feel." ‭ This said, the Grace of Goddesses led home, ‭ He trac'd her steps; and, to the cavern come, ‭ In that rich throne, whence Mercury arose, ‭ He sat. The Nymph herself did then appose, ‭ For food and bev'rage, to him all best meat ‭ And drink, that mortals use to taste and eat. ‭ Then sat she opposite, and for her feast ‭ Was nectar and ambrosia addrest ‭ By handmaids to her. Both, what was prepar'd, ‭ Did freely fall to. Having fitly far'd, ‭ The Nymph Calypso this discourse began: ‭ "Jove-bred Ulysses! Many-witted man! ‭ Still is thy home so wish'd? So soon, away? ‭ Be still of cheer, for all the worst I say. ‭ But, if thy soul knew what a sum of woes, ‭ For thee to cast up, thy stern Fates impose, ‭ Ere to thy country earth thy hopes attain, ‭ Undoubtedly thy choice would here remain, ‭ Keep house with me, and be a liver ever. ‭ Which, methinks, should thy house and thee dissever, ‭ Though for thy wife there thou art set on fire, ‭ And all thy days are spent in her desire; ‭ And though it be no boast in me to say ‭ In form and mind I match her ev'ry way. ‭ Nor can it fit a mortal dame's compare, ‭ T' affect those terms with us that deathless are." ‭ The great-in-counsels made her this reply: ‭ "Renown'd, and to be rev'renc'd, Deity! ‭ Let it not move thee, that so much I vow ‭ My comforts to my wife; though well I know ‭ All cause myself why wise Penelope ‭ In wit is far inferior to thee, ‭ In feature, stature, all the parts of show, ‭ She being a mortal, an immortal thou, ‭ Old ever growing, and yet never old. ‭ Yet her desire shall all my days see told, ‭ Adding the sight of my returning day, ‭ And natural home. If any God shall lay ‭ His hand upon me as I pass the seas, ‭ I'll bear the worst of what his hand shall please, ‭ As having giv'n me such a mind as shall ‭ The more still rise the more his hand lets fall. ‭ In wars and waves my suff'rings were not small. ‭ I now have suffer'd much, as much before, ‭ Hereafter let as much result, and more." ‭ This said, the sun set, and earth shadows gave; ‭ When these two (in an in-room of the cave, ‭ Left to themselves) left love no rites undone. ‭ The early Morn up, up he rose, put on ‭ His in and out weed. She herself enchaces ‭ Amidst a white robe, full of all the Graces, ‭ Ample, and pleated thick like fishy scales; ‭ A golden girdle then her waist impales; ‭ Her head a veil decks; and abroad they come. ‭ And now began Ulysses to go home. ‭ A great axe first she gave, that two ways cut, ‭ In which a fair well-polish'd helm was put, ‭ That from an olive bough receiv'd his frame. ‭ A plainer then. Then led she, till they came ‭ To lofty woods that did the isle confine. ‭ The fir-tree, poplar, and heav'n-scaling pine, ‭ Had there their offspring. Of which, those that were ‭ Of driest matter, and grew longest there, ‭ He choos'd for lighter sail. This place thus shown, ‭ The Nymph turn'd home. He fell to felling down, ‭ And twenty trees he stoop'd in little space, ‭ Plain'd, used his plumb, did all with artful grace. ‭ In mean time did Calypso wimbles bring. ‭ He bor'd, clos'd, nail'd, and order'd ev'ry thing, ‭ And look how much a ship-wright will allow ‭ A ship of burden (one that best doth know ‭ What fits his art) so large a keel he cast, ‭ Wrought up her decks, and hatches, side-boards, mast, ‭ With willow watlings arm'd her to resist ‭ The billows' outrage, added all she miss'd, ‭ Sail-yards, and stern for guide. The Nymph then brought ‭ Linen for sails, which with dispatch he wrought, ‭ Gables, and halsters, tacklings. All the frame ‭ In four days' space to full perfection came. [3] ‭ The fifth day, they dismiss'd him from the shore, ‭ Weeds neat, and odorous, gave him, victuals store, ‭ Wine, strong waters, and a prosp'rous wind, ‭ To which, Ulysses, fit-to-be-divin'd, ‭ His sails expos'd, and hoiséd. Off he gat; ‭ And cheerful was he. At the stern he sat, ‭ And steer'd right artfully. Nor sleep could seize ‭ His eye-lids. He beheld the Pleiades; ‭ The Bear, surnam'd the Wain, that round doth move ‭ About Orion, and keeps still above ‭ The billowy ocean; the slow-setting star ‭ Bootes call'd, by some the Waggoner. ‭ Calypso warn'd him he his course should steer ‭ Still to his left hand. Seventeen days did clear ‭ The cloudy night's command in his moist way, ‭ And by the eighteenth light he might display ‭ The shady hills of the Phæacian shore, ‭ For which, as to his next abode, he bore. ‭ The country did a pretty figure yield, ‭ And look'd from off the dark seas like a shield. ‭ Imperious Neptune, making his retreat ‭ From th' Æthiopian earth, and taking seat ‭ Upon the mountains of the Solymi, ‭ From thence, far off discov'ring, did descry ‭ Ulysses his fields ploughing. All on fire ‭ The sight straight set his heart, and made desire ‭ Of wreak run over, it did boil so high. ‭ When, his head nodding; "O impiety," ‭ He cried out, "now the Gods' inconstancy ‭ Is most apparent, alt'ring their designs ‭ Since I the Æthiops saw, and here confines ‭ To this Ulysses' fate his misery. ‭ The great mark, on which all his hopes rely, ‭ Lies in Phæacia. But I hope he shall ‭ Feel woe at height, ere that dead calm befall." ‭ This said; he, begging, gather'd clouds from land, [4] ‭ Frighted the seas up, snatch'd into his hand ‭ His horrid trident, and aloft did toss, ‭ Of all the winds, all storms he could engross, ‭ All earth took into sea with clouds, grim Night ‭ Fell tumbling headlong from the cope of light, ‭ The East and South winds justled in the air, ‭ The violent Zephyr, and North making-fair, ‭ Roll'd up the waves before them. And then bent ‭ Ulysses' knees, then all his spirit was spent. ‭ In which despair, he thus spake: "Woe is me! ‭ What was I born to, man of misery! ‭ Fear tells me now, that, all the Goddess said, ‭ Truth's self will author, that Fate would be paid ‭ Grief's whole sum due from me, at sea, before ‭ I reach'd the dear touch of my country's shore. ‭ With what clouds Jove heav'n's heighten'd forehead binds! ‭ How tyrannize the wraths of all the winds! ‭ How all the tops he bottoms with the deeps, ‭ And in the bottoms all the tops he steeps! ‭ Thus dreadful is the presence of our death. ‭ Thrice four times blest were they that sunk beneath ‭ Their fates at Troy, and did to nought contend ‭ But to renown Atrides with their end! ‭ I would to God, my hour of death and fate ‭ That day had held the' pow'r to terminate, ‭ When show'rs of darts my life bore undepress'd ‭ About divine Æacides deceas'd! ‭ Then had I been allotted to have died, ‭ By all the Greeks with fun'rals glorified, ‭ (Whence death, encouraging good life, had grown) ‭ Where now I die, by no man mourn'd nor known." ‭ This spoke, a huge wave took him by the head, ‭ And hurl'd him o'er board; ship and all it laid ‭ Inverted quite amidst the waves, but he ‭ Far off from her sprawl'd, strow'd about the sea, ‭ His stern still holding broken off, his mast ‭ Burst in the midst, so horrible a blast ‭ Of mix'd winds struck it. Sails and sail-yards fell ‭ Amongst the billows; and himself did dwell ‭ A long time under water, nor could get ‭ In haste his head out, wave with wave so met ‭ In his depression; and his garments too, ‭ Giv'n by Calypso, gave him much to do, ‭ Hind'ring his swimming; yet he left not so ‭ His drenchéd vessel, for the overthrow ‭ Of her nor him, but gat at length again, ‭ Wrastling with Neptune, hold of her; and then ‭ Sat in her bulk, insulting over death, ‭ Which, with the salt stream prest to stop his breath, ‭ He 'scap'd, and gave the sea again to give ‭ To other men. His ship so striv'd to live, ‭ Floating at random, cuff'd from wave to wave. ‭ As you have seen the North wind when he drave ‭ In autumn heaps of thorn-fed grasshoppers ‭ Hither and thither, one heap this way bears, ‭ Another that, and makes them often meet ‭ in his confus'd gales; so Ulysses' fleet ‭ The winds hurl'd up and down; now Boreas ‭ Toss'd it to Notus, Notus gave it pass ‭ To Eurus, Eurus Zephyr made pursue ‭ The horrid tennis. This sport call'd the view ‭ Of Cadmus' daughter, with the narrow heel, ‭ Ino Leucothea, that first did feel ‭ A mortal dame's desires, and had a tongue, ‭ But now had th' honour to be nam'd among ‭ The marine Godheads. She with pity saw ‭ Ulysses justled thus from flaw to flaw, ‭ And, like a cormorant in form and flight, ‭ Rose from a whirl-pool, on the ship did light, ‭ And thus bespake him: "Why is Neptune thus ‭ In thy pursuit extremely furious, ‭ Oppressing thee with such a world of ill, ‭ Ev'n to thy death? He must not serve his will, ‭ Though 'tis his study. Let me then advise ‭ As my thoughts serve; thou shalt not be unwise ‭ To leave thy weeds and ship to the commands ‭ Of these rude winds, and work out with thy hands ‭ Pass to Phæacia, where thy austere Fate ‭ Is to pursue thee with no more such hate. ‭ Take here this tablet, with this riband strung, ‭ And see it still about thy bosom hung; ‭ By whose eternal virtue never fear ‭ To suffer thus again, nor perish here. ‭ But when thou touchest with thy hand the shore, ‭ Then take it from thy neck, nor wear it more, ‭ But cast it far off from the continent, ‭ And then thy person far ashore present. ‭ Thus gave she him the tablet; and again, ‭ Turn'd to a cormorant, <DW37>'d, past sight, the main. ‭ Patient Ulysses sigh'd at this, and stuck ‭ In the conceit of such fair-spoken luck, ‭ And said: "Alas! I must suspect ev'n this, ‭ Lest any other of the Deities ‭ Add sleight to Neptune's force, to counsel me ‭ To leave my vessel, and so far off see ‭ The shore I aim at. Not with thoughts too clear ‭ Will I obey her, but to me appear ‭ These counsels best: As long as I perceive ‭ My ship not quite dissolv'd, I will not leave ‭ The help she may afford me, but abide, ‭ And suffer all woes till the worst be tried. ‭ When she is split, I'll swim. No miracle can, ‭ Past near and clear means, move a knowing man." ‭ While this discourse employ'd him, Neptune rais'd ‭ A huge, a high, and horrid sea, that seiz'd ‭ Him and his ship, and toss'd them through the lake. ‭ As when the violent winds together take ‭ Heaps of dry chaff, and hurl them ev'ry way; ‭ So his long wood-stack Neptune strook astray ‭ Then did Ulysses mount on rib, perforce, ‭ Like to a rider of a running horse, ‭ To stay himself a time, while he might shift ‭ His drenched weeds, that were Calypso's gift. ‭ When putting straight Leucothea's amulet ‭ About his neck, he all his forces set ‭ To swim, and cast him prostrate to the seas. ‭ When pow'rful Neptune saw the ruthless prease ‭ Of perils siege him thus, he mov'd his head, ‭ And this betwixt him and his heart he said: ‭ "So, now feel ills enow, and struggle so, ‭ Till to your Jove-lov'd islanders you row. ‭ But my mind says, you will not so avoid ‭ This last task too, but be with suff'rance cloy'd." ‭ This said, his rich-man'd horse he mov'd, and reach'd ‭ His house at Ægas. But Minerva fetch'd ‭ The winds from sea, and all their ways but one ‭ Barr'd to their passage; the bleak North alone ‭ She set to blow, the rest she charg'd to keep ‭ Their rages in, and bind themselves in sleep. ‭ But Boreas still flew high to break the seas, ‭ Till Jove-bred Ithacus the more with ease ‭ The navigation-skill'd Phæacian states ‭ Might make his refuge, Death and angry Fates ‭ At length escaping. Two nights, yet, and days ‭ He spent in wrastling with the sable seas; ‭ In which space, often did his heart propose ‭ Death to his eyes. But when Aurora rose, ‭ And threw the third light from her orient hair, ‭ The winds grew calm, and clear was all the air, ‭ Not one breath stirring. Then he might descry, ‭ Rais'd by the high seas, clear, and land was nigh. ‭ And then, look how to good sons that esteem ‭ Their father's life dear, (after pains extreme, ‭ Felt in some sickness, that hath held him long ‭ Down to his bed, and with affections strong ‭ Wasted his body, made his life his load, ‭ As being inflicted by some angry God) ‭ When on their pray'rs they see descend at length ‭ Health from the heav'ns, clad all in spirit and strength, ‭ The sight is precious; so, since here should end ‭ Ulysses' toils, which therein should extend ‭ Health to his country, held to him his sire ‭ And on which long for him disease did tire, ‭ And then, besides, for his own sake to see ‭ The shores, the woods so near, such joy had he, ‭ As those good sons for their recover'd sire. ‭ Then labour'd feet and all parts to aspire ‭ To that wish'd continent; which when as near ‭ He came, as Clamour might inform an ear, ‭ He heard a sound beat from the sea-bred rocks, ‭ Against which gave a huge sea horrid shocks, ‭ That belch'd upon the firm land weeds and foam, ‭ With which were all things hid there, where no room ‭ Of fit capacity was for any port, ‭ Nor from the sea for any man's resort, ‭ The shores, the rocks, the cliff's, so prominent were. ‭ "O," said Ulysses then, "now Jupiter ‭ Hath giv'n me sight of an unhop'd for shore, ‭ Though I have wrought these seas so long, so sore. ‭ Of rest yet no place shows the slend'rest prints, ‭ The rugged shore so bristled is with flints, ‭ Against which ev'ry way the waves so flock, ‭ And all the shore shows as one eminent rock, ‭ So near which 'tis so deep, that not a sand ‭ Is there for any tired foot to stand, ‭ Nor fly his death-fast-following miseries, ‭ Lest, if he land, upon him foreright flies ‭ A churlish wave, to crush him 'gainst a cliff, ‭ Worse than vain rend'ring all his landing strife. ‭ And should I swim to seek a hav'n elsewhere, ‭ Or land less way-beat, I may justly fear ‭ I shall be taken with a gale again, ‭ And cast a huge way off into the main; ‭ And there the great Earth-shaker (having seen ‭ My so near landing, and again his spleen ‭ Forcing me to him) will some whale send out, ‭ (Of which a horrid number here about ‭ His Amphitrite breeds) to swallow me. ‭ I well have prov'd, with what malignity ‭ He treads my steps." While this discourse he held, ‭ A curs'd surge 'gainst a cutting rock impell'd ‭ His naked body, which it gash'd and tore, ‭ And had his bones broke, if but one sea more ‭ Had cast him on it. But She prompted him, ‭ That never fail'd, and bade him no more swim ‭ Still off and on, but boldly force the shore, ‭ And hug the rock that him so rudely tore; ‭ Which he with both hands sigh'd and clasp'd, till past ‭ The billow's rage was; when 'scap'd, back so fast ‭ The rock repuls'd it, that it reft his hold, ‭ Sucking him from it, and far back he roll'd ‭ And as the polypus that (forc'd from home ‭ Amidst the soft sea, and near rough land come ‭ For shelter 'gainst the storms that beat on her ‭ At open sea, as she abroad doth err) ‭ A deal of gravel, and sharp little stones, ‭ Needfully gathers in her hollow bones; ‭ So he forc'd hither by the sharper ill, ‭ Shunning the smoother, where he best hop'd, still ‭ The worst succeeded; for the cruel friend, ‭ To which he cling'd for succour, off did rend ‭ From his broad hands the soaken flesh so sore ‭ That off he fell, and could sustain no more. ‭ Quite under water fell he; and, past fate, ‭ Hapless Ulysses there had lost the state ‭ He held in life, if, still the grey-eyed Maid ‭ His wisdom prompting, he had not assay'd ‭ Another course, and ceas'd t' attempt that shore, ‭ Swimming, and casting round his eye t' explore ‭ Some other shelter. Then the mouth he found ‭ Of fair Callicoe's flood, whose shores were crown'd ‭ With most apt succours: rocks so smooth they seem'd ‭ Polish'd of purpose; land that quite redeem'd ‭ With breathless coverts th' others' blasted shores. ‭ The flood he knew, and thus in heart implores: ‭ "King of this river, hear! Whatever name ‭ Makes thee invok'd, to thee I humbly frame ‭ My flight from Neptune's furies. Rev'rend is ‭ To all the ever-living Deities ‭ What erring man soever seeks their aid. ‭ To thy both flood and knees a man dismay'd ‭ With varied suff'rance sues. Yield then some rest ‭ To him that is thy suppliant profest." ‭ This, though but spoke in thought, the Godhead heard, ‭ Her current straight stay'd, and her thick waves clear'd ‭ Before him, smooth'd her waters, and, just where ‭ He pray'd half-drown'd, entirely sav'd him there. ‭ Then forth he came, his both knees falt'ring, both ‭ His strong hands hanging down, and all with froth ‭ His cheeks and nosthrils flowing, voice and breath ‭ Spent to all use, and down he sunk to death. ‭ The sea had soak'd his heart through; all his veins ‭ His toils had rack'd t' a labouring woman's pains. [5] ‭ Dead weary was he. But when breath did find ‭ A pass reciprocal, and in his mind ‭ His spirit was recollected, up he rose, ‭ And from his neck did th' amulet unloose, ‭ That Ino gave him; which he hurl'd from him ‭ To sea. It sounding fell, and back did swim ‭ With th' ebbing waters, till it straight arriv'd ‭ Where Ino's fair hand it again receiv'd. ‭ Then kiss'd he th' humble earth; and on he goes, ‭ Till bulrushes show'd place for his repose, ‭ Where laid, he sigh'd, and thus said to his soul: ‭ "O me, what strange perplexities control ‭ The whole skill of thy pow'rs in this event! ‭ What feel I? If till care-nurse night be spent ‭ I watch amidst the flood, the sea's chill breath, ‭ And vegetant dews, I fear will be my death, ‭ So low brought with my labours. Towards day ‭ A passing sharp air ever breathes at sea. ‭ If I the pitch of this next mountain scale, ‭ And shady wood, and in some thicket fall ‭ Into the hands of Sleep, though there the cold ‭ May well be check'd, and healthful slumbers hold ‭ Her sweet hand on my pow'rs, all care allay'd, ‭ Yet there will beasts devour me. Best appaid ‭ Doth that course make me yet; for there, some strife, ‭ Strength, and my spirit, may make me make for life; ‭ Which, though impair'd, may yet be fresh applied, ‭ Where peril possible of escape is tried. ‭ But he that fights with heav'n, or with the sea, ‭ To indiscretion adds impiety." ‭ Thus to the woods he hasted; which he found ‭ Not far from sea, but on far-seeing ground, ‭ Where two twin underwoods he enter'd on, ‭ With olive-trees and oil-trees overgrown; ‭ Through which the moist force of the loud-voic'd wind ‭ Did never beat, nor ever Phœbus shin'd, ‭ Nor show'r beat through, they grew so one in one, ‭ And had, by turns, their pow'r t' exclude the sun. ‭ Here enter'd our Ulysses; and a bed ‭ Of leaves huge, and of huge abundance, spread ‭ With all his speed. Large he made it, for there ‭ For two or three men ample cov'rings were, ‭ Such as might shield them from the winter's worst, ‭ Though steel it breathed, and blew as it would burst. [6] ‭ Patient Ulysses joy'd, that ever day ‭ Show'd such a shelter. In the midst he lay, ‭ Store of leaves heaping high on ev'ry side. ‭ And as in some out-field a man doth hide ‭ A kindled brand, to keep the seed of fire, ‭ No neighbour dwelling near, and his desire ‭ Serv'd with self store, he else would ask of none, ‭ But of his fore-spent sparks rakes th' ashes on; ‭ So this out-place Ulysses thus receives, ‭ And thus nak'd virtue's seed lies hid in leaves. ‭ Yet Pallas made him sleep as soon as men ‭ Whom delicacies all their flatt'ries deign, ‭ And all that all his labours could comprise ‭ Quickly concluded in his closed eyes. ‭ FINIS LIBRI QUINTI HOM. ODYSS. ‭[1] _᾽Επἱ σχεδἰης πογυδἐσμον, in rate multis vinculis ligatus._ ‭[2] The piner--Hunger. ‭[3] This four day days' work (you will say) is too much for one man: ‭and Pliny affirms, that Hiero (a king of Sicily) in five-and forty ‭days built two hundred and twenty ships, rigged them, and put to ‭sea with them. ‭[4] _Συναγεἰρω--Mendicando colligo._ ‭[5] _Ὤιδεε_ of _ὠδἰνω ἁ partu doleo._ ‭[6] A metaphorical hyperbole, expressing the winter's extremity of ‭sharpness. ‭ THE SIXTH BOOK OF HOMER'S ODYSSEYS ‭ THE ARGUMENT ‭ Minerva in a vision stands ‭ Before Nausicaa: and commands ‭ She to the flood her weeds should bear; ‭ For now her nuptial day was near. ‭ Nausicaa her charge obeys, ‭ And then with other virgins plays. ‭ Their sports make wak'd Ulysses rise; ‭ Walk to them, and beseech supplies ‭ Of food and clothes. His naked sight ‭ Puts th' other maids, afraid, to flight; ‭ Nausicaa only boldly stays, ‭ And gladly his desire obeys. ‭ He, furnish'd with her favour's shown, ‭ Attends her and the rest to town. ‭ _Ζη̑τα._ ‭ Here olive leaves ‭ T' hide shame began, ‭ The maid receives ‭ The naked man. ‭ The much-sustaining, patient, heav'nly man, ‭ Whom Toil and Sleep had worn so weak and wan, [1] ‭ Thus won his rest. In mean space Pallas went ‭ To the Phæacian city, and descent ‭ That first did broad Hyperia's lands divide, ‭ Near the vast Cyclops, men of monstrous pride, ‭ That prey'd on those Hyperians, since they were ‭ Of greater pow'r; and therefore longer there ‭ Divine Nausithous dwelt not, but arose, ‭ And did for Scheria all his pow'rs dispose; ‭ Far from ingenious art-inventing men ‭ But there did he erect a city then, ‭ First drew a wall round, then he houses builds, ‭ And then a temple to the Gods, the fields ‭ Lastly dividing. But he, stoop'd by Fate, ‭ <DW37>'d to th' infernals; and Alcinous sate ‭ In his command, a man the Gods did teach ‭ Commanding counsels. His house held the reach ‭ Of grey Minerva's project, to provide ‭ That great-soul'd Ithacus might be supplied ‭ With all things fitting his return. She went ‭ Up to the chamber, where the fair descent ‭ Of great Alcinous slept; a maid, whose parts ‭ In wit and beauty wore divine deserts. ‭ Well-deck'd her chamber was; of which the door ‭ Did seem to lighten, such a gloss it bore ‭ Betwixt the posts, and now flew ope to find ‭ The Goddess entry. Like a puft of wind ‭ She reach'd the virgin bed; neat which there lay ‭ Two maids, to whom the Graces did convey ‭ Figure and manners. But above the head ‭ Of bright Nausicaa did Pallas tread ‭ The subtle air, and put the person on ‭ Of Dymas' daughter, from comparison ‭ Exempt in business naval. Like his seed ‭ Minerva look'd now; whom one year did breed [2] ‭ With bright Nausicaa, and who had gain'd ‭ Grace in her love, yet on her thus complain'd: ‭ "Nausicaa! Why bred thy mother one ‭ So negligent in rites so stood upon ‭ By other virgins? Thy fair garments lie ‭ Neglected by thee, yet thy nuptials nigh; ‭ When rich in all attire both thou shouldst be, ‭ And garments give to others honouring thee, ‭ That lead thee to the temple. Thy good name ‭ Grows amongst men for these things; they inflame ‭ Father and rev'rend mother with delight. ‭ Come, when the Day takes any wink from Night, ‭ Let's to the river, and repurify ‭ Thy wedding garments. My society ‭ Shall freely serve thee for thy speedier aid, ‭ Because thou shalt no mote stand on the maid. ‭ The best of all Phæacia woo thy grace, ‭ Where thou wert bred, and ow'st thyself a race. ‭ Up, and stir up to thee thy honour'd sire, ‭ To give thee mules and coach, thee and thy tire, ‭ Veils, girdles, mantles, early to the flood ‭ To bear in state. It suits thy high-born blood, ‭ And far more fits thee, than to foot so far, ‭ For far from town thou know'st the bath-founts are." ‭ This said, away blue-eyed Minerva went ‭ Up to Olympus, the firm continent ‭ That bears in endless being the Deified kind, ‭ That's neither sous'd with show'rs, nor shook with wind, ‭ Nor chill'd with snow, but where Serenity flies ‭ Exempt from clouds, and ever-beamy skies ‭ Circle the glitt'ring hill, and all their days ‭ Give the delights of blesséd Deity praise. ‭ And hither Pallas flew, and left the maid, ‭ When she had all that might excite her said. ‭ Straight rose the lovely Morn, that up did raise ‭ Fair-veil'd Nausicaa, whose dream her praise ‭ To admiration took; who no time spent ‭ To give the rapture of her vision vent ‭ To her lov'd parents, whom she found within. ‭ Her mother set at fire, who had to spin ‭ A rock, whose tincture with sea-purple shin'd; ‭ Her maids about her. But she chanc'd to find ‭ Her father going abroad, to council call'd ‭ By his grave Senate. And to him exhal'd ‭ Her smother'd bosom was: "Lov'd sire," said she, [3] ‭ "Will you not now command a coach for me, ‭ Stately and cómplete, fit for me to bear ‭ To wash at flood the weeds I cannot wear ‭ Before repurified? Yourself it fits ‭ To wear fair weeds, as ev'ry man that sits ‭ In place of council. And five sons you have, ‭ Two wed, three bachelors, that must be brave ‭ In ev'ry day's shift, that they may go dance; ‭ For these three last with these things must advance ‭ Their states in marriage, and who else but I, ‭ Their sister, should their dancing rites supply?" ‭ This gen'ral cause she show'd, and would not name ‭ Her mind of nuptials to her sire, for shame. ‭ He understood her yet, and thus replied: ‭ "Daughter! nor these, nor any grace beside, ‭ I either will deny thee, or defer, ‭ Mules, nor a coach, of state and circular, ‭ Fitting at all parts. Go, my servants shall ‭ Serves thy desires, and thy command in all." ‭ The servants then commanded soon obey'd, ‭ Fetch'd coach, and mules join'd in it. Then the Maid ‭ Brought from the chamber her rich weeds, and laid ‭ All up in coach; in which her mother plac'd ‭ A maund of victuals, varied well in taste, ‭ And other junkets. Wine she likewise fill'd ‭ Within a goat-skin bottle, and distill'd ‭ Sweet and moist oil into a golden cruse, ‭ Both for her daughter's, and her handmaid's, use, ‭ To soften their bright bodies, when they rose ‭ Cleans'd from their cold baths. Up to coach then goes ‭ Th' observéd Maid, takes both the scourge and reins, ‭ And to her side her handmaid straight attains. ‭ Nor these alone, but other virgins, grac'd ‭ The nuptial chariot. The whole bevy plac'd, ‭ Nausicaa scourg'd to make the coach-mules run, ‭ That neigh'd, and pac'd their usual speed, and soon ‭ Both maids and weeds brought to the river-side, ‭ Where baths for all the year their use supplied, ‭ Whose waters were so pure they would not stain, ‭ But still ran fair forth, and did more remain ‭ Apt to purge stains, for that purg'd stain within, ‭ Which by the water's pure store was not seen. ‭ These, here arriv'd, the mules uncoach'd, and drave ‭ Up to the gulfy river's shore, that gave ‭ Sweet grass to them. The maids from coach then took ‭ Their clothes, and steep'd them in the sable brook: ‭ Then put them into springs, and trod them clean ‭ With cleanly feet; adventuring wagers then ‭ Who should have soonest and most cleanly done. ‭ When having thoroughly cleans'd, they spread them on ‭ The flood's shore, all in order. And then, where ‭ The waves the pebbles wash'd, and ground was clear, ‭ They bath'd themselves, and all with glitt'ring oil ‭ Smooth'd their white skins; refreshing then their toil ‭ With pleasant dinner, by the river-side; ‭ Yet still watch'd when the sun their clothes had dried. ‭ Till which time, having din'd, Nausicaa ‭ With other virgins did at stool-ball play, ‭ Their shoulder-reaching head-tires laying by. ‭ Nausicaa, with the wrists of ivory, ‭ The liking stroke struck, singing first a song, ‭ As custom order'd, and amidst the throng ‭ Made such a show, and so past all was seen, ‭ As when the chaste-born, arrow-loving, Queen, ‭ Along the mountains gliding, either over ‭ Spartan Taygetus, whose tops far discover, ‭ Or Eurymanthus, in the wild boar's chace, ‭ Or swift-hov'd hart, and with her Jove's fair race, ‭ The field Nymphs, sporting; amongst whom, to see ‭ How far Diana had priority, ‭ Though all were fair, for fairness yet of all, ‭ As both by head and forehead being more tall, ‭ Latona triumph'd, since the dullest sight ‭ Might eas'ly judge whom her pains brought to light; ‭ Nausicaa so, whom never husband tam'd, ‭ Above them all in all the beauties flam'd. ‭ But when they now made homewards, and array'd, ‭ Ord'ring their weeds disorder'd as they play'd, ‭ Mules and coach ready, then Minerva thought ‭ What means to wake Ulysses might be wrought, ‭ That he might see this lovely-sighted maid, ‭ Whom she intended should become his aid, ‭ Bring him to town, and his return advance. ‭ Her mean was this, though thought a stool-ball chance: [4] ‭ The queen now, for the upstroke, struck the ball ‭ Quite wide off th' other maids, and made it fall ‭ Amidst the whirlpools. At which out shriek'd all, ‭ And with the shriek did wise Ulysses wake; ‭ Who, sitting up, was doubtful who should make ‭ That sudden outcry, and in mind thus striv'd: ‭ "On what a people am I now arriv'd? ‭ At civil hospitable men, that fear ‭ The Gods? Or dwell injurious mortals here? ‭ Unjust, and churlish? Like the female cry ‭ Of youth it sounds. What are they? Nymphs bred high ‭ On tops of hills, or in the founts of floods, ‭ In herby marshes, or in leafy woods? ‭ Or are they high-spoke men I now am near? ‭ I'll prove, and see." With this, the wary peer ‭ Crept forth the thicket, and an olive bough ‭ Broke with his broad hand, which he did bestow ‭ In covert of his nakedness, and then ‭ Put hasty head out. Look how from his den ‭ A mountain lion looks, that, all embrued ‭ With drops of trees, and weather-beaten-hued, ‭ Bold of his strength, goes on, and in his eye ‭ A burning furnace glows, all bent to prey ‭ On sheep, or oxen, or the upland hart, ‭ His belly charging him, and he must part ‭ Stakes with the herdsman in his beasts' attempt, ‭ Ev'n where from rape their strengths are most exempt; ‭ So wet, so weather-beat, so stung with need, ‭ Ev'n to the home-fields of the country's breed ‭ Ulysses was to force forth his access, ‭ Though merely naked; and his sight did press ‭ The eyes of soft-hair'd virgins. Horrid was ‭ His rough appearance to them; the hard pass ‭ He had at sea stuck by him. All in flight ‭ The virgins scatter'd, frighted with this sight, ‭ About the prominent windings of the flood. ‭ All but Nausicaa fled; but she fast stood, ‭ Pallas had put a boldness in her breast, ‭ And in her fair limbs tender fear comprest. ‭ And still she stood him, as resolv'd to know ‭ What man he was, or out of what should grow ‭ His strange repair to them. And here was he ‭ Put to his wisdom; if her virgin knee ‭ He should be bold, but kneeling, to embrace, ‭ Or keep aloof, and try with words of grace, ‭ In humblest suppliance, if he might obtain ‭ Some cover for his nakedness, and gain ‭ Her grace to show and guide him to the town. ‭ The last he best thought, to be worth his own, ‭ In weighing both well; to keep still aloof, ‭ And give with soft words his desires their proof, ‭ Lest, pressing so near as to touch her knee, ‭ He might incense her maiden modesty. ‭ This fair and fil'd speech then shew'd this was he: ‭ "Let me beseech, O queen, this truth of thee, ‭ Are you of mortal, or the defied, race? ‭ If of the Gods, that th' ample heav'ns embrace, ‭ I can resemble you to none above ‭ So near as to the chaste-born birth of Jove, ‭ The beamy Cynthia. Her you full present, ‭ In grace of ev'ry God-like lineament, ‭ Her goodly magnitude, and all th' address ‭ You promise of her very perfectness. ‭ If sprung of humans, that inhabit earth, ‭ Thrice blest are both the authors of your birth, ‭ Thrice blest your brothers, that in your deserts ‭ Must, ev'n to rapture, bear delighted hearts, ‭ To see, so like the first trim of a tree, ‭ Your form adorn a dance. But most blest he, ‭ Of all that breathe, that hath the gift t' engage ‭ Your bright neck in the yoke of marriage, ‭ And deck his house with your commanding merit ‭ I have not seen a man of so much spirit, ‭ Nor man, nor woman, I did ever see, ‭ At all parts equal to the parts in thee. ‭ T' enjoy your sight, doth admiration seize ‭ My eyes, and apprehensive faculties. ‭ Lately in Delos (with a charge of men ‭ Arriv'd, that render'd me most wretched then, ‭ Now making me thus naked) I beheld ‭ The burthen of a palm, whose issue swell'd ‭ About Apollo's fane, and that put on ‭ A grace like thee; for Earth had never none ‭ Of all her sylvan issue so adorn'd. ‭ Into amaze my very soul was turn'd, ‭ To give it observation; as now thee ‭ To view, O virgin, a stupidity ‭ Past admiration strikes me, join'd with fear ‭ To do a suppliant's due, and press so near, ‭ As to embrace thy knees. Nor is it strange, ‭ For one of fresh and firmest spirit would change ‭ T' embrace so bright an object. But, for me, ‭ A cruel habit of calamity ‭ Prepar'd the strong impression thou hast made; ‭ For this last day did fly night's twentieth shade ‭ Since I, at length, escap'd the sable seas; ‭ When in the mean time th' unrelenting prease ‭ Of waves and stern storms toss'd me up and down, ‭ From th' isle Ogygia. And now God hath thrown ‭ My wrack on this shore, that perhaps I may ‭ My mis'ries vary here; for yet their stay, ‭ I fear, Heav'n hath not order'd, though, before ‭ These late afflictions, it hath lent me store. ‭ O queen, deign pity then, since first to you ‭ My fate importunes my distress to vow. ‭ No other dame, nor man, that this Earth own, ‭ And neighbour city, I have seen or known. ‭ The town then show me; give my nakedness ‭ Some shroud to shelter it, if to these seas ‭ Linen or woollen you have brought to cleanse. ‭ God give you, in requital, all th' amends ‭ Your heart can wish, a husband, family, ‭ And good agreement. Nought beneath the sky ‭ More sweet, more worthy is, than firm consent ‭ Of man and wife in household government. ‭ It joys their wishers-well, their enemies wounds, ‭ But to themselves the special good redounds." ‭ She answer'd: "Stranger! I discern in thee ‭ Nor sloth, nor folly, reigns; and yet I see ‭ Th' art poor and wretched. In which I conclude, ‭ That industry nor wisdom make endued ‭ Men with those gifts that make them best to th' eye; ‭ Jove only orders man's felicity. ‭ To good and bad his pleasure fashions still ‭ The whole proportion of their good and ill. ‭ And he, perhaps, hath form'd this plight in thee, ‭ Of which thou must be patient, as he free. ‭ But after all thy wand'rings, since thy way, ‭ Both to our earth, and near our city, lay, ‭ As being expos'd to our cares to relieve, ‭ Weeds, and what else a human hand should give ‭ To one so suppliant and tam'd with woe, ‭ Thou shalt not want. Our city I will show, ‭ And tell our people's name: This neighbour town, ‭ And all this kingdom, the Phæacians own. ‭ And (since thou seem'dst so fain to know my birth, ‭ And mad'st a question, if of heav'n or earth.) ‭ This earth hath bred me; and my father's name ‭ Alcinous is, that in the pow'r and frame ‭ Of this isle's rule is supereminent." ‭ Thus, passing him, she to the virgins went, ‭ And said: "Give stay both to your feet and fright. ‭ Why thus disperse ye for a man's mere sight? ‭ Esteem you him a Cyclop, that long since ‭ Made use to prey upon our citizens? ‭ This man no moist man is, (nor wat'rish thing, [5] ‭ That's ever flitting, ever ravishing ‭ All it can compass; and, like it, doth range ‭ In rape of women, never stay'd in change). ‭ This man is truly manly, wise, and stay'd, [6] ‭ In soul more rich the more to sense decay'd, ‭ Who nor will do, nor suffer to be done, ‭ Acts lewd and abject; nor can such a one ‭ Greet the Phæacians with a mind envíous, ‭ Dear to the Gods they are, and he is pious, ‭ Besides, divided from the world we are, ‭ The out-part of it, billows circular ‭ The sea revolving round about our shore; ‭ Nor is there any man that enters more ‭ Than our own countrymen, with what is brought ‭ From other countries. This man, minding nought ‭ But his relief, a poor unhappy wretch, ‭ Wrack'd here, and hath no other land to fetch, ‭ Him now we must provide for. From Jove come [7] ‭ All strangers, and the needy of a home, ‭ Who any gift, though ne'er so small it be, ‭ Esteem as great, and take it gratefully. ‭ And therefore, virgins, give the stranger food, ‭ And wine; and see ye bathe him in the flood, ‭ Near to some shore to shelter most inclin'd. ‭ _To cold-bath-bathers hurtful is the wind,_ ‭ Not only rugged making th' outward skin, ‭ But by his thin pow'rs pierceth parts within. ‭ This said, their flight in a return they set, ‭ And did Ulysses with all grace entreat, ‭ Show'd him a shore, wind-proof, and full of shade, ‭ By him a shirt and utter mantle laid, ‭ A golden jug of liquid oil did add, ‭ Bad wash, and all things as Nausicaa bad. ‭ Divine Ulysses would not use their aid; ‭ But thus bespake them: "Ev'ry lovely maid, ‭ Let me entreat to stand a little by, [8] ‭ That I, alone, the fresh flood may apply ‭ To cleanse my bosom of the sea-wrought brine, ‭ And then use oil, which long time did not shine ‭ On my poor shoulders. I'll not wash in sight ‭ Of fair-hair'd maidens. I should blush outright, ‭ To bathe all-bare by such a virgin light." ‭ They mov'd, and mus'd a man had so much grace, ‭ And told their mistress what a man he was. ‭ He cleans'd his broad soil'd shoulders, back, and head ‭ Yet never tam'd, but now had foam and weed ‭ Knit in the fair curls. Which dissolv'd, and he ‭ Slick'd all with sweet oil, the sweet charity ‭ The untouch'd virgin show'd in his attire ‭ He cloth'd him with. Then Pallas put a fire, ‭ More than before, into his sparkling eyes, ‭ His late soil set off with his soon fresh guise. ‭ His locks, cleans'd, curl'd the more, and match'd, in pow'r ‭ To please an eye, the hyacinthian flow'r. ‭ And as a workman, that can well combine ‭ Silver and gold, and make both strive to shine, ‭ As being by Vulcan, and Minerva too, ‭ Taught how far either may be urg'd to go ‭ In strife of eminence, when work sets forth ‭ A worthy soul to bodies of such worth, ‭ No thought reproving th' act, in any place, ‭ Nor Art no debt to Nature's liveliest grace; ‭ So Pallas wrought in him a grace as great ‭ From head to shoulders, and ashore did seat ‭ His goodly presence. To which such a guise ‭ He show'd in going, that it ravish'd eyes. ‭ All which continued, as he sat apart, ‭ Nausicaa's eye struck wonder through her heart, ‭ Who thus bespake her consorts: "Hear me, you ‭ Fair-wristed virgins! This rare man, I know, ‭ Treads not our country-earth, against the will ‭ Of some God thronéd on th' Olympian hill. ‭ He show'd to me, till now, not worth the note, ‭ But now he looks as he had godhead got. ‭ I would to heav'n my husband were no worse, ‭ And would be call'd no better, but the course ‭ Of other husbands pleas'd to dwell out here. ‭ Observe and serve him with our utmost cheer." ‭ She said, they heard and did. He drunk and eat ‭ Like to a harpy, having touch'd no meat ‭ A long before time. But Nausicaa now ‭ Thought of the more grace she did lately vow, ‭ Had horse to chariot join'd, and up she rose, ‭ Up cheer'd her guest, and said: "Guest, now dispose ‭ Yourself for town, that I may let you see ‭ My father's court, where all the peers will be ‭ Of our Phæacian state. At all parts, then, ‭ Observe to whom and what place y' are t' attain; ‭ Though I need usher you with no advice, ‭ Since I suppose you absolutely wise. ‭ While we the fields pass, and men's labours there, ‭ So long, in these maids' guides, directly bear ‭ Upon my chariot (I must go before ‭ For cause that after comes, to which this more ‭ Be my induction) you shall then soon end ‭ Your way to town, whose tow'rs you see ascend [9] ‭ To such a steepness. On whose either side ‭ A fair port stands, to which is nothing wide ‭ An ent'rer's passage; on whose both hands ride ‭ Ships in fair harbours; which once past, you win ‭ The goodly market-place (that circles in ‭ A fane to Neptune, built of curious stone, ‭ And passing ample) where munitión, ‭ Gables, and masts, men make, and polish'd oars; ‭ For the Phæacians are not conquerors ‭ By bows nor quivers; oars, masts, ships they are ‭ With which they plough the sea, and wage their war. ‭ And now the cause comes why I lead the way, ‭ Not taking you to coach: The men, that sway ‭ In work of those tools that so fit our state, ‭ Are rude mechanicals, that rare and late ‭ Work in the market-place; and those are they ‭ Whose bitter tongues I shun, who straight would say ‭ (For these vile vulgars are extremely proud, ‭ And foully-languag'd) 'What is he, allow'd ‭ To coach it with Nausicaa, so large set, ‭ And fairly fashion'd? Where were these two met? ‭ He shall be sure her husband. She hath been ‭ Gadding in some place, and, of foreign men ‭ Fitting her fancy, kindly brought him home ‭ In her own ship. He must, of force, be come ‭ From some far region; we have no such man. ‭ It may be, praying hard, when her heart ran ‭ On some wish'd husband, out of heav'n some God ‭ Dropp'd in her lap; and there lies she at road ‭ Her cómplete life time. But, in sooth, if she, ‭ Ranging abroad, a husband, such as he ‭ Whom now we saw, laid hand on, she was wise, ‭ For none of all our nobles are of prize ‭ Enough for her; he must beyond sea come, ‭ That wins her high mind, and will have her home. ‭ Of our peers many have importun'd her, ‭ Yet she will none.' Thus these folks will confer ‭ Behind my back; or, meeting, to my face ‭ The foul-mouth rout dare put home this disgrace; ‭ And this would be reproaches to my fame, ‭ For, ev'n myself just anger would inflame, ‭ If any other virgin I should see, ‭ Her parents living, keep the company ‭ Of any man to any end of love, ‭ Till open nuptials should her act approve. ‭ And therefore hear me, guest, and take such way, ‭ That you yourself may compass, in your stay, ‭ Your quick deduction by my father's grace, ‭ And means to reach the root of all your race. ‭ We shall, not far out of our way to town, ‭ A never-fell'd grove find, that poplars crown, ‭ To Pallas sacred, where a fountain flows, ‭ And round about the grove a meadow grows, ‭ In which my father holds a manor-house, ‭ Deck'd all with orchards, green, and odorous, ‭ As far from town as one may hear a shout. ‭ There stay, and rest your foot-pains, till full out ‭ We reach the city; where, when you may guess ‭ We are arriv'd, and enter our access ‭ Within my father's court, then put you on ‭ For our Phæacian state, where, to be shown ‭ My father's house, desire. Each infant there ‭ Can bring you to it; and yourself will clear ‭ Distinguish it from others, for no shows ‭ The city-buildings make compar'd with those ‭ That king Alcinous' seat doth celebrate. ‭ In whose roofs, and the court (where men of state, ‭ And suitors sit and stay) when you shall hide, ‭ Straight pass it, ent'ring further, where abide ‭ My mother, with her withdrawn housewif'ries, ‭ Who still sits in the fire-shine, and applies ‭ Her rock, all-purple, and of pompous show, ‭ Her chair plac'd 'gainst a pillar, all-a-row ‭ Her maids behind her set; and to her here ‭ My father's dining-throne looks, seated where ‭ He pours his choice of wine in, like a God. ‭ This view once past, for th' end of your abode, ‭ Address suit to my mother, that her mean ‭ May make the day of your redition seen, ‭ And you may frolic straight, though far away ‭ You are in distance from your wishéd stay. ‭ For, if she once be won to wish you well, ‭ Your hope may instantly your passport seal, ‭ And thenceforth sure abide to see your friends, ‭ Fair house, and all to which your heart contends." ‭ This said, she us'd her shining scourge, and lash'd ‭ Her mules, that soon the shore left where she wash'd, ‭ And, knowing well the way, their pace was fleet, ‭ And thick they gather'd up their nimble feet. ‭ Which yet she temper'd so, and us'd her scourge [10] ‭ With so much skill, as not to over-urge ‭ The foot behind, and make them straggle so ‭ From close society. Firm together go ‭ Ulysses and her maids. And now the sun ‭ Sunk to the waters, when they all had won ‭ The never-fell'd, and sound-exciting, wood, ‭ Sacred to Pallas; where the god-like good ‭ Ulysses rested, and to Pallas pray'd: ‭ "Hear me, of goat-kept Jove th' unconquer'd Maid! [11] ‭ Now throughly hear me, since, in all the time ‭ Of all my wrack, my pray'rs could never climb ‭ Thy far-off ears; when noiseful Neptune toss'd ‭ Upon his wat'ry bristles my emboss'd ‭ And rock-torn body. Hear yet now, and deign ‭ I may of the Phæacian state obtain ‭ Pity, and grace." Thus pray'd he, and she heard, ‭ By no means yet, expos'd to sight, appear'd, ‭ For fear t' offend her uncle, the supreme ‭ Of all the Sea-Gods, whose wrath still extreme ‭ Stood to Ulysses; and would never cease, ‭ Till with his country shore he crown'd his peace. ‭ FINIS LIBRI SEXTI HOM. ODYSS. ‭[1] _ϒπνῳ καἱ καμἀτῳ ἁρημένος. Sonno et labore afflictus._ Sleep ‭(_καταχρηστικω̑ς_) for the want of sleep. ‭[2] Intending Dymas' daughter. ‭[3] This familiar and near wanton carriage of Nausicaa to her father, ‭joined with that virgin modesty expressed in her after, is much ‭praised by the gravest of Homer's expositors; with her father's ‭loving allowance of it, knowing her shamefastness and judgment ‭would not let her exceed at any part. Which note is here inserted, ‭not as if this were more worthy the observation than other ‭every-where strewed flowers of precept, but because this more ‭generally pleasing subject may perhaps find more fitness for the ‭stay of most readers. ‭[4] The piety and wisdom of the Poet was such, that (agreeing with ‭the Sacred Letter) not the least of things he makes come to pass ‭_sine Numinis providentiâ._ As Spondanus well notes of him. ‭[5] _Διερὸς βροτός. Cui vitalis vel sensualis humiditas inest. ‭βροτὸς ὰ ῥέω, ut dicatur quasi ῥοτὸς,_ i.e. _ὁ ἐν ῥοᾓ ὢν, quod ‭nihil sit magis fluxum quam <DW25>._ ‭[6] _Ανήρ virili animo præditus, fortis, magnanimus._ Nor are ‭those affirmed to be men, _qui servile quidpiam et abjectum ‭faciunt, vel, facere sustinent_: according to this of Herodotus in ‭Polym. _πολλοὶ μὲν ἄνθρωποι ει͒εν, ὀλίγοι δὲ ἄνδρες._ Many ‭men's forms sustain, but few are men. ‭[7] According to another translator: ‭ _"Ab Jove nam supplex pauper procedit et hospes, ‭ Res brevis, at chara est, magni quoque munaris instar."_ ‭Which I cite to show his good when he keeps him to the original, ‭and near in any degree expounds it. ‭[8] He taught their youths modesty by his aged judgment. As ‭receiving the custom of maids then used to that entertainment of ‭men, notwithstanding the modesty of that age, could not be ‭corrupted inwardly for those outward kind observations of guests ‭and strangers, and was therefore privileged. It is easy to avoid ‭show; and those, that most curiously avoid the outward ‭construction, are ever most tainted with the inward corruption. ‭[9] The city's description so far forth as may in part induce her ‭promised reason why she took not Ulysses to coach with her. ‭[10] Not without some little note of our omnisufficient Homer's ‭general touch of the least fitness lying in his way, may this courtly ‭discretion he describes in Nausicaa be observed, if you please. ‭[11] More of our Poet's curious and sweet piety. ‭ THE SEVENTH BOOK OF HOMER'S ODYSSEYS ‭ THE ARGUMENT ‭ Nausicaa arrives at town; ‭ And then Ulysses. He makes known ‭ His suit to Arete: who view ‭ Takes of his vesture, which she knew, ‭ And asks him from whose hands it came. ‭ He tells, with all the hapless frame ‭ Of his affairs in all the while ‭ Since he forsook Calypso's isle. ‭ ‭ ANOTHER ARGUMENT ‭ _Ητα._ ‭ The honour'd minds, ‭ And welcome things, ‭ Ulysses finds ‭ In Scheria's kings. ‭ Thus pray'd the wise and God-observing man. ‭ The Maid, by free force of her palfreys, wan ‭ Access to town, and the renownéd court ‭ Reach'd of her father; where, within the port, ‭ She stay'd her coach, and round about her came ‭ Her brothers, made as of immortal frame, ‭ Who yet disdain'd not, for her love, mean deeds, ‭ But took from coach her mules, brought in her weeds. [1] ‭ And she ascends her chamber; where purvey'd ‭ A quick fire was by her old chamber-maid, ‭ Eurymedusa, th' Aperæan born, ‭ And brought by sea from Apera t' adorn ‭ The court of great Alcinous, because ‭ He gave to all the blest Phæacians laws, ‭ And, like a heav'n-born pow'r in speech, acquir'd ‭ The people's ears. To one then so admir'd, ‭ Eurymedusa was esteem'd no worse ‭ Than worth the gift; yet now, grown old, was nurse ‭ To ivory-arm'd Nausicaa, gave heat ‭ To all her fires, and dress'd her privy meat. ‭ Then rose Ulysses, and made way to town; ‭ Which ere he reach'd, a mighty mist was thrown ‭ By Pallas round about him, in her care, ‭ Lest, in the sway of envies popular, ‭ Some proud Phæacian might foul language pass, ‭ Justle him up, and ask him what he was. ‭ Ent'ring the lovely town yet, through the cloud ‭ Pallas appear'd, and like a young wench show'd ‭ Bearing a pitcher, stood before him so ‭ As if objected purposely to know ‭ What there he needed; whom he question'd thus: ‭ "Know you not, daughter, where Alcinous, ‭ That rules this town, dwells? I, a poor distrest ‭ Mere stranger here, know none I may request ‭ To make this court known to me." She replied: ‭ "Strange father, I will see you satisfied ‭ In that request. My father dwells just by ‭ The house you seek for; but go silently, ‭ Nor ask, nor speak to any other, I ‭ Shall be enough to show your way. The men ‭ That here inhabit do not entertain ‭ With ready kindness strangers, of what worth ‭ Or state soever, nor have taken forth ‭ Lessons of civil usage or respect ‭ To men beyond them. They, upon their pow'rs ‭ Of swift ships building, top the wat'ry tow'rs, ‭ And Jove hath giv'n them ships, for sail so wrought, ‭ They cut a feather, and command a thought." [2] ‭ This said, she usher'd him, and after he ‭ Trod in the swift steps of the Deity. ‭ The free-sail'd seamen could not get a sight ‭ Of our Ulysses yet, though he forthright ‭ Both by their houses and their persons past, ‭ Pallas about him such a darkness cast ‭ By her divine pow'r, and her rev'rend care, ‭ She would not give the town-born cause to stare. ‭ He wonder'd, as he past, to see the ports; ‭ The shipping in them; and for all resorts ‭ The goodly market-steads; and aisles beside ‭ For the heroës; walls so large and wide; ‭ Rampires so high, and of such strength withall, ‭ It would with wonder any eye appall. ‭ At last they reach'd the court, and Pallas said: ‭ "Now, honour'd stranger, I will see obey'd ‭ Your will, to show our ruler's house; 'tis here; ‭ Where you shall find kings celebrating cheer. ‭ Enter amongst them, nor admit a fear. ‭ _More bold a man is, he prevails the more, ‭ Though man nor place lie ever saw before._ ‭ You first shall find the queen in court, whose name ‭ Is Arete, of parents born the same ‭ That was the king her spouse; their pedigree [3] ‭ I can report. The great Earth-shaker, he ‭ Of Peribœa (that her sex out-shone, ‭ And youngest daughter was t' Eurymedon, ‭ Who of th' unmeasur'd-minded giants sway'd ‭ Th' imperial sceptre, and the pride allay'd ‭ Of men so impious with cold death, and died ‭ Himself soon after) got the magnified ‭ In mind, Nausithous; whom the kingdom's state ‭ First held in supreme rule. Nausithous gat ‭ Rhexenor, and Alcinous, now king. ‭ Rhexenor (whose seed did no male fruit spring, ‭ And whom the silver-bow-grac'd Phœbus slew ‭ Young in the court) his shed blood did renew ‭ In only Arete, who now is spouse ‭ To him that rules the kingdom in this house, ‭ And is her uncle king Alcinous, ‭ Who honours her past equal. She may boast ‭ More honour of him than the honour'd most [4] ‭ Of any wife in earth can of her lord, ‭ How many more soever realms afford, ‭ That keep house under husbands. Yet no more ‭ Her husband honours her, than her blest store ‭ Of gracious children. All the city cast ‭ Eyes on her as a Goddess, and give taste ‭ Of their affections to her in their pray'rs, ‭ Still as she decks the street; for, all affairs ‭ Wrapt in contention, she dissolves to men. ‭ Whom she affects, she wants no mind to deign ‭ Goodness enough. If her heart stand inclin'd ‭ To your dispatch, hope all you wish to find, ‭ Your friends, your longing family, and all ‭ That can within your most affections fall." ‭ This said, away the grey-eyed Goddess flew ‭ Along th' untam'd sea, left the lovely hue ‭ Scheria presented, out-flew Marathon, ‭ And ample-streeted Athens lighted on; ‭ Where to the house, that casts so thick a shade, [5] ‭ Of Erechtheüs she ingression made. ‭ Ulysses to the lofty-builded court ‭ Of king Alcinous made bold resort; ‭ Yet in his heart cast many a thought, before ‭ The brazen pavement of the rich court bore ‭ His enter'd person. Like heav'n's two main lights ‭ The rooms illustrated both days and nights. ‭ On ev'ry side stood firm a wall of brass, ‭ Ev'n from the threshold to the inmost pass, ‭ Which bore a roof up that all-sapphire was. ‭ The brazen thresholds both sides did enfold ‭ Silver pilasters, hung with gates of gold; ‭ Whose portal was of silver; over which ‭ A golden cornice did the front enrich. ‭ On each side, dogs, of gold and silver fram'd, ‭ The house's guard stood: which the Deity lam'd ‭ With knowing inwards had inspir'd, and made ‭ That death nor age should their estates invade. ‭ Along the wall stood ev'ry way a throne, ‭ From th' entry to the lobby, ev'ry one ‭ Cast over with a rich-wrought cloth of state. ‭ Beneath which the Phæacian princes sate ‭ At wine and food, and feasted all the year. ‭ Youths forg'd of gold, at ev'ry table there, ‭ Stood holding flaming torches, that, in night, ‭ Gave through the house each honour'd guest his light ‭ And, to encounter feast with housewif'ry, ‭ In one room fifty women did apply ‭ Their sev'ral tasks. Some apple-colour'd corn ‭ Ground in fair querns, and some did spindles turn, ‭ Some work in looms; no hand least rest receives, ‭ But all had motion apt as aspen leaves. ‭ And from the weeds they wove, so fast they laid, ‭ And so thick thrust together thread by thread, ‭ That th' oil, of which the wool had drunk his fill, ‭ Did with his moisture in light dews distill. ‭ As much as the Phæacian men excell'd ‭ All other countrymen in art to build ‭ A swift-sail'd ship; so much the women there ‭ For work of webs, past other women were. ‭ Past mean, by Pallas' means, they understood ‭ The grace of good works; and had wits as good. ‭ Without the hall, and close upon the gate, ‭ A goodly orchard-ground was situate, ‭ Of near ten acres; about which was led ‭ A lofty quickset. In it flourished ‭ High and broad fruit trees, that pomegranates bore, ‭ Sweet figs, pears, olives; and a number more ‭ Most useful plants did there produce their store, ‭ Whose fruits the hardest winter could not kill, ‭ Nor hottest summer wither. There was still ‭ Fruit in his proper season all the year. ‭ Sweet Zephyr breath'd upon them blasts that were ‭ Of varied tempers. These he made to bear ‭ Ripe fruits, these blossoms. Pear grew after pear, ‭ Apple succeeded apple, grape the grape, ‭ Fig after fig came; time made never rape ‭ Of any dainty there. A spritely vine ‭ Spread here his root, whose fruit a hot sunshine ‭ Made ripe betimes; here grew another green. ‭ Here some were gath'ring, here some pressing, seen. ‭ A large-allotted sev'ral each fruit had; ‭ And all th' adorn'd grounds their appearance made ‭ In flow'r and fruit, at which the king did aim ‭ To the precisest order he could claim. ‭ Two fountains grac'd the garden; of which, one ‭ Pour'd out a winding stream that over-run ‭ The grounds for their use chiefly, th' other went ‭ Close by the lofty palace gate, and lent ‭ The city his sweet benefit. And thus ‭ The Gods the court deck'd of Alcinous. ‭ Patient Ulysses stood a while at gaze, ‭ But, having all observ'd, made instant pace ‭ Into the court; where all the peers he found, ‭ And captains of Phæacia, with cups-crown'd ‭ Off'ring to sharp-eyed Hermes, to whom last ‭ They us'd to sacrifice, when sleep had cast ‭ His inclination through their thoughts. But these ‭ Ulysses pass'd, and forth went; nor their eyes ‭ Took note of him, for Pallas stopp'd the light ‭ With mists about him, that, unstay'd, he might ‭ First to Alcinous, and Arete, ‭ Present his person; and, of both them, she, ‭ By Pallas' counsel, was to have the grace ‭ Of foremost greeting. Therefore his embrace ‭ He cast about her knee. And then off flew ‭ The heav'nly air that hid him. When his view ‭ With silence and with admiration strook ‭ The court quite through; but thus he silence broke: ‭ "Divine Rhexenor's offspring, Arete, ‭ To thy most honour'd husband, and to thee, ‭ A man whom many labours have distrest ‭ Is come for comfort, and to ev'ry guest. ‭ To all whom heav'n vouchsafe delightsome lives, ‭ And after to your issue that survives ‭ A good resignment of the goods ye leave, ‭ With all the honour that yourselves receive ‭ Amongst your people. Only this of me ‭ Is the ambition; that I may but see ‭ (By your vouchsaf'd means, and betimes vouchsaf'd) ‭ My country-earth; since I have long been left ‭ To labours, and to errors, barr'd from end, ‭ And far from benefit of any friend," ‭ He said no more, but left them dumb with that, ‭ Went to the hearth, and in the ashes sat, ‭ Aside the fire. At last their silence brake, ‭ And Echinëus, th' old heroë, spake; ‭ A man that all Phæacians pass'd in years, ‭ And in persuasive eloquence all the peers, ‭ Knew much, and us'd it well; and thus spake he: ‭ "Alcinous! It shews not decently, ‭ Nor doth your honour what you see admit, ‭ That this your guest should thus abjectly sit, ‭ His chair the earth, the hearth his cushion, ‭ Ashes as if appos'd for food. A throne, ‭ Adorn'd with due rites, stands you more in hand ‭ To see his person plac'd in, and command ‭ That instantly your heralds fill-in wine, ‭ That to the God that doth in lightnings shine ‭ We may do sacrifice; for he is there, ‭ Where these his rev'rend suppliants appear. ‭ Let what you have within be brought abroad, ‭ To sup the stranger. All these would have show'd ‭ This fit respect to him, but that they stay ‭ For your precedence, that should grace the way." ‭ When this had added to the well-inclin'd ‭ And sacred order of Alcinous' mind, ‭ Then of the great-in-wit the hand he seis'd, ‭ And from the ashes his fair person rais'd, ‭ Advanc'd him to a well-adornéd throne, ‭ And from his seat rais'd his most lovéd son, ‭ Laodamas, that next himself was set, ‭ To give him place. The handmaid then did get ‭ An ewer of gold, with water fill'd, which plac'd ‭ Upon a caldron, all with silver grac'd, ‭ She pour'd out on their hands. And then was spread ‭ A table, which the butler set with bread, ‭ As others serv'd with other food the board, ‭ In all the choice the present could afford. ‭ Ulysses meat and wine took; and then thus ‭ The king the herald call'd: "Pontonous! ‭ Serve wine through all the house, that all may pay ‭ Rites to the Lightner, who is still in way ‭ With humble suppliants, and them pursues ‭ With all benign and hospitable dues." ‭ Pontonous gave act to all he will'd, ‭ And honey-sweetness-giving-minds wine fill'd, [6] ‭ Disposing it in cups for all to drink. ‭ All having drunk what either's heart could think ‭ Fit for due sacrifice, Alcinous said: ‭ "Hear me, ye dukes that the Phæacians lead, ‭ And you our counsellors, that I may now ‭ Discharge the charge my mind suggests to you, ‭ For this our guest: Feast past, and this night's sleep, ‭ Next morn, our senate summon'd, we will keep ‭ Justs, sacred to the Gods, and this our guest ‭ Receive in solemn court with fitting feast; ‭ Then think of his return, that, under hand ‭ Of our deduction, his natural land ‭ (Without more toil or care, and with delight, ‭ And that soon giv'n him, how far-hence dissite ‭ Soever it can be) he may ascend; ‭ And in the mean time without wrong attend, ‭ Or other want, fit means to that ascent. [7] ‭ What, after, austere Fates shall make th' event ‭ Of his life's thread, now spinning, and began ‭ When his pain'd mother freed his root of man, ‭ He must endure in all kinds. If some God ‭ Perhaps abides with us in his abode, ‭ And other things will think upon than we, ‭ The Gods' wills stand, who ever yet were free ‭ Of their appearance to us, when to them ‭ We offer'd hecatombs of fit esteem, ‭ And would at feast sit with us, ev'n where we ‭ Order'd our session. They would likewise be ‭ Encount'rers of us, when in way alone ‭ About his fit affairs went any one. ‭ Nor let them cloak themselves in any care ‭ To do us comfort, we as near them are, ‭ As are the Cyclops, or the impious race [8] ‭ Of earthy giants, that would heav'n outface." ‭ Ulysses answer'd: "Let some other doubt ‭ Employ your thoughts than what your words give out, ‭ Which intimate a kind of doubt that I ‭ Should shadow in this shape a Deity. ‭ I bear no such least semblance, or in wit, ‭ Virtue, or person. What may well befit ‭ One of those mortals, whom you chiefly know ‭ Bears up and down the burthen of the woe ‭ Appropriate to poor man, give that to me; ‭ Of whose moans I sit in the most degree, ‭ And might say more, sustaining griefs that all ‭ The Gods consent to; no one 'twixt their fall ‭ And my unpitied shoulders letting down ‭ The least diversion. Be the grace then shown, ‭ To let me taste your free-giv'n food in peace. ‭ _Through greatest grief the belly must have ease; ‭ Worse than an envious belly nothing is._ ‭ It will command his strict necessities, ‭ Of men most griev'd in body or in mind, ‭ That are in health, and will not give their kind ‭ A desp'rate wound. When most with cause I grieve, ‭ It bids me still, Eat, man, and drink, and live; ‭ And this makes all forgot. Whatever ill ‭ I ever bear, it ever bids me fill. ‭ But this ease is but forc'd, and will not last, ‭ Till what the mind likes be as well embrac'd; ‭ And therefore let me wish you would partake ‭ In your late purpose; when the morn shall make ‭ Her next appearance, deign me but the grace, ‭ Unhappy man, that I may once embrace ‭ My country-earth. Though I be still thrust at ‭ By ancient ills, yet make me but see that. ‭ And then let life go, when withal I see ‭ My high-roof'd large house, lands, and family." ‭ This all approv'd; and each will'd ev'ry one, ‭ Since he hath said so fairly, set him gone. ‭ Feast past and sacrifice, to sleep all vow ‭ Their eyes at either's house. Ulysses now ‭ Was left here with Alcinous, and his Queen, ‭ The all-lov'd Arete. The handmaids then ‭ The vessel of the banquet took away. ‭ When Arete set eye on his array; ‭ Knew both his out and under weed, which she ‭ Made with her maids; and mus'd by what means he ‭ Obtain'd their wearing; which she made request ‭ To know, and wings gave to these speeches: "Guest! ‭ First let me ask, what, and from whence you are? ‭ And then, who grac'd you with the weeds you wear? ‭ Said you not lately, you had err'd at seas, ‭ And thence arriv'd here?" Laertiades ‭ To this thus answer'd: "'Tis a pain, O Queen, ‭ Still to be op'ning wounds wrought deep, and green, ‭ Of which the Gods have open'd store in me; ‭ Yet your will must be serv'd. Far hence, at sea, ‭ There lies an isle, that bears Ogygia's name, ‭ Where Atlas' daughter, the ingenious dame, ‭ Fair-hair'd Calypso lives; a Goddess grave, ‭ And with whom men nor Gods society have; ‭ Yet I, past man unhappy, liv'd alone, ‭ By Heav'n's wrath forc'd, her house-companion. ‭ For Jove had with a fervent lightning cleft ‭ My ship in twain, and far at black sea left ‭ Me and my soldiers; all whose lives I lost. ‭ I in mine arms the keel took, and was tost ‭ Nine days together up from wave to wave. ‭ The tenth grim night, the angry Deities drave ‭ Me and my wrack on th' isle, in which doth dwell ‭ Dreadful Calypso; who exactly well ‭ Receiv'd and nourish'd me, and promise made ‭ To make me deathless, nor should age invade ‭ My pow'rs with his deserts through all my days. ‭ All mov'd not me, and therefore, on her stays, ‭ Sev'n years she made me lie; and there spent I ‭ The long time, steeping in the misery ‭ Of ceaseless tears the garments I did wear, ‭ From her fair hand. The eighth revolvéd year ‭ (Or by her chang'd mind, or by charge of Jove) ‭ She gave provok'd way to my wish'd remove, ‭ And in a many-jointed ship, with wine ‭ Dainty in savour, bread, and weeds divine, ‭ Sign'd, with a harmless and sweet wind, my pass. ‭ Then sev'nteen days at sea I homeward was, ‭ And by the eighteenth the dark hills appear'd ‭ That your earth thrusts up. Much my heart was cheer'd, ‭ Unhappy man, for that was but a beam, ‭ To show I yet had agonies extreme ‭ To put in suff''rance, which th' Earth-shaker sent, ‭ Crossing my way with tempests violent, ‭ Unmeasur'd seas up-lifting, nor would give ‭ The billows leave to let my vessel live ‭ The least time quiet, that ev'n sigh'd to bear ‭ Their bitter outrage, which, at last, did tear ‭ Her sides in pieces, set on by the winds. ‭ I yet through-swum the waves that your shore binds, ‭ Till wind and water threw me up to it; ‭ When, coming forth, a ruthless billow smit ‭ Against huge rocks, and an accessless shore, ‭ My mangl'd body. Back again I bore, ‭ And swum till I was fall'n upon a flood, ‭ Whose shores, methought, on good advantage stood ‭ For my receipt, rock-free, and fenc'd from wind; ‭ And this I put for, gath'ring up my mind. ‭ Then the divine night came, and treading earth, ‭ Close by the flood that had from Jove her birth, ‭ Within a thicket I repos'd; when round ‭ I ruffled up fall'n leaves in heap; and found, ‭ Let fall from heav'n, a sleep interminate. ‭ And here my heart, long time excruciate, ‭ Amongst the leaves I rested all that night, ‭ Ev'n till the morning and meridian light. ‭ The sun declining then, delightsome sleep ‭ No longer laid my temples in his steep, ‭ But forth I went, and on the shore might see ‭ Your daughter's maids play. Like a Deity ‭ She shin'd above them; and I pray'd to her, ‭ And she in disposition did prefer ‭ Noblesse, and wisdom, no more low than might ‭ Become the goodness of a Goddess' height. ‭ Nor would you therefore hope, suppos'd distrest ‭ As I was then, and old, to find the least ‭ Of any grace from her, being younger far. ‭ _With young folks Wisdom makes her commerce rare._ ‭ Yet she in all abundance did bestow ‭ Both wine, that makes the blood in humans grow, [9] ‭ And food, and bath'd me in the flood, and gave ‭ The weeds to me which now ye see me have. ‭ This through my griefs I tell you, and 'tis true." ‭ Alcinous answer'd: "Guest! my daughter knew ‭ Least of what most you give her; nor became ‭ The course she took, to let with ev'ry dame ‭ Your person lackey; nor hath with them brought ‭ Yourself home too; which first you had besought." ‭ "O blame her not," said he, "heroical lord, ‭ Nor let me hear against her worth a word. ‭ She faultless is, and wish'd I would have gone ‭ With all her women home, but I alone ‭ Would venture my receipt here, having fear ‭ And rev'rend awe of accidents that were ‭ Of likely issue; both your wrath to move, ‭ And to inflame the common people's love ‭ Of speaking ill, to which they soon give place. ‭ _We men are all a most suspicious race."_ ‭ "My guest," said he, "I use not to be stirr'd ‭ To wrath too rashly; and where are preferr'd ‭ To men's conceits things that may both ways fail, ‭ The noblest ever should the most prevail. ‭ Would Jove our Father, Pallas, and the Sun, ‭ That, were you still as now, and could but run ‭ One fate with me, you would my daughter wed, ‭ And be my son-in-law, still vow'd to lead ‭ Your rest of life here! I a house would give, ‭ And household goods, so freely you would live, ‭ Confin'd with us. But 'gainst your will shall none ‭ Contain you here, since that were violence done ‭ To Jove our Father. For your passage home, ‭ That you may well know we can overcome ‭ So great a voyage, thus it shall succeed: ‭ To-morrow shall our men take all their heed, ‭ While you securely sleep, to see the seas ‭ In calmest temper, and, if that will please, ‭ Show you your country and your house ere night, ‭ Though far beyond Eubœa be that sight. ‭ And this Eubœa, as our subjects say ‭ That have been there and seen, is far away, ‭ Farthest from us of all the parts they know; ‭ And made the trial when they help'd to row ‭ The gold-lock'd Rhadamanth, to give him view ‭ Of earth-born Tityus; whom their speeds did show ‭ In that far-off Eubœa, the same day ‭ They set from hence; and home made good their way ‭ With ease again, and him they did convey. ‭ Which I report to you, to let you see ‭ How swift my ships are, and how matchlessly ‭ My young Phæacians with their oars prevail, ‭ To beat the sea through, and assist a sail." ‭ This cheer'd Ulysses, who in private pray'd: ‭ "I would to Jove our Father, what he said, ‭ He could perform at all parts; he should then ‭ Be glorified for ever, and I gain ‭ My natural country." This discourse they had; ‭ When fair-arm'd Arete her handmaids bad ‭ A bed make in the portico, and ply ‭ With clothes, the cov'ring tapestry, ‭ The blankets purple; well-napp'd waistcoats too, ‭ To wear for more warmth. What these had to do, ‭ They torches took and did. The bed purvey'd, ‭ They mov'd Ulysses for his rest, and said: ‭ "Come guest, your bed is fit, now frame to rest." ‭ Motion of sleep was gracious to their guest; ‭ Which now he took profoundly, being laid ‭ Within a loop-hole tow'r, where was convey'd ‭ The sounding portico. The King took rest ‭ In a retir'd part of the house; where drest ‭ The Queen her self a bed, and trundlebed, ‭ And by her lord repos'd her rev'rend head. ‭ FINIS LIBRI SEPTIMI HOM. ODYSS. ‭[1] _Hac fuit illius sæculi simplicitas: nam vel fraternus quoque ‭amor tantus fuit, ut libenter hanc redeunti charissimæ sorori ‭operam præstiterint. Spond._ ‭[2] _Νέες ώκει̑αι ὡσεὶ πτερὸν ἠὲ νόημα, naves veloces veluti penna, ‭atque cogitatio._ ‭[3] For the more perspicuity of this pedigree, I have here set down ‭the diagram, as Spondanus hath it. Neptune begat Nausithous of ‭Peribœa. By Nausithous, Rhexenor, Alcinous, were begot. By ‭Rhexenor, Arete, the wife of her uncle Alcinous. ‭[4] The honour of Arete (or virtue) alleg. ‭[5] Casts so thick a shade--_πυκινός spissus._ ‭[6] The word that bears this long epithet is translated only _dulce:_ ‭which signifies more, _Μελίϕρονα οι͒νον ἐκίρνα Vinum quod ‭melleâ dulcedine animum perfundit, et oblectat._ ‭[7] Ascent to his country's shore. ‭[8] Eustathius will have this comparison of the Phæacians with the ‭Giants and Cyclops to proceed out of the inveterate virulency of ‭Antinous to the Cyclops; who were cause (as is before said) of ‭their remove from their country; and with great endeavour labours ‭the approbation of it; but (under his peace) from the purpose: for ‭the sense of the Poet is clear, that the Cyclops and Giants being in ‭part the issue of the Gods, and yet afterward their defiers, (as ‭Polyp. hereafter dares profess) Antinous (out of bold and manly ‭reason, even to the face of one that might have been a God, for the ‭past manly appearance he made there) would tell him, and the rest ‭in him, that if they graced those Cyclops with their open ‭appearance, that, though descended from them, durst yet deny ‭them, they might much more do them the honour of their open ‭presence that adored them. ‭[9] _Αἴθοψ οι͒νος, Vinum calefaciendi vim habens._ ‭ THE EIGHTH BOOK OF HOMER'S ODYSSEYS ‭ THE ARGUMENT ‭ The Peers of the Phæacian State ‭ A Council call, to consolate ‭ Ulysses with all means for home. ‭ The Council to a banquet come, ‭ Invited by the King. Which done, ‭ Assays for hurling of the stone ‭ The youths make with the stranger-king. ‭ Demodocus, at feast, doth sing ‭ Th' adult'ry of the God of Arms ‭ With Her that rules in amorous charms; ‭ And after sings the entercourse ‭ Of acts about th' Epæan horse. ‭ ANOTHER ARGUMENT ‭ _Θη̑τα._ ‭ The council's frame ‭ At fleet applied. ‭ In strifes of game ‭ Ulysses tried. ‭ Now when the rosy-finger'd Morn arose, ‭ The sacred pow'r Alcinous did dispose ‭ Did likewise rise; and, like him, left his ease ‭ The city-razer Laertiades. ‭ The Council at the navy was design'd; ‭ To which Alcinous, with the sacred mind, ‭ Came first of all. On polish'd stones they sate, ‭ Near to the navy. To increase the state, ‭ Minerva took the herald's form on her, ‭ That serv'd Alcinous, studious to prefer ‭ Ulysses' suit for home. About the town ‭ She made quick way, and fill'd with the renown ‭ Of that design the ears of ev'ry man, ‭ Proclaiming thus: "Peers Phæacensian! ‭ And Men of Council, all haste to the court, ‭ To hear the stranger that made late resort ‭ To King Alcinous, long time lost at sea, ‭ And is in person like a Deity." ‭ This all their pow'rs set up, and spirit instill'd, ‭ And straight the court and seats with men were fill'd. ‭ The whole state wonder'd at Laertes' son, ‭ When they beheld him. Pallas put him on ‭ A supernatural and heav'nly dress, ‭ Enlarg'd him with a height, and goodliness ‭ In breast and shoulders, that he might appear ‭ Gracious, and grave, and reverend, and bear ‭ A perfect hand on his performance there ‭ In all the trials they resolv'd t' impose. ‭ All met, and gather'd in attention close, ‭ Alcinous thus bespake them: "Dukes, and lords, ‭ Hear me digest my hearty thoughts in words. ‭ This stranger here, whose travels found my court, ‭ I know not, nor can tell if his resort ‭ From East or West comes; but his suit is this: ‭ That to his country-earth we would dismiss ‭ His hither-forcéd person, and doth bear ‭ The mind to pass it under ev'ry peer; ‭ Whom I prepare, and stir up, making known ‭ My free desire of his deductión. ‭ Nor shall there ever any other man ‭ That tries the goodness Phæacensian ‭ In me, and my court's entertainment, stay, ‭ Mourning for passage, under least delay. ‭ Come then, a ship into the sacred seas, ‭ New-built, now launch we; and from out our prease ‭ Choose two-and-fifty youths, of all, the best ‭ To use an oar. All which see straight imprest, ‭ And in their oar-bound seats. Let others hie ‭ Home to our court, commanding instantly ‭ The solemn preparation of a feast, ‭ In which provision may for any guest ‭ Be made at my charge. Charge of these low things ‭ I give our youth. You, sceptre-bearing kings, ‭ Consort me home, and help with grace to use ‭ This guest of ours; no one man shall refuse. ‭ Some other of you haste, and call to us ‭ The sacred singer, grave Demodocus, ‭ To whom hath God giv'n song that can excite ‭ The heart of whom he listeth with delight." ‭ This said, he led. The sceptre-bearers lent ‭ Their free attendance; and with all speed went ‭ The herald for the sacred man-in-song. ‭ Youths two-and-fifty, chosen from the throng, ‭ Went, as was will'd, to the untam'd sea's shore; ‭ Where come, they launch'd the ship, the mast it bore ‭ Advanc'd, sails hoiséd, ev'ry seat his oar ‭ Gave with a leather thong. The deep moist then ‭ They further reach'd. The dry streets flow'd with men, ‭ That troop'd up to the king's capacious court, ‭ Whose porticos were chok'd with the resort, ‭ Whose walls were hung with men, young, old, thrust there ‭ In mighty concourse; for whose promis'd cheer ‭ Alcinous slew twelve sheep, eight white-tooth'd swine, ‭ Two crook-haunch'd beeves; which flay'd and dress'd, divine ‭ The show was of so many a jocund guest, ‭ All set together at so set a feast. ‭ To whose accomplish'd state the herald then ‭ The lovely singer led; who past all mean ‭ The Muse affected, gave him good, and ill, ‭ His eyes put out, but put in soul at will. ‭ His place was giv'n him in a chair all grac'd ‭ With silver studs, and 'gainst a pillar plac'd: ‭ Where, as the centre to the state, he rests, ‭ And round about the circle of the guests. ‭ The herald on a pin above his head ‭ His soundful harp hung, to whose height he led ‭ His hand for taking of it down at will, ‭ A board set by with food, and forth did fill ‭ A bowl of wine, to drink at his desire. ‭ The rest then fell to feast, and, when the fire ‭ Of appetite was quench'd, the Muse inflam'd ‭ The sacred singer. Of men highliest fam'd ‭ He sung the glories, and a poem penn'd, ‭ That in applause did ample heav'n ascend. ‭ Whose subject was, the stern Contentión ‭ Betwixt Ulysses and great Thetis' son, ‭ As, at a banquet sacred to the Gods, ‭ In dreadful language they express'd their odds. ‭ When Agamemnon sat rejoic'd in soul ‭ To hear the Greek peers jar in terms so foul; ‭ For augur Phœbus in presage had told ‭ The King of men (desirous to unfold ‭ The war's perplex'd end, and being therefore gone ‭ In heav'nly Pythia to the porch of stone,) ‭ That then the end of all griefs should begin ‭ 'Twixt Greece and Troy, when Greece (with strife to win ‭ That wish'd conclusion) in her kings should jar, ‭ And plead, if force or wit must end the war. ‭ This brave Contention did the poet sing, ‭ Expressing so the spleen of either king, ‭ That his large purple weed Ulysses held ‭ Before his face and eyes, since thence distill'd ‭ Tears uncontain'd; which he obscur'd, in fear ‭ To let th' observing presence note a tear. ‭ But, when his sacred song the mere divine ‭ Had giv'n an end, a goblet crown'd with wine ‭ Ulysses, drying his wet eyes, did seize, [1] ‭ And sacrific'd to those Gods that would please ‭ T' inspire the poet with a song so fit ‭ To do him honour, and renown his wit. ‭ His tears then stay'd. But when again began, ‭ By all the kings' desires, the moving man, ‭ Again Ulysses could not choose but yield ‭ To that soft passion, which again, withheld, ‭ He kept so cunningly from sight, that none, ‭ Except Alcinous himself alone, ‭ Discern'd him mov'd so much. But he sat next, ‭ And heard him deeply sigh; which his pretext ‭ Could not keep hid from him. Yet he conceal'd ‭ His utt'rance of it, and would have it held ‭ From all the rest, brake off the song, and this ‭ Said to those oar-affecting peers of his: ‭ "Princes, and peers! We now are satiate ‭ With sacred song that fits a feast of state, ‭ With wine and food. Now then to field, and try ‭ In all kinds our approv'd activity, ‭ That this our guest may give his friends to know, ‭ In his return, that we as little owe ‭ To fights and wrastlings, leaping, speed-of race, ‭ As these our court-rites; and commend our grace ‭ In all to all superior." Forth he led, ‭ The peers and people troop'd up to their head. ‭ Nor must Demodocus be left within; ‭ Whose harp the herald hung upon the pin, ‭ His hand in his took, and abroad he brought ‭ The heav'nly poet, out the same way wrought ‭ That did the princes, and what they would see ‭ With admiration, with his company ‭ They wish'd to honour. To the place of game ‭ These throng'd; and after routs of other came, ‭ Of all sort, infinite. Of youths that strove, ‭ Many and strong rose to their trial's love. ‭ Up rose Acroneus, and Ocyalus, ‭ Elatreus, Prymneus, and Anchialus, [2] ‭ Nauteus, Eretmeus, Thoen, Proreüs, ‭ Pontëus, and the strong Amphialus ‭ Son to Tectonides Polyneüs. ‭ Up rose to these the great Euryalus, ‭ In action like the Homicide of War. ‭ Naubolides, that was for person far ‭ Past all the rest, but one he could not pass, ‭ Nor any thought improve, Laodamas. ‭ Up Anabesinëus then arose; ‭ And three sons of the Sceptre-state, and those ‭ Were Halius, the fore-prais'd Laodamas, ‭ And Clytonëus like a God in grace. ‭ These first the foot-game tried, and from the lists ‭ Took start together. Up the dust in mists ‭ They hurl'd about, as in their speed they flew; ‭ But Clytonëus first of all the crew ‭ A stitch's length in any fallow field ‭ Made good his pace; when, where the judges yield ‭ The prize and praise, his glorious speed arriv'd. ‭ Next, for the boist'rous wrastling game they striv'd; ‭ At which Euryalus the rest outshone. ‭ At leap Amphialus, At the hollow stone ‭ Elatreüs excell'd. At buffets, last, ‭ Laodamas, the king's fair son, surpast. ‭ When all had striv'd in these assays their fill, ‭ Laodamas said: "Come friends, let's prove what skill ‭ This stranger hath attain'd to in our sport. ‭ Methinks, he must be of the active sort, ‭ His calves, thighs, hands, and well-knit shoulders show ‭ That Nature disposition did bestow ‭ To fit with fact their form. Nor wants he prime. ‭ But sour affliction, made a mate with time, ‭ Makes time the more seen. Nor imagine I, ‭ A worse thing to enforce debility ‭ Than is the sea, though nature ne'er so strong ‭ Knits one together." "Nor conceive you wrong," ‭ Replied Euryalus, "but prove his blood ‭ With what you question." In the midst then stood ‭ Renown'd Laodamas, and prov'd him thus: ‭ "Come, stranger-father, and assay with us ‭ Your pow'rs in these contentions. If your show ‭ Be answer'd with your worth, 'tis fit that you ‭ Should know these conflicts. Nor doth glory stand ‭ On any worth more, in a man's command, ‭ Than to be strenuous both of foot and hand. ‭ Come then, make proof with us, discharge your mind ‭ Of discontentments; for not far behind ‭ Comes your deduction, ship is ready now, [3] ‭ And men, and all things." "Why," said he, "dost thou ‭ Mock me, Laodamas, and these strifes bind ‭ My pow'rs to answer? I am more inclin'd ‭ To cares than conflict. Much sustain'd I have, ‭ And still am suff'ring. I come here to crave, ‭ In your assemblies, means to be dismist, ‭ And pray both kings and subjects to assist." ‭ Euryalus an open brawl began, ‭ And said: "I take you, sir, for no such man ‭ As fits these honour'd strifes. A number more ‭ Strange men there are that I would choose before. ‭ To one that loves to lie aship-board much, ‭ Or is the prince of sailors; or to such ‭ As traffic far and near, and nothing mind ‭ But freight, and passage, and a foreright wind; ‭ Or to a victualler of a ship; or men ‭ That set up all their pow'rs for rampant gain; ‭ I can compare, or hold you like to be: ‭ But, for a wrastler, or of quality ‭ Fit for contentions noble, you abhor ‭ From worth of any such competitor." ‭ Ulysses, frowning, answer'd: "Stranger, far ‭ Thy words are from the fashions regular ‭ Of kind, or honour. Thou art in thy guise ‭ Like to a man that authors injuries. [4] ‭ I see, the Gods to all men give not all ‭ Manly addiction, wisdom, words that fall, ‭ Like dice, upon the square still. Some man takes ‭ Ill form from parents, but God often makes ‭ That fault of form up with observ'd repair ‭ Of pleasing speech, that makes him held for fair, ‭ That makes him speak securely, makes him shine ‭ In an assembly with a grace divine. ‭ Men take delight to see how ev'nly lie ‭ His words asteep in honey modesty. ‭ Another, then, hath fashion like a God, ‭ But in his language he is foul and broad. ‭ And such art thou. A person fair is giv'n, ‭ But nothing else is in thee sent from heav'n; ‭ For in thee lurks a base and earthy soul, ‭ And t' hast compell'd me, with a speech most foul, ‭ To be thus bitter. I am not unseen ‭ In these fair strifes, as thy words overween, ‭ But in the first rank of the best I stand; ‭ At least I did, when youth and strength of hand ‭ Made me thus confident, but now am worn ‭ With woes and labours, as a human born ‭ To bear all anguish. Suffer'd much I have. ‭ The war of men, and the inhuman wave, ‭ Have I driv'n through at all parts. But with all ‭ My waste in suff'rance, what yet may fall ‭ In my performance, at these strifes I'll try. ‭ Thy speech hath mov'd, and made my wrath run high." ‭ This said, with robe and all, he grasp'd a stone, ‭ A little graver than was ever thrown ‭ By these Phæacians in their wrastling rout, ‭ More firm, more massy; which, turn'd round about, ‭ He hurried from him with a hand so strong ‭ It sung, and flew, and over all the throng, ‭ That at the others' marks stood, quite it went; ‭ Yet down fell all beneath it, fearing spent ‭ The force that drave it flying from his hand, ‭ As it a dart were, or a walking wand; ‭ And far past all the marks of all the rest ‭ His wing stole way; when Pallas straight imprest ‭ A mark at fall of it, resembling then ‭ One of the navy-giv'n Phæacian men, ‭ And thus advanc'd Ulysses: "One, though blind, ‭ O stranger, groping, may thy stone's fall find, ‭ For not amidst the rout of marks it fell, ‭ But far before all. Of thy worth think well, ‭ And stand in all strifes. No Phæacian here ‭ This bound can either better or come near." ‭ Ulysses joy'd to hear that one man yet ‭ Us'd him benignly, and would truth abet ‭ In those contentions; and then thus smooth ‭ He took his speech down: "Reach me that now, youth, ‭ You shall, and straight I think, have one such more, ‭ And one beyond it too. And now, whose core ‭ Stands sound and great within him, since ye have ‭ Thus put my spleen up, come again and brave ‭ The guest ye tempted, with such gross disgrace, ‭ At wrastling, buffets, whirlbat, speed o' race; ‭ At all, or either, I except at none, ‭ But urge the whole state of you; only one, ‭ I will not challenge in my forced boast, ‭ And that's Laodamas, for he's mine host. [5] ‭ And who will fight, or wrangle, with his friend? ‭ Unwise he is, and base, that will contend ‭ With him that feeds him in a foreign place; ‭ And takes all edge off from his own sought grace. ‭ None else except I here, nor none despise, ‭ But wish to know, and prove his faculties, ‭ That dares appear now. No strife ye can name ‭ Am I unskill'd in; reckon any game ‭ Of all that are, as many as there are ‭ In use with men. For archery I dare ‭ Affirm myself not mean. Of all a troop ‭ I'll make the first foe with mine arrow stoop, ‭ Though with me ne'er so many fellows bend ‭ Their bows at mark'd men, and affect their end. ‭ Only was Philoctetes with his bow ‭ Still my superior, when we Greeks would show ‭ Our archery against our foes of Troy. ‭ But all, that now by bread frail life enjoy, ‭ I far hold my inferiors. Men of old, ‭ None now alive shall witness me so bold, ‭ To vaunt equality with, such men as these, ‭ Œchalián Eurytus, Hercules, ‭ Who with their bows durst with the Gods contend; ‭ And therefore caught Eurytus soon his end, ‭ Nor died at home, in age, a rev'rend man. ‭ But by the great incenséd Delphian ‭ Was shot to death, for daring competence ‭ With him in all an archer's excellence. ‭ A spear I'll hurl as far as any man ‭ Shall shoot a shaft. How at a race I can ‭ Bestir my feet, I only yield to fear, ‭ And doubt to meet with my superior here. ‭ So many seas so too much have misus'd ‭ My limbs for race, and therefore have diffus'd ‭ A dissolution through my lovéd knees." ‭ This said, he still'd all talking properties. ‭ Alcinous only answer'd: "O my guest, ‭ In good part take we what you have been prest ‭ With speech to answer. You would make appear ‭ Your virtues therefore, that will still shine where ‭ Your only look is. Yet must this man give ‭ Your worth ill language; when, he does not live ‭ In sort of mortals (whencesoe'er he springs, ‭ That judgment hath to speak becoming things) ‭ That will deprave your virtues. Note then now ‭ My speech, and what my love presents to you, ‭ That you may tell heroës, when you come ‭ To banquet with your wife and birth at home, ‭ (Mindful of our worth) what deservings Jove ‭ Hath put on our parts likewise, in remove ‭ From sire to son, as an inherent grace ‭ Kind, and perpetual. We must needs give place ‭ To other countrymen, and freely yield ‭ We are not blameless in our fights of field, ‭ Buffets, nor wrastlings; but in speed of feet, ‭ And all the equipage that fits a fleet, ‭ We boast us best; for table ever spread ‭ With neighbour feasts, for garments varied, ‭ For poesy, music, dancing, baths, and beds. ‭ And now, Phæacians, you that bear your heads ‭ And feet with best grace in enamouring dance, ‭ Enflame our guest here, that he may advance ‭ Our worth past all the world's to his home-friends, ‭ As well for the unmatch'd grace that commends. ‭ Your skill in footing of a dance, as theirs ‭ That fly a race best. And so, all affairs, ‭ At which we boast us best, he best may try, ‭ As sea-race, land-race, dance, and poesy. ‭ Some one with instant speed to court retire, ‭ And fetch Demodocus's soundful lyre." ‭ This said the God-grac'd king; and quick resort ‭ Pontonous made for that fair harp to court. ‭ Nine of the lot-choos'd public rulers rose, ‭ That all in those contentions did dispose, ‭ Commanding a most smooth ground, and a wide, ‭ And all the people in fair game aside. ‭ Then with the rich harp came Pontonous, ‭ And in the midst took place Demodocus. ‭ About him then stood forth the choice young men, [6] ‭ That on man's first youth made fresh entry then, ‭ Had art to make their natural motion sweet, ‭ And shook a most divine dance from their feet, ‭ That twinkled star-like, mov'd as swift, and fine, ‭ And beat the air so thin, they made it shine. ‭ Ulysses wonder'd at it, but amaz'd ‭ He stood in mind to hear the dance so phras'd. ‭ For, as they danc'd, Demodocus did sing, ‭ The bright-crown'd Venus' love with Battle's King; ‭ As first they closely mix'd in th' house of fire. ‭ What worlds of gifts won her to his desire, ‭ Who then the night-and-day-bed did defile ‭ Of good king Vulcan. But in little while ‭ The Sun their mixture saw, and came and told. ‭ The bitter news did by his ears take hold ‭ Of Vulcan's heart. Then to his forge he went, ‭ And in his shrewd mind deep stuff did invent. ‭ His mighty anvil in the stock he put, ‭ And forg'd a net that none could loose or cut, ‭ That when it had them it might hold them fast. ‭ Which having finish'd, he made utmost haste ‭ Up to the dear room where his wife he woo'd, ‭ And, madly wrath with Mars, he all bestrow'd ‭ The bed, and bed-posts, all the beam above ‭ That cross'd the chamber; and a circle strove ‭ Of his device to wrap in all the room. ‭ And 'twas as pure, as of a spider's loom ‭ The woof before 'tis wov'n. No man nor God ‭ Could set his eye on it, a sleight so odd ‭ His art show'd in it. All his craft bespent ‭ About the bed, he feign'd as if he went ‭ To well-built Lemnos, his most lovéd town ‭ Of all towns earthly; nor left this unknown ‭ To golden-bridle-using Mars, who kept ‭ No blind watch over him, but, seeing stept ‭ His rival so aside, he hasted home ‭ With fair-wreath'd Venus' love stung, who was come ‭ New from the court of her most mighty Sire. ‭ Mars enter'd, wrung her hand, and the retire ‭ Her husband made to Lemnos told, and said; ‭ "Now, love, is Vulcan gone, let us to bed, ‭ He's for the barbarous Sintians." Well appay'd ‭ Was Venus with it; and afresh assay'd ‭ Their old encounter. Down they went; and straight ‭ About them cling'd the artificial sleight ‭ Of most wise Vulcan; and were so ensnar'd, ‭ That neither they could stir their course prepar'd ‭ In any limb about them, nor arise. ‭ And then they knew, they would no more disguise ‭ Their close conveyance, but lay, forc'd, stone-still. ‭ Back rush'd the both-foot-cook'd, but straight in skill, ‭ From his near scout-hole turn'd, nor ever went ‭ To any Lemnos, but the sure event ‭ Left Phœbus to discover, who told all. ‭ Then home hopp'd Vulcan, full of grief and gall, ‭ Stood in the portal, and cried out so high, ‭ That all the Gods heard; "Father of the sky, ‭ And ev'ry other deathless God," said he, ‭ "Come all, and a ridiculous object see, ‭ And yet not sufferable neither. Come, ‭ And witness how, when still I step from home, ‭ Lame that I am, Jove's daughter doth profess ‭ To do me all the shameful offices, ‭ Indignities, despites, that can be thought; ‭ And loves this all-things-making-come-to-nought, ‭ Since he is fair forsooth, foot-sound, and I ‭ Took in my brain a little, legg'd awry. ‭ And no fault mine, but all my parent's fault, ‭ Who should not get, if mock me, with my halt. ‭ But see how fast they sleep, while I, in moan, ‭ Am only made an idle looker on. ‭ One bed their turn serves, and it must be mine; ‭ I think yet, I have made their self-loves shine. ‭ They shall no more wrong me, and none perceive; ‭ Nor will they sleep together, I believe, ‭ With too hot haste again. Thus both shall lie ‭ In craft, and force, till the extremity ‭ Of all the dow'r I gave her sire (to gain ‭ A doggéd set-fac'd girl, that will not stain ‭ Her face with blushing, though she shame her head) ‭ He pays me back. She's fair, but was no maid." ‭ While this long speech was making, all were come ‭ To Vulcan's wholly-brazen-founded home, ‭ Earth-shaking Neptune, useful Mercury, ‭ And far-shot Phœbus. No She-Deity, ‭ For shame, would show there. All the give-good Gods ‭ Stood in the portal, and past periods ‭ Gave length to laughters, all rejoic'd to see ‭ That which they said, that no impiety ‭ Finds good success at th' end. "And now," said one, ‭ "The slow outgoes the swift. Lame Vulcan, known ‭ To be the slowest of the Gods, outgoes ‭ Mars the most swift. And this is that which grows ‭ To greatest justice: that adult'ry's sport, ‭ Obtain'd by craft, by craft of other sort ‭ (And lame craft too) is plagued, which grieves the more, ‭ That sound limbs turning lame the lame restore." [7] ‭ This speech amongst themselves they entertain'd, ‭ When Phœbus thus ask'd Hermes: "Thus enchain'd ‭ Wouldst thou be, Hermes, to be thus disclos'd? ‭ Though with thee golden Venus were repos'd?" ‭ He soon gave that an answer: "O," said he, ‭ "Thou king of archers, would 'twere thus with me! ‭ Though thrice so much shame; nay, though infinite ‭ Were pour'd about me, and that ev'ry light, ‭ In great heav'n shining, witness'd all my harms, ‭ So golden Venus slumber'd in mine arms." ‭ The Gods again laugh'd; even the Watery State ‭ Wrung out a laughter, but propitiate ‭ Was still for Mars, and pray'd the God of Fire ‭ He would dissolve him, off'ring the desire ‭ He made to Jove to pay himself, and said, ‭ All due debts should be by the Gods repaid. ‭ "Pay me, no words," said he, "where deeds lend pain, ‭ Wretched the words are giv'n for wretched men. ‭ How shall I bind you in th' Immortals' sight, ‭ If Mars be once loos'd, nor will pay his right?" [8] ‭ "Vulcan," said he, "if Mars should fly, nor see ‭ Thy right repaid, it should be paid by me." ‭ "Your word, so giv'n, I must accept," said he. ‭ Which said, he loos'd them. Mars then rush'd from sky, ‭ And stoop'd cold Thrace. The laughing Deity ‭ For Cyprus was, and took her Paphian state, ‭ Where she a grove, ne'er cut, had consecrate, ‭ All with Arabian odours fum'd, and hath ‭ An altar there, at which the Graces bathe, ‭ And with immortal balms besmooth, her skin, ‭ Fit for the bliss Immortals solace in; ‭ Deck'd her in to-be-studiéd attire, ‭ And apt to set beholders' hearts on fire. ‭ This sung the sacred muse, whose notes and words ‭ The dancers' feet kept as his hands his chords. ‭ Ulysses much was pleas'd, and all the crew. ‭ This would the king have varied with a new ‭ And pleasing measure, and performéd by ‭ Two, with whom none would strive in dancery; ‭ And those his sons were, that must therefore dance ‭ Alone, and only to the harp advance, ‭ Without the words. And this sweet couple was ‭ Young Halius, and divine Laodamas; ‭ Who danc'd a ball-dance. Then the rich-wrought ball, ‭ That Polybus had made, of purple all, ‭ They took to hand. One threw it to the sky, ‭ And then danc'd back; the other, capering high, ‭ Would surely catch it ere his foot touch'd ground, ‭ And up again advanc'd it, and so found ‭ The other cause of dance; and then did he ‭ Dance lofty tricks, till next it came to be ‭ His turn to catch, and serve the other still. ‭ When they had kept it up to either's will, ‭ They then danc'd ground tricks, oft mix'd hand in hand, ‭ And did so gracefully their change command, ‭ That all the other youth that stood at pause, ‭ With deaf'ning shouts, gave them the great applause. ‭ Then said Ulysses: "O, past all men here ‭ Clear, not in pow'r, but in desert as clear, ‭ You said your dancers did the world surpass, ‭ And they perform it clear, and to amaze." ‭ This won Alcinous' heart, and equal prize ‭ He gave Ulysses, saying: "Matchless wise, ‭ Princes and rulers, I perceive our guest, ‭ And therefore let our hospitable best ‭ In fitting gifts be giv'n him: Twelve chief kings ‭ There are that order all the glorious things ‭ Of this our kingdom; and, the thirteenth, I ‭ Exist, as crown to all. Let instantly ‭ Be thirteen garments giv'n him, and of gold ‭ Precious, and fine, a talent. While we hold ‭ This our assembly, be all fetch'd, and giv'n, ‭ That to our feast prepar'd, as to his heav'n, ‭ Our guest may enter. And, that nothing be ‭ Left unperform'd that fits his dignity, ‭ Euryalus shall here conciliate ‭ Himself with words and gifts, since past our rate ‭ He gave bad language." This did all commend ‭ And give in charge; and ev'ry king did send ‭ His herald for his gift. Euryalus, ‭ Answ'ring for his part, said: "Alcinous! ‭ Our chief of all, since you command, I will ‭ To this our guest by all means reconcile, ‭ And give him this entirely-metall'd sword, ‭ The handle massy silver, and the board, ‭ That gives it cover, all of ivory, ‭ New, and in all kinds worth his quality." ‭ This put he straight into his hand, and said: ‭ "Frolic, O guest and father; if words fled ‭ Have been offensive, let swift whirlwinds take ‭ And ravish them from thought. May all Gods make ‭ Thy wife's sight good to thee, in quick retreat ‭ To all thy friends, and best-lov'd breeding seat, ‭ Their long miss quitting with the greater joy; ‭ In whose sweet vanish all thy worst annoy." ‭ "And frolic thou to all height, friend," said he, ‭ "Which heav'n confirm with wish'd felicity; ‭ Nor ever give again desire to thee ‭ Of this sword's use, which with affects so free, ‭ In my reclaim, thou hast bestow'd on me." ‭ This said, athwart his shoulders he put on ‭ The right fair sword; and then did set the sun. ‭ When all the gifts were brought, which back again ‭ (With king Alcinous in all the train) ‭ Were by the honour'd heralds borne to court; ‭ Which his fair sons took, and from the resort ‭ Laid by their rev'rend mother. Each his throne ‭ Of all the peers (which yet were overshone ‭ In king Alcinous' command) ascended; ‭ Whom he to pass as much in gifts contended, ‭ And to his queen said: "Wife! See brought me here ‭ The fairest cabinet I have, and there ‭ Impose a well-cleans'd in, and utter, weed. ‭ A caldron heat with water, that with speed ‭ Our guest well-bath'd, and all his gifts made sure, ‭ It may a joyful appetite procure ‭ To his succeeding feast, and make him hear ‭ The poet's hymn with the securer ear. ‭ To all which I will add my bowl of gold, ‭ In all frame curious, to make him hold ‭ My memory always dear, and sacrifice ‭ With it at home to all the Deities." ‭ Then Arete her maids charg'd to set on ‭ A well-siz'd caldron quickly. Which was done, ‭ Clear water pour'd in, flame made so entire, ‭ It gilt the brass, and made the water fire. ‭ In mean space, from her chamber brought the queen ‭ A wealthy cabinet, where, pure and clean, ‭ She put the garments, and the gold bestow'd ‭ By that free state, and then the other vow'd ‭ By her Alcinous, and said: "Now, guest, ‭ Make close and fast your gifts, lest, when you rest ‭ Aship-board sweetly, in your way you meet ‭ Some loss, that less may make your next sleep sweet." ‭ This when Ulysses heard, all sure he made ‭ Enclos'd and bound safe; for the saving trade ‭ The rev'rend-for-her-wisdom, Circe, had ‭ In foreyears taught him. Then the handmaid bad ‭ His worth to bathing; which rejoic'd his heart, ‭ For, since he did with his Calypso part, ‭ He had no hot baths; none had favour'd him, ‭ Nor been so tender of his kingly limb. ‭ But all the time he spent in her abode, ‭ He liv'd respected as he were a God. ‭ Cleans'd then and balm'd, fair shirt and robe put on, ‭ Fresh come from bath, and to the feasters gone, ‭ Nausicaa, that from the Gods' hands took ‭ The sov'reign beauty of her blessed look, ‭ Stood by a well-carv'd column of the room, ‭ And through her eye her heart was overcome ‭ With admiration of the port imprest ‭ In his aspéct, and said: "God save you, guest! ‭ Be cheerful, as in all the future state ‭ Your home will show you in your better fate. ‭ But yet, ev'n then, let this remember'd be, ‭ Your life's price I lent, and you owe it me." ‭ The varied-in-all-counsels gave reply: ‭ "Nausicaa! Flow'r of all this empery! ‭ So Juno's husband, that the strife for noise ‭ Makes in the clouds, bless me with strife of joys, ‭ In the desir'd day that my house shall show, ‭ As I, as I to a Goddess there shall vow, ‭ To thy fair hand that did my being give, ‭ Which I'll acknowledge ev'ry hour I live." ‭ This said, Alcinous plac'd him by his side. ‭ Then took they feast, and did in parts divide ‭ The sev'ral dishes, fill'd out wine, and then ‭ The striv'd-for-for-his-worth of worthy men, [9] ‭ And rev'renc'd-of-the-state, Demodocus ‭ Was brought in by the good Pontonous. ‭ In midst of all the guests they gave him place, ‭ Against a lofty pillar, when this grace ‭ The grac'd-with-wisdom did him: From the chine, ‭ That stood before him, of a white-tooth'd swine, ‭ Being far the daintiest joint, mix'd through with fat, ‭ He carv'd to him, and sent it where he sat ‭ By his old friend the herald, willing thus: ‭ "Herald, reach this to grave Demodocus, ‭ Say, I salute him, and his worth embrace. ‭ Poets deserve, past all the human race, ‭ Rev'rend respect and honour, since the queen ‭ Of knowledge, and the supreme worth in men, ‭ The Muse, informs them, and loves all their race." ‭ This reach'd the herald to him, who the grace ‭ Receiv'd encourag'd; which, when feast was spent, ‭ Ulysses amplified to this ascent: ‭ "Demodocus! I must prefer you far, ‭ Past all your sort, if, or the Muse of war, ‭ Jove's daughter, prompts you, that the Greeks respects, ‭ Or if the Sun, that those of Troy affects. ‭ For I have heard you, since my coming, sing ‭ The fate of Greece to an admiréd string. ‭ How much our suff'rance was, how much we wrought, ‭ How much the actions rose-to when we fought. ‭ So lively forming, as you had been there, ‭ Or to some free relater lent your ear. ‭ Forth then, and sing the wooden horse's frame, ‭ Built by Epëus, by the martial Dame ‭ Taught the whole fabric; which, by force of sleight, ‭ Ulysses brought into the city's height, ‭ When he had stuff'd it with as many men ‭ As levell'd lofty Ilion with the plain. ‭ With all which if you can as well enchant, ‭ As with expression quick and elegant ‭ You sung the rest, I will pronounce you clear ‭ Inspir'd by God, past all that ever were." ‭ This said, ev'n stirr'd by God up, he began, ‭ And to his song fell, past the forms of man, ‭ Beginning where the Greeks aship-board went, ‭ And ev'ry chief had set on fire his tent, ‭ When th' other kings, in great Ulysses' guide, ‭ In Troy's vast market place the horse did hide, ‭ From whence the Trojans up to Ilion drew ‭ The dreadful engine. Where sat all arew ‭ Their kings about it; many counsels giv'n ‭ How to dispose it. In three ways were driv'n ‭ Their whole distractions. First, if they should feel ‭ The hollow wood's heart, search'd with piercing steel; ‭ Or from the battlements drawn higher yet ‭ Deject it headlong; or that counterfeit ‭ So vast and novel set on sacred fire, ‭ Vow'd to appease each anger'd Godhead's ire. ‭ On which opinion, they, thereafter, saw, ‭ They then should have resolv'd; th' unalter'd law ‭ Of fate presaging, that Troy then should end, ‭ When th' hostile horse she should receive to friend, ‭ For therein should the Grecian kings lie hid, ‭ To bring the fate and death they after did. ‭ He sung, besides, the Greeks' eruptión ‭ From those their hollow crafts, and horse foregone; ‭ And how they made depopulation tread ‭ Beneath her feet so high a city's head. ‭ In which affair, he sung in other place, ‭ That of that ambush some man else did race ‭ The Ilion tow'rs than Laertiades; ‭ But here he sung, that he alone did seize, [10] ‭ With Menelaus, the ascended roof ‭ Of prince Deiphobus, and Mars-like proof ‭ Made of his valour, a most dreadful fight ‭ Daring against him; and there vanquish'd quite, ‭ In little time, by great Minerva's aid, ‭ All Ilion's remnant, and Troy level laid. ‭ This the divine expressor did so give ‭ Both act and passion, that he made it live, ‭ And to Ulysses' facts did breathe a fire ‭ So deadly quick'ning, that it did inspire [11] ‭ Old death with life, and render'd life so sweet, ‭ And passionate, that all there felt it fleet; ‭ Which made him pity his own cruelty, ‭ And put into that ruth so pure an eye ‭ Of human frailty, that to see a man ‭ Could so revive from death, yet no way can ‭ Defend from death, his own quick pow'rs it made ‭ Feel there death's horrors, and he felt life fade, ‭ In tears his feeling brain swet; for, in things [12] ‭ That move past utt'rance, tears ope all their springs. ‭ Nor are there in the pow'rs that all life bears ‭ More true interpreters of all than tears. ‭ And as a lady mourns her sole-lov'd lord, ‭ That fall'n before his city by the sword, ‭ Fighting to rescue from a cruel fate ‭ His town and children, and in dead estate ‭ Yet panting seeing him, wraps him in her arms, ‭ Weeps, shrieks, and pours her health into his arms, ‭ Lies on him, striving to become his shield ‭ From foes that still assail him, spears impell'd ‭ Through back and shoulders, by whose points embrued, ‭ They raise and lead him into servitude, ‭ Labour, and languor; for all which the dame ‭ Eats down her cheeks with tears, and feeds life's flame ‭ With miserable suff'rance; so this king ‭ Of tear-swet anguish op'd a boundless spring; ‭ Nor yet was seen to any one man there ‭ But king Alcinous, who sat so near ‭ He could not 'scape him, sighs, so chok'd, so brake ‭ From all his tempers; which the king did take ‭ Both note and grave respect of, and thus spake: ‭ "Hear me, Phæacian councillors and peers, ‭ And cease Demodocus; perhaps all ears ‭ Are not delighted with his song, for, ever ‭ Since the divine Muse sung, 'our guest hath never ‭ Contain'd from secret mournings. It may fall, ‭ That something sung he hath been grieved with all, ‭ As touching his particular. Forbear, ‭ That feast may jointly comfort all hearts here, ‭ And we may cheer our guest up; 'tis our best ‭ In all due honour. For our rev'rend guest ‭ Is all our celebration, gifts, and all, ‭ His love hath added to our festival. ‭ A guest, and suppliant too, we should esteem ‭ Dear as our brother, one that doth but dream ‭ He hath a soul, or touch but at a mind ‭ Deathless and manly, should stand so inclin'd. ‭ Nor cloak you longer with your curious wit, ‭ Lov'd guest, what ever we shall ask of it. ‭ It now stands on your honest state to tell, ‭ And therefore give your name, nor more conceal ‭ What of your parents, and the town that bears ‭ Name of your native, or of foreigners ‭ That near us border, you are call'd in fame. ‭ There's no man living walks without a name, ‭ Noble nor base, but had one from his birth ‭ Impos'd as fit as to be borne. What earth, ‭ People, and city, own you, give to know. ‭ Tell but our ships all, that your way must show. ‭ For our ships know th' expressed minds of men, ‭ And will so most intentively retain ‭ Their scopes appointed, that they never err, ‭ And yet use never any man to steer, ‭ Nor any rudders have, as others need. ‭ They know men's thoughts, and whither tends their speed, ‭ And there will set them; for you cannot name [13] ‭ A city to them, nor fat soil, that Fame ‭ Hath any notice giv'n, but well they know, ‭ And they will fly to them, though they ebb and flow ‭ In blackest clouds and nights; and never bear ‭ Of any wrack or rock the slend'rest fear. ‭ But this I heard my sire Nausithous say. ‭ Long since, that Neptune, seeing us convey ‭ So safely passengers of all degrees, ‭ Was angry with us; and upon our seas ‭ A well-built ship we had, near harbour come ‭ From safe deduction of some stranger home, ‭ Made in his flitting billows stick stone still; ‭ And dimm'd our city, like a mighty hill ‭ With shade cast round about it. This report, ‭ The old king made; [14] in which miraculous sort, ‭ If God had done such things, or left undone, ‭ At his good pleasure be it. But now, on, ‭ And truth relate us, both whence you err'd, ‭ And to what clime of men would be transferr'd, ‭ With all their fair towns, be they as they are, ‭ If rude, unjust, and all irregular, ‭ Or hospitable, bearing minds that please ‭ The mighty Deity. Which one of these ‭ You would be set at, say, and you are there. ‭ And therefore what afflicts you? Why, to hear ‭ The fate of Greece and Ilion, mourn you so? ‭ The Gods have done it; as to all they do ‭ Destine destruction, that from thence may rise ‭ A poem to instruct posterities. ‭ Fell any kinsman before Ilion? ‭ Some worthy sire-in-law, or like-near son, ‭ Whom next our own blood and self-race we love? ‭ Or any friend perhaps, in whom did move ‭ A knowing soul, and no unpleasing thing? ‭ Since such a good one is no underling ‭ To any brother; for, what fits true friends, ‭ True wisdom is, that blood and birth transcends. ‭ FINIS LIBRI OCTAVI HOM. ODYSS. ‭[1] The continued piety of Ulysses through all places, times, and ‭occasions. ‭[2] Since the Phæacians were not only dwellers by sea, but studious ‭also of sea qualities, their names seem to usurp their faculties ‭therein. All consisting of sea-faring signification, except ‭Laodamas, As Acroneus, _summa seu extrema navis pars._ ‭Ocyalus, _velox in mari._ Elatreus, or _᾽Ελατὴρ, ἐλατη̑ρος, ‭Remex, etc._ ‭[3] The word is _πομπή,_ signifying _deductio, quâ trausvehendum ‭curamus eum qui nobiscum aliquando est versatus._ ‭[4] _᾽Ατάσθαλος damnorum magnorum auctor._ ‭[5] He names Laodamas only for all the other brothers; since in his ‭exception, the others' envies were curbed: for brothers either are ‭or should be of one acceptation in all fit things, And Laodamas, he ‭calls his host, being eldest son to Alcinous: the heir being ever the ‭young master; nor might he conveniently prefer Alcinous in his ‭exception, since he stood not in competition at these contentions. ‭[6] _Μαρμαρυγὰς ποδω̑ν. Μαρμαρυγὴ_ signifies _splendor ‭vibrans_; a twincked splendor; _μαρμαρύσσειν, vibrare veluti ‭radios solares._ ‭[7] Intending the sound of foot, when they outgo the soundest. ‭[8] This is _τὸ τὰ μικρὰ μεγάλως, etc. Parva magnè dicere;_ grave ‭sentence out of lightest vapour. ‭[9] _'Ερίηρον ἀοιδὸν, Poetam cujus hominibus digna est societas._ ‭[10] As by the divine fury directly inspired so, for Ulysses' glory. ‭[11] In that the slaughters he made were expressed so lively. ‭[12] _Τήκετο ᾽Οδυσσεύς. Τήκω,_ metaph. signifying _consumo, ‭tabesco._ ‭[13] This _τερατολογία_ or _affirmation of miracles,_ how impossible ‭soever in these times assured, yet in those ages they were neither ‭absurd nor strange. Those inanimate things having (it seemed) ‭certain Genii, in whose powers they supposed their ships' faculties. ‭As others have affirmed oaks to have sense of hearing; and so the ‭ship of Argos was said to have a mast made of Dodonean oak, that ‭was vocal, and could speak. ‭[14] Intending his father Nausithous. ‭ THE NINTH BOOK OF HOMER'S ODYSSEYS ‭ THE ARGUMENT ‭ Ulysses here is first made known; ‭ Who tells the stern contention ‭ His pow'rs did 'gainst the Cicons try; ‭ And thence to the Lotophagi ‭ Extends his conquest; and from them ‭ Assays the Cyclop Polypheme, ‭ And, by the crafts his wits apply, ‭ He puts him out his only eye. ‭ ANOTHER ARGUMENT ‭ _᾿Ιω̑τα._ ‭ The strangely fed ‭ Lotophagi. ‭ The Cicons fled. ‭ The Cyclop's eye. ‭ Ulysses thus resolv'd the king's demands: ‭ "Alcinous, in whom this empire stands, ‭ You should not of so natural right disherit ‭ Your princely feast, as take from it the spirit. ‭ To hear a poet, that in accent brings ‭ The Gods' breasts down, and breathes them as he sings, ‭ Is sweet, and sacred; nor can I conceive, ‭ In any common-weal, what more doth give ‭ Note of the just and blessed empery, ‭ Than to see comfort universally ‭ Cheer up the people, when in ev'ry roof ‭ She gives observers a most human proof ‭ Of men's contents. To see a neighbour's feast ‭ Adorn it through; and thereat hear the breast ‭ Of the divine Muse; men in order set; ‭ A wine-page waiting; tables crown'd with meat, ‭ Set close to guests that are to use it skill'd; ‭ The cup-boards furnish'd, and the cups still fill'd; ‭ This shows, to my mind, most humanely fair. ‭ Nor should you, for me, still the heav'nly air, ‭ That stirr'd my soul so; for I love such tears ‭ As fall from fit notes, beaten through mine ears ‭ With repetitions of what heav'n hath done, ‭ And break from hearty apprehensión ‭ Of God and goodness, though they show my ill. ‭ And therefore doth my mind excite me still, ‭ To tell my bleeding moan; but much more now, ‭ To serve your pleasure, that to over-flow ‭ My tears with such cause may by sighs be driv'n, ‭ Though ne'er so much plagued I may seem by heav'n. ‭ And now my name; which way shall lead to all ‭ My mis'ries after, that their sounds may fall ‭ Through your ears also, and show (having fled ‭ So much affliction) first, who rests his head ‭ In your embraces, when, so far from home, ‭ I knew not where t' obtain it resting room. ‭ I am Ulysses Laertiades, ‭ The fear of all the world for policies, ‭ For which my facts as high as heav'n resound. ‭ I dwell in Ithaca, earth's most renown'd, ‭ All over-shadow'd with the shake-leaf hill, [1] ‭ Tree-fam'd Neritus; whose near confines fill ‭ Islands a number, well-inhabited, ‭ That under my observance taste their bread; ‭ Dulichius, Samos, and the full-of-food [2] ‭ Zacynthus, likewise grac'd with store of wood. ‭ But Ithaca, though in the seas it lie, ‭ Yet lies she so aloft she casts her eye ‭ Quite over all the neighbour continent; ‭ Far northward situate, and, being lent ‭ But little favour of the morn and sun, ‭ With barren rocks and cliffs is over-run; ‭ And yet of hardy youths a nurse of name; ‭ Nor could I see a soil, where'er I came, ‭ More sweet and wishful. Yet, from hence was I ‭ Withheld with horror by the Deity, ‭ Divine Calypso, in her cavy house, ‭ Enflam'd to make me her sole lord and spouse. ‭ Circe Ææa too, that knowing dame, ‭ Whose veins the like affections did enflame, ‭ Detain'd me likewise. But to neither's love ‭ Could I be tempted; which doth well approve, ‭ Nothing so sweet is as our country's earth, [3] ‭ And joy of those from whom we claim our birth. ‭ Though roofs far richer we far off possess, ‭ Yet, from our native, all our more is less. ‭ To which as I contended, I will tell ‭ The much-distress-conferring facts that fell ‭ By Jove's divine prevention, since I set ‭ From ruin'd Troy my first foot in retreat. ‭ From Ilion ill winds cast me on the coast ‭ The Cicons hold, where I employ'd mine host ‭ For Ismarus, a city built just by ‭ My place of landing; of which victory ‭ Made me expugner. I depeopled it, ‭ Slew all the men, and did their wives remit, ‭ With much spoil taken; which we did divide, ‭ That none might need his part. I then applied ‭ All speed for flight; but my command therein, ‭ Fools that they were, could no observance win ‭ Of many soldiers, who, with spoil fed high, ‭ Would yet fill higher, and excessively ‭ Fell to their wine, gave slaughter on the shore ‭ Clov'n-footed beeves and sheep in mighty store. ‭ In mean space, Cicons did to Cicons cry, ‭ When, of their nearest dwellers, instantly ‭ Many and better soldiers made strong head, ‭ That held the continent, and managéd ‭ Their horse with high skill, on which they would fight, ‭ When fittest cause serv'd, and again alight, ‭ With soon seen vantage, and on foot contend. ‭ Their concourse swift was, and had never end; ‭ As thick and sudden 'twas, as flow'rs and leaves ‭ Dark spring discovers, when she light receives. [4] ‭ And then began the bitter Fate of Jove ‭ To alter us unhappy, which ev'n strove ‭ To give us suff'rance. At our fleet we made ‭ Enforcéd stand; and there did they invade ‭ Our thrust-up forces; darts encounter'd darts, ‭ With blows on both sides; either making parts ‭ Good upon either, while the morning shone, ‭ And sacred day her bright increase held on, ‭ Though much out-match'd in number; but as soon ‭ As Phœbus westward fell, the Cicons won ‭ Much hand of us; six proved soldiers fell, ‭ Of ev'ry ship, the rest they did compel! ‭ To seek of Flight escape from Death and Fate. ‭ Thence sad in heart we sail'd; and yet our state ‭ Was something cheer'd, that (being o'er-match'd so much ‭ In violent number) our retreat was such ‭ As sav'd so many. Our dear loss the less, ‭ That they surviv'd, so like for like success. ‭ Yet left we not the coast, before we call'd ‭ Home to our country-earth the souls exhal'd ‭ Of all the friends the Cicons overcame. ‭ Thrice call'd we on them by their sev'ral name, [5] ‭ And then took leave. Then from the angry North ‭ Cloud-gath'ring Jove a dreadful storm call'd forth ‭ Against our navy, cover'd shore and all ‭ With gloomy vapours. Night did headlong fall ‭ From frowning heav'n. And then hurl'd here and there ‭ Was all our navy; the rude winds did tear ‭ In three, in four parts, all their sails; and down ‭ Driv'n under hatches were we, prest to drown. ‭ Up rush'd we yet again, and with tough hand ‭ (Two days, two nights, entoil'd) we gat near land, ‭ Labours and sorrows eating up our minds. ‭ The third clear day yet, to more friendly winds ‭ We masts advanc'd, we white sails spread, and sate. ‭ Forewinds and guides again did iterate ‭ Our ease and home-hopes; which we clear had reach'd, ‭ Had not, by chance, a sudden north-wind fetch'd, ‭ With an extreme sea, quite about again ‭ Our whole endeavours, and our course constrain ‭ To giddy round, and with our bow'd sails greet ‭ Dreadful Maleia, calling back our fleet ‭ As far forth as Cythera. Nine days more ‭ Adverse winds toss'd me; and the tenth, the shore, ‭ Where dwelt the blossom-fed Lotophagi, ‭ I fetch'd, fresh water took in, instantly ‭ Fell to our food aship-board, and then sent ‭ Two of my choice men to the continent ‭ (Adding a third, a herald) to discover ‭ What sort of people were the rulers over ‭ The land next to us. Where, the first they met, ‭ Were the Lotophagi, that made them eat ‭ Their country-diet, and no ill intent ‭ Hid in their hearts to them; and yet th' event ‭ To ill converted it, for having eat ‭ Their dainty viands, they did quite forget ‭ (As all men else that did but taste their feast) ‭ Both countrymen and country, nor addrest ‭ Any return t' inform what sort of men ‭ Made fix'd abode there, but would needs maintain ‭ Abode themselves there, and eat that food ever. ‭ I made out after, and was feign to sever ‭ Th' enchanted knot by forcing their retreat; ‭ That striv'd, and wept, and would not leave their meat ‭ For heav'n itself. But, dragging them to fleet, ‭ I wrapt in sure bands both their hands and feet, ‭ And cast them under hatches, and away ‭ Commanded all the rest without least stay, ‭ Lest they should taste the lote too, and forget ‭ With such strange raptures their despis'd retreat. ‭ All then aboard, we beat the sea with oars, ‭ And still with sad hearts sail'd by out-way shores, ‭ Till th' out-law'd Cyclops' land we fetch'd; a race ‭ Of proud-liv'd loiterers, that never sow, ‭ Nor put a plant in earth, nor use a plow, ‭ But trust in God for all things; and their earth, ‭ Unsown, unplow'd, gives ev'ry offspring birth ‭ That other lands have; wheat, and barley, vines ‭ That bear in goodly grapes delicious wines; ‭ And Jove sends show'rs for all. No councils there, ‭ Nor councillors, nor laws; but all men bear ‭ Their heads aloft on mountains, and those steep, ‭ And on their tops too; and their houses keep ‭ In vaulty caves, their households govern'd all ‭ By each man's law, impos'd in several, ‭ Nor wife, nor child awed, but as he thinks good, ‭ None for another caring. But there stood ‭ Another little isle, well stor'd with wood, ‭ Betwixt this and the entry; neither nigh ‭ The Cyclops' isle, nor yet far off doth lie, ‭ Men's want it suffer'd, but the men's supplies ‭ The goats made with their inarticulate cries. ‭ Goats beyond number this small island breeds, ‭ So tame, that no access disturbs their feeds, ‭ No hunters, that the tops of mountains scale, ‭ And rub through woods with toil, seek them at all. ‭ Nor is the soil with flocks fed down, not plow'd, ‭ Nor ever in it any seed was sow'd. ‭ Nor place the neighbour Cyclops their delights ‭ In brave vermilion-prow-deck'd ships; nor wrights ‭ Useful, and skilful in such works as need ‭ Perfection to those traffics that exceed ‭ Their natural confines, to fly out and see ‭ Cities of men, and take in mutually ‭ The prease of others; to themselves they live, ‭ And to their island that enough would give ‭ A good inhabitant; and time of year ‭ Observe to all things art could order there. ‭ There, close upon the sea, sweet meadows spring; ‭ That yet of fresh streams want no watering ‭ To their soft burthens, but of special yield. ‭ Your vines would be there; and your common field ‭ But gentle work make for your plow, yet bear ‭ A lofty harvest when you came to shear; ‭ For passing fat the soil is. In it lies ‭ A harbour so oppórtune, that no ties, ‭ Halsers, or gables need, nor anchors cast. ‭ Whom storms put in there are with stay embrac'd, [6] ‭ Or to their full wills safe, or winds aspire ‭ To pilots' uses their more quick desire. ‭ At entry of the haven, a silver ford ‭ Is from a rock-impressing fountain pour'd, ‭ All set with sable poplars. And this port ‭ Were we arriv'd at, by the sweet resort ‭ Of some God guiding us, for 'twas a night ‭ So ghastly dark all port was past our sight, ‭ Clouds hid our ships, and would not let the moon ‭ Afford a beam to us, the whole isle won ‭ By not an eye of ours. None thought the blore, ‭ That then was up, shov'd waves' against the shore, ‭ That then to an unmeasur'd height put on; ‭ We still at sea esteem'd us, till alone ‭ Our fleet put in itself. And then were strook ‭ Our gather'd sails; our rest ashore we took, ‭ And day expected. When the morn gave fire, ‭ We rose, and walk'd, and did the isle admire; ‭ The Nymphs, Jove's daughters, putting up a herd ‭ Of mountain goats to us, to render cheer'd ‭ My fellow soldiers. To our fleet we flew, ‭ Our crooked bows took, long-pil'd darts, and drew ‭ Ourselves in three parts out; when, by the grace ‭ That God vouchsaf'd, we made a gainful chace. ‭ Twelve ships we had, and ev'ry ship had nine ‭ Fat goats allotted [it], ten only mine. ‭ Thus all that day, ev'n till the sun was set, ‭ We sat and feasted, pleasant wine and meat ‭ Plenteously taking; for we had not spent ‭ Our ruddy wine aship-board, supplement ‭ Of large sort each man to his vessel drew, ‭ When we the sacred city overthrew ‭ That held the Cicons. Now then saw we near ‭ The Cyclops' late-prais'd island, and might hear ‭ The murmur of their sheep and goats, and see ‭ Their smokes ascend. The sun then set, and we, ‭ When night succeeded, took our rest ashore. ‭ And when the world the morning's favour wore, ‭ I call'd my friends to council, charging them ‭ To make stay there, while I took ship and stream, ‭ With some associates, and explor'd what men ‭ The neighbour isle held; if of rude disdain, ‭ Churlish and tyrannous, or minds bewray'd ‭ Pious and hospitable. Thus much said, ‭ I boarded, and commanded to ascend ‭ My friends and soldiers, to put off, and lend ‭ Way to our ship. They boarded, sat, and beat ‭ The old sea forth, till we might see the seat ‭ The greatest Cyclop held for his abode, ‭ Which was a deep cave, near the common road ‭ Of ships that touch'd there, thick with laurels spread, ‭ Where many sheep and goats lay shadowéd; ‭ And, near to this, a hall of torn-up stone, ‭ High built with pines, that heav'n and earth attone, ‭ And lofty-fronted oaks; in which kept house ‭ A man in shape immane, and monsterous, ‭ Fed all his flocks alone, nor would afford ‭ Commerce with men, but had a wit abhorr'd, ‭ His mind his body answ'ring. Nor was he ‭ Like any man that food could possibly ‭ Enhance so hugely, but, beheld alone, ‭ Show'd like a steep hill's top, all overgrown ‭ With trees and brambles; little thought had I ‭ Of such vast objects. When, arriv'd so nigh, ‭ Some of my lov'd friends I made stay aboard, ‭ To guard my ship; and twelve with me I shor'd, ‭ The choice of all. I took besides along ‭ A goat-skin flagon of wine, black and strong, ‭ That Maro did present, Evantheus' son, ‭ And priest to Phœbus, who had mansión ‭ In Thracian Ismarus (the town I took). ‭ He gave it me, since I (with rev'rence strook ‭ Of his grave place, his wife and children's good) ‭ Freed all of violence. Amidst a wood, ‭ Sacred to Phœbus, stood his house; from whence ‭ He fetch'd me gifts of varied excellence; ‭ Sev'n talents of fine gold; a bowl all fram'd ‭ Of massy silver; but his gift most fam'd ‭ Was twelve great vessels, fill'd with such rich wine ‭ As was incorruptible and divine. ‭ He kept it as his jewel, which none knew ‭ But he himself, his wife, and he that drew. ‭ It was so strong that never any fill'd ‭ A cup, where that was but by drops instill'd, ‭ And drunk it off, but 'twas before allay'd ‭ With twenty parts in water; yet so sway'd ‭ The spirit of that little, that the whole ‭ A sacred odour breath'd about the bowl. ‭ Had you the odour smelt and scent it cast, ‭ It would have vex'd you to forbear the taste. ‭ But then, the taste gain'd too, the spirit it wrought ‭ To dare things high set-up-an-end my thought. ‭ Of this a huge great flagon full I bore, ‭ And, in a good large knapsack, victuals store; ‭ And long'd to see this heap of fortitude, ‭ That so illit'rate was and upland rude ‭ That laws divine nor human he had learn'd. ‭ With speed we reach'd the cavern; nor discern'd ‭ His presence there, his flocks he fed at field. ‭ Ent'ring his den, each thing beheld did yield ‭ Our admiration; shelves with cheeses heap'd; ‭ Sheds stuff'd with lambs and goats, distinctly kept, ‭ Distinct the biggest, the more mean distinct, ‭ Distinct the youngest. And in their precinct, ‭ Proper and placeful, stood the troughs and pails, ‭ In which he milk'd; and what was giv'n at meals, ‭ Set up a creaming; in the ev'ning still ‭ All scouring bright as dew upon the hill. ‭ Then were my fellows instant to convey ‭ "Kids, cheeses, lambs, aship-board, and away ‭ Sail the salt billow. I thought best not so, ‭ But better otherwise; and first would know, ‭ What guest-gifts he would spare me. Little knew ‭ My friends on whom they would have prey'd. His view ‭ Prov'd after, that his inwards were too rough ‭ For such bold usage. We were bold enough ‭ In what I suffer'd; which was there to stay, ‭ Make fire and feed there, though bear none away. ‭ There sat we, till we saw him feeding come, ‭ And on his neck a burthen lugging home, ‭ Most highly huge, of sere-wood, which the pile ‭ That fed his fire supplied all supper-while. ‭ Down by his den he threw it, and up rose ‭ A tumult with the fall. Afraid, we close ‭ Withdrew ourselves, while he into a cave ‭ Of huge receipt his high-fed cattle drave, ‭ All that he milk'd; the males he left without ‭ His lofty roofs, that all bestrow'd about ‭ With rams and buck-goats were. And then a rock ‭ He lift aloft, that damm'd up to his flock ‭ The door they enter'd; 'twas so hard to wield, ‭ That two-and-twenty waggons, all four-wheel'd, ‭ (Could they be loaded, and have teams that were ‭ Proportion'd to them) could not stir it there. ‭ Thus making sure, he kneel'd and milk'd his ewes, ‭ And braying goats, with all a milker's dues; ‭ Then let in all their young. Then quick did dress ‭ His half milk up for cheese, and in a press ‭ Of wicker press'd it; put in bowls the rest, ‭ To drink and eat, and serve his supping feast. ‭ All works dispatch'd thus, he began his fire; ‭ Which blown, he saw us, and did thus inquire: ‭ ῾Ho! guests! What are ye? Whence sail ye these seas? ‭ Traffic, or rove ye, and like thieves oppress ‭ Poor strange adventurers, exposing so ‭ Your souls to danger, and your lives to woe?' ‭ This utter'd he, when fear from our hearts took ‭ The very life, to be so thunder-strook ‭ With such a voice, and such a monster see; ‭ But thus I answer'd: 'Erring Grecians, we ‭ From Troy were turning homewards, but by force ‭ Of adverse winds, in far diverted course, ‭ Such unknown ways took, and on rude seas toss'd, ‭ As Jove decreed, are cast upon this coast, ‭ Of Agamemnon, famous Atreus' son, ‭ We boast ourselves the soldiers; who hath won [7] ‭ Renown that reacheth heav'n, to overthrow ‭ So great a city, and to ruin so ‭ So many nations. Yet at thy knees lie ‭ Our prostrate bosoms, forc'd with pray'rs to try ‭ If any hospitable right, or boon ‭ Of other nature, such as have been won ‭ By laws of other houses, thou wilt give. ‭ Rev'rence the Gods, thou great'st of all that live. ‭ We suppliants are; and hospitable Jove ‭ Pours wreak on all whom pray'rs want pow'r to move, ‭ And with their plagues together will provide ‭ That humble guests shall have their wants supplied.' ‭ He cruelly answer'd: 'O thou fool,' said he, ‭ To come so far, and to importune me ‭ With any God's fear, or observéd love! ‭ We Cyclops care not for your goat-fed Jove, ‭ Nor other Bless'd ones; we are better far. ‭ To Jove himself dare I bid open war, ‭ To thee, and all thy fellows, if I please. ‭ But tell me, where's the ship, that by the seas ‭ Hath brought thee hither? If far off, or near, ‭ Inform me quickly.' These his temptings were; ‭ But I too much knew not to know his mind, ‭ And craft with craft paid, telling him the wind ‭ (Thrust up from sea by Him that shakes the shore) ‭ Had dash'd our ships against his rocks, and tore ‭ Her ribs in pieces close upon his coast, ‭ And we from high wrack sav'd, the rest were lost. ‭ He answer'd nothing, but rush'd in, and took ‭ Two of my fellows up from earth, and strook ‭ Their brains against it. Like two whelps they flew ‭ About his shoulders, and did all embrue ‭ The blushing earth. No mountain lion tore ‭ Two lambs so sternly, lapp'd up all their gore ‭ Gush'd from their torn-up bodies, limb by limb ‭ (Trembling with life yet) ravish'd into him. ‭ Both flesh and marrow-stufféd bones he eat, ‭ And ev'n th' uncleanséd entrails made his meat. ‭ We, weeping, cast our hands to heav'n, to view ‭ A sight so horrid. Desperation flew, ‭ With all our after lives, to instant death, ‭ In our believ'd destruction. But when breath ‭ The fury of his appetite had got, ‭ Because the gulf his belly reach'd his throat, ‭ Man's flesh, and goat's milk, laying lay'r on lay'r, ‭ Till near chok'd up was all the pass for air, ‭ Along his den, among'st his cattle, down ‭ He rush'd, and streak'd him. 'When my mind was grown ‭ Desp'rate to step in, draw my sword, and part ‭ His bosom where the strings about the heart ‭ Circle the liver, and add strength of hand. ‭ But that rash thought, more stay'd, did countermand, ‭ For there we all had perish'd, since it past ‭ Our pow'rs to lift aside a log so vast, ‭ As barr'd all outscape; and so sigh'd away ‭ The thought all night, expecting active day. ‭ Which come, he first of all his fire enflames, ‭ Then milks his goats and ewes, then to their dams ‭ Lets in their young, and, wondrous orderly, ‭ With manly haste dispatch'd his housewif'ry. ‭ Then to his breakfast, to which other two ‭ Of my poor friends went; which eat, out then go ‭ His herds and fat flocks, lightly putting by ‭ The churlish bar, and clos'd it instantly; ‭ For both those works with ease as much he did, ‭ As you would ope and shut your quiver lid. ‭ With storms of whistlings then his flock he drave ‭ Up to the mountains; and occasion gave ‭ For me to use my wits, which to their height ‭ I striv'd to screw up, that a vengeance might ‭ By some means fall from thence, and Pallas now ‭ Afford a full ear to my neediest vow. ‭ This then my thoughts preferr'd: A huge club lay ‭ Close by his milk-house, which was now in way ‭ To dry and season, being an olive-tree ‭ Which late he fell'd, and, being green, must be ‭ Made lighter for his manage. 'Twas so vast, ‭ That we resembled it to some fit mast, ‭ To serve a ship of burthen that was driv'n ‭ With twenty oars, and had a bigness giv'n ‭ To bear a huge sea. Full so thick, so tall, ‭ We judg'd this club; which I, in part, hew'd small, ‭ And cut a fathom off. The piece I gave ‭ Amongst my soldiers, to take down, and shave; ‭ Which done, I sharpen'd it at top, and then, ‭ Harden'd in fire, I hid it in the den ‭ Within a nasty dunghill reeking there, ‭ Thick, and so moist it issued ev'rywhere. ‭ Then made I lots cast by my friends to try ‭ Whose fortune serv'd to dare the bor'd-out eye ‭ Of that man-eater; and the lot did fall ‭ On four I wish'd to make my aid of all, ‭ And I the fifth made, chosen like the rest. ‭ Then came the even, and he came from the feast ‭ Of his fat cattle, drave in all; nor kept ‭ One male abroad; if, or his memory slept ‭ By Gods' direct will, or of purpose was ‭ His driving in of all then, doth surpass ‭ My comprehension. But he clos'd again ‭ The mighty bar, milk'd, and did still maintain ‭ All other observation as before. ‭ His work all done, two of my soldiers more ‭ At once he snatch'd up, and to supper went. ‭ Then dar'd I words to him, and did present ‭ A bowl of wine, with these words: 'Cyclop! take ‭ A bowl of wine, from my hand, that may make ‭ Way for the man's flesh thou hast eat, and show ‭ What drink our ship held; which in sacred vow ‭ I offer to thee to take ruth on me ‭ In my dismission home. Thy rages be ‭ Now no more sufferable. How shall men, ‭ Mad and inhuman that thou art, again ‭ Greet thy abode, and get thy actions grace, ‭ If thus thou ragest, and eat'st up their race.' ‭ He took, and drunk, and vehemently joy'd ‭ To taste the sweet cup; and again employ'd ‭ My flagon's pow'rs, entreating more, and said: ‭ ῾Good guest, again afford my taste thy aid, ‭ And let me know thy name, and quickly now, ‭ That in thy recompense I may bestow ‭ A hospitable gift on thy desert, ‭ And such a one as shall rejoice thy heart. ‭ For to the Cyclops too the gentle earth ‭ Bears gen'rous wine, and Jove augments her birth, ‭ In store of such, with show'rs; but this rich wine ‭ Fell from the river, that is mere divine, ‭ Of nectar and ambrosia.' This again ‭ I gave him, and again; nor could the fool abstain, ‭ But drunk as often. When the noble juice ‭ Had wrought upon his spirit, I then gave use ‭ To fairer language, saying: 'Cyclop! now, ‭ As thou demand'st, I'll tell my name, do thou ‭ Make good thy hospitable gift to me. ‭ My name is No-Man; No-Man each degree ‭ Of friends, as well as parents, call my name.' ‭ He answer'd, as his cruel soul became: ‭ 'No-Man! I'll eat thee last of all thy friends; ‭ And this is that in which so much amends ‭ I vow'd to thy deservings, thus shall be ‭ My hospitable gift made good to thee.' ‭ This said, he upwards fell, but then bent round ‭ His fleshy neck; and Sleep, with all crowns crown'd, ‭ Subdued the savage. From his throat brake out ‭ My wine, with man's-flesh gobbets, like a spout, ‭ When, loaded with his cups, he lay and snor'd; ‭ And then took I the club's end up, and gor'd ‭ The burning coal-heap, that the point might heat; ‭ Confirm'd my fellow's minds, lest Fear should let ‭ Their vow'd assay, and make them fly my aid. ‭ Straight was the olive-lever, I had laid ‭ Amidst the huge fire to get hard'ning, hot, ‭ And glow'd extremely, though 'twas green; which got ‭ From forth the cinders, close about me stood ‭ My hardy friends; but that which did the good ‭ Was God's good inspiratión, that gave ‭ A spirit beyond the spirit they us'd to have; ‭ Who took the olive spar, made keen before, ‭ And plung'd it in his eye, and up I bore, ‭ Bent to the top close, and help'd pour it in, ‭ With all my forces. And as you have seen ‭ A ship-wright bore a naval beam, he oft ‭ Thrusts at the auger's froofe, works still aloft, ‭ And at the shank help others, with a cord ‭ Wound round about to make it sooner bor'd, ‭ All plying the round still; so into his eye ‭ The fiery stake we labour'd to imply. ‭ Out gush'd the blood that scalded, his eye-ball ‭ Thrust out a flaming vapour, that scorch'd all ‭ His brows and eye-lids, his eye-strings did crack, ‭ As in the sharp and burning rafter brake. ‭ And as a smith, to harden any tool, ‭ Broad axe, or mattock, in his trough doth cool ‭ The red-hot substance, that so fervent is ‭ It makes the cold wave straight to seethe and hiss; ‭ So sod and hiss'd his eye about the stake. ‭ He roar'd withal, and all his cavern brake ‭ In claps like thunder. We did frighted fly, ‭ Dispers'd in corners. He from forth his eye ‭ The fixed stake pluck'd; after which the blood ‭ Flow'd freshly forth; and, mad, he hurl'd the wood ‭ About his hovel. Out he then did cry ‭ For other Cyclops, that in caverns by ‭ Upon a windy promontory dwell'd; ‭ Who, hearing how impetuously he yell'd, ‭ Rush'd ev'ry way about him, and inquir'd, ‭ What ill afflicted him, that he exspir'd ‭ Such horrid clamours, and in sacred Night ‭ To break their sleeps so? Ask'd him, if his fright ‭ Came from some mortal that his flocks had driv'n? ‭ Or if by craft, or might, his death were giv'n? ‭ He answer'd from his den: 'By craft, nor might, ‭ No-Man hath giv'n me death.' They then said right, ‭ 'If no man hurt thee, and thyself alone, ‭ That which is done to thee by Jove is done; ‭ And what great Jove inflicts no man can fly. ‭ Pray to thy Father yet, a Deity, ‭ And prove, from him if thou canst help acquire.' ‭ Thus spake they, leaving him; when all-on-fire ‭ My heart with joy was, that so well my wit ‭ And name deceiv'd him; whom now pain did split, ‭ And groaning up and down he groping tried ‭ To find the stone, which found, he put aside; ‭ But in the door sat, feeling if he could ‭ (As his sheep issued) on some man lay hold; ‭ Esteeming me a fool, that could devise ‭ No stratagem to 'scape his gross surprise. ‭ But I, contending what I could invent ‭ My friends and me from death so eminent ‭ To get deliver'd, all my wiles I wove ‭ (Life being the subject) and did this approve: ‭ Fat fleecy rams, most fair, and great, lay there, ‭ That did a burden like a violet bear. [8] ‭ These, while this learn'd-in-villainy did sleep, ‭ I yok'd with osiers cut there, sheep to sheep, ‭ Three in a rank, and still the mid sheep bore ‭ A man about his belly, the two more ‭ March'd on his each side for defence. I then, ‭ Choosing myself the fairest of the den, ‭ His fleecy belly under-crept, embrac'd ‭ His back, and in his rich wool wrapt me fast ‭ With both my hands, arm'd with as fast a mind. ‭ And thus each man hung, till the morning shin'd; ‭ Which come, he knew the hour, and let abroad ‭ His male-flocks first, the females unmilk'd stood ‭ Bleating and braying, their full bags so sore ‭ With being unemptied, but their shepherd more ‭ With being unsighted; which was cause his mind ‭ Went not a milking. He, to wreak inclin'd, ‭ The backs felt, as they pass'd, of those male dams, ‭ Gross fool! believing, we would ride his rams! ‭ Nor ever knew that any of them bore ‭ Upon his belly any man before. ‭ The last ram came to pass him, with his wool ‭ And me together loaded to the full, ‭ For there did I hang; and that ram he stay'd, ‭ And me withal had in his hands, my head ‭ Troubled the while, not causelessly, nor least. ‭ This ram he grop'd, and talk'd to: 'Lazy beast! ‭ Why last art thou now? Thou hast never us'd ‭ To lag thus hindmost, but still first hast bruis'd ‭ The tender blossom of a flow'r, and held ‭ State in thy steps, both to the flood and field, ‭ First still at fold at even, now last remain? ‭ Dost thou not wish I had mine eye again, ‭ Which that abhorr'd man No-Man did put out, ‭ Assisted by his execrable rout, ‭ When he had wrought me down with wine? But he ‭ Must not escape my wreak so cunningly. ‭ I would to heav'n thou knew'st, and could but speak, ‭ To tell me where he lurks now! I would break ‭ His brain about my cave, strew'd here and there, ‭ To ease my heart of those foul ills, that were ‭ Th' inflictions of a man I priz'd at nought.' ‭ Thus let he him abroad; when I, once brought ‭ A little from his hold, myself first los'd, ‭ And next my friends. Then drave we, and dispos'd, ‭ His straight-legg'd fat fleece-bearers over land, ‭ Ev'n till they all were in my ship's command; ‭ And to our lov'd friends show'd our pray'd-for sight, ‭ Escap'd from death. But, for our loss, outright ‭ They brake in tears; which with a look I stay'd, ‭ And bade them take our boot in. They obey'd, ‭ And up we all went, sat, and us'd our oars. ‭ But having left as far the savage shores ‭ As one might hear a voice, we then might see ‭ The Cyclop at the haven; when instantly ‭ I stay'd our oars, and this insultance us'd: ‭ ῾Cyclop! thou shouldst not have so much abus'd ‭ Thy monstrous forces, to oppose their least ‭ Against a man immartial, and a guest, ‭ And eat his fellows. Thou mightst know there were ‭ Some ills behind, rude swain, for thee to bear, ‭ That fear'd not to devour thy guests, and break ‭ All laws of humans. Jove sends therefore wreak, ‭ And all the Gods, by me.' This blew the more ‭ His burning fury; when the top he tore ‭ From off a huge rock, and so right a throw ‭ Made at our ship, that just before the prow ‭ It overflew and fell, miss'd mast and all ‭ Exceeding little; but about the fall ‭ So fierce a wave it rais'd, that back it bore ‭ Our ship so far, it almost touch'd the shore. ‭ A bead-hook then, a far-extended one, ‭ I snatch'd up, thrust hard, and so set us gone ‭ Some little way; and straight commanded all ‭ To help me with their oars, on pain to fall ‭ Again on our confusion. But a sign ‭ I with my head made, and their oars were mine ‭ In all performance. When we off were set, ‭ (Then first, twice further) my heart was so great, ‭ It would again provoke him, but my men ‭ On all sides rush'd about me, to contain, ‭ And said: 'Unhappy! why will you provoke ‭ A man so rude, that with so dead a stroke, ‭ Giv'n with his rock-dart, made the sea thrust back ‭ Our ship so far, and near hand forc'd our wrack? ‭ Should he again but hear your voice resound, ‭ And any word reach, thereby would be found ‭ His dart's direction, which would, in his fall, ‭ Crush piece-meal us, quite split our ship and all; ‭ So much dart wields the monster.' Thus urg'd they ‭ Impossible things, in fear; but I gave way ‭ To that wrath which so long I held deprest, ‭ By great necessity conquer'd, in my breast: ‭ 'Cyclop! if any ask thee, who impos'd [9] ‭ Th' unsightly blemish that thine eye enclos'd, ‭ Say that Ulysses, old Laertes' son, ‭ Whose seat is Ithaca, and who hath won ‭ Surname of City-razer, bor'd it out.' ‭ At this, he bray'd so loud, that round about ‭ He drave affrighted echoes through the air, ‭ And said: 'O beast! I was premonish'd fair, ‭ By aged prophecy, in one that was ‭ A great and good man, this should come to pass; ‭ And how 'tis prov'd now! Augur Telemus, ‭ Surnam'd Eurymides (that spent with us ‭ His age in augury, and did exceed ‭ In all presage of truth) said all this deed ‭ Should this event take, author'd by the hand ‭ Of one Ulysses, who I thought was mann'd ‭ With great and goodly personage, and bore ‭ A virtue answerable; and this shore ‭ Should shake with weight of such a conqueror; ‭ When now a weakling came, a dwarfy thing, ‭ A thing of nothing; who yet wit did bring, ‭ That brought supply to all, and with his wine ‭ Put out the flame where all my light did shine. ‭ Come, land again, Ulysses! that my hand ‭ May guest-rites give thee, and the great command, ‭ That Neptune hath at sea, I may convert ‭ To the deduction where abides thy heart, ‭ With my solicitings, whose son I am, ‭ And whose fame boasts to bear my father's name. ‭ Nor think my hurt offends me, for my sire ‭ Can soon repose in it the visual fire, ‭ At his free pleasure; which no pow'r beside ‭ Can boast, of men, or of the Deified.' ‭ I answer'd: 'Would to God! I could compell ‭ Both life and soul from thee, and send to hell ‭ Those spoils of nature! Hardly Neptune then ‭ Could cure thy hurt, and give thee all again.' ‭ Then flew fierce vows to Neptune, both his hands ‭ To star-born heav'n cast: 'O thou that all lands ‭ Gird'st in thy ambient circle, and in air ‭ Shak'st the curl'd tresses of thy sapphire hair, ‭ If I be thine, or thou mayst justly vaunt ‭ Thou art my father, hear me now, and grant ‭ That this Ulysses, old Laertes' son, ‭ That dwells in Ithaca, and name hath won ‭ Of City-ruiner, may never reach ‭ His natural region. Or if to fetch ‭ That, and the sight of his fair roofs and friends, ‭ Be fatal to him, let him that amends ‭ For all his miseries, long time and ill, ‭ Smart for, and fail of; nor that fate fulfill, ‭ Till all his soldiers quite are cast away ‭ In others' ships. And when, at last, the day ‭ Of his sole-landing shall his dwelling show, ‭ Let Detriment prepare him wrongs enow.' ‭ Thus pray'd he Neptune; who, his sire, appear'd, ‭ And all his pray'r to ev'ry syllable heard. ‭ But then a rock, in size more amplified ‭ Than first, he ravish'd to him, and implied ‭ A dismal strength in it, when, wheel'd about, ‭ He sent it after us; nor flew it out ‭ From any blind aim, for a little pass ‭ Beyond our fore-deck from the fall there was, ‭ With which the sea our ship gave back upon, ‭ And shrunk up into billows from the stone, ‭ Our ship again repelling near as near ‭ The shore as first. But then our rowers were, ‭ Being warn'd, more arm'd, and stronglier stemm'd the flood ‭ That bore back on us, till our ship made good ‭ The other island, where our whole fleet lay, ‭ In which our friends lay mourning for our stay, ‭ And ev'ry minute look'd when we should land. ‭ Where, now arriv'd, we drew up to the sand, ‭ The Cyclops' sheep dividing, that none there ‭ Of all our privates might be wrung, and bear ‭ Too much on pow'r. The ram yet was alone ‭ By all my friends made all my portion ‭ Above all others; and I made him then ‭ A sacrifice for me and all my men [10] ‭ To cloud-compelling Jove that all commands, ‭ To whom I burn'd the thighs; but my sad hands ‭ Receiv'd no grace from him, who studied how ‭ To offer men and fleet to overthrow. ‭ All day, till sun-set, yet, we sat and eat, ‭ And lib'ral store took in of wine and meat. ‭ The sun then down, and place resign'd to shade, ‭ We slept. Morn came, my men I rais'd, and made ‭ All go aboard, weigh anchor, and away. ‭ They boarded, sat, and beat the aged sea; ‭ And forth we made sail, sad for loss before, ‭ Any yet had comfort since we lost no more." ‭ FINIS LIBRI NONI HOM. ODYSS. ‭[1] _Εἰνοσίϕυλλον, quatientem seu agitantem frondes._ ‭[2] _Quædam quibus corpus alitur et vita sustentatur ὕλη ‭appellantur._ ‭[3] _Amor patriœ._ ‭[4] After night, in the first of the morning. ‭[5] The ancient custom of calling home the dead. ‭[6] The description of all these countries have admirable allegories ‭besides their artly and pleasing relation. ‭[7] This his relation of Agamemnon, and his glory and theirs for ‭Troy's sack, with the piety of suppliants' receipt, to him that was so ‭barbarous and impious, must be intended spoken by Ulysses, with ‭supposition that his hearers would note, still as he spake, how vain ‭they would show to the Cyclops; who respected little Agamemnon, ‭or their valiant exploit against Troy, or the Gods themselves. For ‭otherwise, the serious observation of the words (though good and ‭grave, if spoken to another) want their intentional sharpness and ‭life. ‭[8] Wool of a violet colour. ‭[9] Ulysses' continued insolence, no more to repeat what he said to ‭the Cyclop, than to let his hearers know epithets, and estimation in ‭the world. ‭[10] No occasion let pass to Ulysses' piety in our Poet's singular wit ‭and wisdom. ‭ THE TENTH BOOK OF HOMER'S ODYSSEYS ‭ THE ARGUMENT ‭ Ulysses now relates to us ‭ The grace he had with Æolus, ‭ Great Guardian of the hollow Winds; ‭ Which in a leather bag he binds, ‭ And gives Ulysses; all but one, ‭ Which Zephyr was, who fill'd alone ‭ Ulysses' sails. The bag once seen, ‭ While he slept, by Ulysses' men, ‭ They thinking it did gold enclose, ‭ To find it, all the winds did loose, ‭ Who back flew to their Guard again. ‭ Forth sail'd he; and did next attain ‭ To where the Læstrygonians dwell. ‭ Where he eleven ships lost, and fell ‭ On the Ææan coast, whose shore ‭ He sends Eurylochus t' explore, ‭ Dividing with him half his men. ‭ Who go, and turn no more again, ‭ All, save Eurylochus, to swine ‭ By Circe turn'd. Their stays incline ‭ Ulysses to their search; who got ‭ Of Mercury an antidote, ‭ Which moly was, 'gainst Circe's charms, ‭ And so avoids his soldiers' harms. ‭ A year with Circe all remain, ‭ And then their native forms regain. ‭ On utter shores a time they dwell, ‭ While Ithacus descends to hell. ‭ ANOTHER ARGUMENT ‭ _Κάππα._ ‭ Great Æolus, ‭ And Circe, friends ‭ Finds Ithacus; ‭ And hell descends. ‭ "To the Æolian island we attain'd, ‭ That swum about still on the sea, where reign'd ‭ The God-lov'd Æolus Hippotades. ‭ A wall of steel it had; and in the seas ‭ A wave-beat-smooth rock mov'd about the wall. ‭ Twelve children in his house imperial ‭ Were born to him; of which six daughters were, ‭ And six were sons, that youth's sweet flow'r did bear. ‭ His daughters to his sons he gave as wives; ‭ Who spent in feastful comforts all their lives, ‭ Close seated by their sire and his grave spouse. ‭ Past number were the dishes that the house ‭ Made ever savour; and still full the hall ‭ As long as day shin'd; in the night-time, all ‭ Slept with their chaste wives, each his fair carv'd bed ‭ Most richly furnish'd; and this life they led. ‭ We reach'd the city and fair roofs of these, ‭ Where, a whole month's time, all things that might please ‭ The king vouchsaf'd us; of great Troy inquir'd, ‭ The Grecian fleet, and how the Greeks retir'd. ‭ To all which I gave answer as behov'd. ‭ The fit time come when I dismission mov'd, ‭ He nothing would deny me, but addrest ‭ My pass with such a bounty, as might best ‭ Teach me contentment; for he did enfold ‭ Within an ox-hide, flay'd at nine years old, ‭ All th' airy blasts that were of stormy kinds. ‭ Saturnius made him Steward of his Winds, ‭ And gave him pow'r to raise and to assuage. ‭ And these he gave me, curb'd thus of their rage, ‭ Which in a glitt'ring silver band I bound, ‭ And hung-up in my ship, enclos'd so round ‭ That no egression any breath could find; ‭ Only he left abroad the Western Wind, ‭ To speed our ships, and us with blasts secure. ‭ But our securities made all unsure; ‭ Nor could he consummate our course alone, ‭ When all the rest had got egressión; ‭ Which thus succeeded: Nine whole days and nights ‭ We sail'd in safety; and the tenth, the lights ‭ Borne on our country-earth we might descry, ‭ So near we drew; and yet ev'n then fell I, ‭ Being overwatch'd, into a fatal sleep, ‭ For I would suffer no man else to keep ‭ The foot that rul'd my vessel's course, to lead [1] ‭ The faster home. My friends then Envy fed ‭ About the bag I hung-up, and suppos'd ‭ That gold and silver I had there enclos'd, ‭ As gift from Æolus, and said: 'O heav'n! ‭ What grace and grave price is by all men giv'n ‭ To our commander! Whatsoever coast ‭ Or town he comes to, how much he engrost ‭ Of fair and precious prey, and brought from Troy! ‭ We the same voyage went, and yet enjoy ‭ In our return these empty hands for all. ‭ This bag, now, Æolus was so liberal ‭ To make a guest-gift to him; let us try ‭ Of what consists the fair-bound treasury, ‭ And how much gold and silver it contains.' ‭ _Ill counsel present approbation gains._ ‭ They op'd the bag, and out the vapours brake, ‭ When instant tempest did our vessel take, ‭ That bore us back to sea, to mourn anew ‭ Our absent country. Up amaz'd I flew, ‭ And desp'rate things discours'd; if I should cast ‭ Myself to ruin in the seas, or taste ‭ Amongst the living more moan, and sustain? ‭ Silent, I did so, and lay hid again ‭ Beneath the hatches, while an ill wind took ‭ My ships back to Æolia, my men strook ‭ With woe enough. We pump'd and landed then, ‭ Took food, for all this; and of all my men ‭ I took a herald to me, and away ‭ Went to the court of Æolus, where they ‭ Were feasting still; he, wife, and children, set ‭ Together close. We would not at their meat ‭ Thrust in; but humbly on the threshold sat. ‭ He then, amaz'd, my presence wonder'd at, ‭ And call'd to me: 'Ulysses! How thus back ‭ Art thou arriv'd here? What foul spirit brake ‭ Into thy bosom, to retire thee thus? ‭ We thought we had deduction curious ‭ Giv'n thee before, to reach thy shore and home; ‭ Did it not like thee?' I, ev'n overcome ‭ With worthy sorrow, answer'd: 'My ill men ‭ Have done me mischief, and to them hath been ‭ My sleep th' unhappy motive; but do you, ‭ Dearest of friends, deign succour to my vow. ‭ Your pow'rs command it.' Thus endeavour'd I ‭ With soft speech to repair my misery. ‭ The rest with ruth sat dumb. But thus spake he: ‭ 'Avaunt, and quickly quit my land of thee, ‭ Thou worst of all that breathe. It fits not me ‭ To convoy, and take-in, whom Heav'ns expose. ‭ Away, and with thee go the worst of woes, ‭ That seek'st my friendship, and the Gods thy foes.' ‭ Thus he dismiss'd me sighing. Forth we sail'd, ‭ At heart afflicted. And now wholly fail'd ‭ The minds my men sustain'd, so spent they were ‭ With toiling at their oars, and worse did bear ‭ Their growing labours; and they caus'd their grought ‭ By self-will'd follies; nor now ever thought ‭ To see their country more. Six nights and days ‭ We sail'd; the seventh we saw fair Lamos raise ‭ Her lofty tow'rs, the Læstrygonian state ‭ That bears her ports so far disterminate; ‭ Where shepherd shepherd calls out, he at home [2] ‭ Is call'd out by the other that doth come ‭ From charge abroad, and then goes he to sleep, ‭ The other issuing; he whose turn doth keep ‭ The night observance hath his double hire, ‭ Since day and night in equal length expire ‭ About that region, and the night's watch weigh'd ‭ At twice the day's ward, since the charge that's laid ‭ Upon the night's-man (besides breach of sleep) ‭ Exceeds the days-man's; for one oxen keep, ‭ The other sheep. But when the haven we found, ‭ (Exceeding famous, and environ'd round ‭ With one continuate rock, which so much bent ‭ That both ends almost met, so prominent ‭ They were, and made the haven's mouth passing strait) ‭ Our whole fleet in we got; in whose receit ‭ Our ships lay anchor'd close. Nor needed we ‭ Fear harm on any stays, Tranquillity [3] ‭ So purely sat there, that waves great nor small ‭ Did ever rise to any height at all. ‭ And yet would I no entry make, but stay'd ‭ Alone without the haven, and thence survey'd, ‭ From out a lofty watch-tow'r raised there, ‭ The country round about; nor anywhere ‭ The work of man or beast appear'd to me, ‭ Only a smoke from earth break I might see. ‭ I then made choice of two, and added more, ‭ A herald for associate, to explore ‭ What sort of men liv'd there. They went, and saw ‭ A beaten way, through which carts us'd to draw ‭ Wood from the high hills to the town, and met ‭ A maid without the port, about to get ‭ Some near spring-water. She the daughter was ‭ Of mighty Læstrygonian Antiphas, ‭ And to the clear spring call'd Artacia went, ‭ To which the whole town for their water sent. ‭ To her they came, and ask'd who govern'd there, ‭ And what the people whom he order'd were? ‭ She answer'd not, but led them through the port, ‭ As making haste to show her father's court. ‭ Where enter'd, they beheld, to their affright, ‭ A woman like a mountain-top in height, ‭ Who rush'd abroad, and from the council-place ‭ Call'd home her horrid husband Antiphas, [4] ‭ Who, deadly-minded, straight he snatch'd up one, ‭ And fell to supper. Both the rest were gone; ‭ And to the fleet came. Antiphas a cry ‭ Drave through the city; which heard, instantly ‭ This way and that innumerable sorts, ‭ Not men, but giants, issued through the ports, ‭ And mighty flints from rocks tore, which they threw ‭ Amongst our ships; through which an ill noise flew ‭ Of shiver'd ships, and life-expiring men, ‭ That were, like fishes, by the monsters slain, ‭ And borne to sad feast. While they slaughter'd these, ‭ That were engag'd in all th' advantages ‭ The close-mouth'd and most dead-calm haven could give, ‭ I, that without lay, made some means to live, ‭ My sword drew, cut my gables, and to oars ‭ Set all my men; and, from the plagues those shores ‭ Let fly amongst us, we made haste to fly, ‭ My men close working as men loth to die. ‭ My ship flew freely off; but theirs that lay ‭ On heaps in harbours could enforce no way ‭ Through these stern fates that had engag'd them there. ‭ Forth our sad remnant sail'd, yet still retain'd ‭ The joys of men, that our poor few remain'd. ‭ Then to the isle Ææa we attain'd, ‭ Where fair-hair'd, dreadful, eloquent Circe reign'd, ‭ Ææta's sister both by dame and sire, ‭ Both daughters to Heav'n's man-enlight'ning Fire, ‭ And Perse, whom Oceanus begat, ‭ The ship-fit port here soon we landed at, ‭ Some God directing us. Two days, two nights, ‭ We lay here pining in the fatal spights ‭ Of toil and sorrow; but the next third day ‭ When fair Aurora had inform'd, quick way ‭ I made out of my ship, my sword and lance ‭ Took for my surer guide, and made advance ‭ Up to a prospect; I assay to see ‭ The works of men, or hear mortality ‭ Exspire a voice. When I had climb'd a height, ‭ Rough and right hardly accessible, I might ‭ Behold from Circe's house, that in a grove ‭ Set thick with trees stood, a bright vapour move, ‭ I then grew curious in my thought to try [5] ‭ Some fit inquiry, when so spritely fly ‭ I saw the yellow smoke; but my discourse [6] ‭ A first retiring to my ship gave force, ‭ To give my men their dinner, and to send ‭ (Before th' adventure of myself) some friend. ‭ Being near my ship, of one so desolate ‭ Some God had pity, and would recreate ‭ My woes a little, putting up to me ‭ A great and high-palm'd hart, that (fatally, ‭ Just in my way itself to taste a flood) ‭ Was then descending; the sun heat had sure ‭ Importun'd him, besides the temperature ‭ His natural heat gave. Howsoever, I ‭ Made up to him, and let my jav'lin fly, ‭ That struck him through the mid-part of his chine, ‭ And made him, braying, to the dust confine ‭ His flying forces. Forth his spirit flew; ‭ When I stept in, and from the death's wound drew ‭ My shrewdly-bitten lance; there let him lie ‭ Till I, of cut-up osiers, did imply ‭ A withe a fathom long, with which his feet ‭ I made together in a sure league meet, ‭ Stoop'd under him, and to my neck I heav'd ‭ The mighty burden, of which I receiv'd ‭ A good part on my lance, for else I could ‭ By no means with one hand alone uphold ‭ (Join'd with one shoulder) such a deathful load. ‭ And so, to both my shoulders, both hands stood ‭ Needful assistants; for it was a deer ‭ Goodly-well-grown. When (coming something near ‭ Where rode my ships) I cast it down, and rear'd ‭ My friends with kind words; whom by name I cheer'd, ‭ In note particular, and said: 'See, friends, ‭ We will not yet to Pluto's house; our ends ‭ Shall not be hasten'd, though we be declin'd ‭ In cause of comfort, till the day design'd ‭ By Fate's fix'd finger. Come, as long as food ‭ Or wine lasts in our ship, let's spirit our blood, ‭ And quit our care and hunger both in one.' ‭ This said, they frolick'd, came, and look'd upon ‭ With admiration the huge-bodied beast; ‭ And when their first-serv'd eyes had done their feast, ‭ They wash'd, and made a to-be-striv'd-for meal [7] ‭ In point of honour. On which all did dwell ‭ The whole day long. And, to our venison's store, ‭ We added wine till we could wish no more. ‭ Sun set, and darkness up, we slept, till light ‭ Put darkness down; and then did I excite ‭ My friends to counsel, utt'ring this: 'Now, friends, [8] ‭ Afford unpassionate ear; though ill Fate lends ‭ So good cause to your passion, no man knows ‭ The reason whence and how the darkness grows; ‭ The reason how the morn is thus begun; ‭ The reason how the man-enlight'ning sun ‭ Dives under earth; the reason how again ‭ He rears his golden head. Those counsels, then, ‭ That pass our comprehension, we must leave ‭ To him that knows their causes; and receive ‭ Direction from him in our acts, as far ‭ As he shall please to make them regular, ‭ And stoop them to our reason. In our state ‭ What then behoves us? Can we estimate, ‭ With all our counsels, where we are? Or know ‭ (Without instruction, past our own skills) how, ‭ Put off from hence, to steer our course the more? ‭ I think we cannot. We must then explore ‭ These parts for information; in which way ‭ We thus far are: Last morn I might display ‭ (From off a high-rais'd cliff) an island lie ‭ Girt with th' unmeasur'd sea, and is so nigh ‭ That in the midst I saw the smoke arise ‭ Through tufts of trees. This rests then to advise, ‭ Who shall explore this?' This struck dead their hearts, ‭ Rememb'ring the most execrable parts ‭ That Læstrygonian Antiphas had play'd, ‭ And that foul Cyclop that their fellows bray'd ‭ Betwixt his jaws; which mov'd them so, they cried. ‭ But idle tears had never wants supplied. ‭ I in two parts divided all, and gave ‭ To either part his captain. I must have ‭ The charge of one; and one of God-like look, ‭ Eurylochus, the other. Lots we shook, ‭ Put in a casque together, which of us ‭ Should lead th' attempt; and 'twas Eurylochus. ‭ He freely went, with two-and-twenty more; ‭ All which took leave with tears; and our eyes wore ‭ The same wet badge of weak humanity. ‭ These in a dale did Circe's house descry, ‭ Of bright stone built, in a conspicuous way. ‭ Before her gates hill-wolves, and lions, lay; ‭ Which with her virtuous drugs so tame she made, ‭ That wolf nor lion would one man invade ‭ With any violence, but all arose, ‭ Their huge long tails wagg'd, and in fawns would close, ‭ As loving dogs, when masters bring them home ‭ Relics of feast, in all observance come, ‭ And soothe their entries with their fawns and bounds, ‭ All guests still bringing some scraps for their hounds; ‭ So, on these men, the wolves and lions ramp'd, ‭ Their horrid paws set up. Their spirits were damp'd ‭ To see such monstrous kindness, stay'd at gate, ‭ And heard within the Goddess elevate ‭ A voice divine, as at her web she wrought, ‭ Subtle, and glorious, and past earthly thought, ‭ As all the housewif'ries of Deities are. ‭ To hear a voice so ravishingly rare, ‭ Polités (one exceeding dear to me, ‭ A prince of men, and of no mean degree ‭ In knowing virtue, in all acts whose mind [9] ‭ Discreet cares all ways us'd to turn, and wind) ‭ Was yet surpris'd with it, and said: 'O friends, ‭ Some one abides within here, that commends ‭ The place to us, and breathes a voice divine, ‭ As she some web wrought, or her spindle's twine ‭ She cherish'd with her song; the pavement rings ‭ With imitation of the tunes she sings. ‭ Some woman, or some Goddess, 'tis. Assay ‭ To see with knocking.' Thus said he, and they ‭ Both knock'd, and call'd; and straight her shining gates ‭ She open'd, issuing, bade them in to cates. ‭ Led, and unwise, they follow'd; all but one, ‭ Which was Eurylochus, who stood alone ‭ Without the gates, suspicious of a sleight. ‭ They enter'd, she made sit; and her deceit ‭ She cloak'd with thrones, and goodly chairs of state; ‭ Set herby honey, and the delicate ‭ Wine brought from Smynra, to them; meal and cheese; ‭ But harmful venoms she commix'd with these, ‭ That made their country vanish from their thought. ‭ Which eat, she touch'd them with a rod that wrought ‭ Their transformation far past human wonts; ‭ Swine's snouts, swine's bodies, took they, bristles, grunts, ‭ But still retain'd the souls they had before, ‭ Which made them mourn their bodies' change the more. ‭ She shut them straight in styes, and gave them meat, ‭ Oak-mast, and beech, and cornel-fruit, they eat, ‭ Grov'lling like swine on earth, in foulest sort. ‭ Eurylochus straight hasted the report ‭ Of this his fellows' most remorseful fate, ‭ Came to the ships, but so excruciate ‭ Was with his woe, he could not speak a word, ‭ His eyes stood full of tears, which show'd how stor'd ‭ His mind with moan remain'd. We all admir'd, ‭ Ask'd what had chanc'd him, earnestly desir'd ‭ He would resolve us. At the last, our eyes ‭ Enflam'd in him his fellows' memories, [10] ‭ And out his grief burst thus: 'You will'd; we went ‭ Through those thick woods you saw; when a descent ‭ Show'd us a fair house, in a lightsome ground, ‭ Where, at some work, we heard a heav'nly sound ‭ Breath'd from a Goddess', or a woman's, breast. ‭ They knock'd, she op'd her bright gates; each her guest ‭ Her fair invitement made; nor would they stay, ‭ Fools that they were, when she once led the way. ‭ I enter'd not, suspecting some deceit. ‭ When all together vanish'd, nor the sight ‭ Of anyone (though long I look'd) mine eye ‭ Could any way discover.' Instantly, ‭ My sword and bow reach'd, I bad show the place, ‭ When down he fell, did both my knees embrace, ‭ And pray'd with tears thus: 'O thou kept of God, ‭ Do not thyself lose, nor to that abode ‭ Lead others rashly; both thyself, and all ‭ Thou ventur'st thither, I know well, must fall ‭ In one sure ruin. With these few then fly; ‭ We yet may shun the others' destiny.' ‭ I answer'd him: 'Eurylochus! Stay thou, ‭ And keep the ship then, eat and drink; I now ‭ Will undertake th' adventure; there is cause ‭ In great Necessity's unalter'd laws.' ‭ This said, I left both ship and seas, and on ‭ Along the sacred valleys all alone ‭ Went in discov'ry, till at last I came ‭ Where of the main-med'cine-making Dame ‭ I saw the great house; where encounter'd me ‭ The golden-rod-sustaining Mercury, ‭ Ev'n ent'ring Circe's doors. He met me in ‭ A young man's likeness, of the first-flow'r'd chin, ‭ Whose form hath all the grace of one so young. ‭ He first call'd to me, then my hand he wrung, ‭ And said: 'Thou no-place-finding-for-repose, ‭ Whither, alone, by these hill-confines, goes ‭ Thy erring foot? Th' art ent'ring Circe's house, ‭ Where, by her med'cines, black, and sorcerous, ‭ Thy soldiers all are shut in well-arm'd styes, ‭ And turn'd to swine. Art thou arriv'd with prize ‭ Fit for their ransoms? Thou com'st out no more, ‭ If once thou ent'rest, like thy men before ‭ Made to remain here. But I'll guard thee free, ‭ And save thee in her spite. Receive of me ‭ This fair and good receipt; with which once arm'd, ‭ Enter her roofs, for th' art to all proof charm'd ‭ Against the ill day. I will tell thee all ‭ Her baneful counsel: With a festival ‭ She'll first receive thee, but will spice thy bread ‭ With flow'ry poisons; yet unalteréd ‭ Shall thy firm form be, for this remedy ‭ Stands most approv'd 'gainst all her sorcery, ‭ Which thus particularly shun: When she ‭ Shall with her long rod strike thee, instantly ‭ Draw from thy thigh thy sword, and fly on her ‭ As to her slaughter. She, surpris'd with fear ‭ And love, at first, will bid thee to her bed. ‭ Nor say the Goddess nay, that welcoméd ‭ Thou may'st with all respect be, and procure ‭ Thy fellows' freedoms. But before, make sure ‭ Her favours to thee; and the great oath take ‭ With which the blesséd Gods assurance make ‭ Of all they promise; that no prejudice ‭ (By stripping thee of form, and faculties) ‭ She may so much as once attempt on thee.' ‭ This said, he gave his antidote to me, ‭ Which from the earth he pluck'd, and told me all ‭ The virtue of it, with what Deities call ‭ The name it bears; and Moly [11] they impose ‭ For name to it. The root is hard to loose ‭ From hold of earth by mortals; but God's pow'r ‭ Can all things do. 'Tis black, but bears a flow'r ‭ As white as milk. And thus flew Mercury ‭ Up to immense Olympus, gliding by ‭ The sylvan island. I made back my way ‭ To Circe's house, my mind of my assay ‭ Much thought revolving. At her gates I stay'd ‭ And call'd; she heard, and her bright doors display'd, ‭ Invited, led; I follow'd in, but trac'd ‭ With some distraction. In a throne she plac'd ‭ My welcome person; of a curious frame ‭ 'Twas, and so bright I sat as in a flame; ‭ A foot-stool added. In a golden bowl ‭ She then suborn'd a potion, in her soul ‭ Deform'd things thinking; for amidst the wine ‭ She mix'd her man-transforming medicine; ‭ Which when she saw I had devour'd, she then ‭ No more observ'd me with her soothing vein, ‭ But struck me with her rod, and to her stye ‭ Bad, out, away, and with thy fellows lie. ‭ I drew my sword, and charg'd her, as I meant ‭ To take her life. When out she cried, and bent ‭ Beneath my sword her knees, embracing mine, ‭ And, full of tears, said: 'Who? Of what high line ‭ Art thou the issue? Whence? What shores sustain ‭ Thy native city? I amaz'd remain ‭ That, drinking these my venoms, th' art not turn'd. ‭ Never drunk any this cup but be mourn'd ‭ In other likeness, if it once had pass'd ‭ The ivory bounders of his tongue and taste. ‭ All but thyself are brutishly declin'd. ‭ Thy breast holds firm yet, and unchang'd thy mind. ‭ Thou canst be therefore none else but the man ‭ Of many virtues, Ithacensian, ‭ Deep-soul'd, Ulysses, who; I oft was told, ‭ By that sly God that bears the rod of gold, ‭ Was to arrive here in retreat from Troy. ‭ Sheathe then thy sword, and let my bed enjoy ‭ So much a man, that when the bed we prove, ‭ We may believe in one another's love.' ‭ I then: 'O Circe, why entreat'st thou me ‭ To mix in any human league with thee, ‭ When thou my friends hast beasts turn'd; and thy bed ‭ Tender'st to me, that I might likewise lead ‭ A beast's life with thee, soften'd, naked stripp'd, ‭ That in my blood thy banes may more be steep'd? ‭ I never will ascend thy bed, before, ‭ I may affirm, that in heav'n's sight you swore ‭ The great oath of the Gods, that all attempt ‭ To do me ill is from your thoughts exempt.' ‭ I said, she swore, when, all the oath-rites said, ‭ I then ascended her adornéd bed, ‭ But thus prepar'd: Four handmaids served her there, ‭ That daughters to her silver fountains were, ‭ To her bright-sea-observing sacred floods, ‭ And to her uncut consecrated woods. ‭ One deck'd the throne-tops with rich cloths of state, ‭ And did with silks the foot-pace consecrate. ‭ Another silver tables set before ‭ The pompous throne, and golden dishes' store ‭ Serv'd in with sev'ral feast. A third fill'd wine. ‭ The fourth brought water, and made fuel shine ‭ In ruddy fires beneath a womb of brass. ‭ Which heat, I bath'd; and od'rous water was ‭ Disperpled lightly on my head and neck, ‭ That might my late heart-hurting sorrows check ‭ With the refreshing sweetness; and, for that, ‭ Men sometimes may be something delicate. ‭ Bath'd, and adorn'd, she led me to a throne ‭ Of massy silver, and of fashión ‭ Exceeding curious. A fair foot-stool set, ‭ Water appos'd, and ev'ry sort of meat ‭ Set on th' elaborately-polish'd board, ‭ She wish'd my taste employ'd; but not a word ‭ Would my ears taste of taste; my mind had food ‭ That must digest; eye-meat would do me good. ‭ Circe (observing that I put no hand ‭ To any banquet, having countermand ‭ From weightier cares the light cates could excuse) ‭ Bowing her near me, these wing'd words did use; ‭ 'Why sits Ulysses like one dumb, his mind ‭ Less'ning with languors? Nor to food inclin'd, ‭ Nor wine? Whence comes it? Out of any fear ‭ Of more illusion? You must needs forbear ‭ That wrongful doubt, since you have heard me swear.' ‭ 'O Circe!' I replied, 'what man is he, ‭ Aw'd with the rights of true humanity, ‭ That dares taste food or wine, before he sees ‭ His friends redeem'd from their deformities? ‭ If you be gentle, and indeed incline ‭ To let me taste the comfort of your wine, ‭ Dissolve the charms that their forc'd forms enchain, ‭ And show me here my honour'd friends like men.' ‭ This said, she left her throne, and took her rod, ‭ Went to her stye, and let my men abroad, ‭ Like swine of nine years old. They opposite stood, ‭ Observ'd their brutish form, and look'd for food; ‭ When, with another med'cine, ev'ry one ‭ All over smear'd, their bristles all were gone, ‭ Produc'd by malice of the other bane, ‭ And ev'ry one, afresh, look'd up a man, ‭ Both younger than they were, of stature more, ‭ And all their forms much goodlier than before. ‭ All knew me, cling'd about me, and a cry ‭ Of pleasing mourning flew about so high ‭ The horrid roof resounded; and the queen ‭ Herself was mov'd to see our kind so keen, ‭ Who bad me now bring ship and men ashore, ‭ Our arms, and goods in caves hid, and restore ‭ Myself to her, with all my other men. ‭ I granted, went, and op'd the weeping vein ‭ In all my men; whose violent joy to see ‭ My safe return was passing kindly free ‭ Of friendly tears, and miserably wept. ‭ You have not seen young heifers (highly kept, ‭ Fill'd full of daisies at the field, and driv'n ‭ Home to their hovels, all so spritely giv'n ‭ That no room can contain them, but about ‭ Bace by the dams, and let their spirits out ‭ In ceaseless bleating) of more jocund plight ‭ Than my kind friends, ev'n crying out with sight ‭ Of my return so doubted; circled me ‭ With all their welcomes, and as cheerfully ‭ Dispos'd their rapt minds, as if there they saw ‭ Their natural country, cliffy Ithaca, ‭ And ev'n the roofs where they were bred and born, ‭ And vow'd as much, with tears; 'O your return ‭ As much delights us as in you had come ‭ Our country to us, and our natural home. ‭ But what unhappy fate hath reft our friends?' ‭ I gave unlook'd-for answer, that amends ‭ Made for their mourning, bad them first of all ‭ Our ship ashore draw, then in caverns stall ‭ Our foody cattle, hide our mutual prize, ‭ ῾And then,᾿ said I, ῾attend me, that your eyes, ‭ In Circe's sacred house, may see each friend ‭ Eating and drinking banquets out of end.᾿ ‭ They soon obey'd; all but Eurylochus, ‭ Who needs would stay them all, and counsell'd thus: ‭ ῾O wretches! whither will ye? Why are you ‭ Fond of your mischiefs, and such gladness show ‭ For Circe's house, that will transform ye all ‭ To swine, or wolves, or lions? Never shall ‭ Our heads get out, if once within we be, ‭ But stay compell'd by strong necessity. ‭ So wrought the Cyclop, when t' his cave our friends ‭ This bold one led on, and brought all their ends ‭ By his one indiscretion.᾿ I for this ‭ Thought with my sword (that desp'rate head of his ‭ Hewn from his neck) to gash upon the ground ‭ His mangled body, though my blood was bound ‭ In near alliance to him. But the rest ‭ With humble suit contain'd me, and request, ‭ That I would leave him with my ship alone, ‭ And to the sacred palace lead them on. ‭ I led them; nor Eurylochus would stay ‭ From their attendance on me, our late fray ‭ Struck to his heart so. But mean time, my men, ‭ In Circe's house, were all, in sev'ral bain, ‭ Studiously sweeten'd, smug'd with oil, and deck'd ‭ With in and out weeds, and a feast secret ‭ Serv'd in before them; at which close we found ‭ They all were set, cheer'd, and carousing round, ‭ When mutual sight had, and all thought on, then ‭ Feast was forgotten, and the moan again [12] ‭ About the house flew, driv'n with wings of joy. ‭ But then spake Circe: 'Now, no more annoy, ‭ I know myself what woes by sea, and shore, ‭ And men unjust have plagued enough before ‭ Your injur'd virtues. Here then feast as long, ‭ And be as cheerful, till ye grow as strong ‭ As when ye first forsook your country-earth. ‭ Ye now fare all like exiles; not a mirth, ‭ Flash'd in amongst ye, but is quench'd again ‭ With still-renew'd tears, though the beaten vein ‭ Of your distresses should, me think, be now ‭ Benumb with suff'rance.' We did well allow ‭ Her kind persuasions, and the whole year stay'd ‭ In varied feast with her. When, now array'd ‭ The world was with the spring, and orby hours ‭ Had gone the round again through herbs and flow'rs, ‭ The months absolv'd in order, till the days ‭ Had run their full race in Apollo's rays; ‭ My friends remember'd me of home, and said; ‭ If ever fate would sign my pass, delay'd ‭ It should be now no more. I heard them well, ‭ Yet that day spent in feast, till darkness fell, ‭ And sleep his virtues through our vapours shed. ‭ When I ascended sacred Circe's bed, ‭ Implor'd my pass, and her performéd vow ‭ Which now my soul urg'd, and my soldiers now ‭ Afflicted me with tears to get them gone. ‭ All these I told her, and she answer'd these: ‭ "Much-skill'd Ulysses Laertiades! ‭ Remain no more against your wills with me, ‭ But take your free way; only this must be ‭ Perform'd before you steer your course for home: ‭ You must the way to Pluto overcome, ‭ And stern Persephoné, to form your pass, ‭ By th' aged Theban soul Tiresias, ‭ The dark-brow'd prophet, whose soul yet can see ‭ Clearly, and firmly; grave Persephoné, ‭ Ev'n dead, gave him a mind, that he alone ‭ Might sing truth's solid wisdom, and not one ‭ Prove more than shade in his comparison.᾿ ‭ This broke my heart; I sunk into my bed, ‭ Mourn'd, and would never more be comforted ‭ With light, nor life. But having now exprest ‭ My pains enough to her in my unrest, ‭ That so I might prepare her ruth, and get ‭ All I held fit for an affair so great, ‭ I said: 'O Circe, who shall steer my course ‭ To Pluto's kingdom? Never ship had force ‭ To make that voyage.' The divine-in-voice ‭ Said; 'Seek no guide, raise you your mast, and hoise ‭ Your ship's white sails, and then sit yon at peace, ‭ The fresh North Spirit shall waft ye through the Seas. ‭ But, having past the ocean, you shall see ‭ A little shore, that to Persephoné ‭ Puts up a consecrated wood, where grows ‭ Tall firs, and sallows that their fruits soon lose. ‭ Cast anchor in the gulfs, and go alone ‭ To Pluto's dark house, where, to Acheron ‭ Cocytus runs, and Pyriphlegethon, ‭ Cocytus born of Styx, and where a rock ‭ Of both the met floods bears the roaring shock. ‭ The dark heroë, great Tiresias, ‭ Now coming near, to gain propitious pass, ‭ Dig of a cubit ev'ry way a pit, ‭ And pour to all that are deceas'd in it ‭ A solemn sacrifice. For which, first take ‭ Honey and wine, and their commixtion make; ‭ Then sweet wine neat; and thirdly water pour; ‭ And lastly add to these the whitest flour. ‭ Then vow to all the weak necks of the dead ‭ Off'rings a number; and, when thou shalt tread ‭ The Ithacensian shore, to sacrifice ‭ A heifer never-tam'd, and most of prize, ‭ A pile of all thy most esteeméd goods ‭ Enflaming to the dear streams of their bloods; ‭ And, in secret rites, to Tiresias vow ‭ A ram coal-black at all parts, that doth flow ‭ With fat and fleece, and all thy flocks doth lead. ‭ When the all-calling nation of the dead [13] ‭ Thou thus hast pray'd to, offer on the place ‭ A ram and ewe all black being turn'd in face ‭ To dreadful Erebus, thyself aside ‭ The flood's shore walking. And then, gratified ‭ With flocks of souls of men and dames deceas'd ‭ Shall all thy pious rites be. Straight address'd ‭ See then the off'ring that thy fellows slew, ‭ Flay'd, and impos'd in fire; and all thy crew ‭ Pray to the state of either Deity, ‭ Grave Pluto, and severe Persephoné. ‭ Then draw thy sword, stand firm, nor suffer one ‭ Of all the faint shades of the dead and gone ‭ T' approach the blood, till thou hast heard their king, ‭ The wise Tiresias; who thy offering ‭ Will instantly do honour, thy home-ways, ‭ And all the measure of them by the seas, ‭ Amply unfolding.' This the Goddess told; ‭ And then the Morning in her throne of gold ‭ Survey'd the vast world; by whose orient light ‭ The Nymph adorn'd me with attires as bright, ‭ Her own hands putting on both shirt and weed, ‭ Robes fine, and curious, and upon my head ‭ An ornament that glitter'd like a flame, ‭ Girt me in gold; and forth betimes I came ‭ Amongst my soldiers, rous'd them all from sleep, ‭ And bad them now no more observance keep ‭ Of ease, and feast, but straight a-shipboard fall, ‭ For now the Goddess had inform'd me all. ‭ Their noble spirits agreed; nor yet so clear ‭ Could I bring all off, but Elpenor there ‭ His heedless life left. He was youngest man ‭ Of all my company, and one that wan ‭ Least fame for arms, as little for his brain; ‭ Who (too much steep'd in wine, and so made fain ‭ To get refreshing by the cool of sleep, ‭ Apart his fellows, plung'd in vapours deep, ‭ And they as high in tumult of their way) ‭ Suddenly wak'd and (quite out of the stay ‭ A sober mind had giv'n him) would descend ‭ A huge long ladder, forward, and an end ‭ Fell from the very roof, full pitching on ‭ The dearest joint his head was plac'd upon, ‭ Which, quite dissolv'd, let loose his soul to hell. ‭ I to the rest, and Circe's means did tell ‭ Of our return, as crossing clean the hope ‭ I gave them first, and said: 'You think the scope ‭ Of our endeavours now is straight for home; ‭ No; Circe otherwise design'd, whose doom ‭ Enjoin'd us first to greet the dreadful house ‭ Of austere Pluto and his glorious spouse, ‭ To take the counsel of Tiresias, ‭ The rev'rend Theban, to direct our pass.' ‭ This brake their hearts, and grief made tear their hair. ‭ But grief was never good at great affair; ‭ It would have way yet. We went woful on ‭ To ship and shore, where was arriv'd as soon ‭ Circe unseen, a black ewe and a ram ‭ Binding for sacrifice, and, as she came, ‭ Vanish'd again unwitness'd by our eyes; ‭ Which griev'd not us, nor check'd our sacrifice, ‭ For who would see God, loth to let us see, ‭ This way or that bent; still his ways are free. ‭ FINIS DECIMI LIBRI HOM. ODYSS. ‭[1] _Πόδα νηὸς_--He calls the stern the foot of the ship. ‭[2] This place suffers different construction in all the Commentors: ‭in which all err from the mind of the Poet, as in a hundred other ‭places (which yet I want time to approve) especially about _ἐγγὺς ‭γὰρ νυκτός,_ etc. _Prope enim noetis et diei sunt viœ_ (or _similiter,_ ‭which _ἐγγὺς_ signifies) which they will have to be understood, that ‭the days in that region are long, and the nights short; where Homer ‭intends, that the equinoctial is there; for how else is the course of ‭day and night near or equal? But therefore the night's-man hath his ‭double hire, being as long about his charge as the other; and the ‭night being more dangerous, etc. And if the day were so long, why ‭should the night's-man be preferred in wages? ‭[3] For being cast on the stays, as ships are by weather. ‭[4] Antiphas was king there. ‭[5] _Μερμαίρω, curiosè cogito._ ‭[6] _Αἴθοπα καπνόν. Αι͒θοψ_ signifying _rutilus,_ by reason or the ‭fire mixed with it. _Fumus qui fit dut aliquid accenditur._ ‭[7] _᾿Ερικύδεα δαι̑τα._ ‭[8] The whole end of this counsel was to persuade his soldiers to ‭explore those parts, which he knew would prove a most unpleasing ‭motion to them: for their fellows' terrible entertainment with ‭Antiphas, and Polyph. and therefore he prepares the little he hath to ‭say with this long circumstance; implying a necessity of that ‭service, and necessary resolution to add the trial of the event to ‭their other adventures. ‭[9] _Κεδνὸς, cujus animus curas prudentes versat._ ‭[10] Seeing them, he thought of his fellows. ‭[11] The herb Moly, which, with Ulysses' whole narration, hath in ‭chief an allegorical exposition. Notwithstanding I say with our ‭Spondanus, _Credo in hoc vasto mundi ambitu extare res ‭innumeras mirandæ facultatis: adeo, ut ne quidem ista quæ ad ‭transformanda corpora pertinet, jure è mundo eximi possit, etc._ ‭[12] _Φράσσαντό τε πάντα. Commemorabantque omnia._ Intending ‭all their miseries, escapes, and meetings. ‭[13] _Κλυτὰ ἕθνεα νεκρω̑ν._ Which is expounded _Inclyta examina ‭mortuorum:_ but _κλυτὸς_ is the epithet of Pluto; and by analogy ‭belongs to the dead, _quod ad se omnes advocat._ ‭ THE ELEVENTH BOOK OF HOMER'S ODYSSEYS ‭ THE ARGUMENT ‭ Ulysees' way to Hell appears; ‭ Where he the grave Tiresias hears; ‭ Enquires his own and others' fates; ‭ His mother sees, and th' after states ‭ In which were held by sad decease ‭ Heroës, and Heroesses, ‭ A number, that at Troy wag'd war; ‭ As Ajax that was still at jar ‭ With Ithacus, for th' arms he lost; ‭ And with the great Achilles' ghost. ‭ ANOTHER ARGUMENT ‭ _Λάνβδα._ ‭ Ulysses here ‭ Invokes the dead, ‭ The lives appear ‭ Hereafter led. ‭ "Arriv'd now at our ship, we launch'd, and set ‭ Our mast up, put forth sail, and in did get ‭ Our late-got cattle. Up our sails, we went, ‭ My wayward fellows mourning now th' event. [1] ‭ A good companion yet, a foreright wind, ‭ Circe (the excellent utt'rer of her mind) ‭ Supplied our murmuring consorts with, that was ‭ Both speed and guide to our adventurous pass. ‭ All day our sails stood to the winds, and made ‭ Our voyage prosp'rous. Sun then set, and shade ‭ All ways obscuring, on the bounds we fell ‭ Of deep Oceanus, where people dwell ‭ Whom a perpetual cloud obscures outright, ‭ To whom the cheerful sun lends never light, ‭ Nor when he mounts the star-sustaining heaven, ‭ Nor when he stoops earth, and sets up the even, ‭ But night holds fix'd wings, feather'd all with banes, ‭ Above those most unblest Cimmerians. ‭ Here drew we up our ship, our sheep withdrew, ‭ And walk'd the shore till we attain'd the view, ‭ Of that sad region Circe had foreshow'd; ‭ And then the sacred off'rings to be vow'd ‭ Eurylochus and Persimedes bore. ‭ When I my sword drew, and earth's womb did gore ‭ Till I a pit digg'd of a cubit round, ‭ Which with the liquid sacrifice we crown'd, ‭ First honey mix'd with wine, then sweet wine neat, ‭ Then water pour'd in, last the flour of wheat. ‭ Much I importun'd then the weak-neck'd dead, ‭ And vow'd, when I the barren soil should tread ‭ Of clifty Ithaca, amidst my hall ‭ To kill a heifer, my clear best of all, ‭ And give in off'ring, on a pile compos'd ‭ Of all the choice goods my whole house enclos'd. ‭ And to Tiresias himself, alone, ‭ A sheep coal-black, and the selectest one ‭ Of all my flocks. When to the Pow'rs beneath, ‭ The sacred nation that survive with death, ‭ My pray'rs and vows had done devotions fit, ‭ I took the off'rings, and upon the pit ‭ Bereft their lives. Out gush'd the sable blood, ‭ And round about me fled out of the flood ‭ The souls of the deceas'd. There cluster'd then ‭ Youths, and their wives, much-suff'ring aged men, ‭ Soft tender virgins that but new came there ‭ By timeless death, and green their sorrows were. ‭ There men-at-arms, with armours all embrew'd, ‭ Wounded with lances, and with faulchions hew'd, ‭ In numbers, up and down the ditch, did stalk, ‭ And threw unmeasur'd cries about their walk, ‭ So horrid that a bloodless fear surpris'd ‭ My daunted spirits. Straight then I advis'd ‭ My friends to flay the slaughter'd sacrifice, ‭ Put them in fire, and to the Deities, ‭ Stern Pluto and Persephoné, apply ‭ Exciteful pray'rs. Then drew I from my thigh ‭ My well-edg'd sword, stept in, and firmly stood ‭ Betwixt the prease of shadows and the blood, ‭ And would not suffer anyone to dip ‭ Within our off'ring his unsolid lip, ‭ Before Tiresias that did all controul. ‭ The first that press'd in was Elpenor's soul, ‭ His body in the broad-way'd earth as yet ‭ Unmourn'd, unburied by us, since we swet ‭ With other urgent labours. Yet his smart ‭ I wept to see, and rued it from my heart, ‭ Enquiring how he could before me be ‭ That came by ship? He, mourning, answer'd me: ‭ 'In Circe's house, the spite some spirit did bear, ‭ And the unspeakable good liquor there, ‭ Hath been my bane; for, being to descend ‭ A ladder much in height, I did not tend ‭ My way well down, but forwards made a proof ‭ To tread the rounds, and from the very roof ‭ Fell on my neck, and brake it; and this made ‭ My soul thus visit this infernal shade. ‭ And here, by them that next thyself are dear, ‭ Thy wife, and father, that a little one ‭ Gave food to thee, and by thy only son ‭ At home behind thee left, Telemachus, ‭ Do not depart by stealth, and leave me thus, ‭ Unmourn'd, unburied, lest neglected I ‭ Bring on thyself th' incenséd Deity. ‭ I know that, sail'd from hence, thy ship must touch ‭ On th' isle Ææa; where vouchsafe thus much, ‭ Good king, that, landed, thou wilt instantly ‭ Bestow on me thy royal memory ‭ To this grace, that my body, arms and all, ‭ May rest consum'd in fiery funeral; ‭ And on the foamy shore a sepulchre ‭ Erect to me, that after-times may hear ‭ Of one so hapless. Let me these implore ‭ And fix upon my sepulchre the oar [2] ‭ With which alive I shook the aged seas, ‭ And had of friends the dear societies.' ‭ I told the wretched soul I would fulfill ‭ And execute to th' utmost point his will; ‭ And, all the time we sadly talk'd, I still ‭ My sword above the blood held, when aside ‭ The idol of my friend still amplified ‭ His plaint, as up and down the shades he err'd. ‭ Then my deceaséd mother's soul appear'd, ‭ Fair daughter of Autolycus the great, ‭ Grave Anticlea, whom, when forth I set ‭ For sacred Ilion, I had left alive. ‭ Her sight much mov'd me, and to tears did drive ‭ My note of her decease; and yet not she ‭ (Though in my ruth she held the high'st degree) ‭ Would I admit to touch the sacred blood, ‭ Till from Tiresias I had understood ‭ What Circe told me. At the length did land ‭ Theban Tiresias' soul, and in his hand ‭ Sustain'd a golden sceptre, knew me well, ‭ And said: 'O man unhappy, why to hell ‭ Admitt'st thou dark arrival, and the light ‭ The sun gives leav'st, to have the horrid sight ‭ Of this black region, and the shadows here? ‭ Now sheathe thy sharp sword, and the pit forbear, ‭ That I the blood may taste, and then relate ‭ The truth of those acts that affect thy fate.' ‭ I sheath'd my sword, and left the pit, till he, ‭ The black blood tasting, thus instructed me: ‭ 'Renown'd Ulysses! All unask'd I know ‭ That all the cause of thy arrival now ‭ Is to enquire thy wish'd retreat for home; ‭ Which hardly God will let thee overcome, ‭ Since Neptune still will his opposure try, ‭ With all his laid-up anger, for the eye ‭ His lov'd son lost to thee. And yet through all ‭ Thy suff'ring course (which must be capital) ‭ If both thine own affections, and thy friends, ‭ Thou wilt contain, when thy access ascends ‭ The three-fork'd island, having 'scap'd the seas, ‭ Where ye shall find fed on the flow'ry leas ‭ Fat flocks, and oxen, which the Sun doth own, ‭ To whom are all things as well heard as shown, ‭ And never dare one head of those to slay, ‭ But hold unharmful on your wishéd way, ‭ Though through enough affliction, yet secure ‭ Your Fates shall land ye; but presage says sure, ‭ If once ye spoil them, spoil to all thy friends, ‭ Spoil to thy fleet, and if the justice ends ‭ Short of thyself, it shall be long before, ‭ And that length forc'd out with inflictions store, ‭ When, losing all thy fellows, in a sail ‭ Of foreign built (when most thy Fates prevail ‭ In thy deliv'rance) thus th' event shall sort: ‭ Thou shalt find shipwrack raging in thy port, ‭ Proud men thy goods consuming, and thy wife ‭ Urging with gifts, give charge upon thy life. ‭ But all these wrongs revenge shall end to thee, ‭ And force, or cunning, set with slaughter free ‭ The house of all thy spoilers. Yet again ‭ Thou shalt a voyage make, and come to men ‭ That know no sea, nor ships, nor oars that are ‭ Wings to a ship, nor mix with any fare [3] ‭ Salt's savoury vapour. Where thou first shalt land, ‭ This clear-giv'n sign shall let thee understand, ‭ That there those men remain: Assume ashore ‭ Up to thy royal shoulder a ship oar, ‭ With which, when thou shalt meet one on the way ‭ That will in county admiration say ‭ What dost thou with that wan upon thy neck? ‭ There fix that wan thy oar, and that shore deck ‭ With sacred rites to Neptune; slaughter there ‭ A ram, a bull, and (who for strength doth bear ‭ The name of husband to a herd) a boar. ‭ And, coming home, upon thy natural shore, ‭ Give pious hecatombs to all the Gods, ‭ Degrees observ'd. And then the periods ‭ Of all thy labours in the peace shall end ‭ Of easy death; which shall the less extend ‭ His passion to thee, that thy foe, the Sea, ‭ Shall not enforce it, but Death's victory ‭ Shall chance in only-earnest-pray-vow'd age, [4] ‭ Obtain'd at home, quite emptied of his rage, ‭ Thy subjects round about thee, rich and blest. ‭ And here hath Truth summ'd up thy vital rest.' ‭ I answer'd him: 'We will suppose all these ‭ Decreed in Deity; let it likewise please ‭ Tiresias to resolve me, why so near ‭ The blood and me my mother's soul doth bear, ‭ And yet nor word, nor look, vouchsafe her son? ‭ Doth she not know me?' 'No,' said he, 'nor none ‭ Of all these spirits, but myself alone, ‭ Knows anything till he shall taste the blood. ‭ But whomsoever you shall do that good, ‭ He will the truth of all you wish unfold; ‭ Who you envy it to will all withhold.' ‭ Thus said the kingly soul, and made retreat ‭ Amidst the inner parts of Pluto's seat, ‭ When he had spoke thus by divine instinct. ‭ Still I stood firm, till to the blood's precinct ‭ My mother came, and drunk; and then she knew ‭ I was her son, had passion to renew ‭ Her natural plaints, which thus she did pursue: ‭ 'How is it, O my son, that you alive ‭ This deadly-darksome region underdive? ‭ 'Twixt which, and earth, so many mighty seas, ‭ And horrid currents, interpose their prease, ‭ Oceanus in chief? Which none (unless ‭ More help'd than you) on foot now can transgress. ‭ A well-built ship he needs that ventures there. ‭ Com'st thou from Troy but now, enforc'd to err ‭ All this time with thy soldiers? Nor hast seen, ‭ Ere this long day, thy country, and thy queen?' ‭ I answer'd: 'That a necessary end ‭ To this infernal state made me contend; ‭ That from the wise Tiresias' Theban soul ‭ I might an oracle involv'd unroll; ‭ For I came nothing near Achaia yet, ‭ Nor on our lov'd earth happy foot had set, ‭ But, mishaps suff'ring, err'd from coast to coast, ‭ Ever since first the mighty Grecian host ‭ Divine Atrides led to Ilion, ‭ And I his follower, to set war upon ‭ The rapeful Trojans; and so pray'd she would ‭ The fate of that ungentle death unfold, ‭ That forc'd her thither; if some long disease, ‭ Or that the spleen of her-that-arrows-please, ‭ Diana, envious of most eminent dames, ‭ Had made her th' object of her deadly aims? ‭ My father's state and sons I sought, if they ‭ Kept still my goods? Or they became the prey ‭ Of any other, holding me no more ‭ In pow'r of safe return? Or if my store ‭ My wife had kept together with her son? ‭ If she her first mind held, or had been won ‭ By some chief Grecian from my love and bed?' ‭ All this she answer'd: 'That affliction fed ‭ On her blood still at home, and that to grief ‭ She all the days and darkness of her life ‭ In tears had consecrate. That none possest ‭ My famous kingdom's throne, but th' interest ‭ My son had in it still he held in peace, ‭ A court kept like a prince, and his increase ‭ Spent in his subjects' good, administ'ring laws ‭ With justice, and the general applause ‭ A king should merit, and all call'd him king. ‭ My father kept the upland, labouring, ‭ And shunn'd the city, us'd no sumptuous beds, ‭ Wonder'd-at furnitures, nor wealthy weeds, ‭ But in the winter strew'd about the fire ‭ Lay with his slaves in ashes, his attire ‭ Like to a beggar's; when the summer came, ‭ And autumn all fruits ripen'd with his flame, ‭ Where grape-charg'd vines made shadows most abound, ‭ His couch with fall'n leaves made upon the ground, ‭ And here lay he, his sorrow's fruitful state ‭ Increasing as he faded for my fate; ‭ And now the part of age that irksome is ‭ Lay sadly on him. And that life of his ‭ She led, and perish'd in; not slaughter'd by ‭ The Dame that darts lov'd, and her archery; ‭ Nor by disease invaded, vast and foul, ‭ That wastes the body, and sends out the soul ‭ With shame and horror; only in her moan, ‭ For me and my life, she consum'd her own.' ‭ She thus, when I had great desire to prove ‭ My arms the circle where her soul did move. ‭ Thrice prov'd I, thrice she vanish'd like a sleep, ‭ Or fleeting shadow, which struck much more deep ‭ The wounds my woes made, and made ask her why ‭ She would my love to her embraces fly, ‭ And not vouchsafe that ev'n in hell we might ‭ Pay pious Nature her unalter'd right, ‭ And give Vexation here her cruel fill? ‭ Should not the Queen here, to augment the ill ‭ Of ev'ry suff'rance, which her office is, ‭ Enforce thy idol to afford me this? ‭ 'O son,' she answer'd, 'of the race of men ‭ The most unhappy, our most equal Queen ‭ Will mock no solid arms with empty shade, ‭ Nor suffer empty shades again t' invade ‭ Flesh, bones, and nerves; nor will defraud the fire ‭ Of his last dues, that, soon as spirits expire ‭ And leave the white bone, are his native right, ‭ When, like a dream, the soul assumes her flight. ‭ The light then of the living with most haste, ‭ O son, contend to. This thy little taste ‭ Of this state is enough; and all this life ‭ Will make a tale fit to be told thy wife.' ‭ This speech we had; when now repair'd to me ‭ More female spirits, by Persephoné ‭ Driv'n on before her. All th' heroës' wives, ‭ And daughters, that led there their second lives, ‭ About the black blood throng'd. Of whom yet more ‭ My mind impell'd me to inquire, before ‭ I let them all together taste the gore, ‭ For then would all have been dispers'd, and gone ‭ Thick as they came. I, therefore, one by one ‭ Let taste the pit, my sword drawn from my thigh, ‭ And stand betwixt them made, when, sev'rally, ‭ All told their stocks. The first, that quench'd her fire, ‭ Was Tyro, issued of a noble sire. ‭ She said she sprung from pure Salmoneus' bed, ‭ And Cretheus, son of Æolus, did wed; ‭ Yet the divine flood Enipëus lov'd, ‭ Who much the most fair stream of all floods mov'd. ‭ Near whose streams Tyro walking, Neptune came, ‭ Like Enipëus, and enjoy'd the dame. ‭ Like to a hill, the blue and snaky flood ‭ Above th' immortal and the mortal stood, ‭ And hid them both, as both together lay, ‭ Just where his current falls into the sea. ‭ Her virgin waist dissolv'd, she slumber'd then; ‭ But when the God had done the work of men, ‭ Her fair hand gently wringing, thus he said: ‭ 'Woman! rejoice in our combinéd bed, ‭ For when the year hath run his circle round ‭ (Because the Gods' loves must in fruit abound) ‭ My love shall make, to cheer thy teeming moans, ‭ Thy one dear burden bear two famous sons; ‭ Love well, and bring them up. Go home, and see ‭ That, though of more joy yet I shall be free, ‭ Thou dost not tell, to glorify thy birth; ‭ Thy love is Neptune, shaker of the earth.' ‭ This said, he plung'd into the sea; and she, ‭ Begot with child by him, the light let see ‭ Great Pelias, and Neleus, that became ‭ In Jove's great ministry of mighty fame. ‭ Pelias in broad Iolcus held his throne, ‭ Wealthy in cattle; th' other royal son ‭ Rul'd sandy Pylos. To these issue more ‭ This queen of women to her husband bore, ‭ Æson, and Pheres, and Amythaon ‭ That for his fight on horseback stoop'd to none. ‭ Next her, I saw admir'd Antiope, ‭ Asopus' daughter, who (as much as she ‭ Boasted attraction of great Neptune's love) ‭ Boasted to slumber in the arms of Jove, ‭ And two sons likewise at one burden bore ‭ To that her all-controlling paramour, ‭ Amphion, and fair Zethus; that first laid ‭ Great Thebes' foundations, and strong walls convey'd ‭ About her turrets, that seven ports enclos'd, ‭ For though the Thebans much in strength repos'd, ‭ Yet had not they the strength to hold their own, ‭ Without the added aids of wood and stone. ‭ Alcmena next I saw, that famous wife ‭ Was to Amphitryo, and honour'd life ‭ Gave to the lion-hearted Hercules, ‭ That was of Jove's embrace the great increase. ‭ I saw, besides, proud Creon's daughter there, ‭ Bright Megara, that nuptial yoke did wear ‭ With Jove's great son, who never field did try ‭ But bore to him the flow'r of victory. ‭ The mother then of Œdipus I saw, ‭ Fair Epicasta, that, beyond all law, ‭ Her own son married, ignorant of kind. ‭ And he, as darkly taken in his mind, ‭ His mother wedded, and his father slew. ‭ Whose blind act Heav'n expos'd at length to view, ‭ And he in all-lov'd Thebes the supreme state ‭ With much moan manag'd, for the heavy fate ‭ The Gods laid on him. She made violent flight ‭ To Pluto's dark house from the loathéd light, ‭ Beneath a steep beam strangled with a cord, ‭ And left her son, in life, pains as abhorr'd ‭ As all the Furies pour'd on her in hell. ‭ Then saw I Chloris, that did so excell ‭ In answering beauties, that each part had all. ‭ Great Neleus married her, when gifts not small ‭ Had won her favour, term'd by name of dow'r. ‭ She was of all Amphion's seed the flow'r; ‭ Amphion, call'd Iasides, that then ‭ Rul'd strongly Myniæan Orchomen, ‭ And now his daughter rul'd the Pylian throne, ‭ Because her beauty's empire overshone. ‭ She brought her wife-awed husband, Neleús, ‭ Nestor much honour'd, Periclymenus, ‭ And Chromius, sons with sov'reign virtues grac'd; ‭ But after brought a daughter that surpass'd, ‭ Rare-beautied Pero, so for form exact ‭ That Nature to a miracle was rack'd ‭ In her perfections, blaz'd with th' eyes of men; ‭ That made of all the country's hearts a chain, ‭ And drew them suitors to her. Which her sire ‭ Took vantage of, and, since he did aspire ‭ To nothing more than to the broad-brow'd herd ‭ Of oxen, which the common fame so rear'd, ‭ Own'd by Iphiclus, not a man should be ‭ His Pero's husband, that from Phylace ‭ Those never-yet-driv'n oxen could not drive. ‭ Yet these a strong hope held him to achieve, ‭ Because a prophet, that had never err'd, ‭ Had said, that only he should be preferr'd ‭ To their possession. But the equal fate ‭ Of God withstood his stealth; inextricate ‭ Imprisoning bands, and sturdy churlish swains ‭ That were the herdsmen, who withheld with chains ‭ The stealth-attempter; which was only he ‭ That durst abet the act with prophecy, ‭ None else would undertake it, and he must; ‭ The king would needs a prophet should be just. ‭ But when some days and months expired were, ‭ And all the hours had brought about the year, ‭ The prophet did so satisfy the king ‭ (Iphiclus, all his cunning questioning) ‭ That he enfranchis'd him; and, all worst done, ‭ Jove's counsel made th' all-safe conclusión. ‭ Then saw I Leda, link'd in nuptial chain ‭ With Tyndarus, to whom she did sustain ‭ Sons much renown'd for wisdom; Castor one, ‭ That pass'd for use of horse comparison; ‭ And Pollux, that excell'd in whirlbat fight; ‭ Both these the fruitful earth bore, while the light ‭ Of life inspir'd them; after which, they found ‭ Such grace with Jove, that both liv'd under ground, ‭ By change of days; life still did one sustain, ‭ While th' other died; the dead then liv'd again, ‭ The living dying; both of one self date ‭ Their lives and deaths made by the Gods and Fate. ‭ Iphimedia after Leda came, ‭ That did derive from Neptune too the name ‭ Of father to two admirable sons. ‭ Life yet made short their admiratións, ‭ Who God-opposéd Otus had to name, ‭ And Ephialtes far in sound of fame. ‭ The prodigal earth so fed them, that they grew ‭ To most huge stature, and had fairest hue ‭ Of all men, but Orion, under heav'n. ‭ At nine years old nine cubits they were driv'n ‭ Abroad in breadth, and sprung nine fathoms high. ‭ They threaten'd to give battle to the sky, ‭ And all th' Immortals. They were setting on ‭ Ossa upon Olympus, and upon ‭ Steep Ossa leavy Pelius, that ev'n ‭ They might a highway make with lofty heav'n; ‭ And had perhaps perform'd it, had they liv'd ‭ Till they were striplings; but Jove's son depriv'd ‭ Their limbs of life, before th' age that begins ‭ The flow'r of youth, and should adorn their chins. ‭ Phædra and Procris, with wise Minos' flame, ‭ Bright Ariadne, to the off'ring came. ‭ Whom whilome Theseus made his prise from Crete, ‭ That Athens' sacred soil might kiss her feet, ‭ But never could obtain her virgin flow'r, ‭ Till, in the sea-girt Dia, Dian's pow'r ‭ Detain'd his homeward haste, where (in her fane, ‭ By Bacchus witness'd) was the fatal wane ‭ Of her prime glory, Mæra, Clymene, ‭ I witness'd there; and loath'd Eriphyle, ‭ That honour'd gold more than she lov'd her spouse. [5] ‭ But, all th' heroesses in Pluto's house ‭ That then encounter'd me, exceeds my might ‭ To name or number, and ambrosian night ‭ Would quite be spent, when now the formal hours ‭ Present to sleep our all disposéd pow'rs, ‭ If at my ship, or here. My home-made vow ‭ I leave for fit grace to the Gods and you." ‭ This said; the silence his discourse had made ‭ With pleasure held still through the house's shade, ‭ When white-arm'd Areté this speech began: ‭ "Phæacians! How appears to you this man, ‭ So goodly person'd, and so match'd with mind? ‭ My guest he is, but all you stand combin'd ‭ In the renown he doth us. Do not then ‭ With careless haste dismiss him, nor the main ‭ Of his dispatch to one so needy maim, ‭ The Gods' free bounty gives us all just claim ‭ To goods enow." This speech, the oldest man ‭ Of any other Phæacensian, ‭ The grave heroë, Echinëus, gave ‭ All approbation, saying: "Friends! ye have ‭ The motion of the wise queen in such words ‭ As have not miss'd the mark, with which accords ‭ My clear opinion. But Alcinous, ‭ In word and work, must be our rule." He thus; ‭ And then Alcinous said: "This then must stand, ‭ If while I live I rule in the command ‭ Of this well-skill'd-in-navigation state: ‭ Endure then, guest, though most importunate ‭ Be your affects for home. A little stay ‭ If your expectance bear, perhaps it may ‭ Our gifts make more complete. The cares of all ‭ Your due deduction asks; but principal ‭ I am therein the ruler." He replied: ‭ "Alcinous, the most duly glorified ‭ With rule of all of all men, if you lay ‭ Commandment on me of a whole year's stay, ‭ So all the while your preparations rise, ‭ As well in gifts as time, [6] ye can devise ‭ No better wish for me; for I shall come ‭ Much fuller-handed, and more honoured, home, ‭ And dearer to my people, in whose loves ‭ The richer evermore the better proves." ‭ He answer'd: "There is argued in your sight ‭ A worth that works not men for benefit, ‭ Like prollers or impostors; of which crew, ‭ The gentle black earth feeds not up a few, ‭ Here and there wand'rers, blanching tales and lies, ‭ Of neither praise, nor use. You move our eyes ‭ With form, our minds with matter, and our ears ‭ With elegant oration, such as bears ‭ A music in the order'd history ‭ It lays before us. Not Demodocus ‭ With sweeter strains hath us'd to sing to us ‭ All the Greek sorrows, wept out in your own. ‭ But say: Of all your worthy friends, were none ‭ Objected to your eyes that consorts were ‭ To Ilion with you, and serv'd destiny there? ‭ This night is passing long, unmeasur'd, none ‭ Of all my household would to bed yet; on, ‭ Relate these wondrous things. Were I with you, ‭ If you would tell me but your woes, as now, ‭ Till the divine Aurora show'd her head, ‭ I should in no night relish thought of bed." ‭ "Most eminent king," said he, "times all must keep, ‭ There's time to speak much, time as much to sleep. ‭ But would you hear still, I will tell you still, ‭ And utter more, more miserable ill ‭ Of friends than yet, that scap'd the dismal wars, ‭ And perish'd homewards, and in household jars ‭ Wag'd by a wicked woman. The chaste Queen ‭ No sooner made these lady ghosts unseen, ‭ Here and there flitting, but mine eyesight won ‭ The soul of Agamemnon, Atreus' son, ‭ Sad, and about him all his train of friends, ‭ That in Ægisthus' house endur'd their ends ‭ With his stern fortune. Having drunk the blood, ‭ He knew me instantly, and forth a flood ‭ Of springing tears gush'd; out he thrust his hands, ‭ With will t' embrace me, but their old commands ‭ Flow'd not about him, nor their weakest part. ‭ I wept to see, and moan'd him from my heart, ‭ And ask'd: 'O Agamemnon! King of men! ‭ What sort of cruel death hath render'd slain ‭ Thy royal person? Neptune in thy fleet ‭ Heav'n and his hellish billows making meet, ‭ Rousing the winds? Or have thy men by land ‭ Done thee this ill, for using thy command, ‭ Past their consents, in diminution ‭ Of those full shares their worths by lot had won ‭ Of sheep or oxen? Or of any town, ‭ In covetous strife, to make their rights thine own ‭ In men or women prisoners?' He replied: ‭ 'By none of these in any right I died, ‭ But by Ægisthus and my murd'rous wife ‭ (Bid to a banquet at his house) my life ‭ Hath thus been reft me, to my slaughter led ‭ Like to an ox pretended to be fed. ‭ So miserably fell I, and with me ‭ My friends lay massacred, as when you see ‭ At any rich man's nuptials, shot, or feast, ‭ About his kitchen white-tooth'd swine lie drest. ‭ The slaughters of a world of men thine eyes, ‭ Both private, and in prease of enemies, ‭ Have personally witness'd; but this one ‭ Would all thy parts have broken into moan, ‭ To see how strew'd about our cups and cates, ‭ As tables set with feast, so we with fates, ‭ All gash'd and slain lay, all the floor embrued ‭ With blood and brain. But that which most I rued, ‭ Flew from the heavy voice that Priam's seed, ‭ Cassandra, breath'd, whom, she that wit doth feed ‭ With baneful crafts, false Clytemnestra, slew, ‭ Close sitting by me; up my hands I threw ‭ From earth to heav'n, and tumbling on my sword ‭ Gave wretched life up; when the most abhorr'd, ‭ By all her sex's shame, forsook the room, ‭ Nor deign'd, though then so near this heavy home, ‭ To shut my lips, or close my broken eyes. ‭ Nothing so heap'd is with impieties, ‭ As such a woman that would kill her spouse ‭ That married her a maid. When to my house ‭ I brought her, hoping of her love in heart, ‭ To children, maids, and slaves. But she (in th' art ‭ Of only mischief hearty) not alone ‭ Cast on herself this foul aspersión, ‭ But loving dames, hereafter, to their lords ‭ Will bear, for good deeds, her bad thoughts and words.' ‭ 'Alas,' said I, 'that Jove should hate the lives ‭ Of Atreus' seed so highly for their wives! ‭ For Menelaus' wife a number fell, ‭ For dang'rous absence thine sent thee to hell.' ‭ 'For this,' he answer'd, 'be not thou more kind ‭ Than wise to thy wife. Never all thy mind ‭ Let words express to her. Of all she knows, ‭ Curbs for the worst still, in thyself repose. ‭ But thou by thy wife's wiles shalt lose no blood, ‭ Exceeding wise she is, and wise in good. ‭ Icarius' daughter, chaste Penelope, ‭ We left a young bride, when for battle we ‭ Forsook the nuptial peace, and at her breast ‭ Her first child sucking, who, by this hour, blest, ‭ Sits in the number of surviving men. ‭ And his bliss she hath, that she can contain, ‭ And her bliss thou hast, that she is so wise. ‭ For, by her wisdom, thy returnéd eyes ‭ Shall see thy son, and he shall greet his sire ‭ With fitting welcomes; when in my retire, ‭ My wife denies mine eyes my son's dear sight, ‭ And, as from me, will take from him the light, ‭ Before she adds one just delight to life, ‭ Or her false wit one truth that fits a wife. ‭ For her sake therefore let my harms advise, ‭ That though thy wife be ne'er so chaste and wise, ‭ Yet come not home to her in open view, [7] ‭ With any ship or any personal show, ‭ But take close shore disguis'd, nor let her know, ‭ For 'tis no world to trust a woman now. ‭ But what says Fame? Doth my son yet survive, ‭ In Orchomen, or Pylos? Or doth live ‭ In Sparta with his uncle? Yet I see ‭ Divine Orestes is not here with me.' ‭ I answer'd, asking: 'Why doth Atreus' son ‭ Enquire of me, who yet arriv'd where none ‭ Could give to these news any certain wings? ‭ And 'tis absurd to tell uncertain things.' ‭ Such sad speech past us; and as thus we stood, ‭ With kind tears rend'ring unkind fortunes good, ‭ Achilles' and Patroclus' soul appear'd, ‭ And his soul, of whom never ill was heard, ‭ The good Antilochus, and the soul of him ‭ That all the Greeks past both for force and limb, ‭ Excepting the unmatch'd Æacides, ‭ Illustrious Ajax. But the first of these ‭ That saw, acknowledg'd, and saluted me, ‭ Was Thetis' conqu'ring son, who (heavily ‭ His state here taking) said: 'Unworthy breath! ‭ What act yet mightier imagineth ‭ Thy vent'rous spirit? How dost thou descend ‭ These under-regions, where the dead man's end ‭ Is to be look'd on, and his foolish shade?' ‭ I answer'd him: 'I was induc'd t' invade ‭ These under-parts, most excellent of Greece, ‭ To visit wise Tiresias, for advice ‭ Of virtue to direct my voyage home ‭ To rugged Ithaca; since I could come ‭ To note in no place, where Achaia stood, ‭ And so liv'd ever, tortur'd with the blood ‭ In man's vain veins. Thou, therefore, Thetis' son, ‭ Hast equall'd all, that ever yet have won ‭ The bliss the earth yields, or hereafter shall. ‭ In life thy eminence was ador'd of all, ‭ Ev'n with the Gods; and now, ev'n dead, I see ‭ Thy virtues propagate thy empery ‭ To a renew'd life of command beneath; ‭ So great Achilles triumphs over death.' ‭ This comfort of him this encounter found; ‭ 'Urge not my death to me, nor rub that wound, ‭ I rather wish to live in earth a swain, ‭ Or serve a swain for hire, that scarce can gain ‭ Bread to sustain him, than, that life once gone, ‭ Of all the dead sway the imperial throne. ‭ But say, and of my son some comfort yield, ‭ If he goes on in first fights of the field, ‭ Or lurks for safety in the obscure rear? ‭ Or of my father if thy royal ear ‭ Hath been advertis'd, that the Phthian throne ‭ He still commands, as greatest Myrmidon? ‭ Or that the Phthian and Thessalian rage ‭ (Now feet and hands are in the hold of age) ‭ Despise his empire? Under those bright rays, ‭ In which heav'n's fervour hurls about the days. ‭ Must I no more shine his revenger now, ‭ Such as of old the Ilion overthrow ‭ Witness'd my anger, th' universal host ‭ Sending before me to this shady coast, ‭ In fight for Grecia. Could I now resort, ‭ (But for some small time) to my father's court, ‭ In spirit and pow'r as then, those men should find ‭ My hands inaccessible, and of fire my mind, ‭ That durst with all the numbers they are strong ‭ Unseat his honour, and suborn his wrong.' ‭ This pitch still flew his spirit, though so low, ‭ And this I answer'd thus: 'I do not know ‭ Of blameless Peleus any least report, ‭ But of your son, in all the utmost sort, ‭ I can inform your care with truth, and thus: ‭ From Scyros princely Neoptolemus ‭ By fleet I convey'd to the Greeks, where he ‭ Was chief, at both parts, when our gravity ‭ Retir'd to council, and our youth to fight. ‭ In council still so fiery was Conceit ‭ In his quick apprehension of a cause, ‭ That first he ever spake, nor pass'd the laws ‭ Of any great stay, in his greatest haste. ‭ None would contend with him, that counsell'd last, ‭ Unless illustrious Nestor, he and I ‭ Would sometimes put a friendly contrary ‭ On his opinion. In our fights, the prease ‭ Of great or common, he would never cease, ‭ But far before fight ever. No man there, ‭ For force, he forcéd. He was slaughterer ‭ Of many a brave man in most dreadful fight. ‭ But one and other whom he reft of light, ‭ In Grecian succour, I can neither name, ‭ Nor give in number. The particular fame ‭ Of one man's slaughter yet I must not pass; ‭ Eurypylus Telephides he was, ‭ That fell beneath him, and with him the falls ‭ Of such huge men went, that they show'd like whales [8] ‭ Rampir'd about him. Neoptolemus ‭ Set him so sharply, for the sumptuous ‭ Favours of mistresses he saw him wear; ‭ For past all doubt his beauties had no peer ‭ Of all that mine eyes noted, next to one, ‭ And that was Memnon, Tithon's Sun-like son. ‭ Thus far, for fight in public, may a taste ‭ Give of his eminence. How far surpast ‭ His spirit in private, where he was not seen, ‭ Nor glory could be said to praise his spleen, ‭ This close note I excerpted. When we sat ‭ Hid in Epëus' horse, no optimate ‭ Of all the Greeks there had the charge to ope ‭ And shut the stratagem but I. [9] My scope ‭ To note then each man's spirit in a strait ‭ Of so much danger, much the better might ‭ Be hit by me, than others, as, provok'd, ‭ I shifted place still, when, in some I smok'd ‭ Both privy tremblings, and close vent of tears, ‭ In him yet not a soft conceit of theirs ‭ Could all my search see, either his wet eyes ‭ Ply'd still with wipings, or the goodly guise, ‭ His person all ways put forth, in least part, ‭ By any tremblings, show'd his touch'd-at heart. ‭ But ever he was urging me to make ‭ Way to their sally, by his sign to shake ‭ His sword hid in his scabbard, or his lance ‭ Loaded with iron, at me. No good chance ‭ His thoughts to Troy intended. In th' event, ‭ High Troy depopulate, he made ascent ‭ To his fair ship, with prise and treasure store, ‭ Safe, and no touch away with him he bore ‭ Of far-off-hurl'd lance, or of close-fought sword, ‭ Whose wounds for favours war doth oft afford, ‭ Which he (though sought) miss'd in war's closest wage. ‭ _In close fights Mars doth never fight, but rage.'_ ‭ This made the soul of swift Achilles tread ‭ A march of glory through the herby mead, ‭ For joy to hear me so renown his son; ‭ And vanish'd stalking. But with passión ‭ Stood th' other souls struck, and each told his bane. ‭ Only the spirit Telamonian [10] ‭ Kept far off, angry for the victory ‭ I won from him at fleet; though arbitry ‭ Of all a court of war pronounc'd it mine, ‭ And Pallas' self. Our prise were th' arms divine ‭ Of great Æacides, proposd t' our fames ‭ By his bright Mother, at his funeral games. ‭ I wish to heav'n I ought not to have won; ‭ Since for those arms so high a head so soon ‭ The base earth cover'd, Ajax, that of all ‭ The host of Greece had person capital, ‭ And acts as eminent, excepting his ‭ Whose arms those were, in whom was nought amiss. ‭ I tried the great soul with soft words, and said: ‭ 'Ajax! Great son of Telamon, array'd ‭ In all our glories! What! not dead resign ‭ Thy wrath for those curst arms? The Pow'rs divine ‭ In them forg'd all our banes, in thine own one, ‭ In thy grave fall our tower was overthrown. ‭ We mourn, for ever maim'd, for thee as much ‭ As for Achilles; nor thy wrong doth touch, ‭ In sentence, any but Saturnius' doom; ‭ In whose hate was the host of Greece become ‭ A very horror; who express'd it well ‭ In signing thy fate with this timeless hell. ‭ Approach then, king of all the Grecian merit, ‭ Repress thy great mind and thy flamy spirit, ‭ And give the words I give thee worthy ear.' ‭ All this no word drew from him, but less near ‭ The stern soul kept; to other souls he fled, ‭ And glid along the river of the dead. ‭ Though anger mov'd him, yet he might have spoke, ‭ Since I to him. But my desires were strook ‭ With sight of other souls. And then I saw ‭ Minos, that minister'd to Death a law, ‭ And Jove's bright son was. He was set, and sway'd ‭ A golden sceptre; and to him did plead ‭ A sort of others, set about his throne, ‭ In Pluto's wide-door'd house; when straight came on ‭ Mighty Orion, who was hunting there ‭ The herds of those beasts he had slaughter'd here ‭ In desert hills on earth. A club he bore, ‭ Entirely steel, whose virtues never wore. ‭ Tityus I saw, to whom the glorious earth ‭ Open'd her womb, and gave unhappy birth. ‭ Upwards, and flat upon the pavement, lay ‭ His ample limbs, that spread in their display ‭ Nine acres' compass. On his bosom sat ‭ Two vultures, digging, through his caul of fat, ‭ Into his liver with their crookéd beaks; ‭ And each by turns the concrete entrail breaks ‭ (As smiths their steel beat) set on either side. ‭ Nor doth he ever labour to divide ‭ His liver and their beaks, nor with his hand ‭ Offer them off, but suffers by command ‭ Of th' angry Thund'rer, off'ring to enforce ‭ His love Latona, in the close recourse ‭ She us'd to Pytho through the dancing land, ‭ Smooth Panopëus, I saw likewise stand, ‭ Up to the chin, amidst a liquid lake, ‭ Tormented Tantalus, yet could not slake ‭ His burning thirst. Oft as his scornful cup ‭ Th' old man would taste, so oft 'twas swallow'd up, ‭ And all the black earth to his feet descried, ‭ Divine pow'r (plaguing him) the lake still dried. ‭ About his head, on high trees, clust'ring, hung ‭ Pears, apples, granates, olives ever-young, ‭ Delicious figs, and many fruit-trees more ‭ Of other burden; whose alluring store ‭ When th' old soul striv'd to pluck, the winds from sight, ‭ In gloomy vapours, made them vanish quite. ‭ There saw I Sisyphus in infinite moan, ‭ With both hands heaving up a massy stone, ‭ And on his tip-toes racking all his height, ‭ To wrest up to a mountain-top his freight; ‭ When prest to rest it there, his nerves quite spent, ‭ Down rush'd the deadly quarry, the event ‭ Of all his torture new to raise again; ‭ To which straight set his never-rested pain. ‭ The sweat came gushing out from ev'ry pore ‭ And on his head a standing mist he wore, ‭ Reeking from thence, as if a cloud of dust ‭ Were rais'd about it. Down with these was thrust ‭ The idol of the force of Hercules, ‭ But his firm self did no such fate oppress, ‭ He feasting lives amongst th' Immortal States, ‭ White-ankled Hebe and himself made mates ‭ In heav'nly nuptials. Hebe, Jove's dear race, ‭ And Juno's whom the golden sandals grace. ‭ About him flew the clamours of the dead ‭ Like fowls, and still stoop'd cuffing at his head. ‭ He with his bow, like Night, stalk'd up and down, ‭ His shaft still nock'd, and hurling round his frown ‭ At those vex'd hov'rers, aiming at them still, ‭ And still, as shooting out, desire to still. ‭ A horrid bawdrick wore he thwart his breast, ‭ The thong all-gold, in which were forms imprest, ‭ Where art and miracle drew equal breaths, ‭ In bears, boars, lions, battles, combats, deaths, ‭ Who wrought that work did never such before, ‭ Nor so divinely will do ever more. ‭ Soon as he saw, he knew me, and gave speech: ‭ 'Son of Laertes, high in wisdom's reach, ‭ And yet unhappy wretch, for in this heart, ‭ Of all exploits achiev'd by thy desert, ‭ Thy worth but works out some sinister fate, ‭ As I in earth did. I was generate ‭ By Jove himself, and yet past mean opprest ‭ By one my far inferior, whose proud hest ‭ Impos'd abhorréd labours on my hand. ‭ Of all which one was, to descend this strand, ‭ And hale the dog from thence. He could not think ‭ An act that danger could make deeper sink. ‭ And yet this depth I drew, and fetch'd as high, ‭ As this was low, the dog. The Deity ‭ Of sleight and wisdom, as of downright pow'r, ‭ Both stoop'd, and rais'd, and made me conqueror.' ‭ This said, he made descent again as low ‭ As Pluto's court; when I stood firm, for show ‭ Of more heroës of the times before, ‭ And might perhaps have seen my wish of more, ‭ (As Theseus and Pirithous, deriv'd ‭ From roots of Deity) but before th' achiev'd ‭ Rare sight of these, the rank-soul'd multitude ‭ In infinite flocks rose, venting sounds so rude, ‭ That pale Fear took me, lest the Gorgon's head ‭ Rush'd in amongst them, thrust up, in my dread, ‭ By grim Persephoné. I therefore sent ‭ My men before to ship, and after went. ‭ Where, boarded, set, and launch'd, the ocean wave ‭ Our oars and forewinds speedy passage gave. ‭ FINIS LIBRI UNDECIMI HOM. ODYSS. ‭[1] They mourned the event before they knew it. ‭[2] _Misenus apud Virgilium, ingenti mole, etc._ ‭[3] Men that never eat salt with their food. ‭[4] _Γήπᾳ ὑπὸ λιπαρῳ̑._ Which all translate _senectute sub molli._ ‭The epithet _λιπαρῳ̑;_ not of _λιπαρὸς,_ viz, _pinguis,_ or ‭_λιπαρω̑ς, pinguiter,_ but _λιπαρω̑ς_ signifying _flagitanter ‭orando._ To which pious age is ever altogether addicted. ‭[5] Amphiaraus was her husband, whom she betrayed to his ruin at ‭Thebes, for gold taken of Adrastus her brother. ‭[6] _Venustè et salsè dictum._ ‭[7] This advice he followed at his coming home. ‭[8] This place (and a number more) is most miserably mistaken by ‭all translators and commentors. ‭[9] The horse abovesaid. ‭[10] Ajax the son of Telamon. ‭ THE TWELFTH BOOK OF HOMER'S ODYSSEYS ‭ THE ARGUMENT ‭ He shows from Hell his safe retreat ‭ To th' isle Ææa, Circe's seat; ‭ And how he 'scap'd the Sirens' calls, ‭ With th' erring rocks, and waters' falls, ‭ That Scylla and Charybdis break; ‭ The Sun' s stol' n herds; and his sad wreak ‭ Both of Ulysses' ship and men, ‭ His own head 'scaping scarce the pain. ‭ ‭ ANOTHER ARGUMENT ‭ _Μυ̑_ ‭ The rocks that err'd, ‭ The Sirens' call. ‭ The Sun's stol'n herd. ‭ The soldiers' fall. ‭ "Our ship now past the straits of th' ocean flood, ‭ She plow'd the broad sea's billows, and made good ‭ The isle Ææa, where the palace stands ‭ Of th' early riser with the rosy hands, ‭ Active Aurora, where she loves to dance, ‭ And where the Sun doth his prime beams advance. ‭ When here arriv'd, we drew her up to land, ‭ And trod ourselves the re-saluted sand, ‭ Found on the shore fit resting for the night, ‭ Slept, and expected the celestial light. ‭ Soon as the white-and-red-mix'd finger'd Dame ‭ Had gilt the mountains with her saffron flame, ‭ I sent my men to Circe's house before, ‭ To fetch deceas'd Elpenor to the shore. ‭ Straight swell'd the high banks with fell'd heaps of trees, ‭ And, full of tears, we did due exsequies ‭ To our dead friend. Whose corse consum'd with fire, ‭ And honour'd arms, whose sepulchre entire, ‭ And over that a column rais'd, his oar, ‭ Curiously carv'd, to his desire before, ‭ Upon the top of all his tomb we fix'd. ‭ Of all rites fit his funeral pile was mix'd. ‭ Nor was our safe ascent from Hell conceal'd ‭ From Circe's knowledge; nor so soon reveal'd ‭ But she was with us, with her bread and food, ‭ And ruddy wine, brought by her sacred brood ‭ Of woods and fountains. In the midst she stood, ‭ And thus saluted us; 'Unhappy men, ‭ That have, inform'd with all your senses, been ‭ In Pluto's dismal mansion! You shall die ‭ Twice now, where others, that Mortality ‭ In her fair arms holds, shall but once decease. ‭ But eat and drink out all conceit of these, ‭ And this day dedicate to food and wine, ‭ The following night to sleep. When next shall shine ‭ The cheerful morning, you shall prove the seas. ‭ Your way, and ev'ry act ye must address, ‭ My knowledge of their order shall design, ‭ Lest with your own bad counsels ye incline ‭ Events as bad against ye, and sustain, ‭ By sea and shore, the woful ends that reign ‭ In wilful actions.' Thus did she advise ‭ And, for the time, our fortunes were so wise ‭ To follow wise directions. All that day ‭ We sat and feasted. When his lower way ‭ The Sun had entered, and the Even the high, ‭ My friends slept on their gables; she and I ‭ (Led by her fair hand to place apart, ‭ By her well-sorted) did to sleep convert ‭ Our timid pow'rs; when all things Fate let fall ‭ In our affair she ask'd; I told her all. ‭ To which she answer'd: 'These things thus took end. ‭ And now to those that I inform attend, ‭ Which you rememb'ring, God himself shall be ‭ The blesséd author of your memory. ‭ First to the Sirens ye shall come, that taint ‭ The minds of all men whom they can acquaint ‭ With their attractions. Whosoever shall, ‭ For want of knowledge mov'd, but hear the call ‭ Of any Siren, he will so despise ‭ Both wife and children, for their sorceries, ‭ That never home turns his affection's stream, ‭ Nor they take joy in him, nor he in them. ‭ The Sirens will so soften with their song ‭ (Shrill, and in sensual appetite so strong) ‭ His loose affections, that he gives them head. ‭ And then observe: They sit amidst a mead, ‭ And round about it runs a hedge or wall ‭ Of dead men's bones, their wither'd skins and all ‭ Hung all along upon it; and these men ‭ Were such as they had fawn'd into their fen, ‭ And then their skins hung on their hedge of bones. ‭ Sail by them therefore, thy companions ‭ Beforehand causing to stop ev'ry ear ‭ With sweet soft wax, so close that none may hear ‭ A note of all their charmings. Yet may you, ‭ If you affect it, open ear allow ‭ To try their motion; but presume not so ‭ To trust your judgment, when your senses go ‭ So loose about you, but give strait command ‭ To all your men, to bind you foot and hand ‭ Sure to the mast, that you may safe approve ‭ How strong in instigation to their love ‭ Their rapting tunes are. If so much they move, ‭ That, spite of all your reason, your will stands ‭ To be enfranchis'd both of feet and hands, ‭ Charge all your men before to slight your charge, ‭ And rest so far from fearing to enlarge ‭ That much more sure they bind you. When your friends ‭ Have outsail'd these, the danger that transcends ‭ Rests not in any counsel to prevent, ‭ Unless your own mind finds the tract and bent ‭ Of that way that avoids it. I can say ‭ That in your course there lies a twofold way, ‭ The right of which your own, taught, present wit, ‭ And grace divine, must prompt. In gen'ral yet ‭ Let this inform you: Near these Sirens' shore ‭ Move two steep rocks, at whose feet lie and roar ‭ The black sea's cruel billows; the bless'd Gods ‭ Call them the Rovers. Their abhorr'd abodes ‭ No bird can pass; no not the doves, whose fear [1] ‭ Sire Jove so loves that they are said to bear ‭ Ambrosia to him, can their ravine 'scape, ‭ But one of them falls ever to the rape ‭ Of those sly rocks; yet Jove another still ‭ Adds to the rest, that so may ever fill ‭ The sacred number. Never ship could shun ‭ The nimble peril wing'd there, but did run ‭ With all her bulk, and bodies of her men, ‭ To utter ruin. For the seas retain ‭ Not only their outrageous æsture there, ‭ But fierce assistants of particular fear, ‭ And supernatural mischief, they exspire, ‭ And those are whirlwinds of devouring fire ‭ Whisking about still. Th' Argive ship alone, ‭ Which bore the care of all men, got her gone, [2] ‭ Come from Areta. Yet perhaps ev'n she ‭ Had wrack'd at those rocks, if the Deity, ‭ That lies by Jove's side, had not lent her hand ‭ To their transmission; since the man, that mann'd ‭ In chief that voyage, she in chief did love. ‭ Of these two spiteful rocks, the one doth shove ‭ Against the height of heav'n her pointed brow. ‭ A black cloud binds it round, and never show ‭ Lends to the sharp point; not the clear blue sky ‭ Lets ever view it, not the summer's eye, ‭ Nor fervent autumn's. None that death could end ‭ Could ever scale it, or, if up, descend, ‭ Though twenty hands and feet he had for hold, ‭ A polish'd ice-like glibness doth enfold ‭ The rock so round, whose midst a gloomy cell ‭ Shrouds so far westward that it sees to hell. ‭ From this keep you as far, as from his bow ‭ An able young man can his shaft bestow. ‭ For here the whuling Scylla shrouds her face, [3] ‭ That breathes a voice at all parts no more base ‭ Than are a newly-kitten'd kitling's cries, ‭ Herself a monster yet of boundless size, ‭ Whose sight would nothing please a mortal's eyes, ‭ No nor the eyes of any God, if he ‭ (Whom nought should fright) fell foul on her, and she ‭ Her full shape show'd. Twelve foul feet bear about ‭ Her ugly bulk. Six huge long necks look out ‭ Of her rank shoulders; ev'ry neck doth let ‭ A ghastly head out; ev'ry head three set, ‭ Thick thrust together, of abhorréd teeth, ‭ And ev'ry tooth stuck with a sable death. ‭ She lurks in midst of all her den, and streaks ‭ From out a ghastly whirlpool all her necks; ‭ Where, gloting round her rock, to fish she falls; ‭ And up rush dolphins, dogfish; somewhiles whales ‭ If got within her when her rapine feeds; ‭ For ever-groaning Amphitrite breeds ‭ About her whirlpool an unmeasur'd store. ‭ No sea-man ever boasted touch of shore ‭ That there touch'd with his ship, but still she fed ‭ Of him and his; a man for ev'ry head ‭ Spoiling his ship of. You shall then descry ‭ The other humbler rock, that moves so nigh ‭ Your dart may mete the distance. It receives ‭ A huge wild fig-tree, curl'd with ample leaves, ‭ Beneath whose shades divine Charybdis sits, ‭ Supping the black deeps. Thrice a day her pits ‭ She drinking all dry, and thrice a day again ‭ All up she belches, baneful to sustain. ‭ When she is drinking, dare not near her draught, ‭ For not the force of Neptune, if once caught, ‭ Can force your freedom. Therefore, in your strife ‭ To 'scape Charybdis, labour all for life ‭ To row near Scylla, for she will but have ‭ For her six heads six men; and better save ‭ The rest, than all make off'rings to the wave.' ‭ This need she told me of my loss, when I ‭ Desir'd to know, if that Necessity, ‭ When I had 'scap'd Charybdis' outrages, ‭ My pow'rs might not revenge, though not redress? ‭ She answer'd: 'O unhappy! art thou yet ‭ Enflam'd with war, and thirst to drink thy sweat? ‭ Not to the Gods give up both arms and will? ‭ She deathless is, and that immortal ill ‭ Grave, harsh, outrageous, not to be subdued, ‭ That men must suffer till they be renew'd. ‭ Nor lives there any virtue that can fly ‭ The vicious outrage of their cruelty. ‭ Shouldst thou put arms on, and approach the rock, ‭ I fear six more must expiate the shock. ‭ Six heads six men ask still. Hoise sail, and fly, ‭ And, in thy flight, aloud on Cratis cry ‭ (Great Scylla's mother, who expos'd to light ‭ The bane of men) and she will do such right ‭ To thy observance, that she down will tread ‭ Her daughter's rage, nor let her show a head. ‭ From thenceforth then, for ever past her care, ‭ Thou shalt ascend the isle triangular, ‭ Where many oxen of the Sun are fed, ‭ And fatted flocks. Of oxen fifty head ‭ In ev'ry herd feed, and their herds are seven; ‭ And of his fat flocks is their number even. ‭ Increase they yield not, for they never die. ‭ There ev'ry shepherdess a Deity. ‭ Fair Phaëthusa, and Lampetié, ‭ The lovely Nymphs are that their guardians be, ‭ Who to the daylight's lofty-going Flame ‭ Had gracious birthright from the heav'nly Dame, ‭ Still young Neæra; who (brought forth and bred) ‭ Far off dismiss'd them, to see duly fed ‭ Their father's herds and flocks in Sicily. ‭ These herds and flocks if to the Deity ‭ Ye leave, as sacred things, untouch'd, and on ‭ Go with all fit care of your home, alone, ‭ (Though through some suff'rance) you yet safe shall land ‭ In wishéd Ithaca. But if impious hand ‭ You lay on those herds to their hurts, I then ‭ Presage sure ruin to thy ship and men. ‭ If thou escap'st thyself, extending home ‭ Thy long'd-for landing, thou shalt loaded come ‭ With store of losses, most exceeding late, ‭ And not consorted with a savéd mate.' ‭ This said, the golden-thron'd Aurora rose, ‭ She her way went, and I did mine dispose ‭ Up to my ship, weigh'd anchor, and away. ‭ When rev'rend Circe help'd us to convey ‭ Our vessel safe, by making well inclin'd ‭ A seaman's true companion, a forewind, ‭ With which she fill'd our sails; when, fitting all ‭ Our arms close by us, I did sadly fall ‭ To grave relation what concern'd in fate ‭ My friends to know, and told them that the state ‭ Of our affairs' success, which Circe had ‭ Presag'd to me alone, must yet be made ‭ To one nor only two known, but to all; ‭ That, since their lives and deaths were left to fall ‭ In their elections, they might life elect, ‭ And give what would preserve it fit effect. ‭ I first inform'd them, that we were to fly ‭ The heav'nly-singing Sirens' harmony, ‭ And flow'r-adorned meadow; and that I ‭ Had charge to hear their song, but fetter'd fast ‭ In bands, unfavour'd, to th' erected mast, ‭ From whence, if I should pray, or use command, ‭ To be enlarg'd, they should with much more band ‭ Contain my strugglings. This I simply told ‭ To each particular, nor would withhold ‭ What most enjoin'd mine own affection's stay, ‭ That theirs the rather might be taught t' obey. ‭ In mean time flew our ships, and straight we fetch'd ‭ The Siren's isle; a spleenless wind so stretch'd ‭ Her wings to waft us, and so urg'd our keel. ‭ But having reach'd this isle, we could not feel ‭ The least gasp of it, it was stricken dead, ‭ And all the sea in prostrate slumber spread, ‭ The Sirens' devil charm'd all. Up then flew ‭ My friends to work, struck sail, together drew, ‭ And under hatches stow'd them, sat, and plied ‭ The polish'd oars, and did in curls divide ‭ The white-head waters. My part then came on: ‭ A mighty waxen cake I set upon, ‭ Chopp'd it in fragments with my sword, and wrought ‭ With strong hand ev'ry piece, till all were soft. ‭ The great pow'r of the sun, in such a beam ‭ As then flew burning from his diadem, ‭ To liquefaction help'd us. Orderly ‭ I stopp'd their ears; and they as fair did ply ‭ My feet and hands with cords, and to the mast ‭ With other halsers made me soundly fast. ‭ Then took they seat, and forth our passage strook, ‭ The foamy sea beneath their labour shook. ‭ Row'd on, in reach of an erected voice, ‭ The Sirens soon took note, without our noise, ‭ Tun'd those sweet accents that made charms so strong, ‭ And these learn'd numbers made the Sirens' song: ‭ _'Come here, thou worthy of a world of praise, ‭ That dost so high the Grecian glory raise, ‭ Ulysses! stay thy ship, and that song hear ‭ That none pass'd ever but it bent his ear, ‭ But left him ravish'd, and instructed more ‭ By us, than any ever heard before. ‭ For we know all things whatsoever were ‭ In wide Troy labour'd; whatsoever there ‭ The Grecians and the Trojans both sustain'd ‭ By those high issues that the Gods ordain'd. ‭ And whatsoever all the earth can show ‭ T' inform a knowledge of desert, we know.'_ ‭ This they gave accent in the sweetest strain ‭ That ever open'd an enamour'd vein. ‭ When my constrain'd heart needs would have mine ear ‭ Yet more delighted, force way forth, and hear. ‭ To which end I commanded with all sign ‭ Stern looks could make (for not a joint of mine ‭ Had pow'r to stir) my friends to rise, and give ‭ My limbs free way. They freely striv'd to drive ‭ Their ship still on. When, far from will to loose, ‭ Eurylochus and Perimedes rose ‭ To wrap me surer, and oppress'd me more ‭ With many a halser than had use before. ‭ When, rowing on without the reach of sound, ‭ My friends unstopp'd their ears, and me unbound, ‭ And that isle quite we quitted. But again ‭ Fresh fears employ'd us. I beheld a main ‭ Of mighty billows, and a smoke ascend, ‭ A horrid murmur hearing. Ev'ry friend ‭ Astonish'd sat; from ev'ry hand his Oar ‭ Fell quite forsaken; with the dismal roar ‭ Were all things there made echoes; stone-still stood ‭ Our ship itself, because the ghastly flood ‭ Took all men's motions from her in their own. ‭ I through the ship went, labouring up and down ‭ My friends' recover'd spirits. One by one ‭ I gave good words, and said: That well were known ‭ These ills to them before, I told them all, ‭ And that these could not prove more capital ‭ Than those the Cyclops block'd us up in, yet ‭ My virtue, wit, and heav'n-help'd counsels set ‭ Their freedoms open. I could not believe ‭ But they remember'd it, and wish'd them give ‭ My equal care and means now equal trust. ‭ The strength they had for stirring up they must ‭ Rouse and extend, to try if Jove had laid ‭ His pow'rs in theirs up, and would add his aid ‭ To 'scape ev'n that death. In particular then, ‭ I told our pilot, that past other men ‭ He most must bear firm spirits, since he sway'd ‭ The continent that all our spirits convey'd, ‭ In his whole guide of her. He saw there boil ‭ The fiery whirlpools that to all our spoil ‭ Inclos'd a rock, without which he must steer, ‭ Or all our ruins stood concluded there. ‭ All heard me and obey'd, and little knew ‭ That, shunning that rock, six of them should rue ‭ The wrack another hid. For I conceal'd ‭ The heavy wounds, that never would be heal'd, ‭ To be by Scylla open'd; for their fear ‭ Would then have robb'd all of all care to steer, ‭ Or stir an oar, and made them hide beneath, ‭ When they and all had died an idle death. ‭ But then ev'n I forgot to shun the harm ‭ Circe forewarn'd; who will'd I should not arm, ‭ Nor show myself to Scylla, lest in vain ‭ I ventur'd life. Yet could not I contain, ‭ But arm'd at all parts, and two lances took, ‭ Up to the foredeck went, and thence did look ‭ That rocky Scylla would have first appear'd ‭ And taken my life with the friends I fear'd. ‭ From thence yet no place could afford her sight, ‭ Though through the dark rock mine eye threw her light, ‭ And ransack'd all ways. I then took a strait ‭ That gave myself, and some few more, receit ‭ 'Twixt Scylla and Charybdis; whence we saw ‭ How horridly Charybdis' throat did draw ‭ The brackish sea up, which when all aboard ‭ She spit again out, never caldron sod ‭ With so much fervour, fed with all the store ‭ That could enrage it; all the rock did roar ‭ With troubled waters; round about the tops ‭ Of all the steep crags flew the foamy drops. ‭ But when her draught the sea and earth dissunder'd, ‭ The troubled bottoms turn'd up, and she thunder'd, ‭ Far under shore the swart sands naked lay. ‭ Whose whole stern sight the startled blood did fray ‭ From all our faces. And while we on her ‭ Our eyes bestow'd thus to our ruin's fear, ‭ Six friends had Scylla snatch'd out of our keel, ‭ In whom most loss did force and virtue feel. ‭ When looking to my ship, and lending eye ‭ To see my friends' estates, their heels turn'd high, ‭ And hands cast up, I might discern, and hear ‭ Their calls to me for help, when now they were ‭ To try me in their last extremities. ‭ And as an angler med'cine for surprise ‭ Of little fish sits pouring from the rocks, ‭ From out the crook'd horn of a fold-bred ox, ‭ And then with his long angle hoists them high ‭ Up to the air, then slightly hurls them by, ‭ When helpless sprawling on the land they lie; ‭ So eas'ly Scylla to her rock had rapt ‭ My woeful friends, and so unhelp'd entrapt ‭ Struggling they lay beneath her violent rape, ‭ Who in their tortures, desp'rate of escape, ‭ Shriek'd as she tore, and up their hands to me ‭ Still threw for sweet life. I did never see, ‭ In all my suff'rance ransacking the seas, ‭ A spectacle so full of miseries. ‭ Thus having fled these rocks (these cruel dames ‭ Scylla, Charybdis) where the King of flames ‭ Hath off'rings burn'd to him, our ship put in ‭ The island that from all the earth doth win ‭ The epithet _Faultless,_ where the broad-of-head ‭ And famous oxen for the Sun are fed, ‭ With many fat flocks of that high-gone God. ‭ Set in my ship, mine ear reach'd where we rode ‭ The bellowing of oxen, and the bleat ‭ Of fleecy sheep, that in my memory's seat ‭ Put up the forms that late had been imprest ‭ By dread Ææn Circe, and the best ‭ Of souls and prophets, the blind Theban seer, ‭ The wise Tiresias, who was grave decreer ‭ Of my return's whole means; of which this one ‭ In chief he urg'd--that I should always shun ‭ The island of the man-delighting Sun. ‭ When, sad at heart for our late loss, I pray'd ‭ My friends to hear fit counsel (though dismay'd ‭ With all ill fortunes) which was giv'n to me ‭ By Circe's and Tiresias' prophecy,-- ‭ That I should fly the isle where was ador'd ‭ The Comfort of the world, for ills abhorr'd ‭ Were ambush'd for us there; and therefore will'd ‭ They should put off and leave the isle. This kill'd ‭ Their tender spirits; when Eurylochus ‭ A speech that vex'd me utter'd, answ'ring thus: ‭ 'Cruel Ulysses! Since thy nerves abound ‭ In strength, the more spent, and no toils confound ‭ Thy able limbs, as all beat out of steel, ‭ Thou ablest us too, as unapt to feel ‭ The teeth of Labour, and the spoil of Sleep, ‭ And therefore still wet waste us in the deep, ‭ Nor let us land to eat, but madly now ‭ In night put forth, and leave firm land to strew ‭ The sea with errors. All the rabid flight ‭ Of winds that ruin ships are bred in night. ‭ Who is it that can keep off cruel Death, ‭ If suddenly should rush out th' angry breath ‭ Of Notus, or the eager-spirited West, ‭ That cuff ships dead, and do the Gods their best? ‭ Serve black Night still with shore, meat, sleep, and ease, ‭ And offer to the Morning for the seas.' ‭ This all the rest approv'd, and then knew I ‭ That past all doubt the Devil did apply ‭ His slaught'rous works. Nor would they be withheld; ‭ I was but one, nor yielded but compell'd. ‭ But all that might contain them I assay'd, ‭ A sacred oath on all their pow'rs I laid, ‭ That if with herds or any richest-flocks ‭ We chanc'd t' encounter, neither sheep nor ox ‭ We once should touch, nor (for that constant ill ‭ That follows folly) scorn advice and kill, ‭ But quiet sit us down and take such food ‭ As the immortal Circe had bestow'd. ‭ They swore all this in all severest sort; ‭ And then we anchor'd in the winding port ‭ Near a fresh river, where the long'd-for shore ‭ They all flew out to, took in victuals store, ‭ And, being full, thought of their friends, and wept ‭ Their loss by Scylla, weeping till they slept. ‭ In night's third part, when stars began to stoop, ‭ The Cloud-assembler put a tempest up. ‭ A boist'rous spirit he gave it, drave out all ‭ His flocks of clouds, and let such darkness fall ‭ That Earth and Seas, for fear, to hide were driv'n, ‭ For with his clouds he thrust out Night from heav'n. ‭ At morn we drew our ships into a cave, ‭ In which the Nymphs that Phœbus' cattle drave ‭ Fair dancing-rooms had, and their seats of state. ‭ I urg'd my friends then, that, to shun their fate, ‭ They would observe their oath, and take the food ‭ Our ship afforded, nor attempt the blood ‭ Of those fair herds and flocks, because they were ‭ The dreadful God's that all could see and hear. ‭ They stood observant, and in that good mind ‭ Had we been gone; but so adverse the wind ‭ Stood to our passage, that we could not go. ‭ For one whole month perpetually did blow ‭ Impetuous Notus, not a breath's repair ‭ But his and Eurus' rul'd in all the air. ‭ As long yet as their ruddy wine and bread ‭ Stood out amongst them, so long not a head ‭ Of all those oxen fell in any strife ‭ Amongst those students for the gut and life; ‭ But when their victuals fail'd they fell to prey, ‭ Necessity compell'd them then to stray ‭ In rape of fish and fowl; whatever came ‭ In reach of hand or hook, the belly's flame ‭ Afflicted to it. I then fell to pray'r, ‭ And (making to a close retreat repair, ‭ Free from both friends and winds) I wash'd my hands, ‭ And all the Gods besought, that held commands ‭ In liberal heav'n, to yield some mean to stay ‭ Their desp'rate hunger, and set up the way ‭ Of our return restrain'd. The Gods, instead ‭ Of giving what I pray'd for--pow'r of deed-- ‭ A deedless sleep did on my lids distill, ‭ For mean to work upon my friends their fill. ‭ For whiles I slept, there wak'd no mean to curb ‭ Their headstrong wants; which he that did disturb ‭ My rule in chief at all times, and was chief ‭ To all the rest in counsel to their grief, ‭ Knew well, and of my present absence took ‭ His fit advantage, and their iron strook ‭ At highest heat. For, feeling their desire ‭ In his own entrails, to allay the fire ‭ That Famine blew in them, he thus gave way ‭ To that affection: 'Hear what I shall say, ‭ Though words will staunch no hunger, ev'ry death ‭ To us poor wretches that draw temporal breath ‭ You know is hateful; but, all know, to die ‭ The death of Famine is a misery ‭ Past all death loathsome. Let us, therefore, take ‭ The chief of this fair herd, and off'rings make ‭ To all the Deathless that in broad heav'n live, ‭ And in particular vow, if we arrive ‭ In natural Ithaca, to straight erect ‭ A temple to the Haughty-in-aspect, ‭ Rich and magnificent, and all within ‭ Deck it with relics many and divine. ‭ If yet he stands incens'd, since we have slain ‭ His high-brow'd herd, and, therefore, will sustain ‭ Desire to wrack our ship, he is but one, ‭ And all the other Gods that we atone ‭ With our divine rites will their suffrage give ‭ To our design'd return, and let us live. ‭ If not, and all take part, I rather crave ‭ To serve with one sole death the yawning wave, ‭ Than in a desert island lie and sterve, ‭ And with one pin'd life many deaths observe.' ‭ All cried 'He counsels nobly,' and all speed ‭ Made to their resolute driving; for the feed ‭ Of those coal-black, fair, broad-brow'd, sun-lov'd beeves ‭ Had place close by our ships. They took the lives ‭ Of sence, most eminent; about their fall ‭ Stood round, and to the States Celestial ‭ Made solemn vows; but other rites their ship ‭ Could not afford them, they did, therefore, strip ‭ The curl'd-head oak of fresh young leaves, to make ‭ Supply of service for their barley-cake. ‭ And on the sacredly-enflam'd, for wine, ‭ Pour'd purest water, all the parts divine ‭ Spitting and roasting; all the rites beside ‭ Orderly using. Then did light divide ‭ My low and upper lids; when, my repair ‭ Made near my ship, I met the delicate air ‭ Their roast exhal'd; out instantly I cried, ‭ And said: 'O Jove, and all ye Deified, ‭ Ye have oppress'd me with a cruel sleep, ‭ While ye conferr'd on me a loss as deep ‭ As Death descends to. To themselves alone ‭ My rude men left ungovern'd, they have done ‭ A deed so impious, I stand well assur'd, ‭ That you will not forgive though ye procur'd.' ‭ Then flew Lampetié with the ample robe ‭ Up to her father with the golden globe, ‭ Ambassadress t' inform him that my men ‭ Had slain his oxen. Heart-incensed then, ‭ He cried: 'Revenge me, Father, and the rest ‭ Both ever-living and for ever blest! ‭ Ulysses' impious men have drawn the blood ‭ Of those my oxen that it did me good ‭ To look on, walking all my starry round, ‭ And when I trod earth all with meadows crown'd. ‭ Without your full amends I'll leave heav'n quite, ‭ Dis and the dead adorning with my light.' ‭ The Cloud-herd answer'd: 'Son! Thou shalt be ours, ‭ And light those mortals in that mine of flow'rs! ‭ My red-hot flash shall graze but on their ship, ‭ And eat it, burning, in the boiling deep.' ‭ This by Calypso I was told, and she ‭ Inform'd it from the verger Mercury. ‭ Come to our ship, I chid and told by name ‭ Each man how impiously he was to blame. ‭ But chiding got no peace, and beeves were slain! ‭ When straight the Gods forewent their following pain ‭ With dire ostents. The hides the flesh had lost ‭ Crept all before them. As the flesh did roast, ‭ It bellow'd like the ox itself alive. ‭ And yet my soldiers did their dead beeves drive ‭ Through all these prodigies in daily feasts. ‭ Six days they banqueted and slew fresh beasts; ‭ And when the sev'nth day Jove reduc'd the wind ‭ That all the month rag'd, and so in did bind ‭ Our ship and us, was turn'd and calm'd, and we ‭ Launch'd, put up masts, sails hoised, and to sea. ‭ The island left so far that land nowhere ‭ But only sea and sky had pow'r t' appear, ‭ Jove fix'd a cloud above our ship, so black ‭ That all the sea it darken'd. Yet from wrack ‭ She ran a good free time, till from the West ‭ Came Zephyr ruffling forth, and put his breast ‭ Out in a singing tempest, so most vast ‭ It burst the gables that made sure our mast. ‭ Our masts came tumbling down, our cattle down ‭ Rush'd to the pump, and by our pilot's crown ‭ The main-mast pass'd his fall, pash'd all his skull, ‭ And all this wrack but one flaw made at full. ‭ Off from the stern the sternsman diving fell, ‭ And from his sinews flew his soul to hell. ‭ Together all this time Jove's thunder chid, ‭ And through and through the ship his lightning glid, ‭ Till it embrac'd her round; her bulk was fill'd ‭ With nasty sulphur, and her men were kill'd, ‭ Tumbled to sea, like sea-mews swum about, ‭ And there the date of their return was out. ‭ I toss'd from side to side still, till all-broke ‭ Her ribs were with the storm, and she did choke ‭ With let-in surges; for the mast torn down ‭ Tore her up piecemeal, and for me to drown ‭ Left little undissolv'd. But to the mast ‭ There was a leather thong left, which I cast ‭ About it and the keel, and so sat tost ‭ With baneful weather, till the West had lost ‭ His stormy tyranny. And then arose ‭ The South, that bred me more abhorréd woes; ‭ For back again his blasts expell'd me quite ‭ On ravenous Charybdis. All that night ‭ I totter'd up and down, till Light and I ‭ At Scylla's rock encounter'd, and the nigh ‭ Dreadful Charybdis. As I drave on these, ‭ I saw Charybdis supping up the seas, ‭ And had gone up together, if the tree ‭ That bore the wild figs had not rescued me; ‭ To which I leap'd, and left my keel, and high ‭ Chamb'ring upon it did as close imply ‭ My breast about it as a reremouse could; ‭ Yet might my feet on no stub fasten hold ‭ To ease my hands, the roots were crept so low ‭ Beneath the earth, and so aloft did grow ‭ The far-spread arms that, though good height I gat, ‭ I could not reach them. To the main bole flat ‭ I, therefore, still must cling; till up again ‭ She belch'd my mast, and after that amain ‭ My keel came tumbling. So at length it chanc'd ‭ To me, as to a judge that long advanc'd ‭ To judge a sort of hot young fellows' jars, ‭ At length time frees him from their civil wars, ‭ When glad he riseth and to dinner goes; ‭ So time, at length, releas'd with joys my woes, ‭ And from Charybdis' mouth appear'd my keel. ‭ To which, my hand now loos'd and now my heel, ‭ I altogether with a huge noise dropp'd, ‭ Just in her midst fell, where the mast was propp'd, ‭ And there row'd off with owers of my hands. ‭ God and man's Father would not from her sands ‭ Let Scylla see me, for I then had died ‭ That bitter death that my poor friends supplied. ‭ Nine days at sea I hover'd; the tenth night ‭ In th' isle Ogygia, where, about the bright ‭ And right renown'd Calypso, I was cast ‭ By pow'r of Deity; where I lived embrac'd ‭ With love and feasts. But why should I relate ‭ Those kind occurrents? I should iterate ‭ What I in part to your chaste queen and you ‭ So late imparted. And, for me to grow ‭ A talker-over of my tale again, ‭ Were past my free contentment to sustain." ‭ FINIS DUODECIMI LIBRI HOM. ODYSS. ‭ _Opus novem dierum._ ‭ _Σὺν Θεᾳ._ ‭[1] _Πέλειαι τρήρωνες. Columbæ timidæ._ What these doves were, ‭and the whole mind of this place, the great Macedon asking Chiron ‭Amphipolites, he answered: They were the Pleiades or seven ‭Stars. One of which (besides his proper imperfection of being ‭_ἀμυδρὸς,_ i.e. _adeo exilis, vel subobscurus, ut vix appareat_) is ‭utterly obscured or let by these rocks. Why then, or how, Jove still ‭supplied the lost one, that the number might be full, Athenæus falls ‭to it, and helps the other out, interpreting it to be affirmed of their ‭perpetual septenary number, though there appeared but six. But ‭how lame and loathsome these prosers show in their affected ‭expositions of the poetical mind, this and an hundred others, spent ‭in mere presumptuous guess at this inaccessible Poet, I hope will ‭make plain enough to the most envious of any thing done, besides ‭their own set censures and most arrogant over-weenings. In the 23 ‭of the lliads (being _ψ_) at the games celebrated at Patroclus' ‭funerals, they tied to the top of a mast _πέλειαν τρήρωνα, timidam ‭columbam,_ to shoot at for a game, so that (by these great men's ‭abovesaid expositions) they shot at the Pleiades. ‭[2] _Νηυ̑ς πα̑σι μέλουσα,_ etc. _Navis omnibus curæ: the ship that ‭held the care of all men, or of all things:_ which our critics will ‭needs restrain, _omnibus heroibus, Poetis omnibus, vel Historicis,_ ‭when the care of all men's preservation is affirmed to be the freight ‭of it; as if poets and historians comprehended all things, when I ‭scarce know any that makes them any part of their care. But this ‭likewise is garbage good enough for the monster. Nor will I tempt ‭our spiced consciences with expressing the divine mind it includes. ‭Being afraid to affirm any good of poor poesy, since no man gets ‭any goods by it. And notwithstanding many of our bird-eyed ‭starters at profanation are for nothing so afraid of it; as that lest ‭their galled consciences (scarce believing the most real truth, in ‭approbation of their lives) should be rubbed with the confirmation ‭of it, even in these contemned vanities (as their impieties please to ‭call them) which by much more learned and pious than themselves ‭have ever been called the raptures of divine inspiration, by which, ‭_Homo supra humanam naturam erigitur, et in Deum transit._--Plat. ‭[3] _Δεινὸν λελακυι̑α,_ etc. _Graviter vociferans;_ as all most ‭untruly translate it. As they do in the next verse these words ‭_σκύλακος νεογιλη̑ς catuli leonis,_ no lion being here dreamed of, ‭nor any vociferation. _Δεινὸν λελακυι̑α_ signifying _indignam, ‭dissimilem,_ or _horribilem vocem edens:_ but in what kind ‭_horribilem?_ Not for the gravity or greatness of her voice, but for ‭the unworthy or disproportionable small whuling of it; she being in ‭the vast frame of her body, as the very words _πέλωρ κακὸν_ ‭signify, _monstrum ingens;_ whose disproportion and deformity is ‭too poetically (and therein elegantly) ordered for fat and flat ‭prosers to comprehend. Nor could they make the Poet's words ‭serve their comprehension; and therefore they add of their own, ‭_λάσκω,_ from whence _λελακυι̑α_ is derived, signifying _crepo,_ ‭or _stridulê clamo._ And _σκύλακος νεογιλη̑ς_ is to be ‭expounded, _catuli nuper_ or _recens nati,_ not _leonis._ But thus ‭they botch and abuse the incomparable expressor, because they ‭knew not how otherwise to be monstrous enough themselves to ‭help out the monster. Imagining so huge a great body must needs ‭have a voice as huge; and then would not our Homer have likened ‭it to a lion's whelp's voice, but to the lion's own; and all had been ‭much too little to make a voice answerable to her hugeness. And ‭therefore found our inimitable master a new way to express her ‭monstrous disproportion; performing it so, as there can be _nihil ‭suprâ._ And I would fain learn of my learned detractor, that will ‭needs have me only translate out of the Latin, what Latin ‭translation tells me this? Or what Grecian hath ever found this and ‭a hundred other such? Which may be some poor instance, or ‭proof, of my Grecian faculty, as far as old Homer goes in his two ‭simple Poems, but not a syllable further will my silly spirit ‭presume. ‭ THE THIRTEENTH BOOK OF HOMER'S ODYSSEYS ‭ THE ARGUMENT ‭ Ulysses (shipp'd, but in the even, ‭ With all the presents he was given, ‭ And sleeping then) is set next morn ‭ In full scope of his wish'd return, ‭ And treads unknown his country-shore, ‭ Whose search so many winters wore. ‭ The ship (returning, and arriv'd ‭ Against the city) is depriv'd ‭ Of form, and, all her motion gone, ‭ Transform'd by Neptune to a stone. ‭ Ulysses (let to know the strand ‭ Where the Phæacians made him land) ‭ Consults with Pallas, for the life ‭ Of ev'ry wooer of his wife. ‭ His gifts she hides within a cave, ‭ And him into a man more grave, ‭ All hid in wrinkles, crookéd, gray, ‭ Transform'd; who so goes on his way. ‭ ‭ ANOTHER ARGUMENT ‭ _Νυ̑._ ‭ Phæacia ‭ Ulysses leaves; ‭ Whom Ithaca, ‭ Unwares, receives. ‭ He said; and silence all their tongues contain'd, ‭ In admiration, when with pleasure chain'd ‭ Their ears had long been to him. At last brake ‭ Alcinous silence, and in this sort spake ‭ To th' Ithacensian, Laertes' son: ‭ "O Ithacus! However over-run ‭ With former suff'rings in your way for home, ‭ Since 'twas, at last, your happy fate to come ‭ To my high-roof'd and brass-foundation'd house, ‭ I hope, such speed and pass auspicious ‭ Our loves shall yield you, that you shall no more ‭ Wander, nor suffer, homewards, as before. ‭ You then, whoever that are ever grac'd ‭ With all choice of authoriz'd pow'r to taste ‭ Such wine with me as warms the sacred rage, ‭ And is an honorary giv'n to age, [1] ‭ With which ye likewise hear divinely sing, ‭ In honour's praise, the poet of the king, ‭ I move, by way of my command, to this: ‭ That where in an elaborate chest there lies ‭ A present for our guest, attires of price, ‭ And gold engrav'n with infinite device, ‭ I wish that each of us should add beside ‭ A tripod, and a caldron, amplified ‭ With size, and metal of most rate, and great; ‭ For we, in council of taxation met, ‭ Will from our subjects gain their worth again; ‭ Since 'tis unequal one man should sustain ‭ A charge so weighty, being the grace of all, ‭ Which borne by many is a weight but small." ‭ Thus spake Alcinous, and pleas'd the rest; ‭ When each man clos'd with home and sleep his feast. ‭ But when the colour-giving light arose, ‭ All to the ship did all their speeds dispose, [2] ‭ And wealth, that honest men makes, brought with them. [3] ‭ All which ev'n he that wore the diadem ‭ Stow'd in the ship himself, beneath the seats ‭ The rowers sat in, stooping, lest their lets ‭ In any of their labours he might prove. ‭ Then home he turn'd, and after him did move ‭ The whole assembly to expected feast. ‭ Among whom he a sacrifice addrest, ‭ And slew an ox, to weather-wielding Jove, ‭ Beneath whose empire all things are, and move. ‭ The thighs then roasting, they made glorious cheer ‭ Delighted highly; and amongst them there ‭ The honour'd-of-the-people us'd his voice, ‭ Divine Demodocus. Yet, through this choice ‭ Of cheer and music, had Ulysses still ‭ An eye directed to the Eastern hill, ‭ To see Him rising that illustrates all; ‭ For now into his mind a fire did fall ‭ Of thirst for home. And as in hungry vow ‭ To needful food a man at fixéd plow ‭ (To whom the black ox all day long hath turn'd ‭ The stubborn fallows up, his stomach burn'd ‭ With empty heat and appetite to food, ‭ His knees afflicted with his spirit-spent blood) ‭ At length the long-expected sunset sees, ‭ That he may sit to food, and rest his knees; ‭ So to Ulysses set the friendly light ‭ The sun afforded, with as wish'd a sight. ‭ Who straight bespake that oar-affecting State, ‭ But did in chief his speech appropriate ‭ To him by name, that with their rule was crown'd. ‭ "Alcinous, of all men most renown'd, ‭ Dismiss me with as safe pass as you vow ‭ (Your off'ring past) and may the Gods to you ‭ In all contentment use as full a hand; ‭ For now my landing here and stay shall stand ‭ In all perfection with my heart's desire, ‭ Both my so safe deduction to aspire, ‭ And loving gifts; which may the Gods to me ‭ As blest in use make as your acts are free, ‭ Ev'n to the finding firm in love, and life, ‭ With all desir'd event, my friends, and wife. ‭ When, as myself shall live delighted there, ‭ May you with your wives rest as happy here, ‭ Your sons and daughters, in particular state, ‭ With ev'ry virtue render'd consummate; ‭ And, in your gen'ral empire, may ill never ‭ Approach your land, but good your good quit ever." ‭ This all applauded, and all jointly cried: ‭ "Dismiss the stranger! He hath dignified ‭ With fit speech his dismission." Then the king ‭ Thus charg'd the herald: "Fill for offering ‭ A bowl of wine; which through the whole large house ‭ Dispose to all men, that, propitious ‭ Our father Jove made with our pray'rs, we may ‭ Give home our guest in full and wishéd way." ‭ This said, Pontonous commix'd a bowl ‭ Of such sweet wine as did delight the soul. ‭ Which making sacred to the blessed Gods, ‭ That hold in broad heav'n their supreme abodes, ‭ God-like Ulysses from his chair arose, ‭ And in the hands of th' empress did impose ‭ The all-round cup; to whom, fair spoke, he said: ‭ "Rejoice, O queen, and be your joys repaid ‭ By heav'n, for me, till age and death succeed; ‭ Both which inflict their most unwelcome need ‭ On men and dames alike. And, first, for me, ‭ I must from hence, to both: Live you here free, ‭ And ever may all living blessings spring, ‭ Your joy in children, subjects, and your king." ‭ This said, divine Ulysses took his way; ‭ Before whom the unalterable sway ‭ Of king Alcinous' virtue did command ‭ A herald's fit attendance to the strand, ‭ And ship appointed. With him likewise went ‭ Handmaids, by Arete's injunction sent. ‭ One bore an out and in-weed, fair and sweet, ‭ The other an embroider'd cabinet, ‭ The third had bread to bear, and ruddy wine; ‭ All which, at sea and ship arriv'd, resign ‭ Their freight conferr'd. With fair attendants then, ‭ The sheets and bedding of the man of men, ‭ Within a cabin of the hollow keel, ‭ Spread, and made soft, that sleep might sweetly seel ‭ His restful eyes, he enter'd, and his bed ‭ In silence took. The rowers orderéd ‭ Themselves in sev'ral seats, and then set gone ‭ The ship, the gable from the hollow stone ‭ Dissolv'd and weigh'd-up, all, together, close ‭ Then beat the sea. His lids in sweet repose ‭ Sleep bound so fast, it scarce gave way to breath ‭ Inexcitable, most dear, next of all to death. ‭ And as amids a fair field four brave horse ‭ Before a chariot stung into their course ‭ With fervent lashes of the smarting scourge, ‭ That all their fire blows high, and makes them urge ‭ To utmost speed the measure of their ground; ‭ So bore the ship aloft her fiery bound; ‭ About whom rush'd the billows black and vast, ‭ In which the sea-roars burst. As firm as fast ‭ She ply'd her course yet; nor her wingéd speed ‭ The falcon-gentle could for pace exceed; ‭ So cut she through the waves, and bore a man ‭ Even with the Gods in counsels, that began ‭ And spent his former life in all misease, ‭ Battles of men, and rude waves of the seas, ‭ Yet now securely slept, forgetting all. ‭ And when heav'n's brightest star, that first doth call ‭ The early morning out, advanc'd her head, ‭ Then near to Ithaca the billow-bred ‭ Phræcian ship approach'd. There is a port, ‭ That th' aged sea-God Phorcys makes his fort, ‭ Whose earth the Ithacensian people own, ‭ In which two rocks inaccessible are grown ‭ Far forth into the sea, whose each strength binds ‭ The boist'rous waves in from the high-flown winds ‭ On both the out-parts so, that all within ‭ The well-built ships, that once their harbour win ‭ In his calm bosom, without anchor rest, ‭ Safe, and unstirr'd. From forth the haven's high crest ‭ Branch the well-brawn'd arms of an olive-tree; ‭ Beneath which runs a cave from all sun free, ‭ Cool, and delightsome, sacred to th' access ‭ Of Nymphs whose surnames are the Naiadés; ‭ In which flew humming bees, in which lay thrown ‭ Stone cups, stone vessels, shittles all of stone, ‭ With which the Nymphs their purple mantles wove, ‭ In whose contexture art and wonder strove; ‭ In which pure springs perpetually ran; ‭ To which two entries were; the one for man, ‭ On which the North breath'd; th' other for the Gods, ‭ On which the South; and that bore no abodes ‭ For earthy men, but only deathless feet ‭ Had there free way. This port these men thought meet ‭ To land Ulysses, being the first they knew, ‭ Drew then their ship in, but no further drew ‭ Than half her bulk reach'd, by such cunning hand ‭ Her course was manag'd. Then her men took land, ‭ And first brought forth Ulysses, bed, and all ‭ That richly furnish'd it, he still in thrall ‭ Of all-subduing sleep. Upon the sand ‭ They set him softly down; and then the strand ‭ They strew'd with all the goods he had, bestow'd ‭ By the renown'd Phæacians, since he show'd ‭ So much Minerva. At the olive root ‭ They drew them then in heap, most far from foot ‭ Of any traveller, lest, ere his eyes ‭ Resum'd their charge, they might be others' prise. ‭ These then turn'd home; nor was the sea's Supreme ‭ Forgetful of his threats, for Polypheme ‭ Bent at divine Ulysses, yet would prove ‭ (Ere their performance) the decree of Jove. ‭ "Father! no more the Gods shall honour me, ‭ Since men despise me, and those men that see ‭ The light in lineage of mine own lov'd race. [4] ‭ I vow'd Ulysses should, before the grace ‭ Of his return, encounter woes enow ‭ To make that purchase dear; yet did not vow ‭ Simply against it, since thy brow had bent ‭ To his reduction, in the fore-consent ‭ Thou hadst vouchsaf'd it; yet, before my mind ‭ Hath full pow'r on him, the Phæacians find ‭ Their own minds' satisfaction with his pass, ‭ So far from suff'ring what my pleasure was, ‭ That ease and softness now is habited ‭ In his secure breast, and his careless head ‭ Return'd in peace of sleep to Ithaca, ‭ The brass and gold of rich Phæacia ‭ Rocking his temples, garments richly wov'n, ‭ And worlds of prise, more than was ever strov'n ‭ From all the conflicts he sustain'd at Troy, ‭ If safe he should his full share there enjoy." ‭ The Show'r-dissolver answer'd: "What a speech ‭ Hath pass'd thy palate, O thou great in reach ‭ Of wrackful empire! Far the Gods remain ‭ From scorn of thee, for 'twere a work of pain ‭ To prosecute with ignominies one ‭ That sways our ablest and most ancient throne. ‭ For men, if any so beneath in pow'r ‭ Neglect thy high will, now, or any hour ‭ That moves hereafter, take revenge to thee, ‭ Soothe all thy will, and be thy pleasure free." ‭ "Why then," said he, "thou blacker of the fumes ‭ That dim the sun, my licens'd pow'r resumes ‭ Act from thy speech; but I observe so much ‭ And fear thy pleasure, that, I dare not touch ‭ At any inclination of mine own, ‭ Till thy consenting influence be known. ‭ But now this curious-built Phæacian ship, ‭ Returning from her convoy, I will strip ‭ Of all her fleeting matter, and to stone ‭ Transform and fix it, just when she hath gone ‭ Her full time home, and jets before their prease ‭ In all her trim, amids the sable seas, ‭ That they may cease to convoy strangers still, ‭ When they shall see so like a mighty hill ‭ Their glory stick before their city's grace, ‭ And my hands cast a mask before her face." [5] ‭ "O friend," said Jove, "it shows to me the best ‭ Of all earth's objects, that their whole prease, drest ‭ In all their wonder, near their town shall stand, ‭ And stare upon a stone, so near the land, ‭ So like a ship, and dam up all their lights, ‭ As if a mountain interpos'd their sights." ‭ When Neptune heard this, he for Scheria went, ‭ Whence the Phæacians took their first descent. ‭ Which when he reach'd, and, in her swiftest pride, ‭ The water-treader by the city's side ‭ Came cutting close, close he came swiftly on, ‭ Took her in violent hand, and to a stone ‭ Turn'd all her sylvan substance; all below ‭ Firm'd her with roots, and left her. This strange show ‭ When the Phæacians saw, they stupid stood, ‭ And ask'd each other, who amids the flood ‭ Could fix their ship so in her full speed home, ‭ And quite transparent make her bulk become? ‭ Thus talk'd they; but were far from knowing how ‭ These things had issue. Which their king did show, ‭ And said: "O friends, the ancient prophecies ‭ My father told to me, to all our eyes ‭ Are now in proof. He said, the time would come, ‭ When Neptune, for our safe conducting home ‭ All sorts of strangers, out of envy fir'd, ‭ Would meet our fairest ship as she retir'd, ‭ And all the goodly shape and speed we boast ‭ Should like a mountain stand before us lost ‭ Amids the moving waters; which we see ‭ Perform'd in full end to our prophecy. ‭ Hear then my counsel, and obey me then: ‭ Renounce henceforth our convoy home of men, ‭ Whoever shall hereafter greet our town; ‭ And to th' offended Deity's renown ‭ Twelve chosen oxen let us sacred make, ‭ That he may pity us, and from us take ‭ This shady mountain. They, in fear, obey'd, ‭ Slew all the beeves, and to the Godhead pray'd, ‭ The dukes and princes all ensphering round ‭ The sacred altar; while whose tops were crown'd, ‭ Divine Ulysses, on his country's breast ‭ Laid bound in sleep, now rose out of his rest, ‭ Nor (being so long remov'd) the region knew. ‭ Besides which absence yet, Minerva threw ‭ A cloud about him, to make strange the more ‭ His safe arrival, lest upon his shore ‭ He should make known his face, and utter all ‭ That might prevent th' event that was to fall. ‭ Which she prepar'd so well, that not his wife, ‭ Presented to him, should perceive his life, ‭ No citizen, no friend, till righteous fate ‭ Upon the Wooer's wrongs were consummate. ‭ Through which cloud all things show'd now to the king ‭ Of foreign fashion; the enflow'réd spring ‭ Amongst the trees there, the perpetual waves, ‭ The rocks, that did more high their foreheads raise ‭ To his wrapt eye than naturally they did, ‭ And all the haven, in which a man seem'd hid ‭ From wind and weather, when storms loudest chid. ‭ He therefore, being risen, stood and view'd ‭ His country-earth; which, not perceiv'd, he rued, ‭ And, striking with his hurl'd-down hands his thighs, ‭ He mourn'd, and said: "O me! Again where lies ‭ My desert way? To wrongful men and rude, ‭ And with no laws of human right endued? ‭ Or are they human, and of holy minds? ‭ What fits my deed with these so many kinds ‭ Of goods late giv'n? What with myself will floods ‭ And errors do? I would to God, these goods ‭ Had rested with their owners, and that I ‭ Had fall'n on kings of more regality, ‭ To grace out my return, that lov'd indeed, ‭ And would have giv'n me consorts of fit speed ‭ To my distresses' ending! But, as now ‭ All knowledge flies me where I may bestow ‭ My labour'd purchase, here they shall not stay, ‭ Lest what I car'd for others make their prey. ‭ O Gods! I see the great Phæacians then ‭ Were not all just and understanding men, ‭ That land me elsewhere than their vaunts pretended, ‭ Assuring me my country should see ended ‭ My miseries told them, yet now eat their vaunts. ‭ O Jove! Great Guardian of poor suppliants, ‭ That others sees, and notes too, shutting in ‭ All in thy plagues that most presume on sin, ‭ Revenge me on them. Let me number now ‭ The goods they gave, to give my mind to know ‭ If they have stol'n none in their close retreat." ‭ The goodly caldrons then, and tripods, set ‭ In sev'ral ranks from out the heap, he told, ‭ His rich wrought garments too, and all his gold, ‭ And nothing lack'd; and yet this man did mourn ‭ The but suppos'd miss of his home-return, ‭ And creeping to the shore with much complaint; ‭ Minerva (like a shepherd, young, and quaint, [6] ‭ As king sons are, a double mantle cast ‭ Athwart his shoulders, his fair goers grac'd ‭ With fitted shoes, and in his hand a dart) ‭ Appear'd to him, whose sight rejoic'd his heart, ‭ To whom he came, and said: "O friend! Since first ‭ I meet your sight here, be all good the worst ‭ That can join our encounter. Fare you fair, ‭ Nor with adverse mind welcome my repair, ‭ But guard these goods of mine, and succour me. ‭ As to a God I offer pray'rs to thee, ‭ And low access make to thy lovéd knee. ‭ Say truth, that I may know, what country then, ‭ What common people live here, and what men? ‭ Some famous isle is this? Or gives it vent, ‭ Being near the sea, to some rich continent?" ‭ She answer'd: "Stranger, whatsoe'er you are, ‭ Y'are either foolish, or come passing far, ‭ That know not this isle, and make that doubt trouble, ‭ For 'tis not so exceedingly ignoble, ‭ But passing many know it; and so many, ‭ That of all nations there abides not any, ‭ From where the morning rises and the sun, ‭ To where the even and night their courses run, ‭ But know this country. Rocky 'tis, and rough, ‭ And so for use of horse unapt enough, ‭ Yet with sad barrenness not much infested, [7] ‭ Since clouds are here in frequent rains digested, ‭ And flow'ry dews. The compass is not great, ‭ The little yet well-fill'd with wine and wheat. ‭ It feeds a goat and ox well, being still ‭ Water'd with floods, that ever over-fill ‭ With heav'n's continual show'rs; and wooded so, ‭ It makes a spring of all the kinds that grow. ‭ And therefore, Stranger, the extended name ‭ Of this dominion makes access by fame ‭ From this extreme part of Achaia ‭ As far as Ilion, and 'tis Ithaca." ‭ This joy'd him much, that so unknown a land ‭ Turn'd to his country. Yet so wise a hand ‭ He carried, ev'n of this joy, flown so high, ‭ That other end he put to his reply ‭ Than straight to show that joy, and lay abroad ‭ His life to strangers. Therefore he bestow'd ‭ A veil on truth; for evermore did wind ‭ About his bosom a most crafty mind, ‭ Which thus his words show'd: "I have far at sea, ‭ In spacious Crete, heard speak of Ithaca, ‭ Of which myself, it seems, now reach the shore, ‭ With these my fortunes; whose whole value more ‭ I left in Crete amongst my children there, ‭ From whence I fly for being the slaughterer ‭ Of royal Idomen's most-lovéd son, ‭ Swift-foot Orsilochus, that could out-run ‭ Profess'd men for the race. Yet him I slew, ‭ Because he would deprive me of my due ‭ In Trojan prise; for which I suffer'd so ‭ (The rude waves piercing) the redoubled woe ‭ Of mind and body in the wars of men. ‭ Nor did I gratify his father then ‭ With any service, but, as well as he ‭ Sway'd in command of other soldiery, ‭ So, with a friend withdrawn, we waylaid him, ‭ When gloomy night the cope of heav'n did dim, ‭ And no man knew; but, we lodg'd close, he came, ‭ And I put out to him his vital flame. ‭ Whose slaughter having author'd with my sword, ‭ I instant flight made, and straight fell aboard ‭ A ship of the renown'd Phœnician state; ‭ When pray'r, and pay at a sufficient rate, ‭ Obtain'd my pass of men in her command; ‭ Whom I enjoin'd to set me on the land ‭ Of Pylos, or of Elis the divine, ‭ Where the Epeïans in great empire shine. ‭ But force of weather check'd that course to them, ‭ Though (loth to fail me) to their most extreme ‭ They spent their willing pow'rs. But, forc'd from thence, ‭ We err'd, and put in here, with much expence ‭ Of care and labour; and in dead of night, ‭ When no man there serv'd any appetite ‭ So much as with the memory of food, ‭ Though our estates exceeding needy stood. ‭ But, going ashore, we lay; when gentle sleep ‭ My weary pow'rs invaded, and from ship ‭ They fetching these my riches, with just hand ‭ About me laid them, while upon the sand ‭ Sleep bound my senses; and for Sidon they ‭ (Put off from hence) made sail, while here I lay, ‭ Left sad alone." The Goddess laugh'd, and took ‭ His hand in hers, and with another look ‭ (Assuming then the likeness of a dame, ‭ Lovely and goodly, expert in the frame ‭ Of virtuous housewif'ries) she answer'd thus: ‭ "He should be passing-sly, and covetous ‭ Of stealth, in men's deceits, that coted thee [8] ‭ In any craft, though any God should be ‭ Ambitious to exceed in subtilty. ‭ Thou still-wit-varying wretch! Insatiate [9] ‭ In over-reaches! Not secure thy state ‭ Without these wiles, though on thy native shore ‭ Thou sett'st safe footing, but upon thy store ‭ Of false words still spend, that ev'n from thy birth ‭ Have been thy best friends? Come, our either worth ‭ Is known to either. Thou of men art far, ‭ For words and counsels, the most singular, ‭ But I above the Gods in both may boast ‭ My still-tried faculties. Yet thou hast lost ‭ The knowledge ev'n of me, the Seed of Jove, ‭ Pallas Athenia, that have still out-strove ‭ In all thy labours their extremes, and stood ‭ Thy sure guard ever, making all thy good ‭ Known to the good Phæacians, and receiv'd. ‭ And now again I greet thee, to see weav'd ‭ Fresh counsels for thee, and will take on me ‭ The close reserving of these goods for thee, ‭ Which the renown'd Phæacian states bestow'd ‭ At thy deduction homewards, only mov'd ‭ With my both spirit and counsel. All which grace ‭ I now will amplify, and tell what case ‭ Thy household stands in, utt'ring all those pains ‭ That of mere need yet still must wrack thy veins. ‭ Do thou then freely bear, nor one word give ‭ To man nor dame to show thou yet dost live, ‭ But silent suffer over all again ‭ Thy sorrows past, and bear the wrongs of men." ‭ "Goddess," said he, "unjust men, and unwise, ‭ That author injuries and vanities, ‭ By vanities and wrongs should rather be ‭ Bound to this ill-abearing destiny, ‭ Than just and wise men. What delight hath heav'n, ‭ That lives unhurt itself, to suffer giv'n ‭ Up to all domage those poor few that strive ‭ To imitate it, and like the Deities live? ‭ But where you wonder that I know you not ‭ Through all your changes, that skill is not got ‭ By sleight or art, since thy most hard-hit face ‭ Is still distinguish'd by thy free-giv'n grace; ‭ And therefore, truly to acknowledge thee ‭ In thy encounters, is a mastery ‭ In men most-knowing; for to all men thou ‭ Tak'st sev'ral likeness. All men think they know ‭ Thee in their wits; but, since thy seeming view ‭ Appears to all, and yet thy truth to few, ‭ Through all thy changes to discern thee right ‭ Asks chief love to thee, and inspiréd light. ‭ But this I surely know, that, some years past, ‭ I have been often with thy presence grac'd, ‭ All time the sons of Greece wag'd war at Troy; ‭ But when Fate's full hour let our swords enjoy ‭ Our vows in sack of Priam's lofty town, ‭ Our ships all boarded, and when God had blown ‭ Our fleet in sunder, I could never see ‭ The Seed of Jove, nor once distinguish thee ‭ Boarding my ship, to take one woe from me. ‭ But only in my proper spirit involv'd, ‭ Err'd here and there, quite slain, till heav'n dissolv'd ‭ Me, and my ill; which chanc'd not, till thy grace ‭ By open speech confirm'd me, in a place ‭ Fruitful of people, where, in person, thou ‭ Didst give me guide, and all their city show; ‭ And that was the renown'd Phæacian earth. ‭ Now then, ev'n by the Author of thy birth, ‭ Vouchsafe my doubt the truth (for far it flies ‭ My thoughts that thus should fall into mine eyes ‭ Conspicuous Ithaca, but fear I touch ‭ At some far shore, and that thy wit is such ‭ Thou dost delude me) is it sure the same ‭ Most honour'd earth that bears my country's name?" ‭ "I see," said she, "thou wilt be ever thus ‭ In ev'ry worldly good incredulous, ‭ And therefore have no more the pow'r to see ‭ Frail life more plagued with infelicity ‭ In one so eloquent, ingenious, wise. ‭ Another man, that so long miseries ‭ Had kept from his lov'd home, and thus return'd ‭ To see his house, wife, children, would have burn'd ‭ In headlong lust to visit. Yet t' inquire ‭ What states they hold, affects not thy desire, ‭ Till thou hast tried if in thy wife there be ‭ A sorrow wasting days and nights for thee ‭ In loving tears, that then the sight may prove ‭ A full reward for either's mutual love. ‭ But I would never credit in you both ‭ Least cause of sorrow, but well knew the troth ‭ Of this thine own return, though all thy friends, ‭ I knew as well, should make returnless ends; ‭ Yet would not cross mine uncle Neptune so ‭ To stand their safeguard, since so high did go ‭ His wrath for thy extinction of the eye ‭ Of his lov'd son. Come then, I'll show thee why ‭ I call this isle thy Ithaca, to ground ‭ Thy credit on my words: This haven is own'd ‭ By th' agéd sea-god Phorcys, in whose brow ‭ This is the olive with the ample bough, ‭ And here, close by, the pleasant-shaded cave ‭ That to the Fount-Nymphs th' Ithacensians gave, ‭ As sacred to their pleasures. Here doth run ‭ The large and cover'd den, where thou hast done ‭ Hundreds of off'rings to the Naiades, ‭ Here Mount Neritus shakes his curléd tress ‭ Of shady woods." This said, she clear'd the cloud ‭ That first deceiv'd his eyes; and all things show'd ‭ His country to him. Glad he stood with sight ‭ Of his lov'd soil, and kiss'd it with delight; ‭ And instantly to all the Nymphs he paid ‭ (With hands held up to heav'n) these vows, and said: ‭ "Ye Nymphs the Naiades, great Seed of Jove, ‭ I had conceit that never more should move ‭ Your sight in these spheres of my erring eyes, ‭ And therefore, in the fuller sacrifice ‭ Of my heart's gratitude, rejoice, till more ‭ I pay your names in off'rings as before; ‭ Which here I vow, if Jove's benign descent, ‭ The mighty Pillager, with life convent ‭ My person home, and to my sav'd decease ‭ Of my lov'd son's sight add the sweet increase." ‭ "Be confident," said Pallas, "nor oppress ‭ Thy spirits with care of these performances, ‭ But these thy fortunes let us straight repose ‭ In this divine cave's bosom, that may close ‭ Reserve their value; and we then may see ‭ How best to order other acts to thee." ‭ Thus enter'd she the light-excluding cave, ‭ And through it sought some inmost nook to save ‭ The gold, the great brass, and robes richly-wrought, ‭ Giv'n to Ulysses. All which in he brought, ‭ Laid down in heap; and she impos'd a stone ‭ Close to the cavern's mouth. Then sat they on ‭ The sacred olive's root, consulting how ‭ To act th' insulting Wooers' overthrow; ‭ When Pallas said: "Examine now the means ‭ That best may lay hands on the impudence ‭ Of those proud Wooers, that have now three years ‭ Thy roof's rule sway'd, and been bold offerers ‭ Of suit and gifts to thy renownéd wife, ‭ Who for thy absence all her desolate life ‭ Dissolves in tears till thy desir'd return; ‭ Yet all her Wooers, while she thus doth mourn, ‭ She holds in hope, and ev'ry one affords ‭ (In fore-sent message) promise; but her words ‭ Bear other utt'rance than her heart approves." ‭ "O Gods," said Ithacus, "it now behoves ‭ My fate to end me in the ill decease ‭ That Agamemnon underwent, unless ‭ You tell me, and in time; their close intents. ‭ Advise then means to the reveng'd events ‭ We both resolve on. Be thyself so kind ‭ To stand close to me, and but such a mind ‭ Breathe in my bosom, as when th' Ilion tow'rs ‭ We tore in cinders. O if equal pow'rs ‭ Thou wouldst enflame amidst my nerves as then, ‭ I could encounter with three hundred men, ‭ Thy only self, great Goddess, had to friend, ‭ In those brave ardors thou wert wont t' extend!" ‭ "I will be strongly with thee," answer'd she, ‭ "Nor must thou fail, but do thy part with me. ‭ When both whose pow'rs combine, I hope the bloods ‭ And brains of some of these that waste thy goods ‭ Shall strew thy goodly pavements. Join we then: ‭ I first will render thee unknown to men, ‭ And on thy solid lineaments make dry ‭ Thy now smooth skin; thy bright-brown curls imply ‭ In hoary mattings; thy broad shoulders clothe ‭ In such a cloak as ev'ry eye shall lothe; ‭ Thy bright eyes blear and wrinkle; and so change ‭ Thy form at all parts, that thou shalt be strange ‭ To all the Wooers, thy young son, and wife. ‭ But to thy herdsman first present thy life, ‭ That guards thy swine, and wisheth well to thee, ‭ That loves thy son and wife Penelopé. ‭ Thy search shall find him set aside his herd, ‭ That are with taste-delighting acorns rear'd, ‭ And drink the dark-deep water of the spring, ‭ Bright Arethusa, the most nourishing ‭ Raiser of herds. There stay, and, taking seat ‭ Aside thy herdsman, of the whole state treat ‭ Of home-occurrents, while I make access ‭ To fair-dame-breeding Sparta for regress ‭ Of lov'd Telemachus, who went in quest ‭ Of thy lov'd fame, and liv'd the welcome guest ‭ Of Menelaus." The much-knower said: ‭ "Why wouldst not thou, in whose grave breast is bred ‭ The art to order all acts, tell in this ‭ His error to him? Let those years of his ‭ Amids the rude seas wander, and sustain ‭ The woes there raging, while unworthy men ‭ Devour his fortunes?" "Let not care extend ‭ Thy heart for him," said she, "myself did send ‭ His person in thy search; to set his worth, ‭ By good fame blown, to such a distance forth. ‭ Nor suffers he in any least degree ‭ The grief you fear, but all variety ‭ That Plenty can yield in her quiet'st fare, ‭ In Menelaus' court, doth sit and share. ‭ In whose return from home, the Wooers yet ‭ Lay bloody ambush, and a ship have set ‭ To sea, to intercept his life before ‭ He touch again his birth's attempted shore. ‭ All which, my thoughts say, they shall never do, ‭ But rather, that the earth shall overgo ‭ Some one at least of these love-making men, ‭ By which thy goods so much impair sustain." ‭ Thus using certain secret words to him, ‭ She touch'd him with her rod; and ev'ry limb ‭ Was hid all-over with a wither'd skin; ‭ His bright eyes blear'd; his brow-curls white and thin; ‭ And all things did an agéd man present. ‭ Then, for his own weeds, shirt and coat, all-rent, ‭ Tann'd, and all-sootiéd with noisome smoke, ‭ She put him on; and, over all, a cloke ‭ Made of a stag's huge hide, of which was worn ‭ The hair quite off; a scrip, all-patch'd and torn, ‭ Hung by a cord, oft broke and knit again; ‭ And with a staff did his old limbs sustain. ‭ Thus having both consulted of th' event, ‭ They parted both; and forth to Sparta went ‭ The gray-eyed Goddess, to see all things done ‭ That appertain'd to wise Ulysses' son. ‭ THE END OF THE THIRTEENTH BOOK OF HOMER'S ODYSSEYS. ‭[1] _Γερούσιος οι͒νος, quod pro honorario senibus datur._ And ‭because the word so Englished hath no other to express it, ‭sounding well, and helping our language, it is here used. ‭[2] Intending in chief the senators, with every man's addition of gift. ‭[3] _Εὐήνορα χαλκὸν, bene honestos faciens æs._ ‭[4] The Phæacians were descended originally from Neptune. ‭[5] _Αμϕικαλύπτω, superinjicio aliquid tanquam tegmen seu ‭operimentum._ ‭[6] Minerva like a shepherd (such as kings' sons used at those times ‭to be) appears to Ulysses. ‭[7] _Λυπρὸς, velut tristis, jejunaque naturâ._ ‭[8] _Επίκλοπος, furandi avidus._ ‭[9] _Σχέτλιε, ποικλομη̑τα, varia et multiplicia habens consilia._ ‭ THE FOURTEENTH BOOK OF HOMER'S ODYSSEYS ‭ THE ARGUMENT ‭ Ulysses meets amids the field ‭ His swain Eumæus: who doth yield ‭ Kind guest-rites to him, and relate ‭ Occurrents of his wrong'd estate. ‭ ANOTHER ARGUMENT ‭ _Ξι̑._ ‭ Ulysses fains ‭ For his true good: ‭ His pious swain's ‭ Faith understood. ‭ But he the rough way took from forth the port, ‭ Through woods and hill-tops, seeking the resort ‭ Where Pallas said divine Eumæus liv'd; ‭ Who of the fortunes, that were first achiev'd ‭ By God-like Ithacus in household rights, ‭ Had more true care than all his prosylites. [1] ‭ He found him sitting in his cottage door, ‭ Where he had rais'd to ev'ry airy blore ‭ A front of great height, and in such a place ‭ That round ye might behold, of circular grace ‭ A walk so wound about it; which the swain ‭ (In absence of his far-gone sovereign) ‭ Had built himself, without his queen's supply, ‭ Or old Laertes', to see safely lie ‭ His houséd herd. The inner part he wrought ‭ Of stones, that thither his own labours brought, ‭ Which with an hedge of thorn he fenc'd about, ‭ And compass'd all the hedge with pales cleft out ‭ Of sable oak, that here and there he fix'd ‭ Frequent and thick. Within his yard he mix'd ‭ Twelve styes to lodge his herd; and ev'ry stye ‭ Had room and use for fifty swine to lie; ‭ But those were females all. The male swine slept ‭ Without doors ever; nor was their herd kept ‭ Fair like the females, since they suffer'd still ‭ Great diminution, he being forc'd to kill ‭ And send the fattest to the dainty feasts ‭ Affected by th' ungodly wooing guests. ‭ Their number therefore but three hundred were ‭ And sixty. By them mastiffs, as austere ‭ As savage beasts, lay ever, their fierce strain ‭ Bred by the herdsman, a mere prince of men, ‭ Their number four. Himself was then applied ‭ In cutting forth a fair-hued ox's hide, ‭ To fit his feet with shoes. His servants held ‭ Guard of his swine: three, here and there, at field, ‭ The fourth he sent to city with a sow, ‭ Which must of force be offer'd to the vow ‭ The Wooers made to all satiety, ‭ To serve which still they did those off'rings ply. ‭ The fate-born-dogs-to-bark took sudden view [2] ‭ Of Odyssëus, and upon him flew ‭ With open mouth. He, cunning to appall ‭ A fierce dog's fury, from his hand let fall ‭ His staff to earth, and sat him careless down. ‭ And yet to him had one foul wrong been shown ‭ Where most his right lay, had not instantly ‭ The herdsman let his hide fall, and his cry ‭ (With frequent stones flung at the dogs) repell'd ‭ This way and that their eager course they held; ‭ When through the entry past, he thus did mourn: ‭ "O father! How soon had you near been torn ‭ By these rude dogs, whose hurt had branded me ‭ With much neglect of you! But Deity ‭ Hath giv'n so many other sighs and cares ‭ To my attendant state, that well unwares ‭ You might be hurt for me, for here I lie ‭ Grieving and mourning for the Majesty ‭ That, God-like, wonted to be ruling here, ‭ Since now I fat his swine for others' cheer, ‭ Where he, perhaps, errs hungry up and down, ‭ In countries, nations, cities, all unknown; ‭ If any where he lives yet, and doth see ‭ The sun's sweet beams. But, father, follow me, ‭ That, cheer'd with wine and food, you may disclose ‭ From whence you truly are, and all the woes ‭ Your age is subject to." This said, he led ‭ Into his cottage, and of osiers spread ‭ A thicken'd hurdle, on whose top he strow'd ‭ A wild-goat's shaggy skin, and then bestow'd ‭ His own couch on it, that was soft and great. ‭ Ulysses joy'd to see him so entreat ‭ His uncouth presence, saying: "Jove requite, ‭ And all th' immortal Gods, with that delight ‭ Thou most desir'st, thy kind receipt of me, ‭ friend to human hospitality!" ‭ Eumæus answer'd: "Guest! If one much worse ‭ Arriv'd here than thyself, it were a curse ‭ To my poor means, to let a stranger taste ‭ Contempt for fit food. Poor men, and unplac'd ‭ In free seats of their own, are all from Jove ‭ Commended to our entertaining love. ‭ But poor is th' entertainment I can give, ‭ Yet free and loving. Of such men as live ‭ The lives of servants, and are still in fear ‭ Where young lords govern, this is all the cheer ‭ They can afford a stranger. There was one ‭ That us'd to manage this now desert throne, ‭ To whom the Gods deny return, that show'd ‭ His curious favour to me, and bestow'd ‭ Possessions on me, a most-wishéd wife, ‭ A house, and portion, and a servant's life, ‭ Fit for the gift a gracious king should give; ‭ Who still took pains himself, and God made thrive ‭ His personal endeavour, and to me ‭ His work the more increas'd, in which you see ‭ I now am conversant. And therefore much ‭ His hand had help'd me, had Heav'n's will been such, ‭ He might have here grown old. But he is gone, ‭ And would to God the whole successión ‭ Of Helen might go with him, since for her ‭ So many men died, whose fate did confer ‭ My liege to Troy, in Agamemnon's grace, ‭ To spoil her people, and her turrets race!" ‭ This said, his coat to him he straight did gird, ‭ And to his styes went that contain'd his herd; ‭ From whence he took out two, slew both, and cut ‭ Both fairly up; a fire enflam'd, and put ‭ To spit the joints; which roasted well, he set ‭ With spit and all to him, that he might eat ‭ From thence his food in all the singeing heat, ‭ Yet dredg'd it first with flour; then fill'd his cup ‭ With good sweet wine; sat then, and cheer'd him up ‭ "Eat now, my guest, such lean swine as are meat ‭ For us poor swains; the fat the Wooers eat, ‭ In whose minds no shame, no remorse, doth move, ‭ Though well they know the bless'd Gods do not love ‭ Ungodly actions, but respect the right, ‭ And in the works of pious men delight. ‭ But these are worse than impious, for those ‭ That vow t' injustice, and profess them foes ‭ To other nations, enter on their land, ‭ And Jupiter (to show his punishing hand ‭ Upon th' invaded, for their penance then) ‭ Gives favour to their foes, though wicked men, ‭ To make their prey on them; who, having freight ‭ Their ships with spoil enough, weigh anchor straight, ‭ And each man to his house; (and yet ev'n these, ‭ Doth pow'rful fear of God's just vengeance seize ‭ Ev'n for that prize in which they so rejoice) ‭ But these men, knowing (having heard the voice ‭ Of God by some means) that sad death hath reft ‭ The ruler here, will never suffer left ‭ Their unjust wooing of his wife, nor take ‭ Her often answer, and their own roofs make ‭ Their fit retreats, but (since uncheck'd they may) ‭ They therefore will make still his goods their prey, ‭ Without all spare or end. There is no day, ‭ Nor night, sent out from God, that ever they ‭ Profane with one beast's blood, or only two, ‭ But more make spoil of; and the wrongs they do ‭ In meat's excess to wine as well extend, ‭ Which as excessively their riots spend, ‭ Yet still leave store, for sure his means were great, ‭ And no heroë, that hath choicest seat ‭ Upon the fruitful neighbour-continent, ‭ Or in this isle itself, so opulent ‭ Was as Ulysses; no, nor twenty such, ‭ Put altogether, did possess so much. ‭ Whose herds and flocks I'll tell to ev'ry head: ‭ Upon the continent he daily fed ‭ Twelve herds of oxen, no less flocks of sheep, ‭ As many herds of swine, stalls large and steep, ‭ And equal sorts of goats, which tenants there, ‭ And his own shepherds, kept. Then fed he here ‭ Eleven fair stalls of goats, whose food hath yield ‭ In the extreme part of a neighbour-field. ‭ Each stall his herdsman hath, an honest swain, ‭ Yet ev'ry one must ev'ry day sustain ‭ The load of one beast (the most-fat, and best ‭ Of all the stall-fed) to the Wooers' feast. ‭ And I, for my part, of the swine I keep ‭ (With four more herdsmen) ev'ry day help steep ‭ The Wooers' appetites in blood of one, ‭ The most select our choice can fall upon." ‭ To this Ulysses gave good ear, and fed, ‭ And drunk his wine, and vex'd, and ravishéd ‭ His food for mere vexation. Seeds of ill ‭ His stomach sow'd, to hear his goods go still ‭ To glut of Wooers. But his dinner done, ‭ And stomach fed to satisfactión, ‭ He drunk a full bowl, all of only wine, ‭ And gave it to the guardian of his swine, ‭ Who took it, and rejoic'd; to whom he said: ‭ "O friend, who is it that, so rich, hath paid ‭ Price for thy service, whose commended pow'r, ‭ Thou sayst, to grace the Grecian conquerour, ‭ At Ilion perish'd? Tell me. It may fall ‭ I knew some such. The great God knows, and all ‭ The other deathless Godheads, if I can, ‭ Far having travell'd, tell of such a man." ‭ Eumæus answer'd: "Father, never one, ‭ Of all the strangers that have touch'd upon ‭ This coast, with his life's news could ever yet ‭ Of queen, or lov'd son, any credit get. ‭ These travellers, for clothes, or for a meal, ‭ At all adventures, any lie will tell. ‭ Nor do they trade for truth. Not any man ‭ That saw the people Ithacensian, ‭ Of all their sort, and had the queen's supplies, ‭ Did ever tell her any news, but lies. ‭ She graciously receives them yet, inquires ‭ Of all she can, and all in tears expires. ‭ It is th' accustom'd law, that women keep, ‭ Their husbands elsewhere dead, at home to weep. ‭ But do thou quickly, father, forge a tale, ‭ Some coat, or cloak, to keep thee warm withal, ‭ Perhaps some one may yield thee; but for him, ‭ Vultures and dogs have torn from ev'ry limb ‭ His porous skin, and forth his soul is fled, ‭ His corse at sea to fishes forfeited, ‭ Or on the shore lies hid in heaps of sand, ‭ And there hath he his ebb, his native strand ‭ With friends' tears flowing. But to me past all ‭ Were tears created, for I never shall ‭ Find so humane a royal master more, ‭ Whatever sea I seek, whatever shore. ‭ Nay, to my father, or my mother's love ‭ Should I return, by whom I breathe and move, ‭ Could I so much joy offer; nor these eyes ‭ (Though my desires sustain extremities ‭ For their sad absence) would so fain be blest ‭ With sight of their lives, in my native nest, ‭ As with Ulysses dead; in whose last rest, ‭ O friend, my soul shall love him. He's not here ‭ Nor do I name him like a flatterer, ‭ But as one thankful for his love and care ‭ To me a poor man; in the rich so rare. ‭ And be he past all shores where sun can shine, ‭ I will invoke him as a soul divine." ‭ "O friend," said he, "to say, and to believe, ‭ He cannot live, doth too much licence give ‭ To incredulity; for, not to speak ‭ At needy randon, but my breath to break ‭ In sacred oath, Ulysses shall return. ‭ And when his sight recomforts those that mourn ‭ In his own roofs, then give me cloak, and coat, ‭ And garments worthy of a man of note. ‭ Before which, though need urg'd me never so, ‭ I'll not receive a thread, but naked go. ‭ No less I hate him than the gates of hell, ‭ That poorness can force an untruth to tell. ‭ Let Jove then (Heav'n's chief God) just witness bear, ‭ And this thy hospitable table here, ‭ Together with unblam'd Ulysses' house, ‭ In which I find receipt so gracious, ‭ What I affirm'd of him shall all be true. ‭ This instant year thine eyes ev'n here shall view ‭ Thy lord Ulysses. Nay, ere this month's end, ‭ Return'd full-home, he shall revenge extend ‭ To ev'ry one, whose ever deed hath done ‭ Wrong to his wife and his illustrious son." ‭ "O father," he replied, "I'll neither give ‭ Thy news reward, nor doth Ulysses live. ‭ But come, enough of this, let's drink and eat, ‭ And never more his memory repeat. ‭ It grieves my heart to be remember'd thus ‭ By anyone of one so glorious. ‭ But stand your oath in your assertion strong, ‭ And let Ulysses come, for whom I long, ‭ For whom his wife, for whom his agéd sire, ‭ For whom his son consumes his god-like fire, ‭ Whose chance I now must mourn, and ever shall. ‭ Whom when the Gods had brought to be as tall ‭ As any upright plant, and I had said, ‭ He would amongst a court of men have sway'd ‭ In counsels, and for form have been admir'd ‭ Ev'n with his father, some God misinspir'd, ‭ Or man took from him his own equal mind, ‭ And pass'd him for the Pylian shore to find ‭ His long-lost father. In return from whence, ‭ The Wooers' pride way-lays his innocence, ‭ That of divine Arcesius all the race ‭ May fade to Ithaca, and not the grace ‭ Of any name left to it. But leave we ‭ His state, however, if surpris'd he be, ‭ Or if he scape. And may Saturnius' hand ‭ Protect him safely to his native land. ‭ Do thou then, father, show your griefs, and cause ‭ Of your arrival here; nor break the laws ‭ That truth prescribes you, but relate your name, ‭ And of what race you are, your father's fame, ‭ And native city's; ship and men unfold, ‭ That to this isle convey'd you, since I hold ‭ Your here arrival was not all by shore, ‭ Nor that your feet your agéd person bore." ‭ He answer'd him: "I'll tell all strictly true, ‭ If time, and food, and wine enough, accrue ‭ Within your roof to us, that freely we ‭ May sit and banquet. Let your business be ‭ Discharg'd by others; for, when all is done, ‭ I cannot easily, while the year doth run ‭ His circle round, run over all the woes, ‭ Beneath which, by the course the Gods dispose, ‭ My sad age labours. First, I'll tell you then, ‭ From ample Crete I fetch my native strain; ‭ My father wealthy, whose house many a life ‭ Brought forth and bred besides by his true wife, ‭ But me a bond-maid bore, his concubine. ‭ Yet tender'd was I as his lawful line ‭ By him of whose race I my life profess. ‭ Castor his name, surnam'd Hylacides. ‭ A man, in fore-times, by the Cretan state, ‭ For goods, good children, and his fortunate ‭ Success in all acts, of no mean esteem. ‭ But death-conferring Fates have banish'd him ‭ To Pluto's kingdom. After whom, his sons ‭ By lots divided his possessions, ‭ And gave me passing little; yet bestow'd ‭ A house on me, to which my virtues woo'd ‭ A wife from rich men's roofs; nor was borne low, ‭ Nor last in fight, though all nerves fail me now. ‭ But I suppose, that you, by thus much seen, ‭ Know by the stubble what the corn hath been. ‭ For, past all doubt, affliction past all mean ‭ Hath brought my age on; but, in seasons past, ‭ Both Mars and Pallas have with boldness grac'd, ‭ And fortitude, my fortunes, when I chus'd ‭ Choice men for ambush, prest to have produc'd ‭ Ill to mine enemies; my too vent'rous spirit ‭ Set never death before mine eyes, for merit, ‭ But, far the first advanc'd still, still I strook ‭ Dead with my lance whoever overtook ‭ My speed of foot. Such was I then for war. ‭ But rustic actions ever fled me far, ‭ And household thrift, which breeds a famous race. ‭ In oar-driv'n ships did I my pleasures place, ‭ In battles, light darts, arrows. Sad things all, ‭ And into others' thoughts with horror fall. ‭ But what God put into my mind, to me ‭ I still esteem'd as my felicity. ‭ As men of sev'ral metals are address'd, ‭ So sev'ral forms are in their souls impress'd. ‭ Before the sons of Greece set foot in Troy, ‭ Nine times, in chief, I did command enjoy ‭ Of men and ships against our foreign foe, ‭ And all I fitly wish'd succeeded so. ‭ Yet, after this, I much exploit achiev'd, ‭ When straight my house in all possessions thriv'd. ‭ Yet, after that, I great and rev'rend grew ‭ Amongst the Cretans, till the Thund'rer drew ‭ Our forces out in his foe-Troy decrees; ‭ A hateful service that dissolv'd the knees ‭ Of many a soldier. And to this was I, ‭ And famous Idomen, enjoin'd t' apply ‭ Our ships and pow'rs, Nor was there to be heard ‭ One reason for denial, so preferr'd ‭ Was the unreasonable people's rumour. ‭ Nine years we therefore fed the martial humour, ‭ And in the tenth, de-peopling Priam's town, ‭ We sail'd for home. But God had quickly blown ‭ Our fleet in pieces; and to wretched me ‭ The counsellor Jove did much mishap decree, ‭ For, only one month, I had leave t' enjoy ‭ My wife and children, and my goods t' employ. ‭ But, after this, my mind for Ægypt stood, ‭ When nine fair ships I rigg'd forth for the flood, ‭ Mann'd them with noble soldiers, all things fit ‭ For such a voyage soon were won to it. ‭ Yet six days after stay'd my friends in feast, ‭ While I in banquets to the Gods addrest ‭ Much sacred matter for their sacrifice. ‭ The seventh, we boarded; and the Northern skies ‭ Lent us a frank and passing prosp'rous gale, ‭ 'Fore which we bore us free and easy sail ‭ As we had back'd a full and frolic tide; ‭ Nor felt one ship misfortune for her pride, ‭ But safe we sat, our sailors and the wind ‭ Consenting in our convoy. When heav'n shin'd ‭ In sacred radiance of the fifth fair day, ‭ To sweetly-water'd Egypt reach'd our way, ‭ And there we anchor'd; where I charg'd my men ‭ To stay aboard, and watch. Dismissing then ‭ Some scouts to get the hill-tops, and discover, ‭ They (to their own intemperance giv'n over). ‭ Straight fell to forage the rich fields, and thence ‭ Enforce both wives and infants, with th' expence ‭ Of both their bloods. When straight the rumour flew ‭ Up to the city. Which heard, up they drew ‭ By day's First break, and all the field was fill'd ‭ With foot and horse, whose arms did all things gild. ‭ And then the lightning-loving Deity cast ‭ A foul flight on my soldiers; nor stood fast ‭ One man of all. About whom mischief stood, ‭ And with his stern steel drew in streams the blood ‭ The greater part fed in their dissolute veins; ‭ The rest were sav'd, and made enthralléd swains ‭ To all the basest usages there bred. ‭ And then, ev'n Jove himself supplied my head ‭ With saving counsel; though I wish'd to die, ‭ And there in Egypt with their slaughters lie, ‭ So much grief seiz'd me, but Jove made me yield, ‭ Dishelm my head, take from my neck my shield, ‭ Hurl from my hand my lance, and to the troop ‭ Of horse the king led instantly made up, ‭ Embrace, and kiss his knees; whom pity won ‭ To give me safety, and (to make me shun ‭ The people's outrage, that made in amain, ‭ All jointly fir'd with thirst to see me slain) ‭ He took me to his chariot, weeping, home, ‭ Himself with fear of Jove's wrath overcome, ‭ Who yielding souls receives, and takes most ill ‭ All such as well may save yet love to kill. ‭ Seven years I sojourn'd here, and treasure gat ‭ In good abundance of th' Ægyptian state, ‭ For all would give; but when th' eighth year began, ‭ A knowing fellow (that would gnaw a man [3] ‭ Like to a vermin, with his hellish brain, ‭ And many an honest soul ev'n quick had slain, ‭ Whose name was Phœnix) close accosted me, ‭ And with insinuations, such as he ‭ Practis'd on others, my consent he gain'd ‭ To go into Phœnicia, where remain'd ‭ His house, and living. And with him I liv'd ‭ A cómplete year; but when were all arriv'd ‭ The months and days, and that the year again ‭ Was turning round, and ev'ry season's reign ‭ Renew'd upon us, we for Libya went, ‭ When, still inventing crafts to circumvent, ‭ He made pretext, that I should only go ‭ And help convey his freight; but thought not so, ‭ For his intent was to have sold me there, ‭ And made good gain for finding me a year. ‭ Yet him I follow'd, though suspecting this, ‭ For, being aboard his ship, I must be his ‭ Of strong necessity. She ran the flood ‭ (Driven with a northern gale, right free, and good) ‭ Amids the full stream, full on Crete. But then ‭ Jove plotted death to him and all his men, ‭ For (put off quite from Crete, and so far gone ‭ That shore was lost, and we set eye on none, ‭ But all show'd heav'n and sea) above our keel ‭ Jove pointed right a cloud as black as hell, ‭ Beneath which all the sea hid, and from whence ‭ Jove thunder'd as his hand would never thence, ‭ And thick into our ship he threw his flash; [4] ‭ That 'gainst a rock, or flat, her keel did dash ‭ With headlong rapture. Of the sulphur all ‭ Her bulk did savour; and her men let fall ‭ Amids the surges, on which all lay tost, ‭ Like sea-gulls, round about her sides, and lost. ‭ And so God took all home-return from them. ‭ But Jove himself, though plung'd in that extreme, ‭ Recover'd me by thrusting on my hand ‭ The ship's long mast. And, that my life might stand ‭ A little more up, I embrac'd it round; ‭ And on the rude winds, that did ruins sound, ‭ Nine days we hover'd. In the tenth black night ‭ A huge sea cast me on Thesprotia's height, ‭ Where the heroë Phidon, that was chief ‭ Of all the Thesprots, gave my wrack relief, ‭ Without the price of that redemptión [5] ‭ That Phœnix fish'd for. Where the king's lov'd son ‭ Came to me, took me by the hand, and led ‭ Into his court my poor life, surfeited ‭ With cold and labour; and because my wrack ‭ Chanc'd on his father's shore, he let not lack ‭ My plight or coat, or cloak, or anything ‭ Might cherish heat in me. And here the king ‭ Said, he receiv'd Ulysses as his guest, ‭ Observ'd him friend-like, and his course addrest ‭ Home to his country, showing there to me ‭ Ulysses' goods, a very treasury ‭ Of brass, and gold, and steel of curious frame. ‭ And to the tenth succession of his name ‭ He laid up wealth enough, to serve beside ‭ In that king's house, so hugely amplified ‭ His treasure was. But from his court the king ‭ Affirm'd him shipp'd for the Dodonean spring, ‭ To hear, from out the high-hair'd oak of Jove, ‭ Counsel from him for means to his remove ‭ To his lov'd country, whence so many a year ‭ He had been absent; if he should appear ‭ Disguis'd, or manifest; and further swore ‭ In his mid court, at sacrifice, before ‭ These very eyes, that he had ready there ‭ Both ship and soldiers, to attend and bear ‭ Him to his country. But, before, it chanc'd ‭ That a Thesprotian ship was to be launch'd ‭ For the much-corn-renown'd Dulichian land, ‭ In which the king gave to his men command ‭ To take, and bring me under tender hand ‭ To king Acastus. But, in ill design ‭ Of my poor life, did their desires combine, ‭ So far forth, as might ever keep me under ‭ In fortune's hands, and tear my state in sunder. ‭ And when the water-treader far away ‭ Had left the land, then plotted they the day ‭ Of my long servitude, and took from me ‭ Both coat and cloak, and all things that might be ‭ Grace in my habit, and in place put on ‭ These tatter'd rags, which now you see upon ‭ My wretched bosom. When heav'n's light took sea, [6] ‭ They fetch'd the field-works of fair Ithaca, ‭ And in the arm'd ship, with a well-wreath'd cord, ‭ They straitly bound me, and did all disboard ‭ To shore to supper, in contentious rout. ‭ Yet straight the Gods themselves took from about ‭ My pressed limbs the bands, with equal ease, ‭ And I, my head in rags wrapp'd, took the seas, ‭ Descending by the smooth stern, using then ‭ My hands for oars, and made from these bad men ‭ Long way in little time. At last, I fetch'd ‭ A goodly grove of oaks, whose shore I reach'd, ‭ And cast me prostrate on it. When they knew ‭ My thus-made 'scape, about the shores they flew, ‭ But, soon not finding, held it not their best ‭ To seek me further, but return'd to rest ‭ Aboard their vessel. Me the Gods lodg'd close, ‭ Conducting me into the safe repose ‭ A good man's stable yielded. And thus Fate ‭ This poor hour added to my living date." ‭ "O wretch of guests," said he, "thy tale hath stirr'd ‭ My mind to much ruth, both how thou hast err'd, ‭ And suffer'd, hearing in such good parts shown. ‭ But, what thy chang'd relation would make known ‭ About Ulysses, I hold neither true, ‭ Nor will believe. And what need'st thou pursue ‭ A lie so rashly, since he sure is so ‭ As I conceive, for which my skill shall go? ‭ The safe return my king lacks cannot be, ‭ He is so envied of each Deity, ‭ So clear, so cruelly. For not in Troy ‭ They gave him end, nor let his corpse enjoy ‭ The hands of friends (which well they might have done, ‭ He manag'd arms to such perfection, ‭ And should have had his sepulchre, and all, ‭ And all the Greeks to grace his funeral, ‭ And this had giv'n a glory to his son ‭ Through all times future) but his head is run ‭ Unseen, unhonour'd, into Harpies' maws. ‭ For my part, I'll not meddle with the cause, ‭ I live a separate life amongst my swine, ‭ Come at no town for any need of mine, ‭ Unless the circularly-witted queen [7] ‭ (When any far-come guest is to be seen ‭ That brings her news) commands me bring a brawn, ‭ About which (all things being in question drawn, ‭ That touch the king) they sit, and some are sad ‭ For his long absence, some again are glad ‭ To waste his goods unwreak'd, all talking still. ‭ But, as for me, I nourish'd little will ‭ T' inquire or question of him, since the man ‭ That feign'd himself the fled Ætolian, ‭ For slaught'ring one, through many regions stray'd, ‭ In my stall, as his diversory, stay'd. ‭ Where well entreating him, he told me then, ‭ Amongst the Cretans, with king Idomen, ‭ He saw Ulysses at his ship's repair, ‭ That had been brush'd with the enragéd air; ‭ And that in summer, or in autumn, sure, ‭ With all his brave friends and rich furniture, ‭ He would be here; and nothing so, nor so. ‭ But thou, an old man, taught with so much woe ‭ As thou hast suffer'd, to be season'd true, ‭ And brought by his fate, do not here pursue ‭ His gratulations with thy cunning lies, ‭ Thou canst not soak so through my faculties ‭ For I did never either honour thee ‭ Or give thee love, to bring these tales to me, ‭ But in my fear of hospitable Jove ‭ Thou didst to this pass my affections move." ‭ "You stand exceeding much incredulous," ‭ Replied Ulysses, "to have witness'd thus ‭ My word and oath, yet yield no trust at all. ‭ But make me now a covenant here, and call ‭ The dreadful Gods to witness, that take seat ‭ In large Olympus: If your king's retreat ‭ Prove made, ev'n hither, you shall furnish me ‭ With cloak, and coat, and make my passage free ‭ For lov'd Dulichius; if, as fits my vow, ‭ Your king return not, let your servants throw ‭ My old limbs headlong from some rock most high, ‭ That other poor men may take fear to lie." ‭ The herdsman, that had gifts in him divine, ‭ Replied: "O guest, how shall this fame of mine ‭ And honest virtue, amongst men, remain ‭ Now, and hereafter, without worthy stain, ‭ If I, that led thee to my hovel here, ‭ And made thee fitting hospitable cheer, ‭ Should after kill thee, and thy lovéd mind ‭ Force from thy bones? Or how should stand inclin'd ‭ With any faith my will t' importune Jove, ‭ In any pray'r hereafter for his love? ‭ Come, now 'tis supper's hour, and instant haste ‭ My men will make home, when our sweet repast ‭ We'll taste together." This discourse they held ‭ In mutual kind, when from a neighbour-field ‭ His swine and swine-herds came, who in their cotes ‭ Inclos'd their herds for sleep, which mighty throats ‭ Laid out in ent'ring. Then the God-like swain ‭ His men enjoin'd thus: "Bring me to be slain ‭ A chief swine female, for my stranger guest, ‭ When altogether we will take our feast, ‭ Refreshing now our spirits, that all day take ‭ Pains in our swine's good, who may therefore make ‭ For our pains with them all amends with one, ‭ Since others eat our labours, and take none." ‭ This said, his sharp steel hew'd down wood, and they ‭ A passing fat swine hal'd out of the sty, ‭ Of five years old, which to the fire they put. ‭ When first Eumæus from the front did cut ‭ The sacred hair, and cast it in the fire, ‭ Then pray'd to heav'n; for still before desire ‭ Was serv'd with food, in their so rude abodes, ‭ Not the poor swine-herd would forget the Gods, ‭ Good souls they bore, how bad soever were ‭ The habits that their bodies' parts did bear. ‭ When all the deathless Deities besought, ‭ That wise Ulysses might be safely brought ‭ Home to his house; then with a log of oak ‭ Left lying by, high lifting it, a stroke ‭ He gave so deadly it made life expire. ‭ Then cut the rest her throat, and all in fire ‭ They hid and sing'd her, cut her up; and then, ‭ The master took the office from the men, ‭ Who on the altar did the parts impose ‭ That serv'd for sacrifice; beginning close ‭ About the belly, thorough which he went. ‭ And (all the chief fat gath'ring) gave it vent ‭ (Part dredg'd with flour) into the sacred flame; ‭ Then cut they up the joints, and roasted them, ‭ Drew all from spit, and serv'd in dishes all. ‭ Then rose Eumæus (who was general ‭ In skill to guide each act his fit event) ‭ And, all in seven parts cut, the first part went ‭ To service of the Nymphs and Mercury, ‭ To whose names he did rites of piety ‭ In vows particular; and all the rest ‭ He shar'd to ev'ry one, but his lov'd guest ‭ He grac'd with all the chine, and of that king, ‭ To have his heart cheer'd, set up ev'ry string. ‭ Which he observing said: "I would to Jove, ‭ Eumæus, thou liv'dst in his worthy love ‭ As great as mine, that giv'st to such a guest ‭ As my poor self of all thy goods the best." ‭ Eumæus answer'd: "Eat, unhappy wretch, ‭ And to what here is at thy pleasure reach. ‭ This I have, this thou want'st; thus God will give, ‭ Thus take away, in us, and all that live. ‭ To his will's equal centre all things fall, ‭ His mind he must have, for he can do all." ‭ Thus having eat, and to his wine descended, ‭ Before he serv'd his own thirst, he commended ‭ The first use of it in fit sacrifice ‭ (As of his meat) to all the Deities, ‭ And to the city-racer's hand applied ‭ The second cup, whose place was next his side. ‭ Mesauliús did distribute the meat, ‭ (To which charge was Eumæus solely set, ‭ In absence of Ulysses, by the queen ‭ And old Laertes) and this man had been ‭ Bought by Eumæus, with his faculties, ‭ Employ'd then in the Taphian merchandise. ‭ But now, to food appos'd, and order'd thus, ‭ All fell. Desire suffic'd, Mesauliús ‭ Did take away. For bed then next they were, ‭ All thoroughly satisfied with cómplete cheer. ‭ The night then came, ill, and no taper shin'd; ‭ Jove rain'd her whole date; th' ever-wat'ry wind ‭ Zephyr blew loud; and Laertiades ‭ (Approving kind Eumæus' carefulness ‭ For his whole good) made far about assay, ‭ To get some cast-off cassock (lest he lay ‭ That rough night cold) of him, or anyone ‭ Of those his servants; when he thus begun: ‭ "Hear me, Eumæus, and my other friends, ‭ I'll use a speech that to my glory tends, ‭ Since I have drunk wine past my usual guise. ‭ _Strong wine commands the fool and moves the wise,_ ‭ Moves and impels him too to sing and dance, ‭ And break in pleasant laughters, and, perchance, ‭ Prefer a speech too that were better in. ‭ But when my spirits once to speak begin, ‭ I shall not then dissemble. Would to heav'n, ‭ I were as young, and had my forces driv'n ‭ As close together, as when once our pow'rs ‭ We led to ambush under th' Ilion tow'rs! ‭ Where Ithacus and Menelaus were ‭ The two commanders, when it pleas'd them there ‭ To take myself for third, when to the town ‭ And lofty walls we led, we couch'd close down, ‭ All arm'd, amids the osiers and the reeds, ‭ Which oftentimes th' o'er-flowing river feeds. ‭ The cold night came, and th' icy northern gale ‭ Blew bleak upon us, after which did fall ‭ A snow so cold, it cut as in it beat ‭ A frozen water, which was all concrete ‭ About our shields like crystal. All made feign ‭ Above our arms to clothe, and clothe again. ‭ And so we made good shift, our shields beside ‭ Clapp'd close upon our clothes, to rest and hide ‭ From all discovery. But I, poor fool, ‭ Left my weeds with my men, because so cool ‭ I thought it could not prove; which thought my pride ‭ A little strengthen'd, being loth to hide ‭ A goodly glitt'ring garment I had on; ‭ And so I follow'd with my shield alone, ‭ And that brave weed. But when the night near ended ‭ Her course on earth, and that the stars descended, ‭ I jogg'd Ulysses, who lay passing near, ‭ And spake to him, that had a nimble ear, ‭ Assuring him, that long I could not lie ‭ Amongst the living, for the fervency ‭ Of that sharp night would kill me, since as then ‭ My evil angel made me with my men ‭ Leave all weeds but a fine one. But I know ‭ 'Tis vain to talk; here wants all remedy now. ‭ This said, he bore that understanding part ‭ In his prompt spirit that still show'd his art ‭ In fight and counsel, saying (in a word, ‭ And that low whisper'd) peace, lest you afford ‭ Some Greek note of your softness. No word more, ‭ But made as if his stern austerity bore ‭ My plight no pity; yet, as still he lay ‭ His head reposing on his hand, gave way ‭ To this invention: 'Hear me friends, a dream ‭ (That was of some celestial light a beam) ‭ Stood in my sleep before me, prompting me ‭ With this fit notice: 'We are far,' said he, ‭ 'From out our fleet. Let one go then, and try ‭ If Agamemnon will afford supply ‭ To what we now are strong.' This stirr'd a speed ‭ In Thoas to th' affair; whose purple weed ‭ He left for haste; which then I took, and lay ‭ In quiet after, till the dawn of day. ‭ This shift Ulysses made for one in need, ‭ And would to heav'n, that youth such spirit did feed ‭ Now in my nerves, and that my joints were knit ‭ With such a strength as made me then held fit ‭ To lead men with Ulysses! I should then ‭ Seem worth a weed that fits a herdsman's men, ‭ For two respects, to gain a thankful friend, ‭ And to a good man's need a good extend." ‭ "O father," said Eumæus "thou hast shown ‭ Good cause for us to give thee good renown, ‭ Not using any word that was not freed ‭ From all least ill. Thou, therefore, shalt not need ‭ Or coat, or other thing, that aptly may ‭ Beseem a wretched suppliant for defray ‭ Of this night's need. But, when her golden throne ‭ The morn ascends, you must resume your own, ‭ For here you must not dream of many weeds, ‭ Or any change at all. We serve our needs ‭ As you do yours; one back, one coat. But when ‭ Ulysses' lovéd son returns, he then ‭ Shall give you coat and cassock, and bestow ‭ Your person where your heart and soul is now," ‭ This said, he rose, made near the fire his bed, ‭ Which all with goats' and sheep skins he bespread. ‭ All which Ulysses with himself did line, ‭ With whom; besides, he chang'd a gaberdine, ‭ Thick lin'd, and soft, which still he made his shift ‭ When he would dress him 'gainst the horrid drift ‭ Of tempest, when deep winter's season blows. ‭ Nor pleas'd it him to lie there with his sows, ‭ But while Ulysses slept there, and close by ‭ The other younkers, he abroad would lie, ‭ And therefore arm'd him. Which set cheerful fare ‭ Before Ulysses' heart, to see such care ‭ Of his goods taken, how far off soever ‭ His fate his person and his wealth should sever. ‭ First then, a sharp-edg'd sword he girt about ‭ His well-spread shoulders, and (to shelter out ‭ The sharp West wind that blew) he put him on ‭ A thick-lin'd jacket, and yet cast upon ‭ All that the large hide of a goat well-fed. ‭ A lance then took he, with a keen steel head, ‭ To be his keep-off both 'gainst men and dogs. ‭ And thus went he to rest with his male hogs, ‭ That still abroad lay underneath a rock, ‭ Shield to the North wind's ever-eager shock. ‭ THE END OF THE FOURTEENTH BOOK OF HOMER'S ODYSSEYS. ‭[1] _Πρόσυλος, materiæ adhærens: item, qui rebus mundanis ‭deditus est._ ‭[2] _'ϒλακόμωρος, ad latrandum fato quodam natus._ ‭[3] _Ανὴρ ἀπατήλια εἰδὼς, τρώκτης._ ‭[4] _'Ελελίχθη qui terram rapido motu concutit._ ‭[5] _'Απριάτην sine emptionis seu redemptionis pretio._ ‭[6] At sunset. ‭[7] _Περίϕρων._ ‭ THE FIFTEENTH BOOK OF HOMER'S ODYSSEYS ‭ THE ARGUMENT ‭ Minerva to his native seat. ‭ Exhorts Ulysses' son's retreat, ‭ In bed, and waking. He receives ‭ Gifts of Atrides, and so leaves ‭ The Spartan court. And, going aboard, ‭ Doth favourable way afford ‭ To Theoclymenus, that was ‭ The Argive augur, and sought pass, ‭ Fled for a slaughter he had done. ‭ Eumæus tells Laertes' son, ‭ How he became his father's man, ‭ Being sold by the Phœnician ‭ For some agreed-on faculties, ‭ From forth the Syrian isle made prise. ‭ Telemachus, arrived at home, ‭ Doth to Eumæus' cottage come. ‭ ANOTHER ARGUMENT ‭ O. ‭ From Sparta's strand ‭ Makes safe access ‭ To his own land ‭ Ulyssides. ‭ In Lacedæmon, large, and apt for dances, [1] ‭ Athenian Pallas her access advances ‭ Up to the great-in-soul Ulysses' seed, ‭ Suggesting his return now fit for deed. ‭ She found both him and Nestor's noble son ‭ In bed, in front of that fair mansión, ‭ Nestorides surpris'd with pleasing sleep, ‭ But on the watch Ulysses' son did keep, ‭ Sleep could not enter, cares did so excite ‭ His soul, through all the solitary night, ‭ For his lov'd father. To him, near, she said: ‭ "Telemachus! 'Tis time that now were stay'd ‭ Thy foreign travels, since thy goods are free ‭ For those proud men that all will eat from thee, ‭ Divide thy whole possessións, and leave ‭ Thy too-late presence nothing to receive. ‭ Incite the shrill-voic'd Menelaus then, ‭ To send thee to thy native seat again, ‭ While thou mayst yet find in her honour strong ‭ Thy blameless mother, 'gainst thy fathers' wrong. ‭ For both the father, and the brothers too, ‭ Of thy lov'd mother, will not suffer so ‭ Extended any more her widow's bed, ‭ But make her now her richest wooer wed, ‭ Eurymachus, who chiefly may augment ‭ Her gifts, and make her jointure eminent. ‭ And therefore haste thee, lest, in thy despite, ‭ Thy house stand empty of thy native right. ‭ For well thou know'st what mind a woman bears; ‭ The house of him, whoever she endears ‭ Herself in nuptials to, she sees increas'd, ‭ The issue of her first lov'd lord deceas'd ‭ Forgotten quite, and never thought on more. ‭ In thy return then, the re-counted store ‭ Thou find'st reserv'd, to thy most trusted maid ‭ Commit in guard, till Heav'n's Pow'rs have purvey'd ‭ A wife, in virtue and in beauty's grace, ‭ Of fit sort for thee, to supply her place. ‭ And this note more I'll give thee, which repose ‭ In sure remembrance: The best sort of those ‭ That woo thy mother watchful scouts address ‭ Both in the straits of th' Ithacensian seas, ‭ And dusty Samos, with intent t' invade ‭ And take thy life, ere thy return be made. ‭ Which yet I think will fail, and some of them ‭ That waste thy fortunes taste of that extreme ‭ They plot for thee. But keep off far from shore, ‭ And day and night sail, for a fore-right blore, ‭ Whoever of th' Immortals that vow guard ‭ And 'scape to thy return, will see prepar'd. ‭ As soon as thou arriv'st, dismiss to town ‭ Thy ship and men, and first of all make down ‭ To him that keeps thy swine, and doth conceive ‭ A tender care to see thee well survive. ‭ There sleep; and send him to the town, to tell ‭ The chaste Penelopé, that safe and well ‭ Thou liv'st in his charge, and that Pylos' sands ‭ The place contain'd from whence thy person lands." ‭ Thus she to large Olympus made ascent. ‭ When with his heel a little touch he lent ‭ To Nestor's son, whose sleep's sweet chains he loos'd, ‭ Bad rise, and see in chariot inclos'd ‭ Their one-hoof'd horse, that they might straight be gone. ‭ "No such haste," he replied, "Night holds her throne, ‭ And dims all way to course of chariot. ‭ The morn will soon get up. Nor see forgot ‭ The gifts with haste, that will, I know, be rich, ‭ And put into our coach with gracious speech ‭ By lance-fam'd Menelaus. Not a guest ‭ Shall touch at his house, but shall store his breast ‭ With fit mind of an hospitable man, ‭ To last as long as any daylight can ‭ His eyes recomfort, in such gifts as he ‭ Will proofs make of his hearty royalty." ‭ He had no sooner said, but up arose ‭ Aurora, that the golden hills repose. ‭ And Menelaus, good-at-martial-cries, ‭ From Helen's bed rais'd, to his guest applies ‭ His first appearance. Whose repair made known ‭ T' Ulysses' lov'd son, on his robe was thrown ‭ About his gracious body, his cloak cast ‭ Athwart his ample shoulders, and in haste ‭ Abroad he went, and did the king accost: ‭ "Atrides, guarded with heav'n's deified host, ‭ Grant now remission to my native right, ‭ My mind now urging mine own house's sight." ‭ "Nor will I stay," said he, "thy person long, ‭ Since thy desires to go are grown so strong. ‭ I should myself be angry to sustain ‭ The like detention urg'd by other men. ‭ Who loves a guest past mean, past mean will hate, ‭ _The mean in all acts bears the best estate._ ‭ A like ill 'tis, to thrust out such a guest ‭ As would not go, as to detain the rest. ‭ We should a guest love, while he loves to stay, ‭ And, when he likes not, give him loving way. ‭ Yet suffer so, that we may gifts impose ‭ In coach to thee; which ere our hands inclose, ‭ Thine eyes shall see, lest else our loves may glose. ‭ Besides, I'll cause our women to prepare ‭ What our house yields, and merely so much fare ‭ As may suffice for health. Both well will do, ‭ Both for our honour and our profit too. ‭ And, serving strength with food, you after may ‭ As much earth measure as will match the clay. ‭ If you will turn your course from sea, and go ‭ Through Greece and Argos (that myself may so ‭ Keep kind way with thee) I'll join horse, and guide ‭ T' our human cities. Nor ungratified ‭ Will anyone remit us; some one thing ‭ Will each present us, that along may bring ‭ Our pass with love, and prove our virtues blaz'd: ‭ A caldron, or a tripod, richly-braz'd, ‭ Two mules, a bowl of gold, that hath his price ‭ Heighten'd with emblems of some rare device." ‭ The wise prince answer'd: "I would gladly go ‭ Home to mine own, and see that govern'd so ‭ That I may keep what I for certain hold, ‭ Not hazard that for only hop'd-for gold. ‭ I left behind me none so all ways fit ‭ To give it guard, as mine own trust with it. ‭ Besides, in this broad course which you propose, ‭ My father seeking I myself may lose." ‭ When this the shrill-voic'd Menelaus heard, ‭ He charg'd his queen and maids to see prepar'd ‭ Breakfast, of what the whole house held for best. ‭ To him rose Eteoneus from his rest, ‭ Whose dwelling was not far off from the court, ‭ And his attendance his command did sort ‭ With kindling fires, and furth'ring all the roast, ‭ In act of whose charge heard no time he lost. ‭ Himself then to an odorous room descended, ‭ Whom Megapenthe and his queen attended. ‭ Come to his treasury, a two-ear'd cup ‭ He choos'd of all, and made his son bear up ‭ A silver bowl. The queen then taking stand ‭ Aside her chest, where by her own fair hand ‭ Lay vests of all hues wrought, she took out one ‭ Most large, most artful, chiefly fair, and shone ‭ Like to a star, and lay of all the last. ‭ Then through the house with either's gift they past; ‭ When to Ulysses' son Atrides said: ‭ "Telemachus, since so entirely sway'd ‭ Thy thoughts are with thy vow'd return now tender'd, ‭ May Juno's thund'ring husband see it render'd ‭ Perfect at all parts, action answ'ring thought. ‭ Of all the rich gifts, in my treasure sought, ‭ I give thee here the most in grace and best. ‭ A bowl but silver, yet the brim's comprest ‭ With gold, whose fabric his desert doth bring ‭ From Vulcan's hand, presented by the king ‭ And great heroë of Sidonia's state, ‭ When at our parting he did consummate ‭ His whole house-keeping. This do thou command." ‭ This said, he put the round bowl in his hand, ‭ And then his strong son Megapenthe plac'd ‭ The silver cup before him, amply grac'd ‭ With work and lustre. Helen (standing by, ‭ And in her hand the robe, her housewifery) ‭ His name rememb'ring, said: "And I present, ‭ Lov'd son, this gift to thee, the monument ‭ Of the so-many-lovéd Helen's hands, ‭ Which, at the knitting of thy nuptial bands, ‭ Present thy wife. In mean space, may it lie ‭ By thy lov'd mother; but to me apply ‭ Thy pleasure in it, and thus take thy way ‭ To thy fair house, and country's wishéd stay." ‭ Thus gave she to his hands the veil, and he ‭ The acceptation author'd joyfully. ‭ Which in the chariot's chest Pisistratus ‭ Plac'd with the rest, and held miraculous. ‭ The yellow-headed king then led them all ‭ To seats and thrones plac'd in his spacious hall. ‭ The hand-maid water brought, and gave it stream ‭ From out a fair and golden ewer to them, ‭ From whose hands to a silver caldron fled ‭ The troubled wave. A bright board then she spread, ‭ On which another rev'rend dame set bread. ‭ To which more servants store of victuals serv'd. ‭ Eteonëus was the man that kerv'd, ‭ And Megapenthe fill'd them all their wine. ‭ All fed and drank, till all felt care decline ‭ For those refreshings. Both the guests did go ‭ To horse, and coach, and forth the portico ‭ A little issued, when the yellow King ‭ Brought wine himself, that, with an offering ‭ To all the Gods, they might their journey take. ‭ He stood before the Gods, and thus he spake: ‭ "Farewell young Princes! To grave Nestor's ear ‭ This salutation from my gratitude bear: ‭ That I profess, in all our Ilion wars, ‭ He stood a careful father to my cares." ‭ To whom the wise Ulyssides replied: ‭ "With all our utmost shall be signified, ‭ Jove-kept Atrides, your right royal will; ‭ And would to God, I could as well fulfill ‭ Mine own mind's gratitude, for your free grace, ‭ In telling to Ulysses, in the place ‭ Of my return, in what accomplish'd kind ‭ I have obtain'd the office of a friend ‭ At your deservings; whose fair end you crown ‭ With gifts so many, and of such renown!" ‭ His wish, that he might find in his retreat ‭ His father safe return'd (to so repeat ‭ The king's love to him) was saluted thus: ‭ An eagle rose, and in her seres did truss ‭ A goose, all-white, and huge, a household one, ‭ Which men and women, crying out upon, ‭ Pursued, but she, being near the guests, her flight ‭ Made on their right hand, and kept still fore-right ‭ Before their horses; which observ'd by them, ‭ The spirits in all their minds took joys extreme, ‭ Which Nestor's son thus question'd: "Jove-kept king, [2] ‭ Yield your grave thoughts, if this ostentful thing ‭ (This eagle, and this goose) touch us, or you?" ‭ He put to study, and not knowing how ‭ To give fit answer, Helen took on her ‭ Th' ostent's solution, and did this prefer: ‭ "Hear me, and I will play the prophet's part, ‭ As the Immortals cast it in my heart, ‭ And as, I think, will make the true sense known: ‭ As this Jove's bird, from out the mountains flown, ‭ (Where was her eyrie, and whence rose her race,) ‭ Truss'd up this goose, that from the house did graze, ‭ So shall Ulysses, coming from the wild ‭ Of seas and suff'rings, reach, unreconcil'd, ‭ His native home, where ev'n this hour he is, ‭ And on those house-fed Wooers those wrongs of his ‭ Will shortly wreak, with all their miseries." ‭ "O," said Telemachus, "if Saturnian Jove ‭ To my desires thy dear presage approve, ‭ When I arrive, I will perform to thee ‭ My daily vows, as to a Deity." ‭ This said, he us'd his scourge upon the horse, ‭ That through the city freely made their course ‭ To field, and all day made that first speed good. ‭ But when the sun set, and obscureness stood ‭ In each man's way, they ended their access ‭ At Pheras, in the house of Diocles, ‭ Son to Orsilochus, Alphëus' seed, ‭ Who gave them guest-rites; and sleep's natural need ‭ They that night served there. When Aurora rose, ‭ They join'd their horse, took coach, and did dispose ‭ Their course for Pylos; whose high city soon ‭ They reach'd. Nor would Telemachus be won ‭ To Nestor's house, and therefore order'd thus ‭ His speech to Nestor's son, Pisistratus: ‭ "How shall I win thy promise to a grace ‭ That I must ask of thee? We both embrace ‭ The names of bed-fellows, and in that name ‭ Will glory as an adjunct of our fame; ‭ Our fathers' friendship, our own equal age, ‭ And our joint travel, may the more engage ‭ Our mutual concord. Do not then assay, ‭ My God-lov'd friend, to lead me from my way ‭ To my near ship, but take a course direct ‭ And leave me there, lest thy old sire's respect, ‭ In his desire to love me, hinder so ‭ My way for home, that have such need to go." ‭ This said, Nestorides held all discourse ‭ In his kind soul, how best he might enforce ‭ Both promise and performance; which, at last; ‭ He vow'd to venture, and directly cast ‭ His horse about to fetch the ship and shore. ‭ Where come, his friends' most lovely gifts he bore ‭ Aboard the ship, and in her hind-deck plac'd ‭ The veil that Helen's curious hand had grac'd, ‭ And Menelaus' gold, and said: "Away, ‭ Nor let thy men, in any least date, stay, ‭ But quite put off, ere I get home, and tell ‭ The old duke, you are past; for passing well ‭ I know his mind to so exceed all force ‭ Of any pray'r, that he will stay your course, ‭ Himself make hither, all your course call back, ‭ And, when he hath you, have no thought to rack ‭ Him from his bounty, and to let you part ‭ Without a present, but be vex'd at heart ‭ With both our pleadings, if we once put move ‭ The least repression of his fiery love." ‭ Thus took he coach, his fair-man'd steeds scourg'd on ‭ Along the Pylian city, and anon ‭ His father's court reach'd; while Ulysses' son ‭ Bade board, and arm; which with a thought was done. ‭ His rowers set, and he rich odours firing ‭ In his hind-deck, for his secure retiring, ‭ To great Athenia, to his ship came flying ‭ A stranger, and a prophet, as relying ‭ On wishéd passage, having newly slain ‭ A man at Argos, yet his race's vein ‭ Flow'd from Melampus, who in former date ‭ In Pylos liv'd, and had a huge estate, ‭ But fled his country, and the punishing hand ‭ Of great-soul'd Neleus, in a foreign land, ‭ From that most famous mortal, having held ‭ A world of riches, nor could be compell'd ‭ To render restitution in a year. ‭ In mean space, living as close prisoner ‭ In court of Phylacus, and for the sake ‭ Of Neleus' daughter mighty cares did take, ‭ Together with a grievous languor sent ‭ From grave Erinnys, that did much torment ‭ His vexéd conscience; yet his life's expence ‭ He scap'd, and drave the loud-voiced oxen thence, ‭ To breed-sheep Pylos, bringing vengeance thus ‭ Her foul demerit to great Neleüs, ‭ And to his brother's house reduc'd his wife. ‭ Who yet from Pylos did remove his life ‭ For feed-horse Argos, where his fate set down ‭ A dwelling for him, and in much renown ‭ Made govern many Argives, where a spouse ‭ He took to him, and built a famous house. ‭ There had he born to him Antiphates, ‭ And forceful Mantius. To the first of these ‭ Was great Oïcleus born: Oïcleus gat ‭ Amphiaraus, that the popular state ‭ Had all their health in, whom ev'n from his heart ‭ Jove lov'd, and Phœbus in the whole desert ‭ Of friendship held him; yet not bless'd so much ‭ That age's threshold he did ever touch, ‭ But lost his life by female bribery. [3] ‭ Yet two sons author'd his posterity, ‭ Alcmæon, and renown'd Amphilochus. ‭ Mantius had issue Polyphidius, ‭ And Clytus, but Aurora ravish'd him, ‭ For excellence of his admiréd limb, ‭ And interested him amongst the Gods. ‭ His brother knew men's good and bad abodes ‭ The best of all men, after the decease ‭ Of him that perish'd in unnatural peace ‭ At spacious Thebes. Apollo did inspire ‭ His knowing soul with a prophetic fire. ‭ Who, angry with his father, took his way ‭ To Hyperesia; where, making stay, ‭ He prophesied to all men, and had there ‭ A son call'd Theoclymenus, who here ‭ Came to Telemachus, and found aboard ‭ Himself at sacrifice, whom in a word ‭ He thus saluted: "O friend, since I find, ‭ Ev'n here at ship, a sacrificing mind ‭ Inform your actions, by your sacrifice, ‭ And by that worthy choice of Deities ‭ To whom you offer, by yourself, and all ‭ These men that serve your course maritimal, ‭ Tell one that asks the truth, nor give it glose, ‭ Both who, and whence, you are? From what seed rose ‭ Your royal person? And what city's tow'rs ‭ Hold habitation to your parents' pow'rs?" ‭ He answer'd: "Stranger! The sure truth is this: ‭ I am of Ithaca; my father is ‭ (Or was) Ulysses, but austere death now ‭ Takes his state from him; whose event to know ‭ Himself being long away, I set forth thus ‭ With ship and soldiers." Theoclymenus ‭ As freely said: "And I to thee am fled ‭ From forth my country, for a man struck dead ‭ By my unhappy hand, who was with me ‭ Of one self-tribe, and of his pedigree ‭ Are many friends and brothers, and the sway ‭ Of Achive kindred reacheth far away. ‭ From whom, because I fear their spleens suborn ‭ Blood and black fate against me (being born ‭ To be a wand'rer among foreign men) ‭ Make thy fair ship my rescue, and sustain ‭ My life from slaughter. Thy deservings may ‭ Perform that mercy, and to them I pray." ‭ "Nor will I bar," said he, "thy will to make ‭ My means and equal ship thy aid, but take ‭ (With what we have here, in all friendly use) ‭ Thy life from any violence that pursues." ‭ Thus took he in his lance, and it extended ‭ Aloft the hatches, which himself ascended. ‭ The prince took seat at stern, on his right hand ‭ Set Theoclymenus, and gave command ‭ To all his men to arm, and see made fast ‭ Amidst the hollow keel the beechen mast ‭ With able halsers, hoise sail, launch; which soon ‭ He saw obey'd. And then his ship did run ‭ A merry course; blue-eyed Minerva sent ‭ A fore-right gale, tumultuous, vehement, ‭ Along the air, that her way's utmost yield ‭ The ship might make, and plough the brackish field. ‭ Then set the sun, and night black'd all the ways. ‭ The ship, with Jove's wind wing'd, where th' Epian sways, ‭ Fetch'd Pheras first, then Elis the divine, ‭ And then for those isles made, that sea-ward shine ‭ For form and sharpness like a lance's head, ‭ About which lay the Wooers ambushéd; ‭ On which he rush'd, to try if he could 'scape ‭ His plotted death, or serve her treach'rous rape. ‭ And now return we to Eumæus' shed, ‭ Where, at their food with others marshalléd, ‭ Ulysses and his noble herdsman sate. ‭ To try if whose love's curious estate ‭ Stood firm to his abode, or felt it fade, ‭ And so would take each best cause to persuade ‭ His guest to town, Ulysses thus contends: ‭ "Hear me, Eumæus, and ye other friends. ‭ Next morn to town I covet to be gone, ‭ To beg some others' alms, not still charge one. ‭ Advise me well then, and as well provide ‭ I may be fitted with an honest guide, ‭ For through the streets, since need will have it so, ‭ I'll tread, to try if any will bestow ‭ A dish of drink on me, or bit of bread, ‭ Till to Ulysses' house I may be led; ‭ And there I'll tell all-wise Penelope news, ‭ Mix with the Wooers' pride, and, since they use ‭ To fare above the full, their hands excite ‭ To some small feast from out their infinite: ‭ For which, I'll wait, and play the servingman, ‭ Fairly enough, command the most they can. ‭ For I will tell thee, note me well, and hear, ‭ That, if the will be of Heav'n's Messenger, ‭ (Who to the works of men, of any sort, ‭ Can grace infuse, and glory) nothing short ‭ Am I of him, that doth to most aspire ‭ In any service, as to build a fire, ‭ To cleave sere wood, to roast or boil their meat, ‭ To wait at board, mix wine, or know the neat, ‭ Or any work, in which the poor-call'd worst ‭ To serve the rich-call'd best in Fate are forc'd." ‭ He, angry with him, said: "Alas, poor guest, ‭ Why did this counsel ever touch thy breast? ‭ Thou seek'st thy utter spoil beyond all doubt, ‭ If thou giv'st venture on the Wooers' rout, ‭ Whose wrong and force affects the iron heav'n, ‭ Their light delights are far from being giv'n ‭ To such grave servitors. Youths richly trick'd ‭ In coats or cassocks, locks divinely slick'd, ‭ And looks most rapting, ever have the gift ‭ To taste their crown'd cups, and full trenchers shift. ‭ Their tables ever like their glasses shine, ‭ Loaded with bread, with varied flesh, and wine. ‭ And thou go thither? Stay, for here do none ‭ Grudge at thy presence, nor myself, nor one ‭ Of all I feed. But when Ulysses' son ‭ Again shall greet us, he shall put thee on ‭ Both coat and cassock, and thy quick retreat ‭ Set where thy heart and soul desire thy seat." ‭ Industrious Ulysses gave reply: ‭ "I still much wish, that Heav'n's chief Deity ‭ Lov'd thee, as I do, that hast eas'd my mind ‭ Of woes and wand'rings never yet confin'd. ‭ _Nought is more wretched in a human race, ‭ Than country's want, and shift from place to place._ ‭ But for the baneful belly men take care ‭ Beyond good counsel, whosoever are ‭ In compass of the wants it undergoes ‭ By wand'rings, losses, or dependent woes. ‭ Excuse me therefore, if I err'd at home; ‭ Which since thou wilt make here, as overcome ‭ With thy command for stay, I'll take on me ‭ Cares appertaining to this place, like thee. ‭ Does then Ulysses' sire, and mother, breathe, ‭ Both whom he left in th' age next door to death? ‭ Or are they breathless, and descended where ‭ The dark house is, that never day doth clear?" ‭ "Laertes lives," said he, "but ev'ry hour ‭ Beseecheth Jove to take from him the pow'r ‭ That joins his life and limbs; for with a moan ‭ That breeds a marvel he laments his son ‭ Depriv'd by death, and adds to that another ‭ Of no less depth for that dead son's dead mother, ‭ Whom he a virgin wedded, which the more ‭ Makes him lament her loss, and doth deplore ‭ Yet more her miss, because her womb the truer ‭ Was to his brave son, and his slaughter slew her. ‭ Which last love to her doth his life engage, ‭ And makes him live an undigested age. ‭ O! such a death she died as never may ‭ Seize anyone that here beholds the day, ‭ That either is to any man a friend, ‭ Or can a woman kill in such a kind. ‭ As long as she had being, I would be ‭ A still inquirer (since 'twas dear to me, ‭ Though death to her, to hear his name) when she ‭ Heard of Ulysses, for I might be bold, ‭ She brought me up, and in her love did hold ‭ My life, compar'd with long-veil'd Ctimené, ‭ Her youngest issue (in some small degree ‭ Her daughter yet preferr'd) a brave young dame. ‭ And when of youth the dearly-lovéd flame ‭ Was lighted in us, marriage did prefer ‭ The maid to Samos; whence was sent for her ‭ Infinite riches, when the queen bestow'd ‭ A fair new suit, new shoes, and all, and vow'd ‭ Me to the field, but passing loth to part, ‭ As loving me more than she lov'd her heart. ‭ And these I want now; but their business grows ‭ Upon me daily, which the Gods impose, ‭ To whom I hold all, give account to them, ‭ For I see none left to the diadem ‭ That may dispose all better. So, I drink ‭ And eat of what is here; and whom I think ‭ Worthy or rev'rend, I have giv'n to, still, ‭ These kinds of guest-rites; for the household ill ‭ (Which, where the queen is, riots) takes her still ‭ From thought of these things. Nor is it delight ‭ To hear, from her plight, of or work or word; ‭ The Wooers spoil all. But yet my men will board ‭ Her sorrows often with discourse of all, ‭ Eating and drinking of the festival ‭ That there is kept, and after bring to field ‭ Such things as servants make their pleasures yield. ‭ "O me, Eumæus," said Laertes' son, ‭ "Hast thou then err'd so of a little one, ‭ Like me, from friends and country? Pray thee say, ‭ And say a truth, doth vast Destruction lay ‭ Her hand upon the wide-way'd seat of men, [4] ‭ Where dwelt thy sire and rev'rend mother then, ‭ That thou art spar'd there? Or else, set alone ‭ In guard of beeves, or sheep, set th' enemy on, ‭ Surpris'd, and shipp'd, transferr'd, and sold thee here? ‭ He that bought thee paid well, yet bought not dear." ‭ "Since thou enquir'st of that, my guest," said he, ‭ "Hear and be silent, and, mean space, sit free ‭ In use of these cups to thy most delights; ‭ Unspeakable in length now are the nights. ‭ Those that affect sleep yet, to sleep have leave, ‭ Those that affect to hear, their hearers give. ‭ But sleep not ere your hour; _much sleep doth grieve._ ‭ Whoever lists to sleep, away to bed, ‭ Together with the morning raise his head, ‭ Together with his fellows break his fast, ‭ And then his lord's herd drive to their repast. ‭ We two, still in our tabernacle here ‭ Drinking and eating, will our bosoms cheer ‭ With memories and tales of our annoys. ‭ _Betwixt his sorrows ev'ry human joys,_ ‭ He most, who most hath felt and furthest err'd. ‭ And now thy will to act shall be preferr'd. ‭ There is an isle above Ortygia, ‭ If thou hast heard, they call it Syria, ‭ Where, once a day, the sun moves backward still. ‭ 'Tis not so great as good, for it doth fill ‭ The fields with oxen, fills them still with sheep, ‭ Fills roofs with wine, and makes all corn there cheap. ‭ No dearth comes ever there, nor no disease ‭ That doth with hate us wretched mortals seize, ‭ But when men's varied nations, dwelling there ‭ In any city, enter th' aged year, ‭ The silver-bow-bearer, the Sun, and She ‭ That bears as much renown for archery, ‭ Stoop with their painless shafts, and strike them dead, ‭ As one would sleep, and never keep the bed. ‭ In this isle stand two cities, betwixt whom ‭ All things that of the soil's fertility come ‭ In two parts are divided. And both these ‭ My father rul'd, Ctesius Ormenides, ‭ A man like the Immortals. With these states ‭ The cross-biting Phœnicians traffick'd rates ‭ Of infinite merchandise in ships brought there, ‭ In which they then were held exempt from peer. ‭ There dwelt within my father's house a dame, ‭ Born a Phœnician, skilful in the frame ‭ Of noble housewif'ries, right tall and fair. ‭ Her the Phœnician great-wench-net-lay'r [5] ‭ With sweet words circumvented, as she was ‭ Washing her linen. To his amorous pass ‭ He brought her first, shor'd from his ship to her; ‭ To whom he did his whole life's love prefer, ‭ Which of these breast-exposing dames the hearts ‭ Deceives, though fashion'd of right honest parts. ‭ He ask'd her after, what she was, and whence? ‭ She, passing presently, the excellence ‭ Told of her father's turrets, and that she ‭ Might boast herself sprung from the progeny ‭ Of the rich Sidons, and the daughter was ‭ Of the much-year-revénued Arybas; ‭ But that the Taphian pirates made her prise, ‭ As she return'd from her field-housewif'ries, ‭ Transferr'd her hither, and, at that man's house ‭ Where now she liv'd, for value precious ‭ Sold her to th' owner. He that stole her love ‭ Bade her again to her birth's seat remove, ‭ To see the fair roofs of her friends again, ‭ Who still held state, and did the port maintain ‭ Herself reported. She said: 'Be it so, ‭ So you, and all that in your ship shall row, ‭ Swear to return me in all safety hence.' ‭ All swore. Th' oath past, with ev'ry consequence, ‭ She bade: 'Be silent now, and not a word ‭ Do you, or any of your friends, afford, ‭ Meeting me afterward in any way, ‭ Or at the washing-fount; lest some display ‭ Be made, and told the old man, and he then ‭ Keep me strait bound, to you and to your men ‭ The utter ruin plotting of your lives. ‭ Keep in firm thought then ev'ry word that strives ‭ For dang'rous utt'rance. Haste your ship's full freight ‭ Of what you traffic for, and let me straight ‭ Know by some sent friend she hath all in hold, ‭ And with myself I'll bring thence all the gold ‭ I can by all means finger; and, beside, ‭ I'll do my best to see your freight supplied ‭ With some well-weighing burthen of mine own. ‭ For I bring-up in house a great man's son, ‭ As crafty as myself, who will with me ‭ Run ev'ry way along, and I will be ‭ His leader, till your ship hath made him sure. ‭ He will an infinite great price procure, ‭ Transfer him to what languag'd men ye may.' ‭ This said, she gat her home, and there made stay ‭ A whole year with us, goods of great avail ‭ Their ship enriching. Which now fit for sail, ‭ They sent a messenger t' inform the dame; ‭ And to my father's house a fellow came, ‭ Full of Phœnician craft, that to be sold ‭ A tablet brought, the body all of gold, ‭ The verge all-amber. This had ocular view ‭ Both by my honour'd mother and the crew ‭ Of her house-handmaids, handled, and the price ‭ Beat, ask'd, and promis'd. And while this device ‭ Lay thus upon the forge, this jeweller ‭ Made privy signs, by winks and wiles, to her ‭ That was his object; which she took, and he, ‭ His sign seeing noted, hied to ship. When she, ‭ (My hand still taking, as she us'd to do ‭ To walk abroad with her) convey'd me so ‭ Abroad with her, and in the portico ‭ Found cups, with tasted viands, which the guests ‭ That us'd to flock about my father's feasts ‭ Had left. They gone (some to the council-court, ‭ Some to hear news amongst the talking sort) ‭ Her theft three bowls into her lap convey'd, ‭ And forth she went. Nor was my wit so stay'd ‭ To stay her, or myself. The sun went down, ‭ And shadows round about the world were flown, ‭ When we came to the haven, in which did ride ‭ The swift Phœnician ship; whose fair broad side ‭ They boarded straight, took us up; and all went ‭ Along the moist waves. Wind Saturnius sent. ‭ Six days we day and night sail'd; but when Jove ‭ Put up the seventh day, She that shafts doth love ‭ Shot dead the woman, who into the pump ‭ Like to a dop-chick <DW37>'d, and gave a thump ‭ In her sad settling. Forth they cast her then ‭ To serve the fish and sea-calves, no more men; ‭ But I was left there with a heavy heart; ‭ When wind and water drave them quit apart ‭ Their own course, and on Ithaca they fell, ‭ And there poor me did to Laertes sell. ‭ And thus these eyes the sight of this isle prov'd." ‭ "Eumæus," he replied, "thou much hast mov'd ‭ The mind in me with all things thou hast said, ‭ And all the suff'rance on thy bosom laid, ‭ But, truly, to thy ill hath Jove join'd good, ‭ That one whose veins are serv'd with human blood ‭ Hath bought thy service, that gives competence ‭ Of food, wine, cloth to thee; and sure th' expence ‭ Of thy life's date here is of good desert, ‭ Whose labours not to thee alone impart ‭ Sufficient food and housing, but to me; ‭ Where I through many a heap'd humanity ‭ Have hither err'd, where, though, like thee, not sold, ‭ Nor stay'd like thee yet, nor nought needful hold." ‭ This mutual speech they us'd, nor had they slept ‭ Much time before the much-near morning leapt ‭ To her fair throne. And now struck sail the men ‭ That serv'd Telemachus, arriv'd just then ‭ Near his lov'd shore; where now they stoop'd the mast, ‭ Made to the port with oars, and anchor cast, ‭ Made fast the ship, and then ashore they went, ‭ Dress'd supper, fill'd wine; when (their appetites spent) ‭ Telemachus commanded they should yield ‭ The ship to th' owner, while himself at field ‭ Would see his shepherds; when light drew to end ‭ He would his gifts see, and to town descend, ‭ And in the morning at a feast bestow ‭ Rewards for all their pains. "And whither, now," ‭ Said Theoclymenus, "my lovéd son, ‭ Shall I address myself? Whose mansión, ‭ Of all men, in this rough-hewn isle, shall I ‭ Direct my way to? Or go readily ‭ To thy house and thy mother?" He replied: ‭ "Another time I'll see you satisfied ‭ With my house-entertainment, but as now ‭ You should encounter none that could bestow ‭ Your fit entreaty, and (which less grace were) ‭ You could not see my mother, I not there; ‭ For she's no frequent object, but apart ‭ Keeps from her Wooers, woo'd with her desert, ‭ Up in her chamber, at her housewif'ry ‭ But I'll name one to whom you shall apply ‭ Direct repair, and that's Eurymachus, ‭ Renown'd descent to wise Polybius, ‭ A man whom th' Ithacensians look on now ‭ As on a God, since he of all that woo ‭ Is far superior man, and likest far ‭ To wed my mother, and as circular ‭ Be in that honour as Ulysses was. ‭ But heav'n-hous'd Jove knows the yet hidden pass ‭ Of her disposure, and on them he may ‭ A blacker sight bring than her nuptial day." ‭ As this he utter'd, on his right hand flew ‭ A saker, sacred to the God of view, ‭ That in his talons truss'd and plum'd a dove; ‭ The feathers round about the ship did rove, ‭ And on Telemachus fell; whom th' augur then ‭ Took fast by the hand, withdrew him from his men, ‭ And said: "Telemachus! This hawk is sent ‭ From God; I knew it for a sure ostent ‭ When first I saw it. Be you well assur'd, ‭ There will no Wooer be by heav'n endur'd ‭ To rule in Ithaca above your race, ‭ But your pow'rs ever fill the regal place." ‭ "I wish to heav'n," said he, "thy word might stand, ‭ Thou then shouldst soon acknowledge from my hand ‭ Such gifts and friendship, as would make thee, guest, ‭ Met and saluted as no less than blest." ‭ This said, he call'd Piræus, Clytus' son, ‭ His true associate, saying: "Thou hast done ‭ (Of all my followers to the Pylian shore) ‭ My will in chief in other things, once more ‭ Be chiefly good to me; take to thy house ‭ This lovéd stranger, and be studious ‭ T' embrace and greet him with thy greatest fare, ‭ Till I myself come and take off thy care." ‭ The famous-for-his-lance said: "If your stay ‭ Take time for life here, this man's care I'll lay ‭ On my performance, nor what fits a guest ‭ Shall any penury withhold his feast." ‭ Thus took he ship, bade them board, and away. ‭ They boarded, sat, but did their labour stay ‭ Till he had deck'd his feet, and reached his lance. ‭ They to the city; he did straight advance ‭ Up to his styes, where swine lay for him store, ‭ By whose side did his honest swine-herd snore, ‭ Till his short cares his longest nights had ended, ‭ And nothing worse to both his lords intended. ‭ THE END OF THE FIFTEENTH BOOK OF HOMER'S ODYSSEYS. ‭1 _Εὐρύχορον Λακεδαίμονα in quâ ampli ut pulchri chori duci ‭possunt, vel ducuntur;_ which the vulgar translations turn ‭therefore, _latam, seu amplam._ ‭[2] Nestor's son to Menelaus, his ironical question continuing still ‭Homer's character of Menelaus. ‭[3] His wife betrayed him for money. ‭[4] Supposing him to dwell in a city. ‭[5] _Πολυπαίπαλος, admodum vafer, Der. ex παλεύω, pertraho in ‭retia, et παι̑ς, puella._ ‭ THE SIXTEENTH BOOK OF HOMER'S ODYSSEYS ‭ THE ARGUMENT ‭ The Prince at field, he sends to town ‭ Eumæus, to make truly known ‭ His safe return. By Pallas' will, ‭ Telemachus is giv'n the skill ‭ To know his father. Those that lay ‭ In ambush, to prevent the way ‭ Of young Ulyssides for home, ‭ Retire, with anger overcome. ‭ ANOTHER ARGUMENT ‭ _Πι̑._ ‭ To his most dear ‭ Ulysses shows. ‭ The wise-son here ‭ His father knows. ‭ Ulysses and divine Eumæus rose ‭ Soon as the morning could her eyes unclose, ‭ Made fire, brake fast, and to their pasture send ‭ The gather'd herds, on whom their swains attend. ‭ The self-tire barking dogs all fawn'd upon, ‭ Nor bark'd, at first sight of Ulysses' son. ‭ The whinings of their fawnings yet did greet ‭ Ulysses' ears, and sounds of certain feet, ‭ Who thus bespake Eumæus: "Sure some friend, ‭ Or one well-known, comes, that the mastiffs spend ‭ Their mouths no louder. Only some one near ‭ They whine, and leap about, whose feet I hear." ‭ Each word of this speech was not spent, before ‭ His son stood in the entry of the door. ‭ Out-rush'd amaz'd Eumæus, and let go ‭ The cup to earth, that he had labour'd so, ‭ Cleans'd for the neat wine, did the prince-surprise, ‭ Kiss'd his fair forehead, both his lovely eyes, ‭ Both his white hands, and tender tears distill'd. ‭ There breath'd no kind-soul'd father that was fill'd ‭ Less with his son's embraces, that had liv'd ‭ Ten years in far-off earth, now new retriev'd, ‭ His only child too, gotten in his age, ‭ And for whose absence he had felt the rage ‭ Of griefs upon him, than for this divin'd ‭ So-much-for-form was this divine-for-mind; ‭ Who kiss'd him through, who grew about him kissing, ‭ As fresh from death 'scap'd. Whom so long time missing, ‭ He wept for joy, and said: "Thou yet art come, ‭ Sweet light, sweet sun-rise, to thy cloudy home. ‭ O, never I look'd, when once shipp'd away ‭ For Pylos' shores, to see thy turning day. ‭ Come, enter, lov'd son, let me feast my heart ‭ With thy sweet sight, new-come, so far apart. ‭ Nor, when you liv'd at home, would you walk down ‭ Often enough here, but stay'd still at town; ‭ It pleas'd you then to cast such forehand view ‭ About your house on that most damnéd crew." [1] ‭ "It shall be so then, friend," said he, "but now ‭ I come to glad mine eyes with thee, and know ‭ If still my mother in her house remain, ‭ Or if some Wooer hath aspir'd to gain ‭ Of her in nuptials; for Ulysses' bed, ‭ By this, lies all with spiders's cobwebs spread, ‭ In penury of him that should supply it." ‭ "She still," said he, "holds her most constant quiet, ‭ Aloft thine own house, for the bed's respect; ‭ But, for her lord's sad loss, sad nights and days ‭ Obscure her beauties, and corrupt their rays." ‭ This said, Eumæus took his brazen spear, ‭ And in he went; when, being enter'd near ‭ Within the stony threshold; from his seat ‭ His father rose to him, who would not let ‭ Th' old man remove, but drew him back and prest ‭ With earnest terms his sitting, saying: "Guest, ‭ Take here your seat again, we soon shall get ‭ Within our own house here some other seat. ‭ Here's one will fetch it." This said, down again ‭ His father sat, and to his son his swain ‭ Strew'd fair green osiers, and impos'd thereon ‭ A good soft sheepskin, which made him a throne. ‭ Then he appos'd to them his last-left roast, ‭ And in a wicker basket bread engrost, ‭ Fill'd luscious wine, and then took opposite seat ‭ To the divine Ulysses. When, the meat ‭ Set there before them, all fell-to, and eat. ‭ When they had fed, the prince said: "Pray thee say, ‭ Whence comes this guest? What seaman gave him way ‭ To this our isle? I hope these feet of his ‭ Could walk no water. Who boasts he he is?" ‭ "I'll tell all truly son: From ample Crete ‭ He boasts himself, and says, his erring feet ‭ Have many cities trod, and God was he ‭ Whose finger wrought in his infirmity. ‭ But, to my cottage, the last 'scape of his ‭ Was from a Thesprot's ship. Whate'er he is, ‭ I'll give him you, do what you please; his vaunt ‭ Is, that he is, at most, a suppliant." ‭ "Eumæus," said the prince, "to tell me this, ‭ You have afflicted my weak faculties; ‭ For how shall I receive him to my house ‭ With any safety, that suspicious ‭ Of my young forces (should I be assay'd ‭ With any sudden violence) may want aid ‭ To shield myself? Besides, if I go home, ‭ My mother is with two doubts overcome, ‭ If she shall stay with me, and take fit care ‭ For all such guests as there seek guestive fare, ‭ Her husband's bed respecting, and her fame ‭ Amongst the people; or her blood may frame ‭ A liking to some Wooer, such as best ‭ May bed her in his house, not giving least. ‭ And thus am I unsure of all means free ‭ To use a guest there, fit for his degree. ‭ But, being thy guest, I'll be his supply ‭ For all weeds, such as mere necessity ‭ Shall more than furnish. Fit him with a sword, ‭ And set him where his heart would have been shor'd; ‭ Or, if so pleas'd, receive him in thy shed, ‭ I'll send thee clothes, I vow, and all the bread ‭ His wish would eat, that to thy men and thee ‭ He be no burthen. But that I should be ‭ His mean to my house; where a company ‭ Of wrong-professing Wooers wildly live, ‭ I will in no sort author, lest they give ‭ Foul use to him, and me as gravely grieve. ‭ For what great act can anyone achieve ‭ Against a multitude, although his mind ‭ Retain a courage of the greatest kind? ‭ For all minds have not force in one degree." ‭ Ulysses answer'd: "O friend, since 'tis free ‭ For any man to change fit words with thee, ‭ I'll freely speak: Methinks, a wolfish pow'r ‭ My heart puts on to tear and to devour, ‭ To hear your affirmation, that, in spite ‭ Of what may fall on you, made opposite, ‭ Being one of your proportion, birth, and age, ‭ These Wooers should in such injustice rage. ‭ What should the cause be? Do you wilfully ‭ Endure their spoil? Or hath your empery ‭ Been such amongst your people, that all gather ‭ In troop, and one voice (which ev'n God doth father) ‭ And vow your hate so, that they suffer them? ‭ Or blame your kinsfolk's faiths, before th' extreme ‭ Of your first stroke hath tried them, whom a man, ‭ When strifes to blows rise, trusts, though battle ran ‭ In huge and high waves? Would to heav'n my spirit ‭ Such youth breath'd, as the man that must inherit ‭ Yet-never-touch'd Ulysses, or that he, ‭ But wand'ring this way, would but come, and see ‭ What my age could achieve (and there is Fate ‭ For Hope yet left, that he may recreate ‭ His eyes with such an object) this my head ‭ Should any stranger strike off, if stark dead ‭ I struck not all, the house in open force ‭ Ent'ring with challenge! If their great concourse ‭ Did over-lay me, being a man alone, ‭ (Which you urge for yourself) be you that one, ‭ I rather in mine own house wish to die ‭ One death for all, than so indecently ‭ See evermore deeds worse than death applied, ‭ Guests wrong'd with vile words and blow-giving pride, ‭ The women-servants dragg'd in filthy kind ‭ About the fair house, and in corners blind ‭ Made serve the rapes of ruffians, food devour'd ‭ Idly and rudely, wine exhaust, and pour'd ‭ Through throats profane; and all about a deed ‭ That's ever wooing, and will never speed." ‭ "I'll tell you, guest, most truly," said his son, ‭ "I do not think that all my people run ‭ One hateful course against me; nor accuse ‭ Kinsfolks that I in strifes of weight might use; ‭ But Jove will have it so, our race alone ‭ (As if made singular) to one and one ‭ His hand confining. Only to the king, ‭ Jove-bred Arcesius, did Laertes spring; ‭ Only to old Laertes did descend ‭ Ulysses; only to Ulysses' end ‭ Am I the adjunct, whom he left so young, ‭ That from me to him never comfort sprung. ‭ And to all these now, for their race, arise ‭ Up in their house a brood of enemies. ‭ As many as in these isles bow men's knees, ‭ Samos, Dulichius, and the rich-in-trees ‭ Zacynthus, or in this rough isle's command, ‭ So many suitors for the nuptials stand, ‭ That ask my mother, and, mean space, prefer ‭ Their lusts to all spoil, that dishonour her. ‭ Nor doth she, though she loaths, deny their suits, ‭ Nor they denials take, though taste their fruits. ‭ But all this time the state of all things there ‭ Their throats devour, and I must shortly bear ‭ A part in all. And yet the periods ‭ Of these designs lie in the knees of Gods. ‭ Of all loves then, Eumæus, make quick way ‭ To wise Penelopé, and to her say ‭ My safe return from Pylos, and alone, ‭ Return thou hither, having made it known. ‭ Nor let, besides my mother, any ear ‭ Partake thy message, since a number bear ‭ My safe return displeasure." He replied; ‭ "I know, and comprehend you. You divide ‭ Your mind with one that understands you well. ‭ But, all in one yet, may I not reveal ‭ To th' old hard-fated Arcesiades ‭ Your safe return? Who, through his whole distress ‭ Felt for Ulysses, did not yet so grieve, ‭ But with his household he had will to live, ‭ And serv'd his appetite with wine and food, ‭ Survey'd his husbandry, and did his blood ‭ Some comforts fitting life; but since you took ‭ Your ship for Pylos, he would never brook ‭ Or wine or food, they say, nor cast an eye ‭ On any labour, but sits weeping by, ‭ And sighing out his sorrows, ceaseless moans ‭ Wasting his body, turn'd all skin and bones." ‭ "More sad news still," said he, "yet, mourn he still; ‭ For if the rule of all men's works be will, ‭ And his will his way goes, mine stands inclin'd ‭ T' attend the home-turn of my nearer kind. [2] ‭ Do then what I enjoin; which giv'n effect, ‭ Err nor to field to him, but turn direct, ‭ Entreating first my mother, with most speed, ‭ And all the secrecy that now serves need, ‭ To send this way their store-house guardian, ‭ And she shall tell all to the aged man." [3] ‭ He took his shoes up, put them on, and went. ‭ Nor was his absence hid from Jove's descent, ‭ Divine Minerva, who took straight to view, ‭ A goodly woman's shape that all works knew, ‭ And, standing in the entry, did prefer ‭ Her sight t' Ulysses; but, though meeting her, ‭ His son Telemachus nor saw nor knew. ‭ _The Gods' clear presences are know to few._ ‭ Yet, with Ulysses, ev'n the dogs did see, ‭ And would not bark, but, whining lovingly, ‭ Fled to the stall's far side. When she her eyne ‭ Mov'd to Ulysses; he knew her design, ‭ And left the house, pass'd the great sheep-cote's wall, ‭ And stood before her. She bade utter all ‭ Now to his son, nor keep the least unlos'd, ‭ That, all the Wooers' deaths being now dispos'd, ‭ They might approach the town; affirming; she ‭ Not long would fail t' assist to victory. ‭ This said, she laid her golden rod on him, ‭ And with his late-worn weeds grac'd ev'ry limb, ‭ His body straighten'd, and his youth instill'd, ‭ His fresh blood call'd up, ev'ry wrinkle fill'd ‭ About his broken eyes, and on his chin ‭ The brown hair spread. When his whole trim wrought in, ‭ She issued, and he enter'd to his son, ‭ Who stood amaz'd, and thought some God had done ‭ His house that honour, turn'd away his eyes, ‭ And said; "Now guest, you grace another guise ‭ Than suits your late show. Other weeds you wear, ‭ And other person. Of the starry sphere ‭ You certainly present some deathless God. ‭ Be pleas'd, that to your here-vouchsaf'd abode ‭ We may give sacred rites, and offer gold, ‭ To do us favour." He replied; "I hold ‭ No deified state. Why put you thus on me ‭ A God's resemblance? I am only he ‭ That bears thy father's name; for whose lov'd sake ‭ Thy youth so grieves, whose absence makes thee take ‭ Such wrongs of men." Thus kiss'd he him, nor could ‭ Forbear those tears that in such mighty hold ‭ He held before, still held, still issuing ever; ‭ And now, the shores once broke, the springtide never ‭ Forbore earth from the cheeks he kiss'd. His son, ‭ By all these violent arguments not won ‭ To credit him his father, did deny ‭ His kind assumpt, and said, some Deity ‭ Feign'd that joy's cause, to make him grieve the more; ‭ Affirming, that no man, whoever wore ‭ The garment of mortality, could take, ‭ By any utmost pow'r his soul could make, ‭ Such change into it, since, at so much will, ‭ Not Jove himself could both remove and fill ‭ Old age with youth, and youth with age so spoil, ‭ In such an instant. "You wore all the soil ‭ Of age but now, and were old; and but now ‭ You bear that young grace that the Gods indow ‭ Their heav'n-born forms withal." His father said: ‭ "Telemachus! Admire, nor stand dismay'd, ‭ But know thy solid father; since within ‭ He answers all parts that adorn his skin. ‭ There shall no more Ulyssesses come here. ‭ I am the man, that now this twentieth year ‭ (Still under suff'rance of a world of ill) ‭ My country-earth recover. 'Tis the will ‭ The prey-professor Pallas puts in act, ‭ Who put me thus together, thus distract ‭ In aged pieces as ev'n now you saw, ‭ This youth now rend'ring. 'Tis within the law ‭ Of her free pow'r. Sometimes to show me poor, ‭ Sometimes again thus amply to restore ‭ My youth and ornaments, she still would please. ‭ _The Gods can raise, and throw men down, with ease."_ ‭ This said, he sat; when his Telemachus pour'd ‭ Himself about him; tears on tears he show'r'd, ‭ And to desire of moan increas'd the cloud. ‭ Both wept and howl'd, and laid out shrieks more loud ‭ Than or the bird-bone-breaking eagle rears, ‭ Or brood-kind vulture with the crooked seres, ‭ When rustic hands their tender eyries draw, ‭ Before they give their wings their full-plum'd law. ‭ But miserably pour'd they from beneath ‭ Their lids their tears, while both their breasts did breathe ‭ As frequent cries; and, to their fervent moan, ‭ The light had left the skies, if first the son ‭ Their dumb moans had not vented, with demand ‭ What ship it was that gave the natural land ‭ To his bless'd feet? He then did likewise lay ‭ Hand on his passion, and gave these words way: ‭ "I'll tell thee truth, my son: The men that bear ‭ Much fame for shipping, my reducers were ‭ To long-wish'd Ithaca, who each man else ‭ That greets their shore give pass to where he dwells. ‭ The Phæacensian peers, in one night's date, ‭ While I fast slept, fetch'd th' Ithacensian state, ‭ Grac'd me with wealthy gifts, brass, store of gold, ‭ And robes fair-wrought; all which have secret hold ‭ In caves that by the Gods' advice I chus'd. ‭ And now Minerva's admonitions us'd ‭ For this retreat, that we might here dispose ‭ In close discourse the slaughters of our foes. ‭ Recount the number of the Wooers then, ‭ And let me know what name they hold with men, ‭ That my mind may cast over their estates ‭ A curious measure, and confer the rates ‭ Of our two pow'rs and theirs, to try, if we ‭ Alone may propagate to victory ‭ Our bold encounters of them all, or prove ‭ The kind assistance of some others' love." ‭ "O father," he replied, "I oft have heard ‭ Your counsels and your force of hand preferr'd ‭ To mighty glory, but your speeches now ‭ Your vent'rous mind exceeding mighty show. ‭ Ev'n to amaze they move me; for, in right ‭ Of no fit counsel, should be brought to fight ‭ Two men 'gainst th' able faction of a throng. ‭ No one two, no one ten, no twice ten, strong ‭ These Wooers are, but more by much. For know, ‭ That from Dulichius there are fifty-two, ‭ All choice young men; and ev'ry one of these ‭ Six men attend. From Samos cross'd the seas ‭ Twice-twelve young gallants. From Zacynthus came ‭ Twice-ten. Of Ithaca, the best of name, ‭ Twice-six. Of all which all the state they take ‭ A sacred poet and a herald make. ‭ Their delicacies two, of special sort ‭ In skill of banquets, serve. And all this port ‭ If we shall dare t' encounter, all-thrust-up ‭ In one strong roof, have great care lest the cup, ‭ Your great mind thirsts, exceeding bitter taste, ‭ And your retreat commend not to your haste ‭ Your great attempt, but make you say, you buy ‭ Their pride's revenges at a price too high. ‭ And therefore, if you could; 'twere well you thought ‭ Of some assistant. Be your spirit wrought ‭ In such a man's election, as may lend ‭ His succours freely, and express a friend." ‭ His father answer'd: "Let me ask of thee; ‭ Hear me, consider, and then answer me. ‭ Think'st thou, if Pallas and the King of skies ‭ We had to friend, would their sufficiencies ‭ Make strong our part? Or that some other yet ‭ My thoughts must work for?" "These," said he "are set ‭ Aloft the clouds, and are found aids indeed, ‭ As pow'rs not only that these men exceed, ‭ But bear of all men else the high command, ‭ And hold of Gods an overruling hand." ‭ "Well then," said he, "not these shall sever long ‭ Their force and ours in fights assur'd and strong. ‭ And then 'twixt us and them shall Mars prefer ‭ His strength, to stand our great distinguisher, ‭ When in mine own roofs I am forc'd to blows. ‭ But when the day shall first her fires disclose, ‭ Go thou for home, and troop up with the Wooers, ‭ Thy will with theirs join'd, pow'r with their rude pow'rs; ‭ And after shall the herdsman guide to town ‭ My steps, my person wholly overgrown ‭ With all appearance of a poor old swain, ‭ Heavy, and wretched. If their high disdain ‭ Of my vile presence make them my desert ‭ Affect with contumelies, let thy lov'd heart ‭ Beat in fix'd cónfines of thy bosom still, ‭ And see me suffer, patient of their ill. ‭ Ay, though they drag me by the heels about ‭ Mine own free earth, and after hurl me out, ‭ Do thou still suffer. Nay, though with their darts ‭ They beat and bruise me, bear. But these foul parts ‭ Persuade them to forbear, and by their names ‭ Call all with kind words; bidding, for their shames, ‭ Their pleasures cease. If yet they yield not way, ‭ There breaks the first light of their fatal day. ‭ In mean space, mark this: When the chiefly-wise ‭ Minerva prompts me, I'll inform thine eyes ‭ With some giv'n sign, and then all th' arms that are ‭ Aloft thy roof in some near room prepare ‭ For speediest use. If those brave men inquire ‭ Thy end in all, still rake up all thy fire ‭ In fair cool words, and say: 'I bring them down ‭ To scour the smoke off, being so overgrown ‭ That one would think all fumes, that ever were ‭ Breath'd since Ulysses' loss, reflected here. ‭ These are not like the arms he left behind, ‭ In way for Troy. Besides, Jove prompts my mind ‭ In their remove apart thus with this thought, ‭ That, if in height of wine there should be wrought, ‭ Some harsh contention 'twixt you, this apt mean ‭ To mutual bloodshed may be taken clean ‭ From out your reach, and all the spoil prevented ‭ Of present feast, perhaps ev'n then presented ‭ My mother's nuptials to your long kind vows. ‭ _Steel itself, ready, draws a man to blows.'_ ‭ Thus make their thoughts secure; to us alone ‭ Two swords, two darts, two shields left: which see done ‭ Within our readiest reach, that at our will ‭ We may resume, and charge, and all their skill ‭ Pallas and Jove, that all just counsels breathe, ‭ May darken with secureness to their death. ‭ And let me charge thee now, as thou art mine, ‭ And as thy veins mine own true blood combine: ‭ Let, after this, none know Ulysses near, ‭ Not anyone of all the household there, ‭ Not here the herdsman, not Laertes be ‭ Made privy, not herself Penelopé ‭ But only let thyself and me work out ‭ The women's thoughts of all things borne about ‭ The Wooers' hearts; and then thy men approve, ‭ To know who honours, who with rev'rence love, ‭ Our well-weigh'd memories, and who is won ‭ To fail thy fit right, though my only son." ‭ "You teach," said he, "so punctually now, ‭ As I knew nothing, nor were sprung from you. ‭ I hope, hereafter, you shall better know ‭ What soul I bear, and that it doth not let ‭ The least loose motion pass his natural seat. ‭ But this course you propose will prove, I fear, ‭ Small profit to us; and could wish your care ‭ Would weigh it better as too far about. ‭ For time will ask much, to the sifting out ‭ Of each man's disposition by his deeds; ‭ And, in the mean time, ev'ry Wooer feeds ‭ Beyond satiety, nor knows how to spare. ‭ The women yet, since they more easy are ‭ For our inquiry, I would wish you try, ‭ Who right your state, who do it injury. ‭ The men I would omit, and these things make ‭ Your labour after. But, to undertake ‭ The Wooers' war, I wish your utmost speed, ‭ Especially if you could cheer the deed ‭ With some ostent from Jove." Thus, as the sire ‭ Consented to the son, did here expire ‭ Their mutual speech. And now the ship was come, ‭ That brought the young prince and his soldiers home, ‭ The deep haven reach'd, they drew the ship ashore, ‭ Took all their arms out, and the rich gifts bore ‭ To Clitius' house. But to Ulysses' court ‭ They sent a herald first, to make report ‭ To wise Penelopé, that safe at field ‭ Her son was left; yet, since the ship would yield ‭ Most haste to her, he sent that first, and them ‭ To comfort with his utmost the extreme ‭ He knew she suffer'd. At the court now met ‭ The herald and the herdsman, to repeat ‭ One message to the queen. Both whom arriv'd ‭ Within the gates; both to be foremost striv'd ‭ In that good news. The herald, he for haste ‭ Amongst the maids bestow'd it, thinking plac'd ‭ The queen amongst them. "Now," said he, "O queen, ‭ Your lov'd son is arriv'd." And, then was seen ‭ The queen herself, to whom the herdsman told ‭ All that Telemachus enjoin'd he should; ‭ All which discharg'd, his steps he back bestows, ‭ And left both court and city for his sows. ‭ The Wooers then grew sad; soul-vex'd, and all ‭ Made forth the court; when, by the mighty wall ‭ They took their sev'ral seats, before the gates. ‭ To whom Eurymachus initiates. ‭ Their utter'd grievance. "O," said he, "my friends, ‭ A work right-great begun, as proudly ends, ‭ We said, Telemachus should never make ‭ His voyage good, nor this shore ever take ‭ For his return's receipt; and yet we fail, ‭ And he performs it. Come, let's man a sail, ‭ The best In our election, and bestow ‭ Such soldiers in her as can swiftest row, ‭ To tell our friends that way-lay his retreat ‭ 'Tis safe perform'd, and make them quickly get ‭ Their ship for Ithaca." This was not said ‭ Before Amphinomus in port display'd ‭ The ship arriv'd, her sails then under-stroke, ‭ And oars resum'd; when, laughing, thus he spoke: ‭ "Move for no messenger. These men are come, ‭ Some God hath either told his turning home, ‭ Or they themselves have seen his ship gone by, ‭ Had her in chase, and lost her." Instantly ‭ They rose, and went to port; found drawn to land ‭ The ship, the soldiers taking arms in hand. ‭ The Wooers themselves to council went in throng, ‭ And not a man besides, or old, or young, ‭ Let sit amongst them. Then Eupitheus' son, ‭ Antinous, said: "See, what the Gods have done! ‭ They only have deliver'd from our ill ‭ The men we way-laid. Ev'ry windy hill ‭ Hath been their watch-tow'r, where by turns they stood ‭ Continual sentinel. And we made good ‭ Our work as well, for, sun once set, we never ‭ Slept wink ashore all night, but made sail ever, ‭ This way and that, ev'n till the morning kept ‭ Her sacred station, so to intercept ‭ And take his life, for whom our ambush lay; ‭ And yet hath God to his return giv'n way. ‭ But let us prosecute with counsels here ‭ His necessary death, nor anywhere ‭ Let rest his safety; for if he survive, ‭ Our sails will never-in wish'd havens arrive; ‭ Since he is wise, hath soul, and counsel too, ‭ To work the people, who, will never do ‭ Our faction favour. What we then intend ‭ Against his person, give we present end, ‭ Before he call a council, which, believe, ‭ His spirit will haste, and point where it doth grieve, ‭ Stand up amongst them all, and urge his death ‭ Decreed amongst us. Which complaint will breathe ‭ A fire about their spleens, and blow no praise ‭ On our ill labours. Lest, they therefore raise ‭ Pow'r to exile us from our native earth, ‭ And force our lives' societies to the birth ‭ Of foreign countries, let our speeds prevent, ‭ His coming home to this austere complaint, ‭ At field and far from town, or in some way ‭ Of narrow passage, with his latest day ‭ Shown to his forward youth, his goods and lands ‭ Left to the free division of our hands, ‭ The moveables made all his mother's dow'r, ‭ And his, whoever Fate affords the pow'r ‭ To celebrate, with her sweet Hymen's rites. ‭ Or if this please not, but your appetites ‭ Stand to his safety, and to give him seat ‭ In his whole birth-right, let us look to eat ‭ At his cost never more, but ev'ry man ‭ Haste to his home, and wed, with whom he can ‭ At home, and there lay first about for dow'r ‭ And then the woman give his second pow'r ‭ Of nuptial-liking, and, for last, apply ‭ His purpose with most gifts and destiny." ‭ This silence caus'd; whose breach, at last, begun ‭ Amphinomus, the much renownéd son ‭ Of Nisus surnam'd Aretiades, ‭ Who from Dulichius full of flow'ry leas ‭ Led all the Wooers, and in chief did please ‭ The queen with his discourse, because it grew ‭ From roots of those good minds that did endue [4] ‭ His goodly person; who, exceeding wise, ‭ Us'd this speech: "Friends, I never will advise ‭ The prince's death; for 'tis a damnéd thing ‭ To put to death the issue of a king. ‭ First, therefore, let's examine, what applause ‭ The Gods will give it: If the equal laws ‭ Of Jove approve it, I myself will be ‭ The man shall kill him, and this company ‭ Exhort to that mind: If the Gods remain ‭ Adverse, and hate it, I advise, refrain." ‭ This said Amphinomus, and pleas'd them all ‭ When all arose, and in Ulysses' hall ‭ Took seat again. Then to the queen was come ‭ The Wooers' plot, to kill her son at home, ‭ Since their abroad-design had miss'd success, ‭ The herald Medon (who the whole address ‭ Knew of their counsels) making the report. ‭ The Goddess of her sex, with her fair sort ‭ Of lovely women, at the large hall's door ‭ (Her bright cheeks clouded with a veil she wore) ‭ Stood, and directed to Antinous ‭ Her sharp reproof, which she digested thus: ‭ "Antinous! Compos'd of injury! ‭ Plotter of mischief! Though reports that fly ‭ Amongst our Ithacensian people say ‭ That thou, of all that glory in their sway, ‭ Art best in words and counsels, th' art not so. ‭ Fond, busy fellow, why plott'st thou the woe ‭ And slaughter of my son, and dost not fear ‭ The presidents of suppliants, when the ear ‭ Of Jove stoops to them? 'Tis unjust to do ‭ Slaughter for slaughter, or pay woe for woe, ‭ Mischief for kindness. Death for life sought, then, ‭ Is an injustice to be loath'd of men. ‭ Serves not thy knowledge to remember when ‭ Thy father fled to us? Who (mov'd to wrath ‭ Against the Taphian thieves) pursued with scathe ‭ The guiltless Thesprots; in whose people's fear, ‭ Pursuing him for wreak, he landed here, ‭ They after him, professing both their prize ‭ Of all his chiefly-valued faculties, ‭ And more priz'd life. Of all whose bloodiest ends ‭ Ulysses curb'd them, though they were his friends. ‭ Yet thou, like one that no law will allow ‭ The least true honour, eat'st his house up now ‭ That fed thy father; woo'st for love his wife, ‭ Whom thus thou griev'st and seek'st her sole son's life! ‭ Cease, I command thee, and command the rest ‭ To see all thought of these foul fashions ceas'd." ‭ Eurymachus replied: "Be confident, ‭ Thou all-of-wit-made, the most fam'd descent ‭ Of king Icarius. Free thy spirits of fear. ‭ There lives not anyone, nor shall live here ‭ Now, nor hereafter, while my life gives heat ‭ And light to me on earth, that dares intreat ‭ With any ill touch thy well-lovéd son, ‭ But here I vow, and here will see it done, ‭ His life shall stain my lance. If on his knees ‭ The city-racer, Laertiades, ‭ Hath made me sit, put in my hand his food, ‭ And held his red wine to me, shall the blood ‭ Of his Telemachus on my hand lay ‭ The least pollution, that my life can stay? ‭ No! I have ever charg'd him not to fear ‭ Death's threat from any. And, for that most dear ‭ Love of his father, he shall ever be ‭ Much the most lov'd of all that live to me. ‭ _Who kills a guiltless man from man may fly, ‭ From God his searches all escapes deny."_ ‭ Thus cheer'd his words, but his affections still ‭ Fear'd not to cherish foul intent to kill ‭ Ev'n him whose life to all lives he preferr'd. ‭ The queen went up, and to her love appear'd ‭ Her lord so freshly, that she wept, till sleep ‭ (By Pallas forc'd on her) her eyes did steep ‭ In his sweet humour. When the even was come, ‭ The God-like herdsman reach'd the whole way home. ‭ Ulysses and his son for supper drest ‭ A year-old swine, and ere their host and guest ‭ Had got their presence, Pallas had put by ‭ With her fair rod Ulysses' royalty, ‭ And render'd him an aged man again, ‭ With all his vile integuments, lest his swain ‭ Should know him in his trim, and tell his queen, ‭ In these deep secrets being not deeply seen. ‭ He seen, to him the prince these words did use: ‭ "Welcome divine Eumæus! Now what news ‭ Employs the city? Are the Wooers come ‭ Back from their scout dismay'd? Or here at home ‭ Will they again attempt me?" He replied: ‭ "These touch not my care. I was satisfied ‭ To do, with most speed, what I went to do; ‭ My message done, return. And yet, not so ‭ Came my news first; a herald (met with there) ‭ Forestall'd my tale, and told how safe you were. ‭ Besides which merely necessary thing, ‭ What in my way chanc'd I may over-bring, ‭ Being what I know, and witness'd with mine eyes. ‭ Where the Hermæan sepulchre doth rise ‭ Above the city, I beheld take port ‭ A ship, and in her many a man of sort; ‭ Her freight was shields and lances; and, methought, ‭ They were the Wooers; but, of knowledge, nought ‭ Can therein tell you." The prince smil'd, and knew ‭ They were the Wooers, casting secret view ‭ Upon his father. But what they intended ‭ Fled far the herdsman; whose swain's labours ended, ‭ They dress'd the supper, which, past want, was eat. ‭ When all desire suffic'd of wine and meat, ‭ Of other human wants they took supplies ‭ At Sleep's soft hand, who sweetly clos'd their eyes. ‭ ‭ THE END OF THE SIXTEENTH BOOK OF HOMER'S ODYSSEYS. ‭[1] _'Αΐδηλον ὅμιλον, ἀΐδηλος of ἀΐδης, orcus,_ and signifies ‭properly _tenebricosus,_ or _infernalis,_ so that _perniciosus_ ‭(which is the Latin translation) is not so fit as damned for that crew ‭of dissolute Wooers. The phrase being now used to all so ‭licentious. ‭[2] Intending his father, whose return though he were far from ‭knowing, or fully expecting, yet he desired to order all things as he ‭were present. ‭[3] Intending to Laertes all that Eumæus would have told. ‭[4] _ϕπεσὶ ἀγαθῃ̑σιν, bonis mentibus,_ the plural number used ever ‭by Homer. ‭ THE SEVENTEENTH BOOK OF HOMER'S ODYSSEYS ‭ THE ARGUMENT ‭ Telemachus, return'd to town, ‭ Makes to his curious mother known, ‭ In part, his travels. After whom ‭ Ulysses to the court doth come, ‭ In good Eumæus' guide, and prest ‭ To witness of the Wooers' feast; ‭ Whom, though twice ten years did bestow ‭ In far-off parts, his dog doth know. ‭ ANOTHER ARGUMENT ‭ _Ρω̑._ ‭ Ulysses shows ‭ Through all disguise. ‭ Whom his dog knows; ‭ Who knowing dies. ‭ But when air's rosy birth, the morn, arose, ‭ Telemachus did for the town dispose ‭ His early steps; and took to his command ‭ His fair long lance, well-sorting with his hand, ‭ Thus parting with Eumæus: "Now, my friend, ‭ I must to town, lest too far I extend ‭ My mother's moan for me, who, till her eyes ‭ Mine own eyes witness, varies tears and cries ‭ Through all extremes. Do then this charge of mine, ‭ And guide to town this hapless guest of thine, ‭ To beg elsewhere his further festival. ‭ Give they that please, I cannot give to all, ‭ Mine own wants take up for myself my pain. ‭ If it incense him, he the worst shall gain. ‭ The lovely truth I love, and must be plain." ‭ "Alas, friend," said his father, "nor do I ‭ Desire at all your further charity. ‭ 'Tis better beg in cities than in fields, ‭ And take the worst a beggar's fortune yields. ‭ Nor am I apt to stay in swine-styes more, ‭ However; ever the great chief before ‭ The poor ranks must to ev'ry step obey. ‭ But go; your man in my command shall sway, ‭ Anon yet too, by favour, when your fires ‭ Have comforted the cold heat age expires, ‭ And when the sun's flame hath besides corrected ‭ The early air abroad, not being protected ‭ By these my bare weeds from the morning's frost, ‭ Which (if so much ground is to be engrost ‭ By my poor feet as you report) may give ‭ Too violent charge to th' heat by which I live." ‭ This said, his son went on with spritely pace, ‭ And to the Wooers studied little grace. ‭ Arriv'd at home, he gave his jav'lin stay ‭ Against a lofty pillar, and bold way ‭ Made further in. When having so far gone ‭ That he transcended the fair porch of stone, ‭ The first by far that gave his entry eye ‭ Was nurse Euryclea; who th' embrodery ‭ Of stools there set was giving cushions fair; ‭ Who ran upon him, and her rapt repair ‭ Shed tears for joy. About him gather'd round ‭ The other maids; his head and shoulders crown'd ‭ With kisses and embraces. From above ‭ The Queen herself came, like the Queen of Love, ‭ Or bright Diana; cast about her son ‭ Her kind embraces, with effusión ‭ Of loving tears; kiss'd both his lovely eyes, ‭ His cheeks, and forehead; and gave all supplies ‭ With this entreaty; "Welcome, sweetest light! ‭ I never had conceit to set quick sight ‭ On thee thus soon, when thy lov'd father's fame ‭ As far as Pylos did thy spirit inflame, ‭ In that search ventur'd all-unknown to me. ‭ O say, by what pow'r cam'st thou now to be ‭ Mine eyes' dear object?" He return'd reply: ‭ "Move me not now, when you my 'scape descry ‭ From imminent death, to think me fresh entrapt; ‭ The fear'd wound rubbing, felt before I 'scapt. ‭ Double not needless passion on a heart ‭ Whose joy so green is, and so apt t' invert; ‭ But pure weeds putting on, ascend and take ‭ Your women with you, that ye all may make ‭ Vows of full hecatombs in sacred fire ‭ To all the Godheads, if their only Sire ‭ Vouchsafe revenge of guest-rites wrong'd, which he ‭ Is to protect as being their Deity. ‭ My way shall be directed to the hall ‭ Of common concourse, that I thence may call ‭ A stranger, who from off the Pylian shore ‭ Came friendly with me; whom I sent before ‭ With all my soldiers, but in chief did charge ‭ Piræus with him, wishing him t' enlarge ‭ His love to him at home, in best affair, ‭ And utmost honours, till mine own repair." ‭ Her son thus spoken, his words could not bear ‭ The wings too easily through her either ear, ‭ But putting pure weeds on, made vows entire ‭ Of perfect hecatombs in sacred fire ‭ To all the Deities, if their only Sire ‭ Vouchsaf'd revenge of guest-rites wrong'd, which he ‭ Was to protect as being their Deity. ‭ Her son left house, in his fair hand his lance, ‭ His dogs attending; and, on ev'ry glance ‭ His looks cast from them, Pallas put a grace ‭ That made him seem of the celestial race. ‭ Whom, come to concourse, ev'ry man admir'd, ‭ About him throng'd the Wooers, and desir'd ‭ All good to him in tongues, but in their hearts ‭ Most deep ills threaten'd to his most deserts. ‭ Of whose huge rout once free, he cast glad eye ‭ On some that, long before his infancy, ‭ Were with his father great and gracious, ‭ Grave Halitherses, Mentor, Antiphus: ‭ To whom he went, took seat by them, and they ‭ Inquir'd of all things since his parting day. ‭ To them Piræus came, and brought his guest ‭ Along the city thither, whom not least ‭ The prince respected, nor was long before ‭ He rose and met him. The first word yet bore ‭ Piræus from them both; whose haste besought ‭ The prince to send his women to see brought ‭ The gifts from his house that Atrides gave, ‭ Which his own roofs, he thought, would better save. ‭ The wise prince answer'd: "I can scarce conceive ‭ The way to these works. If the Wooers reave ‭ By privy stratagem my life at home, ‭ I rather wish Piræus may become ‭ The master of them, than the best of these. ‭ But, if I sow in their fields of excess ‭ Slaughter and ruin, then thy trust employ, ‭ And to me joying bring thou those with joy." ‭ This said, he brought home his grief-practis'd guest; ‭ Where both put off, both oil'd, and did invest ‭ Themselves in rich robes, wash'd, and sate, and eat. ‭ His mother, in a fair chair taking seat ‭ Directly opposite, her loom applied; ‭ Who, when her son and guest had satisfied ‭ Their appetites with feast, said: "O my son, ‭ You know that ever since your sire was won ‭ To go in Agamemnon's guide to Troy, ‭ Attempting sleep, I never did enjoy ‭ One night's good rest, but made my quiet bed ‭ A sea blown-up with sighs, with tears still shed ‭ Embrew'd and troubled; yet, though all your miss ‭ In your late voyage hath been made for this, ‭ That you might know th' abode your father made. ‭ You shun to tell me what success you had. ‭ Now then, before the insolent access ‭ The Wooers straight will force on us, express ‭ What you have heard." "I will," said he, "and true. ‭ We came to Pylos, where the studious due ‭ That any father could afford his son, ‭ (But new-arriv'd from some course he had run ‭ To an extreme length, in some voyage vow'd), ‭ Nestor, the pastor of the people, show'd ‭ To me arriv'd, in turrets thrust-up high, ‭ Where not his brave sons were more lov'd than I. ‭ Yet of th' unconquer'd ever-sufferer; ‭ Ulysses, never he could set his ear, ‭ Alive or dead, from any earthy man. ‭ But to the great Lacedæmonian, ‭ Atrides, famous for his lance, he sent, ‭ With horse and chariots, me, to learn th' event ‭ From his relation; where I had the view ‭ Of Argive Helen, whose strong beauties drew, ‭ By wills of Gods, so many Grecian states, ‭ And Trojans, under such laborious fates. ‭ Where Menelaus ask'd me, what affair ‭ To Lacedæmon render'd my repair. ‭ I told him all the truth, who made reply: ‭ 'O deed of most abhorr'd indecency! ‭ A sort of impotents attempt his bed ‭ Whose strength of mind hath cities levelléd! ‭ As to a lion's den, when any hind ‭ Hath brought her young calves, to their rest inclin'd, ‭ When he is ranging hills, and herby dales, ‭ To make of feeders there his festivals, ‭ But, turning to his luster, calves and dam ‭ He shows abhorr'd death, in his anger's flame; ‭ So, should Ulysses find this rabble hous'd ‭ In his free turrets, courting his espous'd, ‭ Foul death would fall them. O, I would to Jove, ‭ Phœbus, and Pallas, that, when he shall prove ‭ The broad report of his exhausted store ‭ True with his eyes, his nerves and sinews wore ‭ That vigour then that in the Lesbian tow'rs, ‭ Provok'd to wrastle with the iron pow'rs ‭ Philomelides vaunted, he approv'd; ‭ When down he hurl'd his challenger, and mov'd ‭ Huge shouts from all the Achives then in view. ‭ If, once come home, he all those forces drew ‭ About him there to work, they all were dead, ‭ And should find bitter his attempted bed. ‭ But what you ask and sue for, I, as far ‭ As I have heard the true-spoke mariner, ‭ Will tell directly, nor delude your ear: ‭ He told me that an island did ensphere, ‭ In much discomfort, great Laertes' son; ‭ And that the Nymph Calypso, overrun ‭ With his affection, kept him in her caves, ‭ Where men, nor ship, of pow'r to brook the waves, ‭ Were near his convoy to his country's shore, ‭ And where herself importun'd evermore ‭ His quiet stay; which not obtain'd, by force ‭ She kept his person from all else recourse.' ‭ This told Atrides, which was all he knew. ‭ Nor stay'd I more, but from the Gods there blew ‭ A prosp'rous wind, that set me quickly here." ‭ This put his mother quite from all her cheer. ‭ When Theoclymenus the augur said: ‭ "O woman, honour'd with Ulysses' bed, ‭ Your son, no doubt, knows clearly nothing more, ‭ Hear me yet speak, that can the truth uncore, ‭ Nor will be curious. Jove then witness bear, ‭ And this thy hospitable table here, ‭ With this whole household of your blameless lord, ‭ That at this hour his royal feet are shor'd ‭ On his lov'd country-earth, and that ev'n here ‭ Coming, or creeping, he will see the cheer ‭ These Wooers make, and in his soul's field sow ‭ Seeds that shall thrive to all their overthrow. ‭ This, set a ship-board, I knew sorted thus, ‭ And cried it out to your Telemachus." ‭ Penelopé replied: "Would this would prove, ‭ You well should witness a most friendly love, ‭ And gifts such of me, as encount'ring Fame ‭ Should greet you with a blesséd mortal's name." ‭ This mutual speech past, all the Wooers were ‭ Hurling the stone, and tossing of the spear, ‭ Before the palace, in the pavéd court, ‭ Where otherwhiles their petulant resort ‭ Sat plotting injuries. But when the hour ‭ Of supper enter'd, and the feeding pow'r ‭ Brought sheep from field, that fill'd up ev'ry way ‭ With those that us'd to furnish that purvey, ‭ Medon, the herald (who of all the rest ‭ Pleas'd most the Wooers, and at ev'ry feast ‭ Was ever near) said: "You whose kind consort ‭ Make the fair branches of the tree our court, ‭ Grace it within now, and your suppers take. ‭ You that for health, and fair contention's sake, ‭ Will please your minds, know, bodies must have meat; ‭ _Play's worse than idleness in times to eat."_ ‭ This said, all left, came in, cast by, on thrones ‭ And chairs, their garments. Their provisións ‭ Were sheep, swine, goats, the chiefly-great and fat, ‭ Besides an ox that from the herd they gat. ‭ And now the king and herdsman, from the field, ‭ In good way were to town; 'twixt whom was held ‭ Some walking conference, which thus begun ‭ The good Eumæus: "Guest, your will was won, ‭ Because the prince commanded, to make way ‭ Up to the city, though I wish'd your stay, ‭ And to have made you guardian of my stall; ‭ But I, in care and fear of what might fall ‭ In after-anger of the prince, forbore. ‭ _The checks of princes touch their subjects sore._ ‭ But make we haste, the day is nearly ended, ‭ And cold airs still are in the even extended." ‭ "I know't," said he, "consider all; your charge ‭ Is giv'n to one that understands at large. ‭ Haste then. Hereafter, you shall lead the way; ‭ Afford your staff too, if it fit your stay, ‭ That I may use it; since you say our pass ‭ Is less friend to a weak foot than it was." ‭ Thus cast he on his neck his nasty scrip, ‭ All-patch'd and torn; a cord, that would not slip ‭ For knots and bracks about the mouth of it, ‭ Made serve the turn; and then his swain did fit ‭ His forc'd state with a staff. Then plied they hard ‭ Their way to town, their cottage left in guard ‭ To swains and dogs. And now Eumæus led ‭ The king along, his garments to a thread ‭ All-bare and burn'd, and he himself hard bore ‭ Upon his staff, at all parts like a poor ‭ And sad old beggar. But when now they got ‭ The rough highway, their voyage wanted not ‭ Much of the city, where a fount they reach'd, ‭ From whence the town their choicest water fetch'd, ‭ That ever overflow'd, and curious art ‭ Was shown about it; in which three had part ‭ Whose names Neritus and Polyctor were, ‭ And famous Ithacus. It had a sphere ‭ Of poplar, that ran round about the wall; ‭ And into it a lofty rock let fall ‭ Continual supply of cool clear stream. ‭ On whose top, to the Nymphs that were supreme ‭ In those parts' loves, a stately altar rose, ‭ Where ev'ry traveller did still impose ‭ Devoted sacrifice. At this fount found ‭ These silly travellers a man renown'd ‭ For guard of goats, which now he had in guide, ‭ Whose huge-stor'd herd two herdsmen kept beside, ‭ For all herds it excell'd, and bred a feed ‭ For Wooers only. He was Dolius' seed, ‭ And call'd Melanthius. Who casting eye ‭ On these two there, he chid them terribly, ‭ And so past mean, that ev'n the wretched fate ‭ Now on Ulysses he did irritate. ‭ His fume to this effect he did pursue: ‭ "Why so,'tis now at all parts passing true, ‭ That ill leads ill, good evermore doth train ‭ With like his like. Why, thou unenvied swain, ‭ Whither dost thou lead this same victless leaguer, ‭ This bane of banquets, this most nasty beggar, ‭ Whose sight doth make one sad, it so abhors? ‭ Who, with his standing in so many doors, ‭ Hath broke his back; and all his beggary tends ‭ To beg base crusts, but to no manly ends, ‭ As asking swords, or with activity ‭ To get a caldron. Wouldst thou give him me, ‭ To farm my stable, or to sweep my yard, ‭ And bring browse to my kids, and that preferr'd ‭ He should be at my keeping for his pains ‭ To drink as much whey as his thirsty veins ‭ Would still be swilling (whey made all his fees) ‭ His monstrous belly would oppress his knees. ‭ But he hath learn'd to lead base life about, ‭ And will not work, but crouch among the rout ‭ For broken meat to cram his bursten gut. ‭ Yet this I'll say, and he will find it put ‭ In sure effect, that if he enters where ‭ Ulysses' roofs cast shade, the stools will there ‭ About his ears fly, all the house will throw, ‭ And rub his ragged sides with cuffs enow." ‭ Past these reviles, his manless rudeness spurn'd ‭ Divine Ulysses; who at no part turn'd ‭ His face from him, but had his spirit fed ‭ With these two thoughts, if he should strike him dead ‭ With his bestowéd staff, or at his feet ‭ Make his direct head and the pavement meet. ‭ But he bore all, and entertain'd a breast ‭ That in the strife of all extremes did rest. ‭ Eumæus, frowning on him, chid him yet, ‭ And, lifting up his hands to heav'n, he set ‭ This bitter curse at him: "O you that bear ‭ Fair name to be the race of Jupiter, ‭ Nymphs of these fountains! If Ulysses ever ‭ Burn'd thighs to you, that, hid in fat, did never ‭ Fail your acceptance, of or lamb or kid, ‭ Grant this grace to me: Let the man thus hid ‭ Shine through his dark fate, make some God his guide, ‭ That, to thee, goatherd, this same palate's pride, [1] ‭ Thou driv'st afore thee, he may come and make ‭ The scatt'rings of the earth, and overtake ‭ Thy wrongs, with forcing thee to ever err ‭ About the city, hunted by his fear. ‭ And in the mean space by some slothful swains ‭ Let lousy sickness gnaw thy cattle's veins." ‭ "O Gods!" replied Melanthius, "what a curse ‭ Hath this dog bark'd out, and can yet do worse! ‭ This man shall I have giv'n into my hands, ‭ When in a well-built ship to far-off lands ‭ I shall transport him, that, should I want here, ‭ My sale of him may find me victuals there. ‭ And, for Ulysses, would to heav'n his joy ‭ The silver-bearing-bow God would destroy, ‭ This day, within his house, as sure as he ‭ The day of his return shall never see." ‭ This said, he left them going silent on; ‭ But he out-went them, and took straight upon ‭ The palace-royal, which he enter'd straight, ‭ Sat with the Wooers, and his trencher's freight ‭ The carvers gave him of the flesh there vented, ‭ But bread the rev'rend butleress presented. ‭ He took against Eurymachus his place, ‭ Who most of all the Wooers gave him grace. ‭ And now Ulysses and his swain got near, ‭ When round about them visited their ear ‭ The hollow harp's delicious-stricken string, ‭ To which did Phemius, near the Wooers, sing. ‭ Then by the hand Ulysses took his swain, ‭ And said: "Eumæus, one may here see plain, ‭ In many a grace, that Laertiades ‭ Built here these turrets, and,'mongst others these, ‭ His whole court arm'd with such a goodly wall, ‭ The cornice, and the cope, majestical, ‭ His double gates, and turrets, built too strong ‭ For force or virtue ever to expugn. ‭ I know the feasters in it now abound, ‭ Their cates cast such a savour; and the sound ‭ The harp gives argues an accomplish'd feast. ‭ _The Gods made music banquet's dearest guest."_ ‭ "These things," said he, "your skill may tell with ease, ‭ Since you are grac'd with greater knowledges. ‭ But now consult we how these works shall sort, ‭ If you will first approach this praiséd court, ‭ And see these Wooers, I remaining here; ‭ Or I shall enter, and yourself forbear? ‭ But be not you too tedious in your stay, ‭ Lest thrust ye be and buffeted away. ‭ _Brain hath no fence for blows;_ look to 't I pray." ‭ "You speak to one that comprehends," said he, ‭ "Go you before, and here adventure me. ‭ I have of old been us'd to cuffs and blows; ‭ My mind is harden'd, having borne the throes ‭ Of many a sour event in waves and wars, ‭ Where knocks and buffets are no foreigners. ‭ And this same harmful belly by no mean ‭ The greatest abstinent can ever wean. ‭ _Men suffer much bane by the belly's rage;_ ‭ For whose sake ships in all their equipage ‭ Are arm'd, and set out to th' untamed seas, ‭ Their bulks full-fraught with ills to enemies." ‭ Such speech they chang'd; when in the yard there lay ‭ A dog, call'd Argus, which, before his way ‭ Assum'd for Ilion, Ulysses bred, ‭ Yet stood his pleasure then in little stead, ‭ As being too young, but, growing to his grace, ‭ Young men made choice of him for ev'ry chace, ‭ Or of their wild goats, of their hares, or harts. ‭ But his king gone, and he, now past his parts, ‭ Lay all abjectly on the stable's store, ‭ Before the oxstall, and mules' stable door, ‭ To keep the clothes cast from the peasants' hands, ‭ While they laid compass on Ulysses' lands, ‭ The dog, with ticks (unlook'd-to) overgrown. ‭ But by this dog no sooner seen but known ‭ Was wise Ulysses, who new-enter'd there, ‭ Up went his dog's laid ears, and, coming near, ‭ Up he himself rose, fawn'd, and wagg'd his stern, ‭ Couch'd close his ears, and lay so; nor discern [2] ‭ Could evermore his dear-lov'd lord again. ‭ Ulysses saw it, nor had pow'r t' abstain ‭ From shedding tears; which (far-off seeing his swain) ‭ He dried from his sight clean; to whom he thus ‭ His grief dissembled: "'Tis miraculous, ‭ That such a dog as this should have his lair ‭ On such a dunghill, for his form is fair. ‭ And yet, I know not, if there were in him ‭ Good pace, or parts, for all his goodly limb; ‭ Or he liv'd empty of those inward things, ‭ As are those trencher-beagles tending kings, ‭ Whom for their pleasure's, or their glory's, sake, ‭ Or fashion, they into their favour take." ‭ "This dog," said he, "was servant to one dead ‭ A huge time since. But if he bore his head, ‭ For form and quality, of such a height, ‭ As when Ulysses, bound for th' Ilion fight, ‭ Or quickly after, left him, your rapt eyes ‭ Would then admire to see him use his thighs ‭ In strength and swiftness. He would nothing fly, ‭ Nor anything let 'scape. If once his eye ‭ Seiz'd any wild beast, he knew straight his scent; ‭ Go where he would, away with him he went. ‭ Nor was there ever any savage stood ‭ Amongst the thickets of the deepest wood ‭ Long time before him, but he pull'd him down; ‭ As well by that true hunting to be shown ‭ In such vast coverts, as for speed of pace ‭ In any open lawn. For in deep chace ‭ He was a passing-wise and well-nos'd hound. ‭ And yet is all this good in him uncrown'd ‭ With any grace here now, nor he more fed ‭ Than any errant cur. His king is dead, ‭ Far from his country; and his servants are ‭ So negligent they lend his hound no care. ‭ _Where masters rule not, but let men alone, ‭ You never there see honest service done. ‭ That man's half-virtue Jove takes quite away, ‭ That once is sun-burnt with the servile day."_ ‭ This said, he enter'd the well-builded-tow'rs, ‭ Up bearing right upon the glorious Wooers, ‭ And left poor Argus dead; his lord's first sight ‭ Since that time twenty years bereft his light. ‭ Telemachus did far the first behold ‭ Eumæus enter, and made signs he should ‭ Come up to him. He, noting, came, and took ‭ On earth his seat. And then the master-cook ‭ Serv'd in more banquet; of which, part he set ‭ Before the Wooers, part the prince did get, ‭ Who sate alone, his table plac'd aside; ‭ To which the herald did the bread divide. ‭ After Eumæus, enter'd straight the king, [3] ‭ Like to a poor and heavy aged thing, ‭ Bore hard upon his staff, and was so clad ‭ As would have made his mere beholder sad. ‭ Upon the ashen floor his limbs he spread, ‭ And 'gainst a cypress-threshold stay'd his head, ‭ The tree wrought smooth, and in a line direct ‭ Tried by the plumb and by the architect. ‭ The prince then bade the herdsman give him bread, ‭ The finest there, and see that prostrated ‭ At-all-parts plight of his giv'n all the cheer ‭ His hands could turn to: "Take," said he, "and bear ‭ These cates to him, and bid him beg of all ‭ These Wooers here, and to their festival ‭ Bear up with all the impudence he can; ‭ _Bashful behaviour fits no needy man."_ ‭ He heard, and did his will. "Hold guest," said he, ‭ "Telemachus commends these cates to thee, ‭ Bids thee bear up, and all these Wooers implore. ‭ _Wit must make impudent whom Fate makes poor."_ ‭ "O Jove," said he, "do my poor pray'rs the grace ‭ To make him blessed'st of the mortal race, ‭ And ev'ry thought now in his gen'rous heart ‭ To deeds that further my desires convert." ‭ Thus took he in with both his hands his store, ‭ And in the uncouth scrip, that lay before ‭ His ill-shod feet, repos'd it; whence he fed ‭ All time the music to the feasters play'd. ‭ Both jointly ending, then began the Wooers ‭ To put in old act their tumultuous pow'rs; ‭ When Pallas standing close did prompt her friend, ‭ To prove how far the bounties would extend ‭ Of those proud Wooers; so, to let him try ‭ Who most, who least, had learn'd humanity. ‭ However, no thought touch'd Minerva's mind, ‭ That anyone should'scape his wreak design'd. ‭ He handsomely became all, crept about ‭ To ev'ry Wooer, held a forc'd hand out, ‭ And all his work did in so like a way, ‭ As he had practis'd begging many a day. ‭ And though they knew all beggars could do this, ‭ Yet they admir'd it as no deed of his; ‭ Though far from thought of other, us'd expence ‭ And pity to him, who he was, and whence, ‭ Inquiring mutually. Melanthius then: ‭ "Hear me, ye Wooers of the far-fam'd queen, ‭ About this beggar. I have seen before ‭ This face of his; and know for certain more, ‭ That this swain brought him hither. What he is, ‭ Or whence he came, flies me." Reply to this ‭ Antinous made, and mock'd Eumæus thus: ‭ "O thou renownéd herdsman, why to us ‭ Brought'st thou this beggar? Serves it not our hands; ‭ That other land-leapers, and cormorands, ‭ Profane poor knaves, lie on us, unconducted, ‭ But you must bring them? So amiss instructed ‭ Art thou in course of thrift, as not to know ‭ Thy lord's goods wrack'd in this their overflow? ‭ Which think'st thou nothing, that thou call'st in these?" ‭ Eumæus answer'd: "Though you may be wise, ‭ You speak not wisely. Who calls in a guest ‭ That is a guest himself? None call to feast ‭ Other than men that are of public use, ‭ Prophets, or poets, whom the Gods produce, ‭ Physicians for men's ills, or architects. ‭ Such men the boundless earth affords respects ‭ Bounded in honour, and may call them well. ‭ But poor men who calls? Who doth so excell ‭ In others' good to do himself an ill? ‭ But all Ulysses' servants have been still ‭ Eyesores in your way more than all that woo, ‭ And chiefly I. But what care I for you, ‭ As long as these roofs hold as thralls to none ‭ The wise Penelope and her god-like son?" ‭ "Forbear," said he, "and leave this tongue's bold ill. ‭ Antinous uses to be crossing still, ‭ And give sharp words; his blood that humour bears, ‭ To set men still together by the ears. ‭ But," turning then t' Antinous, "O," said he, ‭ "You entertain a father's care of me, ‭ To turn these eating guests out. 'Tis advice ‭ Of needful use for my poor faculties, ‭ But God doth not allow this; there must be ‭ Some care of poor men in humanity. ‭ What you yourselves take, give; I not envy, ‭ But give command that hospitality ‭ Be giv'n all strangers. Nor shall my pow'rs fear, ‭ If this mood in me reach my mother's ear; ‭ Much less the servants', that are here to see ‭ Ulysses' house kept in his old degree. ‭ But you bear no such mind, your wits more cast ‭ To fill yourself than let another taste." ‭ Antinous answer'd him: "Brave-spoken man! ‭ Whose mind's free fire see check'd no virtue can. ‭ If all we Wooers here would give as much ‭ As my mind serves, his [4] largess should be such ‭ As would for three months serve his far-off way ‭ From troubling your house with more cause of stay." ‭ This said, he took a stool up, that did rest, ‭ Beneath the board, his spangled feet at feast, ‭ And offer'd at him; but the rest gave all, ‭ And fill'd his fulsome scrip with festival. ‭ And so Ulysses for the present was, ‭ And for the future, furnish'd, and his pass ‭ Bent to the door to eat. Yet could not leave ‭ Antinous so, but said: "Do you too give, ‭ Lov'd lord; your presence makes a show to me ‭ As you not worst were of the company, ‭ But best, and so much that you seem the king, ‭ And therefore you should give some better thing ‭ Than bread, like others. I will spread your praise ‭ Through all the wide world, that have in my days ‭ Kept house myself, and trod the wealthy ways ‭ Of other men ev'n to the title Blest; ‭ And often have I giv'n an erring guest ‭ (How mean soever) to the utmost gain ‭ Of what he wanted, kept whole troops of men, ‭ And had all other comings in, with which ‭ Men live so well, and gain the fame of rich. ‭ Yet Jove consum'd all; he would have it so; ‭ To which, his mean was this: He made me go ‭ Far off, for Egypt, in the rude consort ‭ Of all-ways-wand'ring pirates, where, in port, ‭ I bade my lov'd men draw their ships ashore, ‭ And dwell amongst them; sent out some t' explore ‭ Up to the mountains, who, intemperate, ‭ And their inflam'd bloods bent to satiate, ‭ Forag'd the rich fields, hal'd the women thence, ‭ And unwean'd children, with the foul expence ‭ Both of their fames and bloods. The cry then flew ‭ Straight to the city; and the great fields grew ‭ With horse and foot, and flam'd with iron arms; ‭ When Jove (that breaks the thunder in alarms) ‭ An ill flight cast amongst my men; not one ‭ Inspir'd with spirit to stand, and turn upon ‭ The fierce pursuing foe; and therefore stood ‭ Their ill fate thick about them; some in blood, ‭ And some in bondage; toils led by constraint ‭ Fast'ning upon them. Me along they sent ‭ To Cyprus with a stranger-prince they met, ‭ Dmetor Iasides, who th' imperial seat ‭ Of that sweet island sway'd in strong command. ‭ And thus feel I here need's contemned hand." ‭ "And what God sent," said he, "this suff'ring bane ‭ To vex our banquet? Stand off, nor profane ‭ My board so boldly, lest I show thee here ‭ Cyprus and Egypt made more sour than there. ‭ You are a saucy set-fac'd vagabond. ‭ About with all you go, and they, beyond ‭ Discretion, give thee, since they find not here ‭ The least proportion set down to their cheer. ‭ But ev'ry fountain hath his under-floods. ‭ _It is no bounty to give others' goods."_ ‭ "O Gods," replied Ulysses, "I see now, ‭ You bear no soul in this your goodly show. ‭ Beggars at your board, I perceive, should get ‭ Scarce salt from your hands, if themselves brought meat; ‭ Since, sitting where another's board is spread, ‭ That flows with feast, not to the broken bread ‭ Will your allowance reach." "Nay then," said he, ‭ And look'd austerely, "if so saucy be ‭ Your suffer'd language, I suppose, that clear ‭ You shall not 'scape without some broken cheer." ‭ Thus rapt he up a stool, with which he smit ‭ The king's right shoulder, 'twixt his neck and it. ‭ He stood him like a rock. Antinous' dart ‭ Nor stirr'd Ulysses; who in his great heart ‭ Deep ills projected, which, for time yet, close ‭ He bound in silence, shook his head, and went ‭ Out to the entry, where he then gave vent ‭ To his full scrip, sat on the earth, and eat, ‭ And talk'd still to the Wooers: "Hear me yet, ‭ Ye Wooers of the Queen. It never grieves ‭ A man to take blows, where for sheep, or beeves, ‭ Or other main possessions, a man fights; ‭ But for his harmful belly this man smites, ‭ Whose love to many a man breeds many a woe. ‭ And if the poor have Gods, and Furies too, ‭ Before Antinous wear his nuptial wreath, ‭ He shall be worn upon the dart of death." ‭ "Harsh guest," said he, "sit silent at your meat, ‭ Or seek your desp'rate plight some safer seat, ‭ Lest by the hands or heels youths drag your years, ‭ And rend your rotten rags about your ears." ‭ This made the rest as highly hate his folly, ‭ As he had violated something holy. ‭ When one, ev'n of the proudest, thus began: ‭ "Thou dost not nobly, thus to play the man ‭ On such an errant wretch. O ill dispos'd! ‭ Perhaps some sacred Godhead goes enclos'd ‭ Ev'n in his abject outside; for the Gods ‭ Have often visited these rich abodes ‭ Like such poor stranger pilgrims, since their pow'rs ‭ (Being always shapeful) glide through towns and tow'rs, ‭ Observing, as they pass still, who they be ‭ That piety love, and who impiety." ‭ This all men said, but he held sayings cheap. ‭ And all this time Telemachus did heap ‭ Sorrow on sorrow on his beating heart, ‭ To see his father stricken; yet let part ‭ No tear to earth, but shook his head, and thought ‭ As deep as those ills that were after wrought. ‭ The Queen now, hearing of her poor guest's stroke, ‭ Said to her maid (as to her Wooer she spoke), ‭ "I wish the famous-for-his-bow, the Sun, ‭ Would strike thy heart so." Her wish, thus begun, ‭ Her lady, fair Eurynome, pursued ‭ Her execration, and did thus conclude: ‭ "So may our vows call down from heav'n his end, ‭ And let no one life of the rest extend ‭ His life till morning." "O Eurynomé," ‭ Replied the Queen, "may all Gods speak in thee, ‭ For all the Wooers we should rate as foes, ‭ Since all their weals they place in others' woes! ‭ But this Antinous we past all should hate, ‭ As one resembling black and cruel Fate. ‭ A poor strange wretch begg'd here, compell'd by need, ‭ Ask'd all, and ev'ry one gave in his deed, ‭ Fill'd his sad scrip, and eas'd his heavy wants, ‭ Only this man bestow'd unmanly taunts, ‭ And with a cruel blow, his force let fly, ‭ 'Twixt neck and shoulders show'd his charity." ‭ These minds, above, she and her maids did show, ‭ While, at his scrip, Ulysses sat below. ‭ In which time she Eumæus call'd, and said: ‭ "Go, good Eumæus, and see soon convey'd ‭ The stranger to me; bid him come and take ‭ My salutations for his welcome's sake, ‭ And my desire serve, if he hath not heard ‭ Or seen distress'd Ulysses, who hath err'd ‭ Like such a man, and therefore chance may fall ‭ He hath by him been met and spoke withal?" ‭ "O Queen," said he, "I wish to heav'n your ear ‭ Were quit of this unrev'rend noise you hear ‭ From these rude Wooers, when I bring the guest; ‭ Such words your ear would let into your breast ‭ As would delight it to your very heart. ‭ Three nights and days I did my roof impart ‭ To his fruition (for he came to me ‭ The first of all men since he fled the sea) ‭ And yet he had not giv'n a perfect end ‭ To his relation of what woes did spend ‭ The spite of Fate on him, but as you see [5] ‭ A singer, breathing out of Deity ‭ Love-kindling lines, when all men seated near ‭ Are rapt with endless thirst to ever hear; ‭ So sweeten'd he my bosom at my meat, ‭ Affirming that Ulysses was in Crete, ‭ Where first the memories of Minos were, ‭ A guest to him there dwelling then, as dear ‭ As his true father; and from thence came he ‭ Tir'd on with sorrows, toss'd from sea to sea, ‭ To cast himself in dust, and tumble here, ‭ At Wooers' feet, for blows and broken cheer. ‭ But of Ulysses, where the Thesprots dwell, ‭ A wealthy people, Fame, he says, did tell ‭ The still survival; who his native light ‭ Was bound for now, with treasure infinite." ‭ "Call him," said she, "that he himself may say ‭ This over to me. We shall soon have way ‭ Giv'n by the Wooers; they, as well at gate, ‭ As set within doors, use to recreate ‭ Their high-fed spirits. As their humours lead ‭ They follow; and may well; for still they tread ‭ Uncharg'd ways here, their own wealth lying unwasted ‭ In poor-kept houses, only something tasted ‭ Their bread and wine is by their household swains, ‭ But they themselves let loose continual reins ‭ To our expenses, making slaughter still ‭ Of sheep, goats, oxen, feeding past their fill, ‭ And vainly lavishing our richest wine; ‭ All these extending past the sacred line, ‭ For here lives no man like Ulysses now ‭ To curb these reins. But should he once show ‭ His country-light his presence, he and his ‭ Would soon revenge these Wooers' injuries." ‭ This said, about the house, in echoes round, ‭ Her son's strange neesings made a horrid sound; [6] ‭ At which the Queen yet laugh'd, and said: "Go call ‭ The stranger to me. Heard'st thou not, to all ‭ My words last utter'd, what a neesing brake ‭ From my Telemachus? From whence I make, ‭ This sure conclusion: That the death and fate ‭ Of ev'ry Wooer here is near his date. ‭ Call, then, the guest, and if he tell as true ‭ What I shall ask him, coat, cloak, all things new, ‭ These hands shall yield him." This said, down he went, ‭ And told Ulysses, "that the Queen had sent ‭ To call him to her, that she might enquire ‭ About her husband what her sad desire ‭ Urg'd her to ask; and, if she found him true, ‭ Both coat, and cassock (which he needed) new ‭ Her hands would put on him; and that the bread, ‭ Which now he begg'd amongst the common tread, ‭ Should freely feed his hunger now from her, ‭ Who all he wish'd would to his wants prefer." ‭ His answer was: "I will with fit speed tell ‭ The whole truth to the Queen; for passing well ‭ I know her lord, since he and I have shar'd ‭ In equal sorrows. But I much am scar'd ‭ With this rude multitude of Wooers here, ‭ The rage of whose pride smites heav'n's brazen sphere. ‭ Of whose rout when one struck me for no fault, ‭ Telemachus nor none else turn'd th' assault ‭ From my poor shoulders. Therefore, though she haste, ‭ Beseech the Queen her patience will see past ‭ The day's broad light, and then may she enquire. ‭ 'Tis but my closer pressing to the fire ‭ In th' ev'ning's cold, because my weeds, you know, ‭ Are passing thin; for I made bold to show ‭ Their bracks to you, and pray'd your kind supply." ‭ He heard, and hasted; and met instantly ‭ The Queen upon the pavement in his way, ‭ Who ask'd: "What! Bring'st thou not? What cause of stay ‭ Find his austere supposes? Takes he fear ‭ Of th' unjust Wooers? Or thus hard doth bear ‭ On any other doubt the house objects? ‭ He does me wrong, and gives too nice respects ‭ To his fear'd safety." "He does right," said he, ‭ "And what he fears should move the policy ‭ Of any wise one; taking care to shun ‭ The violent Wooers. He bids bide, till sun ‭ Hath hid his broad light. And, believe it, Queen, ‭ 'Twill make your best course, since you two, unseen, ‭ May pass th' encounter; you to speak more free, ‭ And he your ear gain less distractedly." ‭ "The guest is wise," said she, "and well doth give ‭ The right thought use. Of all the men that live, ‭ Life serves none such as these proud Wooers are, ‭ To give a good man cause to use his care." ‭ Thus, all agreed, amongst the Wooers goes ‭ Eumæus to the prince, and, whisp'ring close, ‭ Said: "Now, my love, my charge shall take up me, ‭ (Your goods and mine). What here is, you must see ‭ In fit protection. But, in chief, regard ‭ Your own dear safeguard; whose state study hard, ‭ Lest suff'rance seize you. Many a wicked thought ‭ Conceal these Wooers; whom just Jove see brought ‭ To utter ruin, ere it touch at us." ‭ "So chance it, friend," replied Telemachus, ‭ "Your bever taken, go. In first of day ‭ Come, and bring sacrifice the best you may. ‭ To me and to th' Immortals be the care ‭ or whatsoever here the safeties are." ‭ This said, he sat in his elaborate throne. ‭ Eumæus (fed to satisfaction) ‭ Went to his charge, left both the court and walls ‭ Full of secure and fatal festivals, ‭ In which the Wooers' pleasures still would sway. ‭ And now begun the even's near-ending day. ‭ THE END OF THE SEVENTEENTH BOOK OF HOMER'S ODYSSEYS. ‭[1] Intending his fat herd, kept only for the Wooers' dainty palates. ‭[2] The dog died as soon as he had seen Ulysses. ‭[3] Ulysses' ruthful fashion of entry to his own hall. ‭[4] His--intending Ulysses. ‭[5] Simile, in which Ulysses is compared with a poet for the ‭sweetness of his speech. ‭[6] Neezing a good omen. ‭ THE EIGHTEENTH BOOK OF HOMER'S ODYSSEYS ‭ ‭ THE ARGUMENT ‭ ‭ Ulysses and rogue Irus fight. ‭ Penelope vouchsafes her sight ‭ To all her Wooers; who present ‭ Gifts to her, ravish'd with content. ‭ A certain parlé then we sing. ‭ Betwixt a Wooer and the King. ‭ ANOTHER ARGUMENT ‭ _Σίγμα._ ‭ The beggar's glee. ‭ The King's high fame. ‭ Gifts giv'n to see ‭ A virtuous dame. ‭ There came a common beggar to the court, ‭ Who in the city begg'd of all resort, ‭ Excell'd in madness of the gut, drunk, ate, ‭ Past intermission, was most hugely great, ‭ Yet had no fibres in him nor no force, ‭ In sight a man, in mind a living corse. ‭ His true name was Arnæus, for his mother ‭ Impos'd it from his birth, and yet another ‭ The city youth would give him (from the course ‭ He after took, deriv'd out of the force ‭ That need held on him, which was up and down ‭ To run on all men's errands through the town) ‭ Which sounded Irus. When whose gut was come, ‭ He needs would bar Ulysses his own home, ‭ And fell to chiding him: "Old man," said he, ‭ "Your way out of the entry quickly see ‭ Be with fair language taken, lest your stay ‭ But little longer see you dragg'd away. ‭ See, sir, observe you not how all these make ‭ Direct signs at me, charging me to take ‭ Your heels, and drag you out? But I take shame. ‭ Rise yet, y' are best, lest we two play a game ‭ At cuffs together." He bent brows, and said: ‭ "Wretch! I do thee no ill, nor once upbraid ‭ Thy presence with a word, nor, what mine eye ‭ By all hands sees thee giv'n, one thought envy. ‭ Nor shouldst thou envy others. Thou may'st see ‭ The place will hold us both; and seem'st to me ‭ A beggar like myself; which who can mend? ‭ _The Gods give most to whom they least are friend. ‭ The chief goods Gods give, is in good to end._ ‭ But to the hands' strife, of which y' are so free, ‭ Provoke me not, for fear you anger me; ‭ And lest the old man, on whose scorn you stood, ‭ Your lips and bosom make shake hands in blood. ‭ I love my quiet well, and more will love ‭ To-morrow than to-day. But if you move ‭ My peace beyond my right, the war you make ‭ Will never after give you will to take ‭ Ulysses' house into your begging walk." ‭ "O Gods," said he, "how volubly doth talk ‭ This eating gulf! And how his fume breaks out, ‭ As from an old crack'd oven! Whom I will clout ‭ So bitterly, and so with both hands mall ‭ His chaps together, that his teeth shall fall ‭ As plain seen on the earth as any sow's, ‭ That ruts the corn-fields, or devours the mows. ‭ Come, close we now, that all may see what wrong ‭ An old man tempts that takes at cuffs a young." ‭ Thus in the entry of those lofty tow'rs ‭ These two, with all spleen, spent their jarring pow'rs. ‭ Antinous took it, laugh'd, and said: "O friends, ‭ We never had such sport! This guest contends ‭ With this vast beggar at the buffet's fight. ‭ Come, join we hands, and screw up all their spite." ‭ All rose in laughters; and about them bore ‭ All the ragg'd rout of beggars at the door. ‭ Then mov'd Antinous the victor's hire ‭ To all the Wooers thus: "There are now at fire ‭ Two breasts of goat; both which let law set down ‭ Before the man that wins the day's renown, ‭ With all their fat and gravy. And of both ‭ The glorious victor shall prefer his tooth, ‭ To which he makes his choice of, from us all, ‭ And ever after banquet in our hall, ‭ With what our boards yield; not a beggar more ‭ Allow'd to share, but all keep out at door." ‭ This he propos'd; and this they all approv'd, ‭ To which Ulysses answer'd: "O most lov'd, ‭ By no means should an old man, and one old ‭ In chief with sorrows, be so over-bold ‭ To combat with his younger; but, alas, ‭ Man's own-ill-working belly needs will pass ‭ This work upon me, and enforce me, too, ‭ To beat this fellow. But then, you must do ‭ My age no wrong, to take my younger's part, ‭ And play me foul play, making your strokes' smart ‭ Help his to conquer; for you eas'ly may ‭ With your strengths crush me. Do then right, and lay ‭ Your honours on it in your oaths, to yield ‭ His part no aid, but equal leave the field." ‭ All swore his will. But then Telemachus ‭ His father's scoffs with comforts serious ‭ Could not but answer, and made this reply: ‭ "Guest! If thine own pow'rs cheer thy victory, ‭ Fear no man's else that will not pass it free. ‭ He fights with many that shall touch but thee. ‭ I'll see thy guest-right paid. Thou here art come ‭ In my protection; and to this the sum ‭ Of all these Wooers (which Antinous are ‭ And King Eurymachus) conjoin their care." ‭ Both vow'd it. When Ulysses, laying by ‭ His upper weed, his inner beggary ‭ Near show'd his shame, which he with rags prevented ‭ Pluck'd from about his thighs, and so presented ‭ Their goodly sight, which were so white and great, ‭ And his large shoulders were to view so set ‭ By his bare rags, his arms, his breast, and all, ‭ So broad, and brawny--their grace natural ‭ Being kept by Pallas, ever standing near-- ‭ That all the Wooers his admirers were ‭ Beyond all measure, mutual whispers driv'n ‭ Through all their cluster, saying: "Sure as heav'n ‭ Poor Irus pull'd upon him bitter blows. ‭ Through his thin garment what a thigh he shows!" ‭ They said; but Irus felt. His coward mind ‭ Was mov'd at root. But now he needs must find ‭ Facts to his brags; and forth at all parts fit ‭ The servants brought him, all his art'ries smit ‭ With fears and tremblings. Which Antinous saw, ‭ And said: "Nay, now too late comes fear. No law ‭ Thou shouldst at first have giv'n thy braggart vein, ‭ Nor should it so have swell'd, if terrors strain ‭ Thy spirits to this pass, for a man so old, ‭ And worn with penuries that still lay hold ‭ On his ragg'd person. Howsoever, take ‭ This vow from me for firm: That if, he make ‭ Thy forces stoop, and prove his own supreme, ‭ I'll put thee in a ship, and down the stream ‭ Send thee ashore where King Echetus reigns, ‭ (The roughest tyrant that the world contains) ‭ And he will slit thy nostrils, crop each ear, ‭ Thy shame cut off, and give it dogs to tear." ‭ This shook his nerves the more. But both were now ‭ Brought to the lists; and up did either throw ‭ His heavy fists. Ulysses, in suspense ‭ To strike so home that he should fright from thence ‭ His coward soul, his trunk laid prostrate there, ‭ Or let him take more leisure to his fear, ‭ And stoop him by degrees. The last show'd best, ‭ To strike him slightly, out of fear the rest ‭ Would else discover him. But, peace now broke, ‭ On his right shoulder Irus laid his stroke. ‭ Ulysses struck him just beneath the ear, ‭ His jawbone broke, and made the blood appear; ‭ When straight he strew'd the dust, and made his cry ‭ Stand for himself; with whom his teeth did lie, ‭ Spit with his blood out; and against the ground ‭ His heels lay sprawling. Up the hands went round ‭ Of all the Wooers, all at point to die ‭ With violent laughters. Then the king did ply ‭ The beggar's feet, and dragg'd him forth the hall, ‭ Along the entry, to the gates and wall; ‭ Where leaving him, he put into his hand ‭ A staff; and bade him there use his command ‭ On swine and dogs, and not presume to be ‭ Lord of the guests, or of the beggary, ‭ Since he of all men was the scum and curse; ‭ And so bade please with that, or fare yet worse. ‭ Then cast he on his scrip, all-patch'd and rent, ‭ Hung by a rotten cord, and back he went ‭ To greet the entry's threshold with his seat. ‭ The Wooers throng'd to him, and did entreat ‭ With gentle words his conquest, laughing still, ‭ Pray'd Jove and all the Gods to give his will ‭ What most it wish'd him and would joy him most, ‭ Since he so happily had clear'd their coast ‭ Of that unsavoury morsel; whom they vow'd ‭ To see with all their utmost haste bestow'd ‭ Aboard a ship, and for Epirus sent ‭ To King Echetus, on whose throne was spent ‭ The worst man's seat that breath'd. And thus was grac'd ‭ Divine Ulysses, who with joy embrac'd ‭ Ev'n that poor conquest. Then was set to him ‭ The goodly goat's breast promis'd (that did swim ‭ In fat and gravy) by Antinous, ‭ And from a basket, by Amphinomus, ‭ Were two breads giv'n him; who, besides, renown'd ‭ His banquet with a golden goblet; crown'd, ‭ And this high salutation: "Frolic, guest, ‭ And be those riches that you first possest ‭ Restor'd again with full as many joys, ‭ As in your poor state I see now annoys." ‭ "Amphinomus," said he, "you seem to me ‭ Exceeding wise, as being the progeny ‭ Of such a father as authentic Fame ‭ Hath told me was so, one of honour'd name, ‭ And great revenues in Dulichius, ‭ His fair name Nisus. He is blazon'd thus; ‭ And you to be his son, his wisdom heiring, ‭ As well as wealth, his state in nought impairing. ‭ To prove which always, let me tell you this, ‭ (As warning you to shun the miseries ‭ That follow full states, if they be not held ‭ With wisdom still at full, and so compell'd ‭ To courses that abode not in their brows, ‭ By too much swing, their sudden overthrows) ‭ _Of all things breathing, or that creep on earth, ‭ Nought is more wretched than a human birth. ‭ Bless'd men think never they can cursed be, ‭ While any power lasts to move a knee._ ‭ But when the bless'd Gods make them feel that smart, ‭ That fled their faith so, as they had no heart ‭ They bear their suff'rings, and, what well they might ‭ Have clearly shunn'd, they then meet in despite. ‭ _The mind of man flies still out of his way, ‭ Unless God guide and prompt it ev'ry day._ ‭ I thought me once a blesséd man with men. ‭ And fashion'd me to all so counted then, ‭ Did all injustice like them, what for lust, ‭ Or any pleasure, never so unjust ‭ I could by pow'r or violence obtain, ‭ And gave them both in all their pow'rs the rein, ‭ Bold of my fathers and my brothers still; ‭ While which held good my arts seem'd never ill. ‭ And thus is none held simply good or bad, ‭ But as his will is either miss'd or had. ‭ All goods God's gifts man calls, howe'er he gets them, ‭ And so takes all; what price soe'er God sets them, ‭ Says nought how ill they come, nor will controul ‭ That ravine in him, though it cost his soul. ‭ And these parts here I see these Wooers play, ‭ Take all that falls, and all dishonours lay ‭ On that man's Queen, that, tell your friends, doth bear ‭ No long time's absence, but is passing near. ‭ Let God then guide thee home, lest he may meet ‭ In his return thy undeparted feet; ‭ For when he enters, and sees men so rude, ‭ The quarrel cannot but in blood conclude." ‭ This said, he sacrific'd, then drunk, and then ‭ Referr'd the giv'n bowl to the guide-of-men; ‭ Who walk'd away, afflicted at his heart, ‭ Shook head, and fear'd that these facts would convert ‭ To ill in th' end; yet had not grace to fly, ‭ Minerva stay'd him, being ordain'd to die ‭ Upon the lance of young Ulyssides. ‭ So down he sat; and then did Pallas please ‭ T' incline the Queen's affections to appear ‭ To all the Wooers, to extend their cheer ‭ To th' utmost lightning that still ushers death, ‭ And made her put on all the painted sheath, ‭ That might both set her Wooers' fancies high, ‭ And get her greater honour in the eye ‭ Ev'n of her son and sov'reign than before. ‭ Who laughing yet, to show her humour bore ‭ No serious appetite to that light show, ‭ She told Eurynomé, that not till now ‭ She ever knew her entertain desire ‭ To please her Wooers' eyes, but oft on fire ‭ She set their hate, in keeping from them still; ‭ Yet now she pleas'd t' appear, though from no will ‭ To do them honour, vowing she would tell ‭ Her son that of them that should fit him well ‭ To make use of; which was, not to converse ‭ Too freely with their pride, nor to disperse ‭ His thoughts amongst them, since they us'd to give ‭ Good words, but through them ill intents did drive. ‭ Eurynomé replied: "With good advise ‭ You vow his counsel, and your open guise. ‭ Go then, advise your son, nor keep more close ‭ Your cheeks, still drown'd in your eyes' overflows, ‭ But bathe your body, and with balms make clear ‭ Your thicken'd count'nance. _Uncomposéd cheer, ‭ And ever mourning, will the marrow wear._ ‭ Nor have you cause to mourn; your son hath now ‭ Put on that virtue which, in chief, your vow ‭ Wish'd, as your blessing, at his birth, might deck ‭ His blood and person." "But forbear to speak ‭ Of baths, or balmings, or of beauty, now," ‭ The Queen replied, "lest, urging comforts, you ‭ Discomfort much; because the Gods have won ‭ The spoil of my looks since my lord was gone. ‭ But these must serve. Call hither then to me ‭ Hippodamia and Autonoé, ‭ That those our train additions may supply ‭ Our own deserts. And yet, besides, not I, ‭ With all my age, have learn'd the boldness yet ‭ T' expose myself to men, unless I get ‭ Some other gracers." This said, forth she went ‭ To call the ladies, and much spirit spent ‭ To make their utmost speed, for now their Queen ‭ Would both herself show, and make them be seen. ‭ But now Minerva other projects laid, ‭ And through Icarius' daughter's veins convey'd ‭ Sweet sleep's desire; in whose soft fumes involv'd ‭ She was as soon as laid, and quite dissolv'd ‭ Were all her lineaments. The Goddess then ‭ Bestow'd immortal gifts on her, that men ‭ Might wonder at her beauties; and the beams ‭ That glister in the Deified Supremes ‭ She clear'd her mourning count'nance up withall. ‭ Ev'n such a radiance as doth round empall ‭ Crown'd Cytherea, when her order'd places ‭ Conduct the bevy of the dancing Graces, ‭ She added to her own; more plump, more high, ‭ And fairer than the polish'd ivory, ‭ Rend'ring her parts and presence. This grace done, ‭ Away the Deity flew; and up did run ‭ Her lovely-wristed ladies, with a noise ‭ That blew the soft chains from her sleeping joys; ‭ When she her fair eyes wip'd, and, gasping, said: ‭ "O me unblest! How deep a sweet sleep spread ‭ His shades about me! Would Diana pleas'd ‭ To shoot me with a death no more diseas'd, ‭ As soon as might be, that no more my moan ‭ Might waste my blood in weepings never done, ‭ For want of that accomplish'd virtue spher'd ‭ In my lov'd lord, to all the Greeks preferr'd!" ‭ Then she descended with her maids, and took ‭ Place in the portal; whence her beamy look ‭ Reach'd ev'ry Wooer's heart; yet cast she on ‭ So thin a veil, that through it quite there shone ‭ A grace so stol'n, it pleas'd above the clear, ‭ And sunk the knees of ev'ry Wooer there, ‭ Their minds so melted in love's vehement fires, ‭ That to her bed she heighten'd all desires. ‭ The prince then coming near, she said: "O son, ‭ Thy thoughts and judgments have not yet put on ‭ That constancy in what becomes their good, ‭ Which all expect in thee. Thy younger blood ‭ Did sparkle choicer spirits; but, arriv'd ‭ At this full growth, wherein their form hath thriv'd ‭ Beyond the bounds of childhood, and when now, ‭ Beholders should affirm, 'This man doth grow ‭ Like the rare son of his matchless Sire, ‭ (His goodliness, his beauty, and his fire ‭ Of soul aspir'd to)' thou mak'st nothing good ‭ Thy fate, nor fortune, nor thy height of blood, ‭ In manage of thy actions. What a deed ‭ Of foul desert hath thy gross suff'rance freed ‭ Beneath thine own roof! A poor stranger here ‭ Us'd most unmanly! How will this appear ‭ To all the world, when Fame shall trumpet out, ‭ That thus, and thus, are our guests beat about ‭ Our court unrighted? 'Tis a blaze will show ‭ Extremely shameful to your name and you." ‭ "I blame you not, O mother," he replied, ‭ "That, this clear wrong sustain'd by me, you chide; ‭ Yet know I both the good and bad of all, ‭ Being past the years in which young errors fall. ‭ But, all this known, skill is not so exact ‭ To give, when once it knows, things fit their fact. ‭ I well may doubt the prease of strangers here, ‭ Who, bent to ill, and only my nerves near, ‭ May do it in despite. And yet the jar ‭ Betwixt our guest and Irus was no war ‭ Wrought by the Wooers; nor our guest sustain'd ‭ Wrong in that action, but the conquest gain'd. ‭ And would to Jove, Minerva, and the Sun, ‭ That all your Wooers might serve Contention ‭ For such a purchase as the beggar made, ‭ And wore such weak heads! Some should death invade, ‭ Strew'd in the entry, some embrue the hall, ‭ Till ev'ry man had vengeance capital, ‭ Sattled like Irus at the gates, his head ‭ Ev'ry way nodding, like one forfeited ‭ To reeling Bacchus, knees nor feet his own, ‭ To bear him where he's better lov'd or known." ‭ Their speeches giv'n this end, Eurymachus ‭ Began his courtship, and express'd it thus: ‭ "Most wise Icarius' daughter! If all those, ‭ That did for Colchos vent'rous sail dispose ‭ For that rich purchase, had before but seen ‭ Earth's richer prize in th' Ithacensian Queen, ‭ They had not made that voyage, but to you ‭ Would all their virtues and their beings vow. ‭ Should all the world know what a worth you store, ‭ To-morrow than to-day, and next light, more ‭ Your court should banquet; since to all dames you ‭ Are far preferr'd, both for the grace of show, ‭ In stature, beauty, form in ev'ry kind ‭ Of all parts outward, and for faultless mind." ‭ "Alas," said she, "my virtue, body, form, ‭ The Gods have blasted with that only storm ‭ That ravish'd Greece to Ilion, since my lord, ‭ For that war shipp'd, bore all my goods aboard. ‭ If he, return'd, should come and govern here ‭ My life's whole state, the grace of all things there ‭ His guide would heighten, as the spirit it bore; ‭ Which dead in me lives, giv'n him long before. ‭ A sad course I live now; Heav'n's stern decree ‭ With many an ill hath numb'd and deaded me. ‭ He took life with him, when he took my hand ‭ In parting from me to the Trojan strand, ‭ These words my witness: 'Woman! I conceive ‭ That not all th' Achives bound for Troy shall leave ‭ Their native earth their safe returnéd bones, ‭ Fame saying, that Troy trains up approvéd sons ‭ In deeds of arms, brave putters-off of shafts, ‭ For winging lances masters of their crafts, ‭ Unmatchéd riders, swift of foot, and straight ‭ Can arbitrate a war of deadliest weight. ‭ Hope then can scarce fill all with life's supply, ‭ And of all any failing, why not I? ‭ Nor do I know, if God hath marshall'd me ‭ Amongst the safe-return'd; or his decree ‭ Hath left me to the thraldom order'd there. ‭ However, all cares be thy burthens here, ‭ My sire and mother tend as much as now, ‭ I further off, more near in cares be you. ‭ Your son to man's state grown, wed whom you will; ‭ And, you gone, his care let his household fill.' ‭ Thus made my lord his will, which Heav'n sees prov'd ‭ Almost at all parts; for the Sun remov'd ‭ Down to his set, ere long, will lead the night ‭ Of those abhorréd nuptials, that should fright ‭ Each worthy woman, which her second are ‭ With any man that breathes, her first lord's care ‭ Dead, because he to flesh and blood is dead; ‭ Which, I fear, I shall yield to, and so wed ‭ A second husband; and my reason is, ‭ Since Jove hath taken from me all his bliss. ‭ _Whom God gives over they themselves forsake, ‭ Their griefs their joys, their God their devil, make._ ‭ And 'tis a great grief, nor was seen till now ‭ In any fashion of such men as woo ‭ A good and wealthy woman, and contend ‭ Who shall obtain her, that those men should spend ‭ Her beeves and best sheep, as their chiefest ends, ‭ But rather that herself and all her friends ‭ They should with banquets and rich gifts entreat. ‭ _Their life is death that live with other's meat."_ ‭ Divine Ulysses much rejoic'd to hear ‭ His Queen thus fish for gifts, and keep in cheer. ‭ Their hearts with hope that she would wed again, ‭ Her mind yet still her first intent retain. ‭ Antinous saw the Wooers won to give, ‭ And said: "Wise Queen, by all your means receive ‭ Whatever bounty any Wooer shall use. ‭ Gifts freely giv'n 'tis folly to refuse. ‭ For know, that we resolve not to be gone ‭ To keep our own roofs, till of all some one, ‭ Whom best you like, your long-woo'd love shall win." ‭ This pleas'd the rest, and ev'ry one sent in ‭ His present by the herald. First had place ‭ Antinous' gift: A robe of special grace, ‭ Exceeding full and fair, and twenty hues ‭ Chang'd lustre to it; to which choice of shows, ‭ Twelve massy plated buttons, all of gold, ‭ Enrich'd the substance, made to fairly hold ‭ The robe together, all lac'd down before, ‭ Where keeps and catches both sides of it wore. ‭ Eurymachus a golden tablet gave, ‭ In which did Art her choicest works engrave; ‭ And round about an amber verge did run, ‭ That cast a radiance from it like the Sun. ‭ Eurydamas two servants had that bore ‭ Two goodly earrings, whose rich hollows wore ‭ Three pearls in either, like so many eyes, ‭ Reflecting glances radiant as the skies. ‭ The king Pisander, great Polyctor's heir, ‭ A casket gave, exceeding rich and fair. ‭ The other other wealthy gifts commended ‭ To her fair hand; which took, and straight ascended ‭ This Goddess of her sex her upper state. ‭ Her ladies all her gifts elaborate ‭ Up bearing after. All to dancing then ‭ The Wooers went, and song's delightful strain; ‭ In which they frolick'd, till the evening came, ‭ And then rais'd sable Hesperus his flame. ‭ When, for their lights within, they set up there ‭ Three lamps, whose wicks were wood exceeding sere, ‭ And passing porous; which they caus'd to burn, ‭ Their matter ever minister'd by turn ‭ Of sev'ral handmaids. Whom Ulysses seeing ‭ Too conversant with Wooers, ill-agreeing ‭ With guise of maids, advis'd in this fair sort: ‭ "Maids of your long-lack'd King, keep you the port ‭ Your Queen's chaste presence bears. Go up to her, ‭ Employ your looms, or rocks, and keep ye there; ‭ I'll serve to feed these lamps, should these lords' dances ‭ Last till Aurora cheer'd us with their glances. ‭ They cannot weary me, for I am one ‭ Born to endure when all men else have done." ‭ They wantonly brake out in laughters all, ‭ Look'd on each other; and to terms did fall ‭ Cheek-proud Melantho, who was Dolius' seed, ‭ Kept by the Queen, that gave her dainty bread ‭ Fit for her daughter; and yet won not so ‭ Her heart to her to share in any woe ‭ She suffer'd for her lord, but she was great ‭ With great Eurymachus, and her love's heat ‭ In his bed quench'd. And this choleric thing ‭ Bestow'd this railing language on the King: ‭ "Base stranger, you are taken in your brain, ‭ You talk so wildly. Never you again ‭ Can get where you were born, and seek your bed ‭ In some smith's hovel, or the marketsted, ‭ But here you must take confidence to prate ‭ Before all these; for fear can get no state ‭ In your wine-hardy stomach. Or 'tis like ‭ To prove your native garb, your tongue will strike ‭ On this side of your mouth still, being at best. ‭ Is the man idle-brain'd for want of rest? ‭ Or proud because he beat the roguish beggar? ‭ Take heed, Sir, lest some better man beleager ‭ Your ears with his fists, and set headlong hence ‭ Your bold abode here with your blood's expence." ‭ He, looking sternly on her, answer'd her: ‭ "Dog! What broad language giv'st thou? I'll prefer ‭ Your usage to the prince, that he may fall ‭ Foul on your fair limbs till he tell them all." ‭ This fray'd the wenches, and all straight got gone ‭ In fear about their business, ev'ry one ‭ Confessing he said well. But he stood now ‭ Close by the cressets, and did looks bestow ‭ On all men there; his brain employ'd about ‭ Some sharper business than to dance it out, ‭ Which had not long to go. Nor therefore would ‭ Minerva let the Wooers' spleens grow cold ‭ With too good usuage of him, that his heart ‭ Might fret enough, and make his choler smart. ‭ Eurymachus provok'd him first, and made ‭ His fellow laugh, with a conceit he had ‭ Fetch'd far from what was spoken long before, ‭ That his poor form perhaps some Deity bore. ‭ "It well may chance," said he, "some God doth bear ‭ This man's resemblance, for, thus standing near ‭ The glist'ring torches, his slick'd head doth throw ‭ Beams round about it as those cressets do, ‭ For not a hair he hath to give it shade. ‭ Say, will thy heart serve t' undertake a trade ‭ For fitting wages? Should I take thee hence ‭ To walk my grounds, and look to ev'ry fence, ‭ Or plant high trees, thy hire should raise thy forces ‭ Food store, and clothes. But these same idle courses ‭ Thou art so prompt in that thou wilt not work, ‭ But forage up and down, and beg, and lurk ‭ In ev'ry house whose roofs hold any will ‭ To feed such fellows. That thy gut may fill, ‭ Gives end to all thy being." He replied: ‭ "I wish, at any work we two were tried, ‭ In height of spring-time, when heav'n's lights are long, ‭ I a good crook'd scythe that were sharp and strong, ‭ You such another, where the grass grew deep, ‭ Up by day-break, and both our labours keep ‭ Up till slow darkness eas'd the labouring light, ‭ Fasting all day, and not a crumb till night; ‭ We then should prove our either workmanship. ‭ Or if, again, beeves, that the goad or whip ‭ Were apt t' obey before a tearing plow, ‭ Big lusty beasts, alike in bulk and brow, ‭ Alike in labour, and alike in strength, ‭ Our task four acres, to be till'd in length ‭ Of one sole day; again: then you should try ‭ If the dull glebe before the plow-should fly, ‭ Or I a long stitch could bear clean and even. ‭ Or lastly, if the Guide of earth and heaven ‭ Should stir stern war up, either here or there, ‭ And that at this day I had double spear, ‭ And shield, and steel casque fitting for my brows; ‭ At this work likewise, 'midst the foremost blows, ‭ Your eyes should note me, and get little cause ‭ To twit me with my belly's sole applause. ‭ But you affect t' affect with injury, ‭ Your mind ungentle, seem in valour high, ‭ Because 'gainst few, and those not of the best, ‭ Your conversation hath been still profest. ‭ But if Ulysses, landed on his earth, ‭ And enter'd on the true right of his birth, ‭ Should come and front ye, straight his ample gates ‭ Your feet would hold too narrow for your fates." ‭ He frown'd, rag'd, call'd him wretch, and vow'd ‭ To be his death, since he durst prove so proud ‭ Amongst so many, to tell him so home ‭ What he affected; ask'd, if overcome ‭ With wine he were, or, as his minion said, ‭ Talk'd still so idly, and were palsiéd ‭ In his mind's instruments, or was proud because ‭ He gat from Irus off with such applause? ‭ With all which, snatching up a stool, he threw; ‭ When old Ulysses to the knees withdrew ‭ Of the Dulichian lord, Amphinomus, ‭ As if he fear'd him. His dart missing thus ‭ His aged object, and his page's hand ‭ (A boy that waited on his cup's command, ‭ Now holding of an ewer to him) he smit, ‭ Down fell the sounding ewer, and after it ‭ The guiltless page lay sprawling in the dust, ‭ And crying out. When all the Wooers thrust ‭ A tumult up amongst them, wishing all ‭ The rogue had perish'd in some hospital, ‭ Before his life there stirr'd such uproars up, ‭ And with rude speeches spice their pleasures' cup. ‭ And all this for a beggar to fulfill ‭ A filthy proverb: _Good still yields to ill._ ‭ The prince cried out on them, to let the bad ‭ Obscure the good so; told them they were mad, ‭ Abus'd their banquet, and affirm'd some God ‭ Tried mast'ries with them; bade them take their load ‭ Of food and wine, sit up, or fall to bed ‭ At their free pleasures; and since he gave head ‭ To all their freedoms, why should they mistake ‭ Their own rich humours for a beggar's sake? ‭ All bit their lips to be so taken down, ‭ And taught the course that should have been their own, ‭ Admir'd the prince; and said he bravely spoke. ‭ But Nisus' son then struck the equal stroke, ‭ And said: "O friends, let no man here disdain ‭ To put up equal speeches, nor maintain ‭ With serious words an humour, nor with stroke ‭ A stranger in another's house provoke, ‭ Nor touch the meanest servant, but confine ‭ All these dissentions in a bowl of wine; ‭ Which fill us, cup-bearer, that, having done ‭ Our nightly sacrifice, we may atone ‭ Our pow'rs with sleep, resigning first the guest ‭ Up to the prince, that holds all interest ‭ In his disposure here; the house being his ‭ In just descent, and all the faculties." ‭ This all approv'd; when noble Mulius, ‭ Herald-in-chief to lord Amphinomus, ‭ The wine distributed with rev'rend grace ‭ To ev'ry Wooer; when the Gods giv'n place; ‭ With service fit; they serv'd themselves, and took ‭ Their parting cups, till, when they all had shook ‭ The angry humour off, they bent to rest, ‭ And ev'ry Wooer to sev'ral roofs addrest. ‭ THE END OF THE EIGHTEENTH BOOK OF HOMER'S ODYSSEYS. ‭ THE NINETEENTH BOOK OF HOMER'S ODYSSEYS ‭ ‭ THE ARGUMENT ‭ Ulysses and his son eschew ‭ Offending of the Wooers' view ‭ With any armour. His birth's seat, ‭ Ulysses tells his Queen, is Crete, ‭ Euryclea the truth yet found, ‭ Discover'd by a scar-heal'd wound, ‭ Which in Parnassus' tops a boar, ‭ Struck by him in his chace, did gore. ‭ ANOTHER ARGUMENT ‭ _Ταυ̑._ ‭ The King still hid ‭ By what he said; ‭ By what he did ‭ Informs his maid. ‭ Yet did divine Ulysses keep his roof, ‭ And with Minerva plotted still the proof ‭ Of all the Wooers' deaths; when thus his son ‭ He taught with these fore-counsels: "We must run ‭ A close course with these arms, and lay them by, ‭ And to the Wooers make so fair a sky ‭ As it would never thunder. Let me then, ‭ That you may well retain, repeat again ‭ What in Eumæus' cottage I advis'd: ‭ If when they see no leisure exercis'd, ‭ In fetching down your arms, and ask what use ‭ Your mind will give them, say, 'tis their abuse ‭ With smoke and rust that makes you take them down, ‭ This not being like the armory well-known ‭ To be the leavings of Laertes' son ‭ Consorting the design for Ilion; ‭ Your eyes may see how much they are infected, ‭ As all fires' vapours ever since reflected ‭ On those sole arms. Besides, a graver thought ‭ Jove graves within you, lest, their spirits wrought ‭ Above their pitch with wine, they might contend ‭ At some high banquet, and to wounds transcend, ‭ Their feast inverting; which, perhaps, may be ‭ Their nuptial feast with wise Penelopé. ‭ _The ready weapon, when the blood is up, ‭ Doubles the uproar heighten'd by the cup. ‭ Wrath's means for act, curb all the ways ye can, ‭ As loadstones draw the steel, so steel draws man._ ‭ Retain these words; nor what is good think, thus ‭ Receiv'd at second hand, superfluous." ‭ The son, obeying, did Euryclea call, ‭ And bade her shut in th' utter porches all ‭ The other women, till himself brought down ‭ His father's arms, which all were overgrown ‭ By his neglect with rust, his father gone, ‭ And he too-childish to spend thoughts upon ‭ Those manly implements; but he would now ‭ Reform those young neglects, and th' arms bestow ‭ Past reach of smoke. The loving nurse replied: ‭ "I wish, O son, your pow'rs would once provide ‭ For wisdom's habit, see your household were ‭ In thrifty manage, and tend all things there. ‭ But if these arms must down, and ev'ry maid ‭ Be shut in utter rooms, who else should aid ‭ Your work with light?" He answer'd: "This my guest. ‭ There shall no one in my house taste my feast, ‭ Or join in my nave, that shall idly live, [1] ‭ However far hence he his home derive." ‭ He said, and his words stood. The doors she shut ‭ Of that so well-fill'd house. And th' other put ‭ Their thoughts in act; best shields, helms, sharpen'd lances, ‭ Brought down; and Pallas before both advances ‭ A golden cresset, that did cast a light ‭ As if the Day sat in the throne of Night. ‭ When, half-amaz'd, the prince said: "O my father, ‭ Mine eyes my soul's pow'rs all in wonder gather, ‭ For though the walls, and goodly wind-beams here, ‭ All all these pillars, that their heads so rear, ‭ And all of fir, they seem yet all of fire. ‭ Some God is surely with us." His wise sire ‭ Bade peace, and keep the counsels of the Gods, ‭ Nor ask a word: "These Pow'rs, that use abodes ‭ Above the stars, have pow'r from thence to shine ‭ Through night and all shades to earth's inmost mine. ‭ Go thou for sleep, and leave me here to wake ‭ The women, and the Queen whose heart doth ache ‭ To make inquiry for myself of me." ‭ He went to sleep where lights did endlessly ‭ Burn in his night-rooms; where he feasted rest, ‭ Till day's fair weed did all the world invest. ‭ Thus was divine Ulysses left alone ‭ With Pallas, plotting foul confusion ‭ To all the Wooers. Forth then came the Queen; ‭ Phœbe, with golden Cytherea seen, ‭ Her port presented. Whom they set a chair ‭ Aside the fire, the fashion circular, ‭ The substance silver and rich elephant; ‭ Whose fabric did the cunning finger vaunt ‭ Of great Icmalius, who besides had done ‭ A footstool for her that did suit her throne, ‭ On which they cast an ample skin, to be ‭ The cushion for her other royalty. ‭ And there she sat; about whom came her maids, ‭ Who brought upon a table store of breads, ‭ And bowls that with the Wooers' wine were crown'd. ‭ The embers then they cast upon the ground ‭ From out the lamps, and other fuel added, ‭ That still with cheerful flame the sad house gladded. ‭ Melantha seeing still Ulysses there, ‭ Thus she held out her spleen: "Still, stranger, here? ‭ Thus late in night? To see what ladies do? ‭ Avaunt you, wretch, hence, go without doors, go; ‭ And quickly, too, lest ye be singed away ‭ With burning firebrands." He, thus seeing their fray ‭ Continued by her with such spleen, replied: ‭ "Minion! What makes your angry blood thus chide ‭ My presence still? Is it because you see ‭ I shine not in your wanton bravery, ‭ But wear these rags? It fits the needy fate ‭ That makes me beg thus of the common state. ‭ Such poor souls, and such beggars, yet are men; ‭ And ev'n my mean means means had to maintain ‭ A wealthy house, and kept a manly press, ‭ Was counted blessed, and the poor access ‭ Of any beggar did not scorn, but feed, ‭ With often hand, and any man of need ‭ Reliev'd as fitted; kept my servants, too, ‭ Not few, but did with those additions go ‭ That call choice men _The Honest_, who are styl'd ‭ The rich, the great. But what such great ones build ‭ Jove oft pulls down, as thus he ruin'd me; ‭ His will was such, which is his equity. ‭ And therefore, woman, bear you fitting hand ‭ On your behaviour, lest your spirit thus mann'd, ‭ And cherish'd with your beauties, when they wane, ‭ Comes down, your pride now being then your bane; ‭ And in the mean space shun the present danger, ‭ Lest your bold fashion breed your sov'reign's anger, ‭ Or lest Ulysses come, of whom ev'n yet ‭ Hope finds some life in Fate. Or, be his seat ‭ Amongst the merely ruin'd, yet his son, ‭ Whose life's heat Phœbus saves, is such a one ‭ As can discover who doth well deserve ‭ Of any woman here his years now serve." ‭ The Queen gave ear, and thus suppress'd the flame: ‭ "Thou quite without a brow, past female shame, ‭ I hear thy monstrous boldness, which thy head ‭ Shall pay me pains for. Thou hast heard it said, ‭ And from myself too, and ev'ry part ‭ Thy knowledge serves thee, that, to ease my heart ‭ So punish'd in thy witness, my desire ‭ Dwelt on this stranger, that I might inquire ‭ My lost friend's being. But 'tis ever tried, ‭ _Both man and God are still forgot with pride._ ‭ Eurynomé, bring here this guest a seat, ‭ And cushion on it, that we two may treat ‭ Of the affair in question. Set it near, ‭ That I may softly speak, yet he well hear." ‭ She did this little freely; and he sat ‭ Close by the Queen, who ask'd him, Whence, and what ‭ He was himself? And what th' inhabited place ‭ Where liv'd his parents? Whence he fetch'd his race? ‭ "O woman," he replied, "with whom no man, ‭ That moves in earth's unbounded circle, can ‭ Maintain contention for true honour giv'n, ‭ Whose fame hath reach'd the fairly-flowing heav'n, ‭ Who, like a never-ill-deserving king, ‭ That is well-spoke of, first, for worshipping, ‭ And striving to resemble God in empire; ‭ Whose equal hand impartially doth temper ‭ Greatness and Goodness; to whom therefore bears ‭ The black earth store of all grain, trees confers ‭ Cracking with burthen, long-liv'd herds creates, ‭ All which the sea with her sorts emulates; ‭ And all this feeds beneath his pow'rful hand ‭ Men, valiant, many, making strong his land ‭ With happy lives led; nothing else the cause ‭ Of all these blessings, but well-order'd laws; ‭ Like such a king are you, in love, in fame, ‭ And all the bliss that deifies a dame. ‭ And therefore do not mix this with a moan ‭ So wretched as is now in question; ‭ Ask not my race nor country, lest you fill ‭ My heart yet fuller with repeated ill; ‭ For I must follow it with many tears, ‭ Though 'tis not seemly to sit wounding ears ‭ In public roofs with our particular life. ‭ _Time's worst expense is still-repeated grief._ ‭ I should be irksome to your ladies here, ‭ And you yourself would say you urg'd your ear ‭ To what offends it, my still-broken eyne ‭ Supposing wounded with your too-much wine." ‭ "Stranger," said she, "you fear your own excess ‭ With giving me too great a nobleness. ‭ The Gods my person, beauty, virtue too, ‭ Long since subverted, when the Ilion woe ‭ The Greek design attempted; in which went ‭ My praise and honour. In his government ‭ Had I deserv'd your utmost grace, but now ‭ Sinister Deity makes dishonour woo, ‭ In show of grace, my ruin. All the peers ‭ Sylvan Zacynthus, and Dulichius, spheres, ‭ Samos and Ithaca, strange strifes have shown ‭ To win me, spending on me all mine own; ‭ Will wed me, in my spite; and these are those ‭ That take from me all virtue to dispose ‭ Or guest or suppliant, or take any course ‭ Amongst my heralds, that should all disburse, ‭ To order anything. Though I need none ‭ To give me grief at home, abroad errs one ‭ That my veins shrink for, whom these holding gone, ‭ Their nuptials hasten, and find me as slow. ‭ Good spirits prompted me to make a show ‭ Of undertaking a most curious task, ‭ That an unmeasur'd space of time would ask; ‭ Which they enduring long would often say, ‭ When ends thy work? I soon had my delay, ‭ And pray'd their stay; for though my lord were dead, ‭ His father's life yet matter ministred ‭ That must employ me; which, to tell them true, ‭ Was that great work I nam'd. For now near drew ‭ Laertes' death, and on my hand did lie ‭ His funeral-robe, whose end, being now so nigh, ‭ I must not leave, and lose so much begun, ‭ The rather lest the Greek dames might be won ‭ To tax mine honour, if a man so great ‭ Should greet his grave without his winding sheet. ‭ Pride made them credulous, and I went on; ‭ When whatsoever all the day had done ‭ I made the night help to undo again, ‭ Though oil and watch it cost, and equal pain. ‭ Three years my wit secur'd me undiscern'd, ‭ Yet, when the fourth came, by my maids discern'd, ‭ False careless wenches, how they were deluded; ‭ When, by my light discern'd, they all intruded, ‭ Used threat'ning words, and made me give it end; ‭ And then could I to no more length extend ‭ My linger'd nuptials; not a counsel more ‭ Was to be stood upon; my parents bore ‭ Continual hand on me to make me wed; ‭ My son grew angry that so ruinéd ‭ His goods were by them. He is now a man ‭ Wise in a great degree, and one that can ‭ Himself give order to his household fare; ‭ And Jove give equal glory to his care. ‭ But thus you must not pass me; I must know, ‭ It may be for more end, from whence doth grow ‭ Your race and you; for I suppose you none ‭ Sprung of old oak, or justled out of stone." ‭ He answer'd: "O Ulysses' rev'rend wife! ‭ Yet hold you purpose to inquire my life? ‭ I'll tell you, though it much afflict me more ‭ Than all the sorrows I have felt before. ‭ As worthily it may, since so long time ‭ As I have wander'd from my native clime, ‭ Through human cities, and in suff'rance still, ‭ To rip all wounds up, though of all their ill ‭ I touch but part, must actuate all their pain. ‭ But, ask you still, I'll tell, though still sustain. ‭ In middle of the sable sea there lies ‭ An isle call'd Crete, a ravisher of eyes, ‭ Fruitful, and mann'd with many an infinite store; ‭ Where ninety cities crown the famous shore, ‭ Mix'd with all-languag'd men. There Greeks survive, ‭ There the great-minded Eteocretans live, ‭ There the Dorensians never out of war, ‭ The Cydons there, and there the singular ‭ Pelasgian people. There doth Cnossus stand, ‭ That mighty city, where had most command ‭ Great Jove's disciple, Minos, who nine years ‭ Conferr'd with Jove, both great familiars ‭ In mutual counsels. And this Minos' son, ‭ The mighty-minded king Deucalion, ‭ Was sire to me and royal Idomen, ‭ Who with Atrides went to Ilion then, ‭ My elder brother and the better man, ‭ My name Aethon. At that time began ‭ My knowledge of Ulysses, whom my home ‭ Receiv'd with guest-rites. He was thither come ‭ By force of weather, from the Malean coast ‭ But new got off, where he the navy lost, ‭ Then under sail for Troy, and wind-bound lay ‭ Long in Amnisus; hardly got away ‭ From horrid storms, that made him anchor there, ‭ In havens that sacred to Lucina were, ‭ Dreadful and dang'rous, in whose bosom crept ‭ Lucina's cavern. But in my roof slept ‭ Ulysses, shor'd in Crete; who first inquir'd ‭ For royal Idomen, and much desir'd ‭ To taste his guest-rites, since to him had been ‭ A welcome guest my brother Idomen. ‭ The tenth or 'leventh light on Ulysses shin'd ‭ In stay at Crete, attending then the wind ‭ For threaten'd Ilion. All which time my house ‭ With love and entertainments curious ‭ Embrac'd his person, though a number more ‭ My hospitable roofs receiv'd before, ‭ His men I likewise call'd, and from the store ‭ Allow'd them meal and heat-exciting wine, ‭ And oxen for their slaughter, to confine ‭ In my free hand the utmost of their need. ‭ Twelve days the Greeks stay'd, ere they got them freed, ‭ A gale so bitter blew out of the north, ‭ That none could stand on earth, being tumbled forth ‭ By some stern God. But on the thirteenth day ‭ The tempest ceas'd, and then went Greeks their way." ‭ Thus many tales Ulysses told his wife, ‭ At most but painting, yet most like the life; ‭ Of which her heart such sense took through her ears, ‭ It made her weep as she would turn to tears. ‭ And as from off the mountains melts the snow, ‭ Which Zephyr's breath conceal'd, but was made flow ‭ By hollow Eurus, which so fast pours down, ‭ That with their torrent floods have overflown; ‭ So down her fair cheeks her kind tears did glide, ‭ Her miss'd lord mourning set so near her side. ‭ Ulysses much was mov'd to see her mourn, ‭ Whose eyes yet stood as dry as iron or horn ‭ In his untroubled lids, which in his craft ‭ Of bridling passion he from issue saft. ‭ When she had giv'n her moan so many tears, ‭ That now 'twas satiate, her yet loving fears ‭ Ask'd thus much further: "You have thus far tried ‭ My love's credulity, but if gratified ‭ With so long stay he was with you, you can ‭ Describe what weed he wore, what kind of man ‭ Both he himself was, and what followers ‭ Observ'd him there." "Alas," said he, "the years ‭ Have grown so many since--this making now ‭ Their twentieth revolution--that my show ‭ Of these slight notes will set my memory sore, ‭ But, to my now remembrance, this he wore: ‭ A double purple robe, drawn close before ‭ With golden buttons, plaited thick, and bore ‭ A facing where a hundred colours shin'd. ‭ About the skirts a hound a freckled hind ‭ In full course hunted; on the fore skirts, yet, ‭ He pinch'd and pull'd her down, when with her feet, ‭ And all her force, she struggled hard for flight. ‭ Which had such life in gold, that to the sight ‭ It seem'd the hind itself for ev'ry hue, ‭ The hound and all so answering the view, ‭ That all admir'd all. I observ'd beside ‭ His inner weed, so rarely beautified ‭ That dumb amaze it bred, and was as thin ‭ As any dry and tender onion skin; ‭ As soft 'twas, too, and glister'd like the sun. ‭ The women were to loving wonder won ‭ By him and by his weeds. But, by the way, ‭ You must excuse me, that I cannot say ‭ He brought this suit from home, or had it there ‭ Sent for some present, or, perhaps, elsewhere ‭ Receiv'd it for his guest-gift; for your lord ‭ Had friends not few, the fleet did not afford ‭ Many that had not fewer. I bestow'd ‭ A well-edg'd sword on him, a robe that flow'd ‭ In folds and fulness, and did reach his feet, ‭ Of richest purple; brought him to his fleet ‭ With all my honour; and besides, to add ‭ To all this sifted circumstance, he had ‭ A herald there, in height a little more ‭ Put from the earth, that thicker shoulders wore, ‭ A swarth complexion and a curléd head, ‭ His name Eurybates; and much in stead ‭ He stood your king, employ'd in most command, ‭ Since most of all his mind could understand." ‭ When all these signs she knew for chiefly true, ‭ Desire of moan upon her beauties grew, ‭ And yet, ev'n that desire suffic'd, she said: ‭ "Till this, my guest, a wretched state array'd ‭ Your ill-us'd person, but from this hour forth ‭ You shall be honour'd, and find all the worth ‭ That fits a friend. Those weeds these hands bestow'd ‭ From out my wardrobe; those gold buttons sew'd ‭ Before for closure and for ornament. ‭ But never more must his return present ‭ The person that gave those adornments state; ‭ And therefore, under an abhorréd fate, ‭ Was he induc'd to feed the common fame, ‭ To visit vile Troy, ay too vile to name." ‭ "No more yet mourn," said he, "nor thus see pin'd ‭ Your lovely person. _Weeping wastes the mind._ ‭ And yet I blame you not; for any dame ‭ That weds one young, and brings to him his name, ‭ Whatever man he is, will mourn his loss. ‭ Much more respectful then must show your woes ‭ That weep thus for Ulysses, who, Fame says, ‭ Was equal with the Gods in all his ways. ‭ But where no cause is there must be no moan, ‭ And therefore hear me, my relation ‭ Shall lay the clear truth naked to your view: ‭ I heard amongst the Thesprots for most true, ‭ That lord Ulysses liv'd, and stood just now ‭ On his return for home; that wealth did flow ‭ In his possession, which he made not known, ‭ But begg'd amongst the people, since alone ‭ He quite was left, for all his men were lost ‭ In getting off from the Trinacrian coast; ‭ Jove and the Sun was wroth with them for rape ‭ Made of his oxen, and no man let 'scape ‭ The rugged deeps of Neptune; only he, ‭ The ship's keel only keeping, was by sea ‭ Cast on the fair Phæacian continent, ‭ Where men survive that are the Gods' descent, ‭ And like a God receiv'd him, gave him heaps ‭ Of wealthy gifts, and would conduct his steps ‭ Themselves safe home; which he might long ago ‭ His pleasure make, but profit would not so. ‭ He gather'd going, and had mighty store ‭ Of gold in safeguard; so beyond the shore ‭ That common sails kept, his high flood of wit ‭ Bore glorious top, and all the world for it ‭ Hath far exceeded. All this Phædon told, ‭ That doth the sceptre of Thesprotia hold, ‭ Who swore to me, in household sacrifice, ‭ The ship was launch'd, and men to man the prise, ‭ That soon should set him on his country earth, ‭ Show'd me the goods, enough to serve the birth ‭ That in the tenth age of his seed should spring, ‭ Yet in his court contain'd. But then the king, ‭ Your husband, for Dodona was in way, ‭ That from th' Oraculous Oak he might display ‭ Jove's will what course for home would best prevail, ‭ To come in pomp, or bear a secret sail. ‭ But me the king dispatch'd in course before, ‭ A ship then bound for the Dulichian shore. ‭ So thus you see his safety whom you mourn; ‭ Who now is passing near, and his return ‭ No more will punish with delays, but see ‭ His friends and country. All which truth to thee ‭ I'll seal with sacred oath. Be witness, Jove, ‭ Thou first and best of all the thron'd above! ‭ And thou house of the great Laertes' heir, ‭ To whose high roofs I tender my repair, ‭ That what I tell the Queen event shall crown! ‭ This year Ulysses shall possess his own, ‭ Nay ere the next month ends shall here arrive, ‭ Nay, ere it enters, here abide alive!" ‭ "O may this prove," said she; "gifts, friendship, then ‭ Should make your name the most renown'd of men. ‭ But 'tis of me receiv'd, and must so sort, ‭ That nor my lord shall ever see his court, ‭ Nor you gain your deduction thence, for now ‭ The alter'd house doth no such man allow ‭ As was Ulysses, if he ever were, ‭ To entertain a rev'rend passenger, ‭ And give him fair dismission. But, maids, see ‭ Ye bathe his feet, and then with tapestry, ‭ Best sheets and blankets, make his bed, and lay ‭ Soft waistcoats by him, that, lodg'd warm, he may ‭ Ev'n till the golden-seated morning's ray ‭ Enjoy good rest; and then, with her first light, ‭ Bathe, and give alms, that cherish'd appetite ‭ He may apply within our hall, and sit ‭ Safe by Telemachus. Or, if th' unfit ‭ And harmful mind of any be so base ‭ To grieve his age again, let none give grace ‭ Of doing any deed he shall command, ‭ How wroth soever, to his barbarous hand. ‭ For how shall you, guest, know me for a dame ‭ That pass so far, nay, turn and wind the fame ‭ Of other dames for wisdom, and the frame ‭ Of household usage, if your poor thin weeds ‭ I let draw on you want, and worser deeds, ‭ That may, perhaps, cause here your latest day? ‭ _The life of man is short and flies away._ ‭ And if the ruler's self of households be ‭ Ungentle, studying inhumanity, ‭ The rest prove worse, but he bears all the blame; ‭ All men will, living, vow against his name ‭ Mischiefs and miseries, and, dead, supply ‭ With bitter epitaphs his memory. ‭ But if himself be noble--noble things ‭ Doing and knowing--all his underlings ‭ Will imitate his noblesse, and all guests ‭ Give it, in many, many interests." ‭ "But, worthiest Queen," said he, "where you command ‭ Baths and rich beds for me, I scorn to stand ‭ On such state now nor ever thought it yet, ‭ Since first I left the snowy hills of Crete. ‭ When once I fell a-shipboard those thoughts fled; ‭ I love to take now, as long since, my bed. ‭ Though I began the use with sleepless nights, ‭ I many a darkness with right homely rites ‭ Have spent ere this hour, and desir'd the morn ‭ Would come, and make sleep to the world a scorn. ‭ Nor run these dainty baths in my rude head; ‭ Nor any handmaid, to your service bred, ‭ Shall touch my ill-kept feet, unless there live ‭ Some poor old drudge here, that hath learn'd to give ‭ Old men good usage, and no work will fly, ‭ As having suffer'd ill as much as I. ‭ But if there live one such in your command, ‭ I will not shame to give my foot her hand." ‭ She gave this answer: "O my lovéd guest, ‭ There never enter'd these kind roofs for rest ‭ Stranger or friend that so much wisdom laid ‭ In gage for guest-rites, as your lips have paid. ‭ There lives an old maid in my charge that knows ‭ The good you speak of by her many woes; ‭ That nourish'd and brought up, with curious care, ‭ Th' unhappy man; your old familiar, ‭ Ev'n since his mother let him view the light, ‭ And oft hath felt in her weak arms his weight; ‭ And she, though now much weaker, shall apply ‭ Her maiden service to your modesty. ‭ Euryclea, rise, and wash the feet of one ‭ That is of one age with your sov'reign gone, ‭ Such hands, such feet hath, though of alter'd grace. ‭ _Much grief in men will bring on change apace."_ ‭ She, from her aged slumber wak'd, did clear ‭ Her heavy eyes, and instantly, to hear ‭ Her sov'reign's name, had work enough to dry ‭ Her cheeks from tears, and to his memory ‭ These moans did offer: "O my son," said she, ‭ "I never can take grief enough for thee, ‭ Whom Goodness hurts, and whom ev'n Jove's high spleen, ‭ Since thou art Jove-like, hates the most of men. ‭ For none hath offer'd him so many thighs, ‭ Nor such whole hecatombs of sacrifice, ‭ Fat and selected, as thy zeal hath done; ‭ For all, but praying that thy noble son, ‭ Thy happy age might see at state of man. ‭ And yet hath Jove with mists Cimmerian ‭ Put out the light of his returning day. ‭ And as yourself, O father, in your way ‭ Took these fair roofs for hospitable rites, ‭ Yet find, for them, our dogged women's spites; ‭ So he, in like course, being driven to proof, ‭ Long time ere this, what such a royal roof ‭ Would yield his mis'ries, found such usage there. ‭ And you, now flying the foul language here, ‭ And many a filthy fact of our fair dames, ‭ Fly me like them, and put on causeless shames ‭ To let me cleanse your feet. For not the cause ‭ The Queen's command yields is the pow'r that draws ‭ My will to wash your feet, but what I do ‭ Proceeds from her charge and your rev'rence too; ‭ Since I in soul am stricken with a ruth ‭ Of your distresses, and past show of truth; [2] ‭ Your strangeness claiming little interest ‭ In my affections. And yet many a guest ‭ Of poor condition hath been harbour'd here, ‭ But never any did so right appear ‭ Like king Ulysses as yourself, for state ‭ Both of your stature, voice, and very gait." ‭ "So all have said," said he, "that ever yet ‭ Had the proportions of our figures met ‭ In their observance; so right your eye ‭ Proves in your soul your judging faculty." ‭ Thus took she up a caldron brightly scour'd, ‭ To cleanse his feet in; and into it pour'd ‭ Store of cold wave, which on the fire she set; ‭ And therein bath'd, being temperately heat, ‭ Her sov'reign's feet. Who turn'd him from the light, ‭ Since suddenly he doubted her conceit, ‭ So rightly touching at his state before, ‭ A scar now seeing on his foot, that bore ‭ An old note, to discern him, might descry ‭ The absolute truth; which, witness'd by her eye, ‭ Was straight approv'd. He first receiv'd this sore ‭ As in Parnassus' tops a white-tooth'd boar ‭ He stood in chase withal, who struck him there, ‭ At such time as he liv'd a sojourner ‭ With his grandsire, Autolycus; who th' art ‭ Of theft and swearing (not out of the heart, ‭ But by equivocation) first adorn'd ‭ Your witty man withal, and was suborn'd ‭ By Jove's descent, ingenious Mercury, ‭ Who did bestow it, since so many a thigh ‭ Of lambs and kids he had on him bestow'd ‭ In sacred flames, who therefore when he vow'd ‭ Was ever with him. And this man impos'd ‭ Ulysses' name, the light being first disclos'd ‭ To his first sight then, when his grandsire came ‭ To see the then preferrer of his fame, ‭ His lovéd daughter. The first supper done, ‭ Euryclea put in his lap her son, ‭ And pray'd him to bethink and give his name, ‭ Since that desire did all desires inflame. ‭ "Daughter and son-in-law," said he, "let then ‭ The name that I shall give him stand with men. ‭ Since I arriv'd here at the hour of pain, ‭ In which mine own kind entrails did sustain ‭ Moan for my daughter's yet unended throes, ‭ And when so many men's and women's woes, ‭ In joint compassion met of human birth, ‭ Brought forth t' attend the many-feeding earth, ‭ Let Odyssëus be his name, as one [3] ‭ Expos'd to just constraint of all men's moan. ‭ When here at home he is arriv'd at state ‭ Of man's first youth he shall initiate ‭ His practis'd feet in travel made abroad, ‭ And to Parnassus, where mine own abode ‭ And chief means lie, address his way, where I ‭ Will give him from my open'd treasury ‭ What shall return him well, and fit the fame ‭ Of one that had the honour of his name." ‭ For these fair gifts he went, and found all grace ‭ Of hands and words in him and all his race. ‭ Amphithea, his mother's mother, too, ‭ Applied her to his love, withal, to do ‭ In grandame's welcomes, both his fair eyes kist, ‭ And brows; and then commanded to assist ‭ Were all her sons by their respected sire ‭ In furnishing a feast, whose ears did fire ‭ Their minds with his command; who home straight led ‭ A five-years-old male ox, fell'd, slew, and flay'd, ‭ Gather'd about him, cut him up with art, ‭ Spitted, and roasted, and his ev'ry part ‭ Divided orderly. So all the day ‭ They spent in feast; no one man went his way ‭ Without his fit fill. When the sun was set, ‭ And darkness rose, they slept, till day's fire het ‭ Th' enlighten'd earth; and then on hunting went ‭ Both hounds and all Autolycus' descent. ‭ In whose guide did divine Ulysses go, ‭ Climb'd steep Parnassus, on whose forehead grow ‭ All sylvan offsprings round. And Soon they reach'd ‭ The concaves, whence air's sounding vapours fetch'd ‭ Their loud descent. As soon as any sun ‭ Had from the ocean, where his waters run ‭ In silent deepness, rais'd his golden head, ‭ The early huntsmen all the hill had spread, ‭ Their hounds before them on the searching trail, ‭ They near, and ever eager to assail: ‭ Ulysses brandishing a lengthful lance, ‭ Of whose first flight he long'd to prove the chance. ‭ Then found they lodg'd a boar of bulk extreme, ‭ In such a queach as never any beam ‭ The sun shot pierc'd, nor any pass let find ‭ The moist impressions of the fiercest wind, ‭ Nor any storm the sternest winter drives, ‭ Such proof it was; yet all within lay leaves ‭ In mighty thickness; and through all this flew ‭ The hounds' loud mouths. The sounds the tumult threw, ‭ And all together, rous'd the boar, that rush'd ‭ Amongst their thickest, all his bristles push'd ‭ From forth his rough neck, and with flaming eyes ‭ Stood close, and dar'd all. On which horrid prise ‭ Ulysses first charg'd; whom above the knee ‭ The savage struck, and rac'd it crookedly ‭ Along the skin, yet never reach'd the bone. ‭ Ulysses' lance yet through him quite was thrown, ‭ At his right shoulder ent'ring, at his left ‭ The bright head passage to his keenness cleft, ‭ And show'd his point gilt with the gushing gore. ‭ Down in the dust fell the extended boar, ‭ And forth his life flew. To Ulysses round ‭ His uncle drew; who, woeful for his wound, ‭ With all art bound it up, and with a charm ‭ Stay'd straight the blood, went home, and, when the harm ‭ Receiv'd full cure, with gifts, and all event ‭ Of joy and love to his lov'd home they sent ‭ Their honour'd nephew; whose return his sire ‭ And rev'rend mother took with joys entire, ‭ Enquir'd all passages, all which he gave ‭ In good relation, nor of all would save ‭ His wound from utt'rance; by whose scar he came ‭ To be discover'd by this aged dame. ‭ Which when she cleansing felt, and noted well, ‭ Down from her lap into the caldron fell ‭ His weighty foot, that made the brass resound, ‭ Turn'd all aside, and on th' embrewéd ground ‭ Spilt all the water. Joy and grief together ‭ Her breast invaded; and of weeping weather ‭ Her eyes stood full; her small voice stuck within ‭ Her part expressive; till at length his chin ‭ She took and spake to him: "O son," said she, ‭ "Thou art Ulysses, nor canst other be; ‭ Nor could I know thee yet, till all my king ‭ I had gone over with the warméd spring." ‭ Then look'd she for the Queen to tell her all; ‭ And yet knew nothing sure, though nought could fall ‭ In compass of all thoughts to make her doubt, ‭ Minerva that distraction struck throughout ‭ Her mind's rapt forces that she might not tell. ‭ Ulysses, noting yet her aptness well, ‭ With one hand took her chin, and made all show ‭ Of favour to her, with the other drew ‭ Her offer'd parting closer, ask'd her why ‭ She, whose kind breast had nurs'd so tenderly ‭ His infant life, would now his age destroy, ‭ Though twenty years had held him from the joy ‭ Of his lov'd country? But, since only she, ‭ God putting her in mind, now knew 'twas he, ‭ He charg'd her silence, and to let no ear ‭ In all the court more know his being there, ‭ Lest, if God gave into his wreakful hand ‭ Th' insulting Wooers' lives, he did not stand ‭ On any partial respect with her, ‭ Because his nurse, and to the rest prefer ‭ Her safety therefore, but, when they should feel ‭ His punishing finger, give her equal steel. ‭ "What words," said she, "fly your retentive pow'rs? ‭ You know you lock your counsels in your tow'rs ‭ In my firm bosom, and that I am far ‭ From those loose frailties. Like an iron bar, ‭ Or bolt of solid'st stone, I will contain; ‭ And tell you this besides; that if you gain, ‭ By God's good aid, the Wooers' lives in yours, ‭ What dames are here their shameless paramours; ‭ And have done most dishonour to your worth, ‭ My information well shall paint you forth." ‭ "It shall not need," said he, "myself will soon, ‭ While thus I mask here, set on ev'ry one ‭ My sure observance of the worst and best. ‭ Be thou then silent, and leave God the rest." ‭ This said, the old dame for more water went, ‭ The rest was all upon the pavement spent ‭ By known Ulysses' foot. More brought, and he ‭ Supplied beside with sweetest ointments, she ‭ His seat drew near the fire, to keep him warm, ‭ And with his piec'd rags hiding close his harm. ‭ The Queen came near, and said: "Yet, guest, afford ‭ Your further patience, till but in a word ‭ I'll tell my woes to you; for well I know ‭ That Rest's sweet hour her soft foot orders now, ‭ When all poor men, how much soever griev'd, ‭ Would gladly get their woe-watch'd pow'rs reliev'd. ‭ But God hath giv'n my grief a heart so great ‭ It will not down with rest, and so I set ‭ My judgment up to make it my delight. ‭ All day I mourn, yet nothing let the right ‭ I owe my charge both in my work and maids; ‭ And when the night brings rest to others' aids ‭ I toss my bed; Distress, with twenty points, ‭ Slaught'ring the pow'rs that to my turning joints ‭ Convey the vital heat. And as all night ‭ Pandareus' daughter, poor Edone, sings, ‭ Clad in the verdure of the yearly springs, ‭ When she for Itylus, her lovéd son, ‭ By Zethus' issue in his madness done ‭ To cruel death, pours out her hourly moan, ‭ And draws the ears to her of ev'ry one; ‭ So flows my moan that cuts in two my mind, ‭ And here and there gives my discourse the wind, ‭ Uncertain whether I shall with my son ‭ Abide still here, the safe possession ‭ And guard of all goods, rev'rence to the bed ‭ Of my lov'd lord, and to my far-off spread ‭ Fame with the people, putting still in use, ‭ Or follow any best Greek I can chuse ‭ To his fit house, with treasure infinite, ‭ Won to his nuptials. While the infant plight ‭ And want of judgment kept my son in guide, ‭ He was not willing with my being a bride, ‭ Nor with my parting from his court; but now, ‭ Arriv'd at man's state, he would have me vow ‭ My love to some one of my Wooers here, ‭ And leave his court; offended that their cheer ‭ Should so consume his free possessions. ‭ To settle then a choice in these my moans, ‭ Hear and expound a dream that did engrave ‭ My sleeping fancy: Twenty geese I have, ‭ All which, me thought, mine eye saw tasting wheat ‭ In water steep'd, and joy'd to see them eat; ‭ When straight a crook-beak'd eagle from a hill ‭ Stoop'd, and truss'd all their necks, and all did kill; ‭ When, all left scatter'd on the pavement there, ‭ She took her wing up to the Gods' fair sphere. ‭ I, ev'n amid my dream, did weep and mourn ‭ To see the eagle, with so shrewd a turn, ‭ Stoop my sad turrets; when, methought, there came ‭ About my mournings many a Grecian dame, ‭ To cheer my sorrows; in whose most extreme ‭ The hawk came back, and on the prominent beam ‭ That cross'd my chamber fell, and us'd to me ‭ A human voice, that sounded horribly, ‭ And said: 'Be confident, Icarius' seed, ‭ This is no dream, but what shall chance indeed. ‭ The geese the Wooers are, the eagle, I, ‭ Was heretofore a fowl, but now imply ‭ Thy husband's being, and am come to give ‭ The Wooers' death, that on my treasure live.' ‭ With this sleep left me, and my waking way ‭ I took, to try if any violent prey ‭ Were made of those my fowls, which well enough ‭ I, as before, found feeding at their trough ‭ Their yoted wheat." "O woman," he replied, ‭ "Thy dream can no interpretation bide ‭ But what the eagle made, who was your lord, ‭ And said himself would sure effect afford ‭ To what he told you; that confusion ‭ To all the Wooers should appear, and none ‭ Escape the fate and death he had decreed." ‭ She answer'd him: "O guest, these dreams exceed ‭ The art of man t' interpret; and appear ‭ Without all choice or form; nor ever were ‭ Perform'd to all at all parts. But there are ‭ To these light dreams, that like thin vapours fare, ‭ Two two-leav'd gates, the one of ivory, ‭ The other horn. Those dreams, that fantasy ‭ Takes from the polish'd ivory port, delude ‭ The dreamer ever, and no truth include; ‭ Those, that the glitt'ring horn-gate lets abroad, ‭ Do evermore some certain truth abode. ‭ But this my dream I hold of no such sort ‭ To fly from thence; yet, whichsoever port ‭ It had access from, it did highly please ‭ My son and me. And this my thoughts profess: ‭ That day that lights me from Ulysses' court ‭ Shall both my infamy and curse consort. ‭ I, therefore, purpose to propose them now, ‭ In strong contention, Ulysses' bow; ‭ Which he that eas'ly draws, and from his draft ‭ Shoots through twelve axes (as he did his shaft, ‭ All set up in a row, and from them all ‭ His stand-far-off kept firm) my fortunes shall ‭ Dispose, and take me to his house from hence, ‭ Where I was wed a maid, in confluence ‭ Of feast and riches; such a court here then ‭ As I shall ever in my dreams retain." ‭ "Do not," said he, "defer the gameful prize, ‭ But set to task their importunities ‭ With something else than nuptials; for your lord ‭ Will to his court and kingdom be restor'd ‭ Before they thread those steels, or draw his bow." ‭ "O guest," replied Penelope, "would you ‭ Thus sit and please me with your speech, mine ears ‭ Would never let mine eyelids close their spheres! ‭ But none can live without the death of sleep, ‭ Th' Immortals in our mortal memories keep ‭ Our ends and deaths by sleep, dividing so, ‭ As by the fate and portion of our woe, ‭ Our times spent here, to let us nightly try ‭ That while we live, as much live as we die. ‭ In which use I will to my bed ascend, ‭ Which I bedew with tears, and sigh past end ‭ Through all my hours spent, since I lost my joy ‭ For vile, lewd, never-to-be-naméd, Troy, ‭ Yet there I'll prove for sleep, which take you here, ‭ Or on the earth, if that your custom were, ‭ Or have a bed, dispos'd for warmer rest." ‭ Thus left she with her ladies her old guest, ‭ Ascended her fair chamber, and her bed, ‭ Whose sight did ever duly make her shed ‭ Tears for her lord; which still her eyes did steep, ‭ Till Pallas shut them with delightsome sleep. ‭ THE END OF THE NINETEENTH BOOK OF HOMER'S ODYSSEYS. ‭[1] _Χοὶνικος ἅπτηται,_ they will needs turn this, _quadram_ (for ‭_modium) gustet._ Though the words bear no such signification, ‭but give a proverb then in use repetition, which was: _he shall not ‭join or make a spoke in the nave of my chariot, or chariot-wheel. ‭Χοίνικον,_ or _χοίνικις,_ signifying _modiolus rotæ,_ and _ἅπτω, ‭recto._ ‭[2] Intending with truth itself, not his show only. ‭[3] Autolycus gives his grandchild Ulysses his name: from whence ‭the Odysseys is derived, _'Οδυσσεύς,_ derived of _ὀδύζομαι, ex ‭ὀδύνη factum;_ signifying _dolorem proprie corporis, nam ira ex ‭dolore oritur._ ‭ THE TWENTIETH BOOK OF HOMER'S ODYSSEYS ‭ THE ARGUMENT ‭ Ulysses, in the Wooers' beds, ‭ Resolving first to kill the maids. ‭ That sentence giving off, his care ‭ For other objects doth prepare. ‭ ANOTHER ARGUMENT ‭ _ψ._ ‭ Jove's thunder chides, ‭ But cheers the King, ‭ The Wooers' prides ‭ Discomfiting. ‭ Ulysses in the entry laid his head, ‭ And under him an ox-hide newly-flay'd, ‭ Above him sheep-fells store; and over those ‭ Eurynomé cast mantles. His repose ‭ Would bring no sleep yet, studying the ill ‭ He wish'd the Wooers; who came by him still ‭ With all their wenches, laughing, wantoning, ‭ In mutual lightness; which his heart did sting, ‭ Contending two ways, if, all patience fled, ‭ He should rush up and strike those strumpets dead, ‭ Or let that night be last, and take th' extreme ‭ Of those proud Wooers, that were so supreme ‭ In pleasure of their high-fed fantasies. ‭ His heart did bark within him to surprise ‭ Their sports with spoils; no fell she-mastiff can, ‭ Amongst her whelps, fly eag'rer on a man ‭ She doth not know, yet scents him something near, ‭ And fain would come to please her tooth, and tear, ‭ Than his disdain, to see his roof so fil'd ‭ With those foul fashions, grew within him wild ‭ To be in blood of them. But, finding best ‭ In his free judgment to let passion rest, ‭ He chid his angry spirit, and beat his breast, ‭ And said: "Forbear, my mind, and think on this: ‭ There hath been time when bitter agonies ‭ Have tried thy patience. Call to mind the day ‭ In which the Cyclop, which pass'd manly sway ‭ Of violent strength, devour'd thy friends; thou then ‭ Stood'st firmly bold, till from that hellish den ‭ Thy wisdom brought thee off, when nought but death ‭ Thy thoughts resolv'd on." This discourse did breathe ‭ The fiery boundings of his heart, that still ‭ Lay in that æsture, without end his ill ‭ Yet manly suff'ring. But from side to side ‭ It made him toss apace. You have not tried ‭ A fellow roasting of a pig before ‭ A hasty fire, his belly yielding store ‭ Of fat and blood, turn faster, labour more ‭ To have it roast, and would not have it burn, ‭ Than this and that way his unrest made turn ‭ His thoughts and body, would not quench the fire, ‭ And yet not have it heighten his desire ‭ Past his discretion, and the fit enough ‭ Of haste and speed, that went to all the proof ‭ His well-laid plots, and his exploits requir'd, ‭ Since he, but one, to all their deaths aspir'd. ‭ In this contention Pallas stoop'd from heav'n, ‭ Stood over him, and had her presence giv'n ‭ A woman's form, who sternly thus began: ‭ "Why, thou most sour and wretched-fated man ‭ Of all that breathe, yet liest thou thus awake? ‭ The house in which thy cares so toss and take ‭ Thy quiet up is thine; thy wife is there; ‭ And such a son, as if thy wishes were ‭ To be suffic'd with one they could not mend." ‭ "Goddess," said he, "'tis true; but I contend ‭ To right their wrongs, and, though I be but one, ‭ To lay unhelp'd and wreakful hand upon ‭ This whole resort of impudents, that here ‭ Their rude assemblies never will forbear. ‭ And yet a greater doubt employs my care, ‭ That if their slaughters in my reaches are, ‭ And I perform them, Jove and you not pleas'd, ‭ How shall I fly their friends? And would stand seis'd ‭ Of counsel to resolve this care in me." ‭ "Wretch," she replied, "a friend of worse degree ‭ Might win thy credence, that a mortal were, I ‭ And us'd to second thee, though nothing near ‭ So pow'rful in performance nor in care; ‭ Yet I, a Goddess, that have still had share ‭ In thy achievements, and thy person's guard, ‭ Must still be doubted by thy brain, so hard ‭ To credit anything above thy pow'r; ‭ And that must come from heav'n; if ev'ry hour ‭ There be not personal appearance made, ‭ And aid direct giv'n, that may sense invade. ‭ I'll tell thee, therefore, clearly: If there were ‭ Of divers-languag'd men an army here ‭ Of fifty companies, all driving hence ‭ Thy sheep and oxen, and with violence ‭ Offer'd to charge us, and besiege us round, ‭ Thou shouldst their prey reprise, and them confound. ‭ Let sleep then seize thee. _To keep watch all night ‭ Consumes the spirits, and makes dull the sight."_ ‭ Thus pour'd the Goddess sleep into his eyes, ‭ And reascended the Olympian skies. ‭ When care-and-lineament-resolving sleep ‭ Had laid his temples in his golden steep, ‭ His-wise-in-chaste-wit-worthy wife did rise, ‭ First sitting up in her soft bed, her eyes ‭ Open'd with tears, in care of her estate, ‭ Which now her friends resolv'd to terminate ‭ To more delays, and make her marry one. ‭ Her silent tears then ceas'd, her orison ‭ This Queen of women to Diana made: ‭ "Rev'rend Diana, let thy darts invade ‭ My woeful bosom, and my life deprive, ‭ Now at this instant, or soon after drive ‭ My soul with tempests forth, and give it way ‭ To those far-off dark vaults, where never day ‭ Hath pow'r to shine, and let them cast it down ‭ Where refluent Oceanus doth crown ‭ His curléd head, where Pluto's orchard is, ‭ And entrance to our after miseries. ‭ As such stern whirlwinds ravish'd to that stream ‭ Pandareus' daughters, when the Gods to them ‭ Had reft their parents, and them left alone, ‭ Poor orphan children, in their mansion; ‭ Whose desolate life did Love's sweet Queen incline ‭ To nurse with presséd milk and sweetest wine; ‭ Whom Juno deck'd beyond all other dames ‭ With wisdom's light, and beauty's moving flames; ‭ Whom Phœbe goodliness of stature render'd; ‭ And to whose fair hands wise Minerva tender'd ‭ The loom and needle in their utmost skill; ‭ And while Love's Empress scal'd th' Olympian hill ‭ To beg of lightning-loving Jove (since he ‭ The means to all things knows, and doth decree ‭ Fortunes, infortunes, to the mortal race) ‭ For those poor virgins, the accomplish'd grace ‭ Of sweetest nuptials, the fierce Harpies prey'd ‭ On ev'ry good and miserable maid, ‭ And to the hateful Furies gave them all ‭ In horrid service; yet, may such fate fall ‭ From steep Olympus on my loathéd head, ‭ Or fair-chair'd Phœbe strike me instant dead, ‭ That I may undergo the gloomy shore ‭ To visit great Ulysses' soul, before ‭ I soothe my idle blood and wed a worse. ‭ And yet, beneath how desperate a curse ‭ Do I live now! It is an ill that may ‭ Be well endur'd, to mourn the whole long day, ‭ So night's sweet sleeps, that make a man forget ‭ Both bad and good, in some degree would let ‭ My thoughts leave grieving; but, both day and night, ‭ Some cruel God gives my sad memory sight. ‭ This night, methought, Ulysses grac'd my bed ‭ In all the goodly state with which he led ‭ The Grecian army; which gave joys extreme ‭ To my distress, esteeming it no dream, ‭ But true indeed; and that conceit I had, ‭ That when I saw it false I might be mad. ‭ Such cruel fates command in my life's guide." ‭ By this the morning's orient dews had dyed ‭ The earth in all her colours; when the King, ‭ In his sweet sleep, suppos'd the sorrowing ‭ That she us'd waking in her plaintive bed ‭ To be her mourning, standing by his head, ‭ As having known him there; who straight arose, ‭ And did again within the hall dispose ‭ The carpets and the cushions, where before ‭ They serv'd the seats. The hide without the door ‭ He carried back, and then, with held-up hands, ‭ He pray'd to Him that heav'n and earth commands: ‭ "O Father Jove, if through the moist and dry ‭ You, willing, brought me home, when misery ‭ Had punish'd me enough by your free dooms, ‭ Let some of these within those inner rooms, ‭ Startled with horror of some strange ostent, ‭ Come here, and tell me that great Jove hath bent ‭ Threat'nings without at some lewd men within." ‭ To this his pray'r Jove shook his sable chin, ‭ And thunder'd from those pure clouds that, above ‭ The breathing air, in bright Olympus move. ‭ Divine Ulysses joy'd to hear it roar. ‭ Report of which a woman-miller bore ‭ Straight to his ears; for near to him there ground ‭ Mills for his corn, that twice six women found ‭ Continual motion, grinding barley-meal, ‭ And wheat, man's marrow. Sleep the eyes did seal ‭ Of all the other women, having done ‭ Their usual task; which yet this dame alone ‭ Had scarce giv'n end to, being, of all the rest, ‭ Least fit for labour. But when these sounds prest ‭ Her ears, above the rumbling of her mill, ‭ She let that stand, look'd out, and heav'n's steep hill ‭ Saw clear and temp'rate; which made her (unware ‭ Of giving any comfort to his care ‭ In that strange sign he pray'd for) thus, invoke: ‭ "O King of men and Gods, a mighty stroke ‭ Thy thund'ring hand laid on the cope of stars, ‭ No cloud in all the air; and therefore wars ‭ Thou bidst to some men in thy sure ostent! ‭ Perform to me, poor wretch, the main event, ‭ And make this day the last, and most extreme, ‭ In which the Wooers' pride shall solace them ‭ With whorish banquets in Ulysses' roof, ‭ That, with sad toil to grind them meal enough, ‭ Have quite dissolv'd my knees. Vouchsafe, then, now ‭ Thy thunders may their latest feast foreshow." ‭ This was the boon Ulysses begg'd of Jove, [1] ‭ Which, with his thunder, through his bosom drove ‭ A joy, that this vaunt breath'd: "Why now these men, ‭ Despite their pride, will Jove make pay me pain." ‭ By this had other maids, than those that lay ‭ Mix'd with the Wooers, made a fire like day ‭ Amidst the hearth of the illustrious hall; ‭ And then the Prince, like a Celestial, ‭ Rose from his bed, to his embalm'd feet tied ‭ Fair shoes, his sword about his breast applied, ‭ Took to his hand his sharp-pil'd lance, and met, ‭ Amidst the entry, his old nurse, that set ‭ His haste at sudden stand; to whom he said: ‭ "O, my lov'd nurse, with what grace have you laid ‭ And fed my guest here? Could you so neglect ‭ His age, to lodge him thus? Though all respect ‭ I give my mother's wisdom, I must yet ‭ Affirm it fail'd in this; for she hath set ‭ At much more price a man of much less worth, ‭ Without his person's note, and yet casts forth ‭ With ignominious hands, for his form sake, ‭ A man much better." "Do not faulty make, ‭ Good son, the faultless. He was giv'n his seat ‭ Close to her side, and food till he would eat, ‭ Wine till his wish was serv'd; for she requir'd ‭ His wants, and will'd him all things he desir'd; ‭ Commanded her chief maids to make his bed, ‭ But he, as one whom sorrow only fed ‭ And all infortune, would not take his rest ‭ In bed, and cov'rings fit for any guest, ‭ But in the entry, on an ox's hide ‭ Never at tanner's, his old limbs implied, ‭ In warm sheep-fells; yet over all we cast ‭ A mantle, fitting for a man more grac'd." ‭ He took her answer, left the house, and went, ‭ Attended with his dogs, to sift th' event ‭ Of private plots, betwixt him and his sire ‭ In common counsel. Then the crew entire ‭ Of all the household maids Euryclea bad ‭ Bestir them through the house, and see it clad ‭ In all best form; gave all their parts; and one ‭ She set to furnish ev'ry seat and throne ‭ With needle works, and purple clothes of state; ‭ Another set to scour and cleanse the plate; ‭ Another all the tables to make proud ‭ With porous sponges; others she bestow'd ‭ In all speed to the spring, to fetch from thence ‭ Fit store of water; all at all expence ‭ Of pains she will'd to be; for this to all ‭ Should be a day of common festival, ‭ And not a Wooer now should seek his home, ‭ Elsewhere than there, but all were bid to come ‭ Exceeding early, and be rais'd to heav'n ‭ With all the entertainment could be giv'n. ‭ They heard with greedy ears, and ev'rything ‭ Put straight in practice. Twenty to the spring ‭ Made speed for water; many in the house ‭ Took pains; and all were both laborious ‭ And skill'd in labour; many fell to fell ‭ And cleave their wood; and all did more than well. ‭ Then troop'd the lusty Wooers in; and then ‭ Came all from spring; at their heels loaded men ‭ With slaughter'd brawns, of all the herd the prize, ‭ That had been long fed-up in sev'ral styes; ‭ Eumæus and his men convey'd them there, ‭ He, seeing now the king, began to cheer, ‭ And thus saluted him: "How now, my guest? ‭ Have yet your virtues found more interest ‭ In these great Wooers' good respects? Or still ‭ Pursue they you with all their wonted ill?" ‭ "I would to heav'n, Eumæus," he replied, ‭ "The Deities once would take in hand their pride, ‭ That such unseemly fashions put in frame ‭ In others' roofs, as show no spark of shame." ‭ Thus these; and to these came Melanthius, ‭ Great guardian of the most egregious ‭ Rich Wooers' herds, consisting all of goats; ‭ Which he, with two more, drave, and made their cotes ‭ The sounding porticos of that fair court. ‭ Melanthius, seeing the king, this former sort ‭ Of upland language gave: "What? Still stay here, ‭ And dull these Wooers with thy wretched cheer? ‭ Not gone for ever yet? Why now I see ‭ This strife of cuffs betwixt the beggary, ‭ That yesterday assay'd to get thee gone, ‭ And thy more roguery, needs will fall upon ‭ My hands to arbitrate. Thou wilt not hence ‭ Till I set on thee; thy ragg'd impudence ‭ Is so fast-footed. Are there not beside ‭ Other great banquetants, but you must tide ‭ At anchor still with us?" He nothing said, ‭ But thought of ill enough, and shook his head. ‭ Then came Philœtius, a chief of men, ‭ That to the Wooers' all-devouring den ‭ A barren steer drave, and fat goats; for they ‭ In custom were with traffickers by sea, ‭ That who they would sent, and had utt'rance there. ‭ And for these likewise the fair porches were ‭ Hurdles and sheep-pens, as in any fair. ‭ Philœtius took note in his repair ‭ Of seen Ulysses, being a man as well ‭ Giv'n to his mind's use as to buy and sell, ‭ Or do the drudg'ry that the blood desir'd, ‭ And, standing near Eumæus, this enquir'd: ‭ "What guest is this that makes our house of late ‭ His entertainer? Whence claims he the state ‭ His birth in this life holds? What nation? ‭ What race? What country stands his speech upon? ‭ O'er hardly portion'd by the terrible Fates. ‭ The structure of his lineaments relates ‭ A king's resemblance in his pomp of reign ‭ Ev'n thus in these rags. But poor erring men, ‭ That have no firm home, but range here and there ‭ As need compels, God keeps in this earth's sphere, ‭ As under water, and this tune he sings, ‭ When he is spinning ev'n the cares of kings." ‭ Thus coming to him, with a kind of fear ‭ He took his hand, and, touch'd exceeding near ‭ With mere imagination of his worth, ‭ This salutation he sent loudly forth: ‭ "Health! Father stranger! In another world ‭ Be rich and happy, though thou here art hurl'd ‭ At feet of never such insulting Need. ‭ O Jove, there lives no one God of thy seed ‭ More ill to man than thou. Thou tak'st no ruth-- ‭ When thou thyself hast got him in most truth-- ‭ To wrap him in the straits of most distress, ‭ And in the curse of others' wickedness. ‭ My brows have swet to see it, and mine eyes ‭ Broke all in tears, when this being still the guise ‭ Of worthiest men, I have but only thought, ‭ That down to these ills was Ulysses wrought, ‭ And that, thus clad, ev'n he is error-driv'n, ‭ If yet he live and sees the light of heav'n. ‭ But, if now dead, and in the house of hell, ‭ O me! O good Ulysses! That my weal ‭ Did ever wish, and when, but half a man ‭ Amongst the people Cephallenian, ‭ His bounty to his oxen's charge preferr'd ‭ One in that youth; which now is grown a herd ‭ Unspeakable for number, and feed there ‭ With their broad heads, as thick as of his ear ‭ A field of corn is to a man. Yet these ‭ Some men advise me with this noted prease ‭ Of Wooers may devour, and wish me drive ‭ Up to their feasts with them, that neither give ‭ His son respect, though in his own free roof, ‭ Nor have the wit to fear th' infallible proof ‭ Of Heav'nly vengeance, but make offer now ‭ The long-lack'd King's possessions to bestow ‭ In their self-shares. Methinks the mind in me ‭ Doth turn as fast, as in a flood or sea ‭ A raging whirlpit doth, to gather in ‭ To fishy death those swimmers in their sin; ‭ Or feeds a motion as circular ‭ To drive my herds away. But while the son ‭ Bears up with life, 'twere heinous wrong to run ‭ To other people with them, and to trust ‭ Men of another earth. And yet more just ‭ It were to venture their laws, the main right ‭ Made still their masters, than at home lose quite ‭ Their right and them, and sit and grieve to see ‭ The wrong authoriz'd by their gluttony. ‭ And I had long since fled, and tried th' event ‭ With other proud kings, since more insolent ‭ These are than can be borne, but that ev'n still ‭ I had a hope that this, though born to ill, ‭ Would one day come from some coast, and their last ‭ In his roofs strew with ruins red and vast." ‭ "Herdsman," said he, "because thou art in show ‭ Nor lewd nor indiscreet, and that I know ‭ There rules in thee an understanding soul, ‭ I'll take an oath, that in thee shall control ‭ All doubt of what I swear: Be witness, Jove, ‭ That sway'st the first seat of the thron'd above, ‭ This hospitable table, and this house, ‭ That still hold title for the strenuous ‭ Son of Laertes, that, if so you please, ‭ Your eyes shall witness Laertiades ‭ Arriv'd at home, and all these men that reign ‭ In such excesses here shall here lie slain!" ‭ He answer'd: "Stranger! Would just Jove would sign ‭ What you have sworn! In your eyes' beams should shine ‭ What pow'rs I manage, and how these my hands ‭ Would rise and follow where he first commands." ‭ So said Eumæus, praying all the Sky ‭ That wise Ulysses might arrive and try. ‭ Thus while they vow'd, the Wooers sat as hard ‭ On his son's death, but had their counsels scar'd, ‭ For on their left hand did an eagle soar, ‭ And in her seres a fearful pigeon bore. ‭ Which seen, Amphinomus presag'd: "O friends, ‭ Our counsels never will receive their ends ‭ In this man's slaughter. Let us therefore ply ‭ Our bloody feast, and make his oxen die." ‭ Thus came they in, cast off on seats their cloaks, ‭ And fell to giving sacrificing strokes ‭ Of sheep and goats, the chiefly fat and great, ‭ Slew fed-up swine, and from the herd a neat. ‭ The inwards roasted they dispos'd bewixt ‭ Their then observers, wine in flagons mixt. ‭ The bowls Eumæus brought, Philœtius bread, ‭ Melanthius fill'd the wine. Thus drank and fed ‭ The feastful Wooers. Then the prince, in grace ‭ Of his close project, did his father place ‭ Amidst the pavéd entry, in a seat ‭ Seemless and abject, a small board and meat ‭ Of th' only inwards; in a cup of gold ‭ Yet sent him wine, and bade him now drink bold, ‭ All his approaches he himself would free ‭ 'Gainst all the Wooers, since he would not see ‭ His court made popular, but that his sire ‭ Built it to his use. Therefore all the fire ‭ Blown in the Wooers' spleens he bade suppress, ‭ And that in hands nor words they should digress ‭ From that set peace his speech did then proclaim. ‭ They bit their lips and wonder'd at his aim ‭ In that brave language; when Antinous said: ‭ "Though this speech, Grecians, be a mere upbraid, ‭ Yet this time give it pass. The will of Jove ‭ Forbids the violence of our hands to move, ‭ But of our tongues we keep the motion free, ‭ And, therefore, if his further jollity ‭ Tempt our encounter with his braves, let's check ‭ His growing insolence, though pride to speak ‭ Fly passing high with him." The wise prince made ‭ No more spring of his speech, but let it fade. ‭ And now the heralds bore about the town ‭ The sacred hecatomb; to whose renown ‭ The fair-hair'd Greeks assembled, and beneath ‭ Apollo's shady wood the holy death ‭ They put to fire; which, made enough, they drew, ‭ Divided all, that did in th' end accrue ‭ To glorious satisfaction. Those that were ‭ Disposers of the feast did equal cheer ‭ Bestow on wretched Laertiades, ‭ With all the Wooers' souls; it so did please ‭ Telemachus to charge them. And for these ‭ Minerva would not see the malices ‭ The Wooers bore too much contain'd, that so ‭ Ulysses' mov'd heart yet might higher flow ‭ In wreakful anguish. There was wooing there, ‭ Amongst the rest, a gallant that did bear ‭ The name of one well-learn'd in jests profane, ‭ His name Ctesippus, born a Samian; ‭ Who, proud because his father was so rich, ‭ Had so much confidence as did bewitch ‭ His heart with hope to wed Ulysses' wife; ‭ And this man said: "Hear me, my lords, in strife ‭ For this great widow. This her guest did share ‭ Even feast with us, with very comely care ‭ Of him that order'd it; for 'tis not good ‭ Nor equal to deprive guests of their food, ‭ And specially whatever guest makes way ‭ To that house where Telemachus doth sway; ‭ And therefore I will add to his receit ‭ A gift of very hospitable weight, ‭ Which he may give again to any maid ‭ That bathes his grave feet, and her pains see paid, ‭ Or any servant else that the divine ‭ Ulysses' lofty battlements confine." ‭ Thus snatch'd he with a valiant hand, from out ‭ The poor folks' common basket, a neat's foot, ‭ And threw it at Ulysses; who his head ‭ Shrunk quietly aside, and let it shed ‭ His malice on the wall; the suff'ring man ‭ A laughter raising most Sardinian, ‭ With scorn and wrath mix'd, at the Samian. ‭ Whom thus the prince reprov'd: "Your valour wan ‭ Much grace, Ctesippus, and hath eas'd your mind ‭ With mighty profit, yet you see it find ‭ No mark it aim'd at; the poor stranger's part ‭ Himself made good enough, to 'scape your dart. ‭ But should I serve thee worthily, my lance ‭ Should strike thy heart through, and, in place t' advance ‭ Thyself in nuptials with his wealth, thy sire ‭ Should make thy tomb here; that the foolish fire ‭ Of all such valours may not dare to show ‭ These foul indecencies to me. I now ‭ Have years to understand my strength, and know ‭ The good and bad of things, and am no more ‭ At your large suff'rance, to behold my store ‭ Consum'd with patience, see my cattle slain, ‭ My wine exhausted, and my bread in vain ‭ Spent on your license; for to one then young ‭ So many enemies were match too strong. ‭ But let me never more be witness to ‭ Your hostile minds, nor those base deeds ye do; ‭ For, should ye kill me in my offer'd wreak, ‭ I wish it rather, and my death would speak ‭ Much more good of me, than to live and see ‭ Indignity upon indignity, ‭ My guests provok'd with bitter words and blows, ‭ My women-servants dragg'd about my house ‭ To lust and rapture." This made silence seize ‭ The house throughout; till Damastorides ‭ At length the calm brake, and said: "Friend, forbear ‭ To give a just speech a disdainful ear; ‭ The guest no more touch, nor no servant here. ‭ Myself will to the Prince and Queen commend ‭ A motion grateful, if they please to lend ‭ Grateful receipt. As long as any hope ‭ Left wise Ulysses any passage ope ‭ To his return in our conceits, so long ‭ The Queen's delays to our demands stood strong ‭ In cause and reason, and our quarrels thus ‭ With guests, the Queen, or her Telemachus, ‭ Set never foot amongst our lib'ral feast; ‭ For should the King return, though thought deceas'd, ‭ It had been gain to us, in finding him, ‭ To lose his wife. But now, since nothing dim ‭ The days break out that show he never more ‭ Shall reach the dear touch of his country-shore, ‭ Sit by your mother, in persuasion ‭ That now it stands her honour much upon ‭ To choose the best of us, and, who gives most, ‭ To go with him home. For so, all things lost ‭ In sticking on our haunt so, you shall clear ‭ Recover in our no more concourse here, ‭ Possess your birth-right wholly, eat and drink, ‭ And never more on our disgraces think." ‭ "By Jove, no, Agelaus! For I swear ‭ By all my father's sorrows, who doth err ‭ Far off from Ithaca, or rests in death, ‭ I am so far from spending but my breath ‭ To make my mother any more defer ‭ Her wishéd nuptials, that I'll counsel her ‭ To make her free choice; and besides will give ‭ Large gifts to move her. But I fear to drive ‭ Or charge her hence; for God will not give way ‭ To any such course, if I should assay." ‭ At this, Minerva made for foolish joy ‭ The Wooers mad, and rous'd their late annoy ‭ To such a laughter as would never down. ‭ They laugh'd with others' cheeks, ate meat o'erflown ‭ With their own bloods, their eyes stood full of tears ‭ For violent joys; their souls yet thought of fears, ‭ Which Theoclymenus express'd, and said: ‭ "O wretches! Why sustain ye, well apaid, ‭ Your imminent ill? A night, with which death sees, ‭ Your heads and faces hides beneath your knees; ‭ Shrieks burn about you; your eyes thrust out tears; ‭ These fixéd walls, and that main beam that bears ‭ The whole house up, in bloody torrents fall; ‭ The entry full of ghosts stands; full the hall ‭ Of passengers to hell; and under all ‭ The dismal shades; the sun sinks from the poles; ‭ And troubled air pours bane about your souls." ‭ They sweetly laughed at this. Eurymachus ‭ To mocks dispos'd, and said: "This new-come-t'-us ‭ Is surely mad, conduct him forth to light ‭ In th' open market-place; he thinks 'tis night ‭ Within the house." "Eurymachus," said he, ‭ "I will not ask for any guide of thee, ‭ I both my feet enjoy, have ears and eyes, ‭ And no mad soul within me; and with these ‭ Will I go forth the doors, because I know ‭ That imminent mischief must abide with you, ‭ Which not a man of all the Wooers here ‭ Shall fly or 'scape. Ye all too highly bear ‭ Your uncurb'd heads. Impieties ye commit, ‭ And ev'ry man affect with forms unfit." ‭ This said, he left the house, and took his way ‭ Home to Piræus; who, as free as day, ‭ Was of his welcome. When the Wooers' eyes ‭ Chang'd looks with one another, and, their guise ‭ Of laughters still held on, still eas'd their breasts ‭ Of will to set the Prince against his guests, ‭ Affirming that of all the men alive ‭ He worst luck had, and prov'd it worst to give ‭ Guests entertainment; for he had one there ‭ A wand'ring hunter-out of provender, ‭ An errant beggar ev'ry way, yet thought ‭ (He was so hungry) that he needed nought ‭ But wine and victuals, nor knew how to do, ‭ Nor had a spirit to put a knowledge to, ‭ But liv'd an idle burthen to the earth. ‭ Another then stepp'd up, and would lay forth ‭ His lips in prophecy, thus: "But, would he hear ‭ His friends' persuasions, he should find it were ‭ More profit for him to put both aboard ‭ For the Sicilian people, that afford ‭ These feet of men good price; and this would bring [2] ‭ Good means for better guests." These, words made wing ‭ To his ears idly, who had still his eye ‭ Upon his father, looking fervently ‭ When he would lay his long-withholding hand ‭ On those proud Wooers. And, within command ‭ Of all this speech that pass'd, Icarius' heir, ‭ The wise Penelope, her royal chair ‭ Had plac'd of purpose. Their high dinner then ‭ With all-pleas'd palates these ridiculous men ‭ Fell sweetly to, as joying they had slain ‭ Such store of banquet. But there did not reign ‭ A bitterer banquet-planet in all heav'n ‭ Than that which Pallas had to that day driv'n, ‭ And, with her able friend now, meant t' appose, ‭ Since they till then were in deserts so gross. ‭ THE END OF THE TWENTIETH BOOK OF HOMER'S ODYSSEYS. ‭[1] Viz. That some from within might issue, and witness in his ‭hearing some wreakful ostent to his enemies from heaven. ‭[2] These feet of men, etc. _ἀνδραποδισταί._ ‭ THE TWENTY-FIRST BOOK OF HOMER'S ODYSSEYS ‭ THE ARGUMENT ‭ Penelope proposeth now ‭ To him that draws Ulysses' bow ‭ Her instant nuptials. Ithacus ‭ Eumæus and Philœtius ‭ Gives charge for guarding of the gates; ‭ And he his shaft shoots through the plates. ‭ ANOTHER ARGUMENT ‭ _Φι̑._ ‭ The nuptial vow ‭ And game rehears'd, ‭ Drawn is the bow, ‭ The steels are pierc'd. ‭ Pallus, the Goddess with the sparkling eyes, ‭ Excites Penelope t' object the prize, ‭ The bow and bright steels, to the Wooers' strength ‭ And here began the strife and blood at length. ‭ She first ascended by a lofty stair ‭ Her utmost chamber; of whose door her fair ‭ And half transparent hand receiv'd the key, ‭ Bright, brazen, bitted passing curiously, ‭ And at it hung a knob of ivory. ‭ And this did lead her where was strongly kept ‭ The treasure-royal; in whose store lay heapt ‭ Gold, brass, and steel, engrav'n with infinite art; ‭ The crooked bow, and arrowy quiver, part ‭ Of that rich magazine. In the quiver were ‭ Arrows a number, sharp and sighing gear. ‭ The bow was giv'n by kind Eurytides ‭ Iphitus, fashion'd like the Deities, ‭ To young Ulysses, when within the roof ‭ Of wise Orsilochus their pass had proof ‭ Of mutual meeting in Messena; where ‭ Ulysses claim'd a debt, to whose pay were ‭ The whole Messenian people bound, since they ‭ From Ithaca had forc'd a wealthy prey ‭ Of sheep and shepherds. In their ships they thrust ‭ Three hundred sheep together; for whose just ‭ And instant rendry old Laertes sent ‭ Ulysses his ambassador, that went ‭ A long way in the ambassy, yet then ‭ Bore but the foremost prime of youngest men; ‭ His father sending first to that affair ‭ His gravest counsellors, and then his heir. ‭ Iphitus made his way there, having lost ‭ Twelve female horse, and mules commended most ‭ For use of burthen; which were after cause ‭ Of death and fate to him; for, past all laws ‭ Of hospitality, Jove's mighty son, ‭ Skill'd in great acts, was his confusion ‭ Close by his house, though at that time his guest, ‭ Respecting neither the apposéd feast, ‭ And hospitable table, that in love ‭ He set before him, nor the voice of Jove, ‭ But, seizing first his mares, he after slew ‭ His host himself. From those mares' search now grew ‭ Ulysses known t' Iphitus; who that bow ‭ At their encounter did in love bestow, ‭ Which great Eurytus' hand had borne before, ‭ (Iphitus' father) who, at death's sad door, ‭ In his steep turrets, left it to his son. ‭ Ulysses gave him a keen falchion, ‭ And mighty lance. And thus began they there ‭ Their fatal loves; for after never were ‭ Their mutual tables to each other known, ‭ Because Jove's son th' unworthy part had shown ‭ Of slaughtering this God-like loving man, ‭ Eurytus' son, who with that bow began ‭ And ended love t' Ulysses; who so dear ‭ A gift esteem'd it, that he would not bear ‭ In his black fleet that guest-rite to the war, ‭ But, in fit memory of one so far ‭ In his affection, brought it home, and kept ‭ His treasure with it; where till now it slept. ‭ And now the Queen of women had intent ‭ To give it use, and therefore made ascent ‭ Up all the stairs' height to the chamber door, ‭ Whose shining leaves two bright pilasters bore ‭ To such a close when both together went ‭ It would resist the air in their consent. ‭ The ring she took then, and did draw aside ‭ A bar that ran within, and then implied ‭ The key into the lock, which gave a sound, ‭ The bolt then shooting, as in pasture ground ‭ A bull doth low, and make the valleys ring; ‭ So loud the lock humm'd when it loos'd the spring, ‭ And ope the doors flew. In she went, along ‭ The lofty chamber, that was boarded strong ‭ With heart of oak, which many years ago ‭ The architect did smooth and polish so ‭ That now as then he made it freshly shine, ‭ And tried the evenness of it with a line. ‭ There stood in this room presses that enclos'd ‭ Robes odoriferous, by which repos'd ‭ The bow was upon pins; nor from it far ‭ Hung the round quiver glitt'ring like a star; ‭ Both which her white extended hand took down. ‭ Then sat she low, and made her lap a crown ‭ Of both these relics, which she wept to see, ‭ And cried quite out with loving memory ‭ Of her dear lord; to whose worth paying then ‭ Kind debts enow, she left, and, to the men ‭ Vow'd to her wooing, brought the crooked bow, ‭ And shaft-receiving quiver, that did flow ‭ With arrows beating sighs up where they fell. ‭ Then, with another chest, replete as well ‭ With games won by the King, of steel and brass, ‭ Her maids attended. Past whom making pass ‭ To where her Wooers were, she made her stay ‭ Amidst the fair hall door, and kept the ray ‭ Of her bright count'nance hid with veils so thin, ‭ That though they seem'd t' expose, they let love in; ‭ Her maids on both sides stood; and thus she spake: ‭ "Hear me, ye Wooers, that a pleasure take ‭ To do me sorrow, and my house invade ‭ To eat and drink, as if 'twere only made ‭ To serve your rapines; my lord long away, ‭ And you allow'd no colour for your stay ‭ But his still absence; striving who shall frame ‭ Me for his wife; and, since 'tis made a game, ‭ I here propose divine Ulysses' bow ‭ For that great master-piece to which ye vow. ‭ He that can draw it with least show to strive, ‭ And through these twelve axe-heads an arrow drive, ‭ Him will I follow, and this house forego ‭ That nourish'd me a maid, now furnish'd so ‭ With all things fit, and which I so esteem ‭ That I shall still live in it in my dream." ‭ This said, she made Eumæus give it them. ‭ He took and laid it by, and wept for woe; ‭ And like him wept Philœtius, when the bow ‭ Of which his king was bearer he beheld. ‭ Their tears Antinous' manhood much refell'd, ‭ And said: "Ye rustic fools! that still each day ‭ Your minds give over to this vain dismay, ‭ Why weep ye, wretches, and the widow's eyes ‭ Tempt with renew'd thought, that would otherwise ‭ Depose her sorrows, since her lord is dead, ‭ And tears are idle? Sit, and eat your bread, ‭ Nor whisper more a word; or get ye gone, ‭ And weep without doors. Let this bow alone ‭ To our out-match'd contention. For I fear ‭ The bow will scarce yield draught to any here; ‭ Here no such man lives as Laertes' son ‭ Amongst us all. I knew him; thought puts on ‭ His look's sight now, methinks, though then a child." ‭ Thus show'd his words doubt, yet his hopes instill'd ‭ His strength the stretcher of Ulysses' string, ‭ And his steels' piercer. But his shaft must sing ‭ Through his pierc'd palate first; whom so he wrong'd ‭ In his free roof, and made the rest ill-tongued ‭ Against his virtues. Then the sacred heat ‭ That spirited his son did further set ‭ Their confidence on fire, and said: "O friends, ‭ Jove hath bereft my wits. The Queen intends, ‭ Though I must grant her wise, ere long to leave ‭ Ulysses' court, and to her bed receive ‭ Some other lord; yet, notwithstanding, I ‭ Am forc'd to laugh, and set my pleasures high ‭ Like one mad sick. But, Wooers, since ye have ‭ An object for your trials now so brave, ‭ As all the broad Achaian earth exceeds, ‭ As sacred Pylos, as the Argive breeds, ‭ As black Epirus, as Mycena's birth, ‭ And as the more fam'd Ithacensian earth, ‭ All which, yourselves well know, and oft have said-- ‭ For what need hath my mother of my aid ‭ In her advancement?--tender no excuse ‭ For least delay, nor too much time profuse ‭ In stay to draw this bow, but draw it straight, ‭ Shoot, and the steels pierce; make all see how slight ‭ You make these poor bars to so rich a prize. ‭ No eag'rer yet? Come all. My faculties ‭ Shall try the bow's strength, and the piercéd steel. ‭ I will not for my rev'rend mother feel ‭ The sorrows that I know will seize my heart, ‭ To see her follow any, and depart ‭ From her so long-held home; but first extend ‭ The bow and arrow to their tender'd end. ‭ For I am only to succeed my sire ‭ In guard of his games, and let none aspire ‭ To their besides possession." This said, ‭ His purple robe he cast off; by he laid ‭ His well-edg'd sword; and, first, a sev'ral pit ‭ He digg'd for ev'ry axe, and strengthen'd it ‭ With earth close ramm'd about it; on a rew ‭ Set them, of one height, by a line he drew ‭ Along the whole twelve; and so orderly ‭ Did ev'ry deed belonging (yet his eye ‭ Never before beholding how 'twas done) ‭ That in amaze rose all his lookers-on. ‭ Then stood he near the door, and prov'd to draw ‭ The stubborn bow. Thrice tried, and thrice gave law ‭ To his uncrown'd attempts; the fourth assay ‭ With all force off'ring, which a sign gave stay ‭ Giv'n by his father; though he show'd a mind ‭ As if he stood right heartily inclin'd ‭ To perfect the exploit, when all was done ‭ In only drift to set the Wooers on. ‭ His weakness yet confess'd, he said: "O shame! ‭ I either shall be ever of no name, ‭ But prove a wretch; or else I am too young, ‭ And must not now presume on pow'rs so strong ‭ As sinews yet more growing may engraft, ‭ To turn a man quite over with a shaft. ‭ Besides, to men whose nerves are best prepar'd, ‭ _All great adventures at first proof are hard._ ‭ But come, you stronger men, attempt this bow, ‭ And let us end our labour." Thus, below ‭ A well-join'd board he laid it, and close by ‭ The brightly-headed shaft; then thron'd his thigh ‭ Amidst his late-left seat. Antinous then ‭ Bade all arise; but first, who did sustain ‭ The cup's state ever, and did sacrifice ‭ Before they ate still, and that man bade rise, ‭ Since on the other's right hand he was plac'd, ‭ Because he held the right hand's rising, grac'd ‭ With best success still. This discretion won ‭ Supreme applause; and first rose Œnops' son, ‭ Liodes, that was priest to all the rest, ‭ Sat lowest with the cup still, and their jest ‭ Could never like, but ever was the man ‭ That check'd their follies; and he now began ‭ To taste the bow, the sharp shaft took, tugg'd hard, ‭ And held aloft, and, till he quite had marr'd ‭ His delicate tender fingers, could not stir ‭ The churlish string; who therefore did refer ‭ The game to others, saying, that same bow, ‭ In his presage, would prove the overthrow ‭ Of many a chief man there; nor thought the fate ‭ Was any whit austere, since death's short date ‭ Were much the better taken, than long life ‭ Without the object of their amorous strife, ‭ For whom they had burn'd-out so many days ‭ To find still other, nothing but delays ‭ Obtaining in them; and affirm'd that now ‭ Some hop'd to have her, but when that tough bow ‭ They all had tried, and seen the utmost done, ‭ They must rest pleas'd to cease; and now some one ‭ Of all their other fair-veil'd Grecian dames ‭ With gifts, and dower, and Hymeneal flames, ‭ Let her love light to him that most will give, ‭ And whom the nuptial destiny did drive." ‭ Thus laid he on the well-join'd polish'd board ‭ The bow and bright-pil'd shaft, and then restor'd ‭ His seat his right. To him Antinous ‭ Gave bitter language, and reprov'd him thus: ‭ "What words, Liodes, pass thy speech's guard, ‭ That 'tis a work to bear, and set so hard ‭ They set up my disdain! This bow must end ‭ The best of us? Since thy arms cannot lend ‭ The string least motion? Thy mother's throes ‭ Brought never forth thy arms to draught of bows, ‭ Or knitting shafts off. Though thou canst not draw ‭ The sturdy plant, thou art to us no law. ‭ Melanthius! Light a fire, and set thereat ‭ A chair and cushions, and that mass of fat ‭ That lies within bring out, that we may set ‭ Our pages to this bow, to see it het ‭ And suppled with the suet, and then we ‭ May give it draught, and pay this great decree ‭ Utmost performance." He a mighty fire ‭ Gave instant flame, put into act th' entire ‭ Command laid on him, chair and cushions set, ‭ Laid on the bow, which straight the pages het, ‭ Chaf'd, suppled with the suet to their most; ‭ And still was all their unctuous labour lost, ‭ All Wooers' strengths too indigent and poor ‭ To draw that bow; Antinous' arms it tore, ‭ And great Eurymachus', the both clear best, ‭ Yet both it tir'd, and made them glad to rest. ‭ Forth then went both the swains, and after them ‭ Divine Ulysses; when, being past th' extreme ‭ Of all the gates, with winning words he tried ‭ Their loves, and this ask'd: "Shall my counsels hide ‭ Their depths from you? My mind would gladly know ‭ If suddenly Ulysses had his vow ‭ Made good for home, and had some God to guide ‭ His steps and strokes to wreak these Wooers' pride, ‭ Would your aids join on his part, or with theirs? ‭ How stand your hearts affected?" They made pray'rs ‭ That some God would please to return their lord, ‭ He then should see how far they would afford ‭ Their lives for his. He, seeing their truth, replied; ‭ "I am your lord, through many a suff'rance tried, ‭ Arriv'd now here, whom twenty years have held ‭ From forth my country. Yet are not conceal'd ‭ From my sure knowledge your desires to see ‭ My safe return. Of all the company ‭ Now serving here besides, not one but you ‭ Mine ear hath witness'd willing to bestow ‭ Their wishes of my life, so long held dead. ‭ I therefore vow, which shall be perfected, ‭ That if God please beneath my hand to leave ‭ These Wooers lifeless, ye shall both receive ‭ Wives from that hand, and means, and near to me ‭ Have houses built to you, and both shall be ‭ As friends and brothers to my only son. ‭ And, that ye well may know me, and be won ‭ To that assurance, the infallible sign ‭ The white-tooth'd boar gave, this mark'd knee of mine, ‭ When in Parnassus he was held in chase ‭ By me, and by my famous grandsire's race, ‭ I'll let you see." Thus sever'd he his weed ‭ From that his wound; and ev'ry word had deed ‭ In their sure knowledges. Which made them cast ‭ Their arms about him, his broad breast embrac'd, ‭ His neck and shoulders kiss'd. And him as well ‭ Did those true pow'rs of human love compell ‭ To kiss their heads and hands, and to their moan ‭ Had sent the free light of the cheerful sun, ‭ Had not Ulysses broke the ruth, and said; ‭ "Cease tears and sorrows, lest we prove display'd ‭ By some that issue from the house, and they ‭ Relate to those within. Take each his way, ‭ Not altogether in, but one by one, ‭ First I, then you; and then see this be done; ‭ The envious Wooers will by no means give ‭ The offer of the bow and arrow leave ‭ To come at me; spite then their pride, do thou, ‭ My good Eumæus, bring both shaft and bow ‭ To my hand's proof; and charge the maids before ‭ That instantly they shut in ev'ry door, ‭ That they themselves (if any tumult rise ‭ Beneath my roofs by any that envies ‭ My will to undertake the game) may gain ‭ No passage forth, but close at work contain ‭ With all free quiet, or at least constrain'd, ‭ And therefore, my Philœtius, see maintain'd, ‭ When close the gates are shut, their closure fast, ‭ To which end be it thy sole work to cast ‭ Their chains before them." This said, in he led, ‭ Took first his seat; and then they seconded ‭ His entry with their own. Then took in hand ‭ Eurymachus the bow, made close his stand ‭ Aside the fire, at whose heat here and there ‭ He warm'd and suppled it, yet could not stere ‭ To any draught the string, with all his art; ‭ And therefore swell'd in him his glorious heart, ‭ Affirming, "that himself and all his friends ‭ Had cause to grieve, not only that their ends ‭ They miss'd in marriage, since enough besides ‭ Kind Grecian dames there liv'd to be their brides ‭ In Ithaca, and other bord'ring towns, ‭ But that to all times future their renowns ‭ Would stand disparag'd, if Ulysses' bow ‭ They could not draw, and yet his wife would woo." ‭ Antinous answer'd; "That there could ensue ‭ No shame at all to them; for well he knew ‭ That this day was kept holy to the Sun ‭ By all the city, and there should be done ‭ No such profane act, therefore bade lay by ‭ The bow for that day; but the mastery ‭ Of axes that were set up still might stand, ‭ Since that no labour was, nor any hand ‭ Would offer to invade Ulysses' house, ‭ To take, or touch with surreptitious ‭ Or violent hand, what there was left for use. ‭ He, therefore, bade the cup-bearer infuse ‭ Wine to the bowls, that so with sacrifice ‭ They might let rest the shooting exercise, ‭ And in the morning make Melanthius bring ‭ The chief goats of his herd, that to the King ‭ Of bows and archers they might burn the thighs ‭ For good success, and then attempt the prize." ‭ The rest sat pleas'd with this. The heralds straight ‭ Pour'd water on their hands; each page did wait ‭ With his crown'd cup of wine, serv'd ev'ry man ‭ Till all were satisfied. And then began ‭ Ulysses' plot of his close purpose thus: ‭ "Hear me, ye much renown'd Eurymachus, ‭ And king Antinous, in chief, who well, ‭ And with decorum sacred, doth compell ‭ This day's observance, and to let lay down ‭ The bow all this light, giving Gods their own. ‭ The morning's labour God the more will bless, ‭ And strength bestow where he himself shall please. ‭ Against which time let me presume to pray ‭ Your favours with the rest, that this assay ‭ May my old arms prove, trying if there lie ‭ In my poor pow'rs the same activity ‭ That long since crown'd them; or if needy fare ‭ And desolate wand'ring have the web worn bare ‭ Of my life's thread at all parts, that no more ‭ Can furnish these affairs as heretofore." ‭ This het their spleens past measure, blown with fear ‭ Lest his loath'd temples would the garland wear ‭ Of that bow's draught; Antinous using speech ‭ To this sour purpose: "Thou most arrant wretch ‭ Of all guests breathing, in no least degree ‭ Grac'd with a human soul, it serves not thee ‭ To feast in peace with us, take equal share ‭ Of what we reach to, sit, and all things hear ‭ That we speak freely,--which no begging guest ‭ Did ever yet,--but thou must make request ‭ To mix with us in merit of the Queen. ‭ But wine inflames thee, that hath ever been ‭ The bane of men whoever yet would take ‭ Th' excess it offers and the mean forsake. ‭ Wine spoil'd the Centaur great Eurytion, ‭ In guest-rites with the mighty-minded son ‭ Of bold Ixion, in his way to war ‭ Against the Lapithes; who, driv'n as far ‭ As madness with the bold effects of wine, ‭ Did outrage to his kind host, and decline ‭ Other heroës from him feasted there ‭ With so much anger that they left their cheer, ‭ And dragg'd him forth the fore-court, slit his nose, ‭ Cropp'd both his ears, and, in the ill-dispose ‭ His mind then suffer'd, drew the fatal day ‭ On his head with his host; for thence the fray ‭ Betwixt the Centaurs and the Lapithes ‭ Had mortal act. But he for his excess ‭ In spoil of wine fared worse himself; as thou ‭ For thy large cups, if thy arms draw the bow, ‭ My mind fortells shalt fear; for not a man ‭ Of all our consort, that in wisdom can ‭ Boast any fit share, will take prayers then, ‭ But to Echetus, the most stern of men, ‭ A black sail freight with thee, whose worst of ill, ‭ Be sure, is past all ransom. Sit, then, still, ‭ Drink temp'rately, and never more contend ‭ With men your youngers." This the Queen did end ‭ With her defence of him, and told his foe ‭ It was not fair nor equal t' overcrow ‭ The poorest guest her son pleas'd t' entertain ‭ In his free turrets with so proud a strain ‭ Of threats and bravings; asking if he thought, ‭ That if the stranger to his arms had brought ‭ The stubborn bow down, he should marry her, ‭ And bear her home? And said, himself should err ‭ In no such hope; nor of them all the best ‭ That griev'd at any good she did her guest ‭ Should banquet there; since it in no sort show'd ‭ Noblesse in them, nor paid her what she ow'd ‭ Her own free rule there. This Eurymachus ‭ Confirm'd and said: "Nor feeds it hope in us, ‭ Icarius' daughter, to solemnize rites ‭ Of nuptials with thee; nor in noblest sights ‭ It can show comely; but to our respects ‭ The rumour both of sexes and of sects ‭ Amongst the people would breed shame and fear, ‭ Lest any worst Greek said: 'See, men that were ‭ Of mean deservings will presume t' aspire ‭ To his wife's bed, whom all men did admire ‭ For fame and merit, could not draw his bow, ‭ And yet his wife had foolish pride to woo, ‭ When straight an errant beggar comes and draws ‭ The bow with ease, performing all the laws ‭ The game besides contain'd'; and this would thus ‭ Prove both indignity and shame to us." ‭ The Queen replied: "The fame of men, I see, ‭ Bears much price in your great suppos'd degree; ‭ Yet who can prove amongst the people great, ‭ That of one so esteem'd of them the seat ‭ Doth so defame and ruin? And beside, ‭ With what right is this guest thus vilified ‭ In your high censures, when the man in blood ‭ Is well compos'd and great, his parents good? [1] ‭ And therefore give the bow to him, to try ‭ His birth and breeding by his chivalry. ‭ If his arms draw it, and that Phœbus stands ‭ So great a glory to his strength, my hands ‭ Shall add this guerdon: Ev'ry sort of weed, ‭ A two-edg'd sword, and lance to keep him freed ‭ From dogs and men hereafter, and dismiss ‭ His worth to what place tends that heart of his." ‭ Her son gave answer: "That it was a wrong ‭ To his free sway in all things that belong ‭ To guard of that house, to demand the bow ‭ Of any Wooer, and the use bestow ‭ Upon the stranger: for the bow was his ‭ To give or to withhold; no masteries ‭ Of her proposing giving any pow'r ‭ T' impair his right in things for any Wooer, ‭ Or any that rough Ithaca affords, ‭ Any that Elis; of which no man's words ‭ Nor pow'rs should curb him, stood he so inclin'd, ‭ To see the bow in absolute gift resign'd ‭ To that his guest to bear and use at will, ‭ And therefore bade his mother keep her still ‭ Amongst her women at her rock and loom; ‭ Bows were for men; and this bow did become ‭ Past all men's his disposure, since his sire ‭ Left it to him, and all the house entire." ‭ She stood dismay'd at this, and in her mind ‭ His wise words laid up, standing so inclin'd ‭ As he had will'd, with all her women going ‭ Up to her chamber, there her tears bestowing, ‭ As ev'ry night she did, on her lov'd lord, ‭ Till sleep and Pallas her fit rest restor'd. ‭ The bow Eumæus took, and bore away; ‭ Which up in tumult, and almost in fray, ‭ Put all the Wooers, one enquiring thus: ‭ "Whither, rogue, abject, wilt thou bear from us ‭ That bow propos'd? Lay down, or I protest ‭ Thy dogs shall eat thee, that thou nourishest ‭ To guard thy swine; amongst whom, left of all, ‭ Thy life shall leave thee, if the festival, ‭ We now observe to Phœbus, may our zeals ‭ Grace with his aid, and all the Deities else." ‭ This threat made good Eumæus yield the bow ‭ To his late place, not knowing what might grow ‭ From such a multitude. And then fell on ‭ Telemachus with threats, and said: "Set gone ‭ That bow yet further; 'tis no servant's part ‭ To serve too many masters; raise your heart ‭ And bear it off, lest, though you're younger, yet ‭ With stones I pelt you to the field with it. ‭ If you and I close, I shall prove too strong. ‭ I wish as much too hard for all this throng ‭ The Gods would make me, I should quickly send ‭ Some after with just sorrow to their end, ‭ They waste my victuals so, and ply my cup, ‭ And do me such shrewd turns still." This put up ‭ The Wooers all in laughters, and put down ‭ Their angers to him, that so late were grown ‭ So grave and bloody; which resolv'd that fear ‭ Of good Eumæus, who did take and bear ‭ The King the bow; call'd nurse, and bade her make ‭ The doors all sure, that if men's tumults take ‭ The ears of some within, they may not fly, ‭ But keep at work still close and silently. ‭ These words put wings to her, and close she put ‭ The chamber door. The court-gates then were shut ‭ By kind Philœtius, who straight did go ‭ From out the hall, and in the portico ‭ Found laid a gable of a ship, compos'd ‭ Of spongy bulrushes; with which he clos'd, ‭ In winding round about them, the court-gates, ‭ Then took his place again, to view the fates ‭ That quickly follow'd. When he came, he saw ‭ Ulysses viewing, ere he tried to draw, ‭ The famous bow, which ev'ry way he mov'd, ‭ Up and down turning it; in which be prov'd ‭ The plight it was in, fearing, chiefly, lest ‭ The horns were eat with worms in so long rest. ‭ But what his thoughts intended turning so, ‭ And keeping such a search about the bow, ‭ The Wooers little knowing fell to jest, ‭ And said: "Past doubt he is a man profest ‭ In bowyers' craft, and sees quite through the wood; ‭ Or something, certain, to be understood ‭ There is in this his turning of it still. ‭ A cunning rogue he is at any ill." ‭ Then spake another proud one: "Would to heav'n, ‭ I might, at will, get gold till he hath giv'n ‭ That bow his draught!" With these sharp jests did these ‭ Delightsome Woo'rs their fatal humours please. ‭ But when the wise Ulysses once had laid ‭ His fingers on it, and to proof survey'd ‭ The still sound plight it held, as one of skill ‭ In song, and of the harp, doth at his will, ‭ In tuning of his instrument, extend ‭ A string out with his pin, touch all, and lend ‭ To ev'ry well-wreath'd string his perfect sound, ‭ Struck all together; with such ease drew round ‭ The King the bow. Then twang'd he up the string, ‭ That as a swallow in the air doth sing ‭ With no continued tune, but, pausing still, ‭ Twinks out her scatter'd voice in accents shrill; ‭ So sharp the string sung when he gave it touch, ‭ Once having bent and drawn it. Which so much ‭ Amaz'd the Wooers, that their colours went ‭ And came most grievously. And then Jove rent ‭ The air with thunder; which at heart did cheer ‭ The now-enough-sustaining traveller, ‭ That Jove again would his attempt enable. ‭ Then took he into hand, from off the table, ‭ The first drawn arrow: and a number more ‭ Spent shortly on the Wooers; but this one ‭ He measur'd by his arm, as if not known ‭ The length were to him, nock'd it then, and drew; ‭ And through the axes, at the first hole, flew ‭ The steel-charg'd arrow; which when he had done ‭ He thus bespake the Prince: "You have not won ‭ Disgrace yet by your guest; for I have strook ‭ The mark I shot at, and no such toil took ‭ In wearying the bow with fat and fire ‭ As did the Wooers. Yet reserv'd entire, ‭ Thank Heav'n, my strength is, and myself am tried, ‭ No man to be so basely vilified ‭ As these men pleas'd to think me. But, free way ‭ Take that, and all their pleasures; and while day ‭ Holds her torch to you, and the hour of feast ‭ Hath now full date, give banquet, and the rest, ‭ Poem and harp, that grace a well-fill'd board." ‭ This said, he beckon'd to his son; whose sword ‭ He straight girt to him, took to hand his lance, ‭ And cómplete-arm'd did to his sire advance. ‭ THE END OF THE TWENTY-FIRST BOOK OF HOMER'S ODYSSEYS. ‭[1] _Εὐπηγής, bene compactus et coagmentatus._ ‭ THE TWENTY-SECOND BOOK OF HOMER'S ODYSSEYS ‭ THE ARGUMENT ‭ The Wooers in Minerva's sight ‭ Slain by Ulysses; all the light ‭ And lustful housewives by his son ‭ And servants are to slaughter done. ‭ ANOTHER ARGUMENT ‭ _Χι̑._ ‭ The end of pride, ‭ And lawless lust, ‭ Is wretched tried ‭ With slaughters just. ‭ The upper rags that wise Ulysses wore ‭ Cast off, he rusheth to the great hall door ‭ With bow and quiver full of shafts, which down ‭ He pour'd before his feet, and thus made known ‭ His true state to the Wooers: "This strife thus ‭ Hath harmless been decided; now for us ‭ There rests another mark, more hard to hit, ‭ And such as never man before hath smit; ‭ Whose full point likewise my hands shall assay, ‭ And try if Phœbus will give me his day." ‭ He said, and off his bitter arrow thrust ‭ Right at Antinous; and struck him just ‭ As he was lifting up the bowl, to show ‭ That 'twixt the cup and lip much ill may grow. ‭ Death touch'd not at his thoughts at feast; for who ‭ Would think that he alone could perish so ‭ Amongst so many, and he best of all? ‭ The arrow in his throat took full his fall, ‭ And thrust his head far through the other side. ‭ Down fell his cup, down he, down all his pride; ‭ Straight from his nostrils gush'd the human gore; ‭ And, as he fell, his feet far overbore ‭ The feastful table; all the roast and bread ‭ About the house strew'd. When his high-born head ‭ The rest beheld so low, up rush'd they all, ‭ And ransack'd ev'ry corner of the hall ‭ For shields and darts; but all fled far their reach. ‭ Then fell they foul on him with terrible speech, ‭ And told him it should prove the dearest shaft ‭ That ever pass'd him; and that now was saft ‭ No shift for him, but sure and sudden death; ‭ For he had slain a man, whose like did breathe ‭ In no part of the kingdom; and that now ‭ He should no more for games strive with his bow, ‭ But vultures eat him there. These threats they spent, ‭ Yet ev'ry man believ'd that stern event ‭ Chanc'd 'gainst the author's will. O fools, to think ‭ That all their rest had any cup to drink ‭ But what their great Antinous began! ‭ He, frowning, said: "Dogs, see in me the man ‭ Ye all held dead at Troy. My house it is ‭ That thus ye spoil, and thus your luxuries ‭ File with my women's rapes; in which ye woo ‭ The wife of one that lives, and no thought show ‭ Of man's fit fear, or God's, your present fame, ‭ Or any fair sense of your future name; ‭ And, therefore, present and eternal death ‭ Shall end your base life." This made fresh fears breathe ‭ Their former boldness. Ev'ry man had eye ‭ On all the means, and studied ways to fly ‭ So deep deaths imminent. But seeing none, ‭ Eurymachus began with suppliant moan ‭ To move his pity, saying: "If you be ‭ This isle's Ulysses, we must all agree, ‭ In grant of your reproof's integrity, ‭ The Greeks have done you many a wrong at home, ‭ At field as many. But of all the sum ‭ Lies here contract in death; for only he ‭ Impos'd the whole ill-offices that we ‭ Are now made guilty of, and not so much ‭ Sought his endeavours, or in thought did touch ‭ At any nuptials, but a greater thing ‭ Employ'd his forces; for to be our king ‭ Was his chief object; his sole plot it was ‭ To kill your son, which Jove's hand would not pass, ‭ But set it to his own most merited end. ‭ In which end your just anger, nor extend ‭ Your stern wreak further; spend your royal pow'rs ‭ In mild ruth of your people; we are yours; ‭ And whatsoever waste of wine or food ‭ Our liberties have made, we'll make all good ‭ In restitutions. Call a court, and pass ‭ A fine of twenty oxen, gold, and brass, ‭ On ev'ry head, and raise your most rates still, ‭ Till you are pleas'd with your confesséd fill. ‭ Which if we fail to tender, all your wrath ‭ It shall be justice in our bloods to bathe." ‭ "Eurymachus," said he, "if you would give ‭ All that your fathers' hoard, to make ye live, ‭ And all that ever you yourselves possess, ‭ Or shall by any industry increase, ‭ I would not cease from slaughter, till your bloods ‭ Had bought out your intemp'rance in my goods. ‭ It rests now for you that you either fight ‭ That will 'scape death, or make your way by flight. ‭ In whose best choice, my thoughts conceive, not one ‭ Shall shun the death your first hath undergone." ‭ This quite dissolv'd their knees. Eurymachus, ‭ Enforcing all their fears, yet counsell'd thus: ‭ "O friends! This man, now he hath got the bow ‭ And quiver by him, ever will bestow ‭ His most inaccessible hands at us, ‭ And never leave, if we avoid him thus, ‭ Till he hath strewn the pavement with us all; ‭ And, therefore, join we swords, and on him fall ‭ With tables forc'd up, and borne in oppos'd ‭ Against his sharp shafts; when, being round-enclos'd ‭ By all our onsets, we shall either take ‭ His horrid person, or for safety make ‭ His rage retire from out the hall and gates; ‭ And then, if he escape, we'll make our states ‭ Known to the city by our gen'ral cry. ‭ And thus this man shall let his last shaft fly ‭ That ever his hand vaunted." Thus he drew ‭ His sharp-edg'd sword; and with a table flew ‭ In on Ulysses, with a terrible throat ‭ His fierce charge urging. But Ulysses smote ‭ The board, and cleft it through from end to end ‭ Borne at his breast; and made his shaft extend ‭ His sharp head to his liver, his broad breast ‭ Pierc'd at his nipple; when his hand releast ‭ Forthwith his sword, that fell and kiss'd the ground, ‭ With cups and victuals lying scatter'd round ‭ About the pavement; amongst which his brow ‭ Knock'd the imbrued earth, while in pains did flow ‭ His vital spirits, till his heels shook out ‭ His feastful life, and hurl'd a throne about ‭ That way-laid death's convulsions in his feet; ‭ When from his tender eyes the light did fleet. ‭ Then charg'd Amphinomus with his drawn blade ‭ The glorious king, in purpose to have made ‭ His feet forsake the house; but his assay ‭ The prince prevented, and his lance gave way ‭ Quite through his shoulder, at his back; his breast ‭ The fierce pile letting forth. His ruin prest ‭ Groans from the pavement, which his forehead strook. ‭ Telemachus his long lance then forsook-- ‭ Left in Amphinomus--and to his sire ‭ Made fiery pass, not staying to acquire ‭ His lance again, in doubt that, while he drew ‭ The fixéd pile, some other might renew ‭ Fierce charge upon him, and his unharm'd head ‭ Cleave with his back-drawn sword; for which he fled ‭ Close to his father, bade him arm, and he ‭ Would bring him shield and jav'lins instantly, ‭ His own head arming, more arms laying by ‭ To serve the swine-herd and the oxen-herd. ‭ _Valour well arm'd is ever most preferr'd._ ‭ "Run then," said he, "and come before the last ‭ Of these auxiliary shafts are past, ‭ For fear, lest, left alone, they force my stand ‭ From forth the ports." He flew, and brought to hand ‭ Eight darts, four shields, four helms. His own parts then ‭ First put in arms, he furnish'd both his men, ‭ That to their king stood close; but he, as long ‭ As he had shafts to friend, enough was strong ‭ For all the Wooers, and some one man still ‭ He made make even with earth, till all a hill ‭ Had rais'd in th' even-floor'd hall. His last shaft spent, ‭ He set his bow against a beam, and went ‭ To arm at all parts, while the other three ‭ Kept off the Wooers, who, unarm'd, could be ‭ No great assailants. In the well-built wall ‭ A window was thrust out, at end of all ‭ The house's entry; on whose utter side ‭ There lay a way to town, and in it wide ‭ And two-leav'd folds were forg'd, that gave fit mean ‭ For flyers-out; and, therefore, at it then ‭ Ulysses plac'd Eumæus in close guard; ‭ One only pass ope to it, which (prepar'd ‭ In this sort by Ulysses 'gainst all pass) ‭ By Agelaus' tardy memory was ‭ In question call'd, who bade some one ascend ‭ At such a window, and bring straight to friend ‭ The city with his clamour, that this man ‭ Might quickly shoot his last. "This no one can ‭ Make safe access to," said Melanthius, ‭ "For 'tis too near the hall's fair doors, whence thus ‭ The man afflicts ye; for from thence there lies ‭ But one strait passage to it, that denies ‭ Access to all, if any one man stand, ‭ Being one of courage, and will countermand ‭ Our offer to it. But I know a way ‭ To bring you arms, from where the King doth lay ‭ His whole munition; and believe there is ‭ No other place to all the armories ‭ Both of himself and son." This said, a pair ‭ Of lofty stairs he climb'd, and to th' affair ‭ Twelve shields, twelve lances brought, as many casques ‭ With horsehair plumes; and set to bitter tasks ‭ Both son and sire. Then shrunk Ulysses' knees, ‭ And his lov'd heart, when thus in arms he sees ‭ So many Wooers, and their shaken darts; ‭ For then the work show'd as it ask'd more parts ‭ To safe performance, and he told his son ‭ That or Melanthius or his maids had done ‭ A deed that foul war to their hands conferr'd. ‭ "O father," he replied, "'tis I have err'd ‭ In this caus'd labour; I, and none but I, ‭ That left the door ope of your armoury. ‭ But some, it seems, hath set a sharper eye ‭ On that important place. Eumæus! Haste ‭ And shut the door, observing who hath past ‭ To this false action; any maid, or one ‭ That I suspect more, which is Dolius' son." ‭ While these spake thus, Melanthius went again ‭ For more fair arms; when the renownéd swain ‭ Eumæus saw, and told Ulysses straight ‭ It was the hateful man that his conceit ‭ Before suspected, who had done that ill; ‭ And, being again there, ask'd if he should kill, ‭ If his pow'r serv'd, or he should bring the swain ‭ To him, t' inflict on him a sev'ral pain ‭ For ev'ry forfeit he had made his house. ‭ He answer'd: "I and my Telemachus ‭ Will here contain these proud ones in despite, ‭ How much soever these stol'n arms excite ‭ Their guilty courages, while you two take ‭ Possession of the chamber. The doors make ‭ Sure at your back, and then, surprising him, ‭ His feet and hands bind, wrapping ev'ry limb ‭ In pliant chains; and with a halter cast ‭ Above the wind-beam--at himself made fast-- ‭ Aloft the column draw him; where alive ‭ He long may hang, and pains enough deprive ‭ His vexéd life before his death succeed." ‭ This charge, soon heard, as soon they put to deed, ‭ Stole on his stealth, and at the further end ‭ Of all the chamber saw him busily bend ‭ His hands to more arms, when they, still at door, ‭ Watch'd his return. At last he came, and bore ‭ In one hand a fair helm, in th' other held ‭ A broad and ancient rusty-rested shield, ‭ That old Laertes in his youth had worn, ‭ Of which the cheek-bands had with age been torn. ‭ They rush'd upon him, caught him by the hair, ‭ And dragg'd him in again; whom, crying out, ‭ They cast upon the pavement, wrapp'd about ‭ With sure and pinching cords both foot and hand, ‭ And then, in full act of their King's command, ‭ A pliant chain bestow'd on him, and hal'd ‭ His body up the column, till he scal'd ‭ The highest wind-beam; where made firmly fast, ‭ Eumæus on his just infliction past ‭ This pleasurable cavil: "Now you may ‭ All night keep watch here, and the earliest day ‭ Discern, being hung so high, to rouse from rest ‭ Your dainty cattle to the Wooers' feast. ‭ There, as befits a man of means so fair, ‭ Soft may you sleep, nought under you but air; ‭ And so long hang you." Thus they left him there, ‭ Made fast the door, and with Ulysses were ‭ All arm'd in th' instant. Then they all stood close, ‭ Their minds fire breath'd in flames against their foes, ‭ Four in th' entry fighting all alone; ‭ When from the hall charg'd many a mighty one. ‭ But to them then Jove's seed, Minerva, came, ‭ Resembling Mentor both in voice and frame ‭ Of manly person. Passing well apaid ‭ Ulysses was, and said: "Now, Mentor, aid ‭ 'Gainst these odd mischiefs; call to memory now ‭ My often good to thee, and that we two ‭ Of one year's life are." Thus he said, but thought ‭ ft was Minerva, that had ever brought ‭ To her side safety. On the other part, ‭ The Wooers threaten'd; but the chief in heart ‭ Was Agelaus, who to Mentor spake: ‭ "Mentor! Let no words of Ulysses make ‭ Thy hand a fighter on his feeble side ‭ 'Gainst all us Wooers; for we firm abide ‭ In this persuasion, that when sire and son ‭ Our swords have slain, thy life is sure to run ‭ One fortune with them. What strange acts hast thou ‭ Conceit to form here? Thy head must bestow ‭ The wreak of theirs on us. And when thy pow'rs ‭ Are taken down by these fierce steels of ours, ‭ All thy possessions, in-doors and without, ‭ Must raise on heap with his; and all thy rout ‭ Of sons and daughters in thy turrets bleed ‭ Wreak off'rings to us; and our town stand freed ‭ Of all charge with thy wife." Minerva's heart ‭ Was fir'd with these braves, the approv'd desert ‭ Of her Ulysses chiding, saying: "No more ‭ Thy force nor fortitude as heretofore ‭ Will gain thee glory; when nine years at Troy ‭ White-wristed Helen's rescue did employ ‭ Thy arms and wisdom, still and ever us'd, ‭ The bloods of thousands through the field diffus'd ‭ By thy vast valour; Priam's broad-way'd town ‭ By thy grave parts was sack'd and overthrown; ‭ And now, amongst thy people and thy goods, ‭ Against the Wooers' base and petulant bloods ‭ Stint'st thou thy valour? Rather mourning here ‭ Than manly fighting? Come, friend, stand we near, ‭ And note my labour, that thou may'st discern ‭ Amongst thy foes how Mentor's nerves will earn ‭ All thy old bounties." This she spake, but stay'd ‭ Her hand from giving each-way-often-sway'd ‭ Uncertain conquest to his certain use, ‭ But still would try what self-pow'rs would produce ‭ Both in the father and the glorious son. ‭ Then on the wind-beam that along did ron ‭ The smoky roof, transform'd, Minerva sat, ‭ Like to a swallow; sometimes cuffing at ‭ The swords and lances, rushing from her seat, ‭ And up and down the troubl'd house did beat ‭ Her wing at ev'ry motion. And as she ‭ Had rous'd Ulysses; so the enemy ‭ Damastor's son excited, Polybus, ‭ Amphinomus, and Demoptolemus, ‭ Eurynomus, and Polyctorides; ‭ For these were men that of the wooing prease ‭ Were most egregious, and the clearly best ‭ In strength of hand of all the desp'rate rest ‭ That yet surviv'd, and now fought for their souls; ‭ Which straight swift arrows sent among the fowls. ‭ But first, Damastor's son had more spare breath ‭ To spend on their excitements ere his death, ‭ And said: That now Ulysses would forbear ‭ His dismal hand, since Mentor's spirit was there, ‭ And blew vain vaunts about Ulysses' ears; ‭ In whose trust he would cease his massacres, ‭ Rest him, and put his friend's huge boasts in proof; ‭ And so was he beneath the entry's roof ‭ Left with Telemachus and th' other two. ‭ "At whom," said he, "discharge no darts, but throw ‭ All at Ulysses, rousing his faint rest; ‭ Whom if we slaughter, by our interest ‭ In Jove's assistance, all the rest may yield ‭ Our pow'rs no care, when he strews once the field." ‭ As he then will'd, they all at random threw ‭ Where they suppos'd he rested; and then flew ‭ Minerva after ev'ry dart, and made ‭ Some strike the threshold, some the walls invade, ‭ Some beat the doors, and all acts render'd vain ‭ Their grave steel offer'd. Which escap'd, again" ‭ Came on Ulysses, saying: "O that we ‭ The Wooers' troop with our joint archery ‭ Might so assail, that where their spirits dream ‭ On our deaths first, we first may slaughter them!" ‭ Thus the much-suff'rer said; and all let-fly, ‭ When ev'ry man struck dead his enemy. ‭ Ulysses slaughter'd Demoptolemus. ‭ Euryades by young Telemachus ‭ His death encounter'd. Good Eumæus slew ‭ Elatus. And Philœtius overthrew ‭ Pisander. All which tore the pavéd floor ‭ Up with their teeth. The rest retir'd before ‭ Their second charge to inner rooms; and then ‭ Ulysses follow'd; from the slaughter'd men ‭ Their darts first drawing. While which work was done, ‭ The Wooers threw with huge contention ‭ To kill them all; when with her swallow-wing ‭ Minerva cuff'd, and made their jav'lins ring ‭ Against the doors and thresholds, as before. ‭ Some yet did graze upon their marks. One tore ‭ The prince's wrist, which was Amphimedon, ‭ Th' extreme part of the skin but touch'd upon. ‭ Ctesippus over good Eumeeus' shield ‭ His shoulder's top did taint; which yet did yield ‭ The lance free pass, and gave his hurt the ground. ‭ Again then charg'd the Wooers, and girt round ‭ Ulysses with their lances; who turn'd head, ‭ And with his jav'lin struck Eurydamas dead. ‭ Telemachus disliv'd Amphimedon; ‭ Eumæus, Polybus; Philœtius won ‭ Ctesippus' bosom with his dart, and said, ‭ In quittance of the jester's part he play'd, ‭ The neat's foot hurling at Ulysses: "Now, ‭ Great son of Polytherses, you that vow ‭ Your wit to bitter taunts, and love to wound ‭ The heart of any with a jest, so crown'd ‭ Your wit be with a laughter, never yielding ‭ To fools in folly, but your glory building ‭ On putting down in fooling, spitting forth ‭ Puff'd words at all sorts, cease to scoff at worth, ‭ And leave revenge of vile words to the Gods, ‭ Since their wits bear the sharper edge by odds; ‭ And, in the mean time, take the dart I drave, ‭ For that right hospitable foot you gave ‭ Divine Ulysses, begging but his own." ‭ Thus spake the black-ox-herdsman; and straight down ‭ Ulysses struck another with his dart-- ‭ Damastor's son. Telemachus did part, ‭ Just in the midst, the belly of the fair ‭ Evenor's son; his fierce pile taking air ‭ Out at his back. Flat fell he on his face, ‭ His whole brows knocking, and did mark the place. ‭ And now man-slaught'ring Pallas took in hand ‭ Her snake-fring'd shield, and on that beam took stand ‭ In her true form, where swallow-like she sat. ‭ And then, in this way of the house and that, ‭ The Wooers, wounded at the heart with fear, ‭ Fled the encounter; as in pastures where ‭ Fat herds of oxen feed, about the field ‭ (As if wild madness their instincts impell'd) ‭ The high-fed bullocks fly, whom in the spring, ‭ When days are long, gad-bees or breezes sting. ‭ Ulysses and his son the flyers chas'd, ‭ As when, with crooked beaks and seres, a cast ‭ Of hill-bred eagles, cast-off at some game, ‭ That yet their strengths keep, but, put up, in flame ‭ The eagle stoops; from which, along the field ‭ The poor fowls make wing, this and that way yield ‭ Their hard-flown pinions, then the clouds assay ‭ For 'scape or shelter, their forlorn dismay ‭ All spirit exhaling, all wings' strength to carry ‭ Their bodies forth, and, truss'd up, to the quarry ‭ Their falconers ride-in, and rejoice to see ‭ Their hawks perform a flight so fervently; ‭ So, in their flight, Ulysses with his heir ‭ Did stoop and cuff the Wooers, that the air ‭ Broke in vast sighs, whose heads they shot and cleft, ‭ The pavement boiling with the souls they reft. ‭ Liodes, running to Ulysses, took ‭ His knees, and thus did on his name invoke; ‭ "Ulysses! Let me pray thee to my place ‭ Afford the rev'rence, and to me the grace; ‭ That never did or said, to any dame ‭ Thy court contain'd, or deed, or word to blame; ‭ But others so affected I have made ‭ I lay down their insolence; and, if the trade ‭ They kept with wickedness have made them still ‭ Despise my speech, and use their wonted ill, ‭ They have their penance by the stroke of death, ‭ Which their desert divinely warranteth. ‭ But I am priest amongst them, and shall I ‭ That nought have done worth death amongst them die? ‭ From thee this proverb then will men derive: ‭ _Good turns do never their mere deeds survive."_ ‭ He, bending his displeaséd forehead, said: ‭ "If you be priest among them, as you plead, ‭ Yet you would marry, and with my wife too, ‭ And have descent by her. For all that woo ‭ Wish to obtain, which they should never do, ‭ Dames' husbands living. You must therefore pray ‭ Of force, and oft in Court here, that the day ‭ Of my return for him might never shine; ‭ The death to me wish'd, therefore, shall be thine." ‭ This said, he took a sword up that was cast ‭ From Agelaus, having struck his last, ‭ And on the priest's mid neck he laid a stroke ‭ That struck his head off, tumbling as he spoke. ‭ Then did the poet Phemius (whose surname ‭ Was call'd Terpiades; who thither came ‭ Forc'd by the Wooers) fly death; but being near ‭ The court's great gate, he stood, and parted there ‭ In two his counsels; either to remove ‭ And take the altar of Herceian Jove ‭ (Made sacred to him, with a world of art ‭ Engrav'n about it, where were wont t' impart ‭ Laertes and Ulysses many a thigh ‭ Of broad-brow'd oxen to the Deity) ‭ Or venture to Ulysses, clasp his knee, ‭ And pray his ruth. The last was the decree ‭ His choice resolv'd on. 'Twixt the royal throne ‭ And that fair table that the bowl stood on ‭ With which they sacrific'd, his harp he laid ‭ Along the earth, the King's knees hugg'd, and said: ‭ "Ulysses! Let my pray'rs obtain of thee ‭ My sacred skill's respect, and ruth to me! ‭ It will hereafter grieve thee to have slain ‭ A poet, that doth sing to Gods and men. ‭ I of myself am taught, for God alone ‭ All sorts of song hath in my bosom sown, ‭ And I, as to a God, will sing to thee; ‭ Then do not thou deal like the priest with me. ‭ Thine own lov'd son Telemachus will say, ‭ That not to beg here, nor with willing way ‭ Was my access to thy high court addrest, ‭ To give the Wooers my song after feast, ‭ But, being many, and so much more strong, ‭ They forced me hither, and compell'd my song." ‭ This did the prince's sacred virtue hear, ‭ And to the King, his father, said: "Forbear ‭ To mix the guiltless with the guilty's blood. ‭ And with him likewise let our mercies save ‭ Medon the herald, that did still behave ‭ Himself with care of my good from a child; ‭ If by Eumæus yet he be not kill'd, ‭ Or by Philœtius, nor your fury met, ‭ While all this blood about the house it swet." ‭ This Medon heard, as lying hid beneath ‭ A throne set near, half-dead with fear of death; ‭ A new-flay'd ox-hide, as but there thrown by, ‭ His serious shroud made, he lying there to fly. ‭ But hearing this he quickly left the throne, ‭ His ox-hide cast as quickly, and as soon ‭ The prince's knees seiz'd, saying: "O my love, ‭ I am not slain, but here alive and move. ‭ Abstain yourself, and do not see your sire ‭ Quench with my cold blood the unmeasur'd fire ‭ That flames in his strength, making spoil of me, ‭ His wrath's right, for the Wooers' injury." ‭ Ulysses smil'd, and said: "Be confident ‭ This man hath sav'd and made thee different, ‭ To let thee know, and say, and others see, ‭ _Good life is much more safe than villany._ ‭ Go then, sit free without from death within. ‭ This much-renownéd singer from the sin ‭ Of these men likewise quit. Both rest you there, ‭ While I my house purge as it fits me here." ‭ This said, they went and took their seat without ‭ At Jove's high altar, looking round about, ‭ Expecting still their slaughter. When the King ‭ Search'd round the hall, to try life's hidden wing ‭ Made from more death. But all laid prostrate there ‭ In blood and gore he saw. Whole shoals they were, ‭ And lay as thick as in a hollow creek ‭ Without the white sea, when the fishers break ‭ Their many-mesh'd draught-net up, there lie ‭ Fish frisking on the sands, and fain the dry ‭ Would for the wet change, but th' all-seeing beam ‭ The sun exhales hath suck'd their lives from them; ‭ So one by other sprawl'd the Wooers there. ‭ Ulysses and his son then bid appear ‭ The nurse Euryclea, to let her hear ‭ His mind in something fit for her affair. ‭ He op'd the door, and call'd, and said: "Repair, ‭ Grave matron long since born, that art our spy ‭ To all this house's servile housewif'ry; ‭ My father calls thee, to impart some thought ‭ That asks thy action." His word found in nought ‭ Her slack observance, who straight op'd the door ‭ And enter'd to him; when himself before ‭ Had left the hall. But there the King she view'd ‭ Amongst the slain, with blood and gore imbrued. ‭ And as a lion skulking all in night, ‭ Far-off in pastures, and come home, all dight ‭ In jaws and breast-locks with an ox's blood ‭ New feasted on him, his looks full of mood; ‭ So look'd Ulysses, all his hands and feet ‭ Freckled with purple. When which sight did greet ‭ The poor old woman (such works being for eyes ‭ Of no soft temper) out she brake in cries, ‭ Whose vent, though throughly open'd, he yet clos'd, ‭ Call'd her more near, and thus her plaints compos'd: ‭ "'Forbear, nor shriek thus, but vent joys as loud. ‭ _It is no piety to bemoan the proud,_ ‭ Though ends befall them moving ne'er so much, ‭ These are the portions of the Gods to such. ‭ _Men's own impieties in their instant act ‭ Sustain their plagues, which are with stay but rackt._ ‭ But these men Gods nor men had in esteem, ‭ Nor good nor bad had any sense in them, ‭ Their lives directly ill were, therefore, cause ‭ That Death in these stern forms so deeply draws. ‭ Recount, then, to me those licentious dames ‭ That lost my honour and their sex's shames." ‭ "I'll tell you truly," she replied: "There are ‭ Twice five-and-twenty women here that share ‭ All work amongst them; whom I taught to spin, ‭ And bear the just bands that they suffer'd in. ‭ Of all which only there were twelve that gave ‭ Themselves to impudence and light behave, ‭ Nor me respecting, nor herself--the Queen. ‭ And for your son he hath but lately been ‭ Of years to rule; nor would his mother bear ‭ His empire where her women's labours were, ‭ But let me go and give her notice now ‭ Of your arrival. Sure some God doth show ‭ His hand upon her in this rest she takes, ‭ That all these uproars bears and never wakes." ‭ "Nor wake her yet," said he, "but cause to come ‭ Those twelve light women to this utter room." ‭ She made all utmost haste to come and go, ‭ And bring the women he had summon'd so. ‭ Then both his swains and son he bade go call ‭ The women to their aid, and clear the hall ‭ Of those dead bodies, cleanse each board and throne ‭ With wetted sponges. Which with fitness done, ‭ He bade take all the strumpets 'twixt the wall ‭ Of his first court and that room next the hall, ‭ In which the vessels of the house were scour'd, ‭ And in their bosoms sheath their ev'ry sword, ‭ Till all their souls were fled, and they had then ‭ Felt 'twas but pain to sport with lawless men. ‭ This said, the women came all drown'd in moan, ‭ And weeping bitterly. But first was done ‭ The bearing thence the dead; all which beneath ‭ The portico they stow'd, where death on death ‭ They heap'd together. Then took all the pains ‭ Ulysses will'd. His son yet and the swains ‭ With paring-shovels wrought. The women bore ‭ Their parings forth, and all the clotter'd gore. ‭ The house then cleans'd, they brought the women out, ‭ And put them in a room so wall'd about ‭ That no means serv'd their sad estates to fly. ‭ Then said Telemachus: "These shall not die ‭ A death that lets out any wanton blood, ‭ And vents the poison that gave lust her food, ‭ The body cleansing, but a death that chokes ‭ The breath, and altogether that provokes ‭ And seems as bellows to abhorréd lust, ‭ That both on my head pour'd depraves unjust, ‭ And on my mother's, scandalling the Court, ‭ With men debauch'd, in so abhorr'd a sort." ‭ This said, a halser of a ship they cast ‭ About a cross-beam of the roof, which fast ‭ They made about their necks, in twelve parts cut, ‭ And hal'd them up so high they could not put ‭ Their feet to any stay. As which was done, ‭ Look how a mavis, or a pigeon, ‭ In any grove caught with a springe or net, ‭ With struggling pinions 'gainst the ground doth beat ‭ Her tender body, and that then strait bed ‭ Is sour to that swing in which she was bred; ‭ So striv'd these taken birds, till ev'ry one ‭ Her pliant halter had enforc'd upon ‭ Her stubborn neck, and then aloft was haul'd ‭ To wretched death. A little space they sprawl'd, ‭ Their feet fast moving, but were quickly still. ‭ Then fetch'd they down Melanthius, to fulfill ‭ The equal execution; which was done ‭ In portal of the hall, and thus begun: ‭ They first slit both his nostrils, cropp'd each ear, ‭ His members tugg'd off, which the dogs did tear ‭ And chop up bleeding sweet; and, while red-hot ‭ The vice-abhorring blood was, off they smote ‭ His hands and feet; and there that work had end. ‭ Then wash'd they hands and feet that blood had stain'd, ‭ And took the house again. And then the King ‭ Euryclea calling, bade her quickly bring ‭ All-ill-expelling brimstone, and some fire, ‭ That with perfumes cast he might make entire ‭ The house's first integrity in all. ‭ And then his timely will was, she should call ‭ Her Queen and ladies; still yet charging her ‭ That all the handmaids she should first confer. ‭ She said he spake as fitted; but, before, ‭ She held it fit to change the weeds he wore, ‭ And she would others bring him, that not so ‭ His fair broad shoulders might rest clad, and show ‭ His person to his servants was to blame. ‭ "First bring me fire," said he. She went and came ‭ With fire and sulphur straight; with which the hall ‭ And of the huge house all rooms capital ‭ He throughly sweeten'd. Then went nurse to call ‭ The handmaid servants down; and up she went ‭ To tell the news, and will'd them to present ‭ Their service to their sov'reign. Down they came ‭ Sustaining torches all, and pour'd a flame ‭ Of love about their lord, with welcomes home, ‭ With huggings of his hands, with laboursome ‭ Both heads and foreheads kisses, and embraces, ‭ And plied him so with all their loving graces ‭ That tears and sighs took up his whole desire; ‭ For now he knew their hearts to him entire. ‭ THE END OF THE TWENTY-SECOND BOOK OF HOMER'S ODYSSEYS. ‭ THE TWENTY-THIRD BOOK OF HOMER'S ODYSSEYS ‭ THE ARGUMENT ‭ Ulysses to his wife is known. ‭ A brief sum of his travels shown. ‭ Himself, his son, and servants go ‭ T' approve the Wooers' overthrow. ‭ ANOTHER ARGUMENT ‭ _Ψι̑._ ‭ For all annoys ‭ Sustain'd before, ‭ The true wife's joys ‭ Now made the more. ‭ The servants thus inform'd, the matron goes ‭ Up where the Queen was cast in such repose, ‭ Affected with a fervent joy to tell ‭ What all this time she did with pain conceal. ‭ Her knees revok'd their first strength, and her feet ‭ Were borne above the ground with wings to greet ‭ The long-griev'd Queen with news her King was come; ‭ And, near her, said: "Wake, leave this withdrawn room, ‭ That now your eyes may see at length, though late, ‭ The man return'd, which, all the heavy date ‭ Your woes have rack'd out, you have long'd to see. ‭ Ulysses is come home, and hath set free ‭ His court of all your Wooers, slaught'ring all ‭ For wasting so his goods with festival, ‭ His house so vexing, and for violence done ‭ So all ways varied to his only son." ‭ She answer'd her: "The Gods have made thee mad, ‭ Of whose pow'r now thy pow'rs such proof have had. ‭ The Gods can blind with follies wisest eyes, ‭ And make men foolish so to make them wise. ‭ For they have hurt ev'n thy grave brain, that bore ‭ An understanding spirit heretofore. ‭ Why hast thou wak'd me to more tears, when Moan ‭ Hath turn'd my mind, with tears into her own? ‭ Thy madness much more blameful, that with lies ‭ Thy haste is laden, and both robs mine eyes ‭ Of most delightsome sleep, and sleep of them, ‭ That now had bound me in his sweet extreme, ‭ T' embrace my lids and close my visual spheres: ‭ I have not slept so much this twenty years, ‭ Since first my dearest sleeping-mate was gone ‭ For that too-ill-to-speak-of Ilion. ‭ Hence, take your mad steps back. If any maid ‭ Of all my train besides a part had play'd ‭ So bold to wake, and tell mine ears such lies, ‭ I had return'd her to her housewif'ries ‭ With good proof of my wrath to such rude dames. ‭ But go, your years have sav'd their younger blames." ‭ She answer'd her: "I nothing wrong your ear, ‭ But tell the truth. Your long-miss'd lord is here, ‭ And, with the Wooers' slaughter, his own hand, ‭ In chief exploit, hath to his own command ‭ Reduc'd his house; and that poor guest was he, ‭ That all those Wooers wrought such injury. ‭ Telemachus had knowledge long ago ‭ That 'twas his father, but his wisdom so ‭ Observ'd his counsels, to give surer end ‭ To that great work to which they did contend." ‭ This call'd her spirits to their conceiving places; ‭ She sprung for joy from blames into embraces ‭ Of her grave nurse, wip'd ev'ry tear away ‭ From her fair cheeks, and then began to say ‭ What nurse said over thus: "O nurse, can this ‭ Be true thou say'st? How could that hand of his ‭ Alone destroy so many? They would still ‭ Troop all together. How could he then kill ‭ Such numbers so united?" "How," said she, ‭ "I have not seen nor heard; but certainly ‭ The deed is done. We sat within in fear, ‭ The doors shut on us, and from thence might hear ‭ The sighs and groans of ev'ry man he slew, ‭ But heard nor saw more, till at length there flew ‭ Your son's voice to mine ear, that call'd to me, ‭ And bade me then come forth, and then I see ‭ Ulysses standing in the midst of all ‭ Your slaughter'd Wooers, heap'd up, like a wall, ‭ One on another round about his side. ‭ It would have done you good to have descried ‭ Your conqu'ring lord all-smear'd with blood and gore ‭ So like a lion. Straight, then, off they bore ‭ The slaughter'd carcasses, that now before ‭ The fore-court gates lie, one on another pil'd. ‭ And now your victor all the hall, defil'd ‭ With stench of hot death, is perfuming round, ‭ And with a mighty fire the hearth hath crown'd. ‭ "Thus, all the death remov'd, and ev'ry room ‭ Made sweet and sightly, that yourself should come ‭ His pleasure sent me. Come, then, take you now ‭ Your mutual fills of comfort. Grief on you ‭ Hath long and many suff'rings laid; which length, ‭ Which many suff'rings, now your virtuous strength ‭ Of uncorrupted chasteness hath conferr'd ‭ A happy end to. He that long hath err'd ‭ Is safe arriv'd at home; his wife, his son, ‭ Found safe and good; all ill that hath been done ‭ On all the doers' heads, though long prolong'd, ‭ His right hath wreak'd, and in the place they wrong'd." ‭ She answer'd: "Do not you now laugh and boast ‭ As you had done some great act, seeing most ‭ Into his being; for you know he won-- ‭ Ev'n through his poor and vile condition-- ‭ A kind of prompted thought that there was plac'd ‭ Some virtue in him fit to be embrac'd ‭ By all the house, but most of all by me, ‭ And by my son that was the progeny ‭ Of both our loves. And yet it is not he, ‭ For all the likely proofs ye plead to me,-- ‭ Some God hath slain the Wooers in disdain ‭ Of the abhorréd pride he saw so reign ‭ In those base works they did. No man alive, ‭ Or good or bad, whoever did arrive ‭ At their abodes once, ever could obtain ‭ Regard of them; and therefore their so vain ‭ And vile deserts have found as vile an end. ‭ But, for Ulysses, never will extend ‭ His wish'd return to Greece, nor he yet lives." ‭ "How strange a Queen are you," said she, "that gives ‭ No truth your credit, that your husband, set ‭ Close in his house at fire, can purchase yet ‭ No faith of you, but that he still is far ‭ From any home of his! Your wit's at war ‭ With all credulity ever! And yet now, ‭ I'll name a sign shall force belief from you: ‭ I bath'd him lately, and beheld the scar ‭ That still remains a mark too ocular ‭ To leave your heart yet blinded; and I then ‭ Had run and told you, but his hand was fain ‭ To close my lips from th' acclamation ‭ My heart was breathing, and his wisdom won ‭ My still retention, till he gave me leave ‭ And charge to tell you this. Now then receive ‭ My life for gage of his return; which take ‭ In any cruel fashion, if I make ‭ All this not clear to you." "Lov'd nurse," said she, ‭ "Though many things thou know'st, yet these things be ‭ Veil'd in the counsels th' uncreated Gods ‭ Have long time mask'd in; whose dark periods ‭ 'Tis hard for thee to see into. But come, ‭ Let's see my son, the slain, and him by whom ‭ They had their slaughter." This said, down they went; ‭ When, on the Queen's part, divers thoughts were spent, ‭ If, all this giv'n no faith, she still should stand ‭ Aloof, and question more; or his hugg'd hand ‭ And lovéd head she should at first assay ‭ With free-giv'n kisses. When her doubtful way ‭ Had pass'd the stony pavement, she took seat ‭ Against her husband, in the opposite heat ‭ The fire then cast upon the other wall. ‭ Himself set by the column of the hall, ‭ His looks cast downwards, and expected still ‭ When her incredulous and curious will ‭ To shun ridiculous error, and the shame ‭ To kiss a husband that was not the same, ‭ Would down, and win enough faith from his sight. ‭ She silent sat, and her perplexéd plight ‭ Amaze encounter'd. Sometimes she stood clear ‭ He was her husband; sometimes the ill wear ‭ His person had put on transform'd him so ‭ That yet his stamp would hardly current go. ‭ Her son, her strangeness seeing, blam'd her thus: ‭ "Mother, ungentle mother! tyrannous! ‭ In this too-curious modesty you show. ‭ Why sit you from my father, nor bestow ‭ A word on me t' enquire and clear such doubt ‭ As may perplex you? Found man ever out ‭ One other such a wife that could forbear ‭ Her lov'd lord's welcome home, when twenty year ‭ In infinite suff'rance he had spent apart. ‭ _No flint so hard is as a woman's heart."_ ‭ "Son," said she, "amaze contains my mind, ‭ Nor can I speak and use the common kind ‭ Of those enquiries, nor sustain to see ‭ With opposite looks his count'nance. If this be ‭ My true Ulysses now return'd, there are ‭ Tokens betwixt us of more fitness far ‭ To give me argument he is my lord; ‭ And my assurance of him may afford ‭ My proofs of joy for him from all these eyes ‭ With more decorum than objéct their guise ‭ To public notice." The much-suff'rer brake ‭ In laughter out, and to his son said: "Take ‭ Your mother from the prease, that she may make ‭ Her own proofs of me, which perhaps may give ‭ More cause to the acknowledgments that drive ‭ Their show thus off. But now, because I go ‭ So poorly clad, she takes disdain to know ‭ So loath'd a creature for her lovéd lord. ‭ Let us consult, then, how we may accord ‭ The town to our late action. Some one slain ‭ Hath made the all-left slaughterer of him fain ‭ To fly his friends and country; but our swords ‭ Have slain a city's most supportful lords, ‭ The chief peers of the kingdom, therefore see ‭ You use wise means t' uphold your victory." ‭ "See you to that, good father," said the son, ‭ "Whose counsels have the sov'reign glory won ‭ From all men living. None will strive with you, ‭ But with unquestion'd girlands grace your brow, ‭ To whom our whole alacrities we vow ‭ In free attendance. Nor shall our hands leave ‭ Your onsets needy of supplies to give ‭ All the effects that in our pow'rs can fall." ‭ "Then this," said he, "to me seems capital ‭ Of all choice courses: Bathe we first, and then ‭ Attire we freshly; all our maids and men ‭ Enjoining likewise to their best attire. ‭ The sacred singer then let touch his lyre, ‭ And go before us all in graceful dance, ‭ That all without, to whose ears shall advance ‭ Our cheerful accents, or of travellers by, ‭ Or firm inhabitants, solemnity ‭ Of frolic nuptials may imagine here. ‭ And this perform we, lest the massacre ‭ Of all our Wooers be divulg'd about ‭ The ample city, ere ourselves get out ‭ And greet my father in his grove of trees, ‭ Where, after, we will prove what policies ‭ Olympius shall suggest to overcome ‭ Our latest toils, and crown our welcome home." ‭ This all obey'd; bath'd, put on fresh attire ‭ Both men and women did. Then took his lyre ‭ The holy singer, and set thirst on fire ‭ With songs and faultless dances; all the court ‭ Rung with the footings that the numerous sport ‭ From jocund men drew and fair-girdled dames; ‭ Which heard abroad, thus flew the common fames: ‭ "This sure the day is when the much-woo'd Queen ‭ Is richly wed. O wretch! That hath not been ‭ So constant as to keep her ample house ‭ Till th' utmost hour had brought her foremost spouse." ‭ Thus some conceiv'd, but little knew the thing. ‭ And now Eurynomé had bath'd the King, ‭ Smooth'd him with oils, and he himself attir'd ‭ In vestures royal. Her part then inspir'd ‭ The Goddess Pallas, deck'd his head and face ‭ With infinite beauties, gave a goodly grace ‭ Of stature to him, a much plumper plight ‭ Through all his body breath'd, curls soft and bright ‭ Adorn'd his head withal, and made it show ‭ As if the flow'ry hyacinth did grow ‭ In all his pride there, in the gen'ral trim ‭ Of ev'ry lock and ev'ry curious limb. ‭ Look how a skilful artizan, well-seen ‭ In all arts metalline, as having been ‭ Taught by Minerva and the God of fire, ‭ Doth gold with silver mix so that entire ‭ They keep their self-distinction, and yet so ‭ That to the silver from the gold doth flow ‭ A much more artificial lustre than his own, ‭ And thereby to the gold itself is grown ‭ A greater glory than if wrought alone, ‭ Both being stuck off by either's mixtion; ‭ So did Minerva her's and his combine, ‭ He more in her, she more in him, did shine. ‭ Like an Immortal from the bath he rose, ‭ And to his wife did all his grace dispose, ‭ Encount'ring this her strangeness: "Cruel dame ‭ Of all that breathe, the Gods past steel and flame ‭ Have made thee ruthless. Life retains not one ‭ Of all dames else that bears so overgrown ‭ A mind with abstinence, as twenty years ‭ To miss her husband drown'd in woes and tears, ‭ And at his coming keep aloof, and fare ‭ As of his so long absence and his care ‭ No sense had seiz'd her. Go, nurse, make a bed, ‭ That I alone may sleep; her heart is dead ‭ To all reflection!" To him thus replied ‭ The wise Penelope: "Man half-deified, ‭ 'Tis not my fashion to be taken straight ‭ With bravest men, nor poorest use to sleight. ‭ Your mean appearance made not me retire, ‭ Nor this your rich show makes me now admire, ‭ Nor moves at all; for what is all to me ‭ If not my husband? All his certainty ‭ I knew at parting; but, so long apart, ‭ The outward likeness holds no full desert ‭ For me to trust to. Go, nurse, see addrest ‭ A soft bed for him, and the single rest ‭ Himself affects so. Let it be the bed ‭ That stands within our bridal chamber-sted, ‭ Which he himself made. Bring it forth from thence, ‭ And see it furnish'd with magnificence." ‭ This said she to assay him, and did stir ‭ Ev'n his establish'd patience; and to her ‭ Whom thus he answer'd: "Woman! your words prove ‭ My patience strangely. Who is it can move ‭ My bed out of his place? It shall oppress ‭ Earth's greatest understander; and, unless ‭ Ev'n God himself come, that can eas'ly grace ‭ Men in their most skills, it shall hold his place; ‭ For man he lives not that (as not most skill'd, ‭ So not most young) shall easily make it yield, ‭ If, building on the strength in which he flows, ‭ He adds both levers too and iron crows: ‭ For in the fixture of the bed is shown ‭ A master-piece, a wonder; and 'twas done ‭ By me, and none but me, and thus was wrought: ‭ There was an olive-tree that had his grought ‭ Amidst a hedge, and was of shadow proud, ‭ Fresh, and the prime age of his verdure show'd, ‭ His leaves and arms so thick that to the eye ‭ It show'd a column for solidity. ‭ To this had I a comprehension ‭ To build my bridal bow'r; which all of stone, ‭ Thick as the tree of leaves, I rais'd, and cast ‭ A roof about it nothing meanly grac'd, ‭ Put glued doors to it, that op'd art enough, ‭ Then from the olive ev'ry broad-leav'd bough ‭ I lopp'd away; then fell'd the tree; and then ‭ Went over it both with my axe and plane, ‭ Both govern'd by my line, And then I hew'd ‭ My curious bedstead out; in which I shew'd ‭ Work of no common hand. All this begun, ‭ I could not leave till to perfection ‭ My pains had brought it; took my wimble, bor'd ‭ The holes, as fitted, and did last afford ‭ The varied ornament, which show'd no want ‭ Of silver, gold, and polish'd elephant. ‭ An ox-hide dyed in purple then I threw ‭ Above the cords. And thus to curious view ‭ I hope I have objected honest sign ‭ To prove I author nought that is not mine. ‭ But if my bed stand unremov'd or no, ‭ O woman, passeth human wit to know." ‭ This sunk her knees and heart, to hear so true ‭ The signs she urg'd; and first did tears ensue ‭ Her rapt assurance; then she ran and spread ‭ Her arms about his neck, kiss'd oft his head, ‭ And thus the curious stay she made excus'd: ‭ "Ulysses! Be not angry that I us'd ‭ Such strange delays to this, since heretofore ‭ Your suff'ring wisdom hath the garland wore ‭ From all that breathe; and 'tis the Gods that, thus ‭ With mutual miss so long afflicting us, ‭ Have caus'd my coyness; to our youths envied ‭ That wish'd society that should have tied ‭ Our youths and years together; and since now ‭ Judgment and Duty should our age allow ‭ As full joys therein as in youth and blood, ‭ See all young anger and reproof withstood ‭ For not at first sight giving up my arms, ‭ My heart still trembling lest the false alarms ‭ That words oft strike-up should ridiculize me. ‭ Had Argive Helen known credulity ‭ Would bring such plagues with it, and her again, ‭ As authoress of them all, with that foul stain ‭ To her and to her country, she had stay'd ‭ Her love and mixture from a stranger's bed; ‭ But God impell'd her to a shameless deed, ‭ Because she had not in herself decreed, ‭ Before th' attempt, that such acts still were shent ‭ As simply in themselves as in th' event ‭ By which not only she herself sustains, ‭ But we, for her fault, have paid mutual pains. ‭ Yet now, since these signs of our certain bed ‭ You have discover'd, and distinguishéd ‭ From all earth's others, no one man but you ‭ Yet ever getting of it th' only show, ‭ Nor one of all dames but myself and she ‭ My father gave, old Actor's progeny, ‭ Who ever guarded to ourselves the door ‭ Of that thick-shaded chamber, I no more ‭ Will cross your clear persuasion, though till now ‭ I stood too doubtful and austere to you," ‭ These words of hers, so justifying her stay, ‭ Did more desire of joyful moan convey ‭ To his glad mind than if at instant sight ‭ She had allow'd him all his wishes' right. ‭ He wept for joy, t' enjoy a wife so fit ‭ For his grave mind, that knew his depth of wit, ‭ And held chaste virtue at a price so high, ‭ And as sad men at sea when shore is nigh, ‭ Which long their hearts have wish'd, their ship quite lost ‭ By Neptune's rigour, and they vex'd and tost ‭ 'Twixt winds and black waves, swimming for their lives, ‭ A few escap'd, and that few that survives, ‭ All drench'd in foam and brine, crawl up to land, ‭ With joy as much as they did worlds command; ‭ So dear to this wife was her husband's sight, ‭ Who still embrac'd his neck, and had, till light ‭ Display'd her silver ensign, if the Dame, ‭ That bears the blue sky intermix'd with flame ‭ In her fair eyes, had not infix'd her thought ‭ On other joys, for loves so hardly brought ‭ To long'd-for meeting; who th' extended night ‭ Withheld in long date, nor would let the light ‭ Her wing-hoov'd horse join--Lampus, Phaeton-- ‭ Those ever-colts that bring the morning on ‭ To worldly men, but, in her golden chair, ‭ Down to the ocean by her silver hair ‭ Bound her aspirings. Then Ulysses said: ‭ "O wife! Nor yet are my contentions stay'd. ‭ A most unmeasur'd labour long and hard ‭ Asks more performance; to it being prepar'd ‭ By grave Tiresiás, when down to hell ‭ I made dark passage, that his skill might tell ‭ My men's return and mine. But come, and now ‭ Enjoy the sweet rest that our Fates allow." ‭ "The place of rest is ready," she replied, ‭ "Your will at full serve, since the Deified ‭ Have brought you where your right is to command. ‭ But since you know, God making understand ‭ Your searching mind, inform me what must be ‭ Your last set labour; since 'twill fall to me, ‭ I hope, to hear it after, tell me now. ‭ _The greatest pleasure is before to know."_ ‭ "Unhappy!" said Ulysses; "To what end ‭ Importune you this labour? It will lend ‭ Nor you nor me delight, but you shall know ‭ I was commanded yet more to bestow ‭ My years in travel, many cities more ‭ By sea to visit; and when first for shore ‭ I left my shipping, I was will'd to take ‭ A naval oar in hand, and with it make ‭ My passage forth till such strange men I met ‭ As knew no sea, nor ever salt did eat ‭ With any victuals, who the purple beaks ‭ Of ships did never see, nor that which breaks ‭ The waves in curls, which is a fan-like oar, ‭ And serves as wings with which a ship doth soar. ‭ To let me know, then, when I was arriv'd ‭ On that strange earth where such a people liv'd, ‭ He gave me this for an unfailing sign: ‭ When any one that took that oar of mine, ‭ Borne on my shoulder, for a corn-cleanse fan, ‭ I met ashore, and show'd to be a man ‭ Of that land's labour, there had I command ‭ To fix mine oar, and offer on that strand ‭ T' imperial Neptune, whom I must implore, ‭ A lamb, a bull, and sow-ascending boar; ‭ And then turn home, where all the other Gods ‭ That in the broad heav'n made secure abodes ‭ I must solicit--all my curious heed ‭ Giv'n to the sev'ral rites they have decreed-- ‭ With holy hecatombs; and then, at home, ‭ A gentle death should seize me that would come ‭ From out the sea, and take me to his rest ‭ In full ripe age, about me living blest ‭ My loving people; to which, he presag'd, ‭ The sequel of my fortunes were engag'd." ‭ "If then," said she, "the Gods will please t' impose ‭ A happier being to your fortune's close ‭ Than went before, your hope gives comfort strength ‭ That life shall lend you better days at length." ‭ While this discourse spent mutual speech, the bed ‭ Eurynomé and nurse had made, and spread ‭ With richest furniture, while torches spent ‭ Their parcel-gilt thereon. To bed then went ‭ The aged nurse; and, where their sov'reigns were, ‭ Eurynomé, the chambermaid, did bear ‭ A torch, and went before them to their rest; ‭ To which she left them and for her's addrest. ‭ The King and Queen then now, as newly-wed, ‭ Resum'd the old laws of th' embracing bed. ‭ Telemachus and both his herdsmen then ‭ Dissolv'd the dances both to maids and men; ‭ Who in their shady roofs took timely sleep. ‭ The bride and bridegroom having ceas'd to keep ‭ Observéd love-joys, from their fit delight ‭ They turn'd to talk. The Queen then did recite ‭ What she had suffer'd by the hateful rout ‭ Of harmful Wooers, who had eat her out ‭ So many oxen and so many sheep, ‭ How many tun of wine their drinking deep ‭ Had quite exhausted. Great Ulysses then ‭ Whatever slaughters he had made of men, ‭ Whatever sorrows he himself sustain'd, ‭ Repeated amply; and her ears remain'd ‭ With all delight attentive to their end, ‭ Nor would one wink sleep till he told her all, ‭ Beginning where he gave the Cicons fall; ‭ From thence his pass to the Lotophagi; ‭ The Cyclop's acts, the putting out his eye, ‭ And wreak of all the soldiers he had eat, ‭ No least ruth shown to all they could entreat; ‭ His way to Æolus; his prompt receit ‭ And kind dismission; his enforc'd retreat ‭ By sudden tempest to the fishy main, ‭ And quite distraction from his course again; ‭ His landing at the Læstrigonian port, ‭ Where ships and men in miserable sort ‭ Met all their spoils, his ship and he alone ‭ Got off from the abhorr'd confusión; ‭ His pass to Circe, her deceits and arts; ‭ His thence descension to th' Infernal parts; ‭ His life's course of the Theban prophet learn'd, ‭ Where all the slaughter'd Grecians he discern'd, ‭ And lovéd mother; his astonish'd ear ‭ With what the Siren's voices made him hear; ‭ His 'scape from th' erring rocks, which Scylla was, ‭ And rough Charybdis, with the dang'rous pass ‭ Of all that touch'd there; his Sicilian ‭ Offence giv'n to the Sun; his ev'ry man ‭ Destroy'd by thunder vollied out of heav'n, ‭ That split his ship; his own endeavours driv'n ‭ To shift for succours on th' Ogygian shore, ‭ Where Nymph Calypso such affection bore ‭ To him in his arrival, that with feast ‭ She kept him in her caves, and would have blest ‭ His welcome life with an immortal state ‭ Would he have stay'd and liv'd her nuptial mate, ‭ All which she never could persuade him to; ‭ His pass to the Phæacians spent in woe; ‭ Their hearty welcome of him, as he were ‭ A God descended from the starry sphere; ‭ Their kind dismission of him home with gold, ‭ Brass, garments, all things his occasions would. ‭ This last word us'd, sleep seiz'd his weary eye ‭ That salves all care to all mortality. ‭ In mean space Pallas entertain'd intent ‭ That when Ulysses thought enough time spent ‭ In love-joys with his wife, to raise the day, ‭ And make his grave occasions call away. ‭ The morning rose and he, when thus he said: ‭ "O Queen, now satiate with afflictions laid ‭ On both our bosoms,--you oppresséd here ‭ With cares for my return, I ev'rywhere ‭ By Jove and all the other Deities tost ‭ Ev'n till all hope of my return was lost,-- ‭ And both arriv'd at this sweet haven, our bed, ‭ Be your care us'd to see administ'red ‭ My house-possessions left. Those sheep, that were ‭ Consum'd in surfeits by your Wooers here, ‭ I'll forage to supply with some; and more ‭ The suff'ring Grecians shall be made restore, ‭ Ev'n till our stalls receive their wonted fill. ‭ "And now, to comfort my good father's ill ‭ Long suffer'd for me, to the many-tree'd ‭ And ample vineyard grounds it is decreed ‭ In my next care that I must haste and see ‭ His long'd-for presence. In the mean time, be ‭ Your wisdom us'd, that since, the sun ascended, ‭ The fame will soon be through the town extended ‭ Of those I here have slain, yourself, got close ‭ Up to your chamber, see you there repose, ‭ Cheer'd with your women, and nor look afford ‭ Without your court, nor any man a word." ‭ This said, he arm'd; to arms both son and swain ‭ His pow'r commanding, who did entertain ‭ His charge with spirit, op'd the gates and out, ‭ He leading all. And now was hurl'd about ‭ Aurora's ruddy fire; through all whose light ‭ Minerva led them through the town from sight. ‭ THE END OF THE TWENTY-THIRD BOOK OF HOMER'S ODYSSEYS. ‭ THE TWENTY-FOURTH BOOK OF HOMER'S ODYSSEYS ‭ THE ARGUMENT ‭ By Mercury the Wooers' souls ‭ Are usher'd to th' infernal pools. ‭ Ulysses with Laertes met, ‭ The people are in uproar set ‭ Against them, for the Wooers' ends; ‭ Whom Pallas stays and renders friends. ‭ ANOTHER ARGUMENT ‭ _Ω._ ‭ The uproar's fire, ‭ The people's fall: ‭ The grandsire, sire, ‭ And son, to all. ‭ Cyllenian Hermes, with his golden rod, ‭ The Wooers' souls, that yet retain'd abode ‭ Amidst their bodies, call'd in dreadful rout ‭ Forth to th' Infernals; who came murmuring out. ‭ And as amidst the desolate retreat ‭ Of some vast cavern, made the sacred seat ‭ Of austere spirits, bats with breasts and wings ‭ Clasp fast the walls, and each to other clings, ‭ But, swept off from their coverts, up they rise ‭ And fly with murmurs in amazeful guise ‭ About the cavern; so these, grumbling, rose ‭ And flock'd together. Down before them goes ‭ None-hurting Mercury to Hell's broad ways, ‭ And straight to those straits; where the ocean stays ‭ His lofty current in calm deeps, they flew, ‭ Then to the snowy rock they next withdrew, ‭ And to the close of Phœbus' orient gates, ‭ The nation then of dreams, and then the states ‭ Of those souls' idols that the weary dead ‭ Gave up in earth, which in a flow'ry mead ‭ Had habitable situatión. ‭ And there they saw the soul of Thetis' son, ‭ Of good Patroclus, brave Antilochus, ‭ And Ajax, the supremely strenuous ‭ Of all the Greek host next Pelëion; ‭ All which assembled about Maia's son. ‭ And to them, after, came the mournful ghost ‭ Of Agamemnon, with all those he lost ‭ In false Ægisthus' court. Achilles then ‭ Beholding there that mighty king of men, ‭ Deplor'd his plight, and said: "O Atreus' son! ‭ Of all heroës, all opinion ‭ Gave thee for Jove's most lov'd, since most command ‭ Of all the Greeks he gave thy eminent hand ‭ At siege of Ilion, where we suffer'd so. ‭ And is the issue this, that first in woe ‭ Stern Fate did therefore set thy sequel down? ‭ _None borne past others' Fates can pass his own._ ‭ I wish to heav'n that in the height of all ‭ Our pomp at Ilion Fate had sign'd thy fall, ‭ That all the Greeks might have advanc'd to thee ‭ A famous sepulchre, and Fame might see ‭ Thy son giv'n honour in thy honour'd end! ‭ But now a wretched death did Fate extend ‭ To thy confusion and thy issue's shame." ‭ "O Thetis' son," said he, "the vital flame ‭ Extinct at Ilion, far from th' Argive fields, ‭ The style of Blessed to thy virtue yields. ‭ About thy fall the best of Greece and Troy ‭ Were sacrific'd to slaughter. Thy just joy ‭ Conceiv'd in battle with some worth forgot ‭ In such a death as great Apollo shot ‭ At thy encounters. Thy brave person lay ‭ Hid in a dusty whirlwind, that made way ‭ With human breaths spent in thy ruin's state ‭ Thou, great, wert greatly valued in thy fate. ‭ All day we fought about thee; nor at all ‭ Had ceas'd our conflict, had not Jove let fall ‭ A storm that forc'd off our unwilling feet. ‭ But, having brought thee from the fight to fleet, ‭ Thy glorious person, bath'd and balm'd, we laid ‭ Aloft a bed; and round about thee paid ‭ The Greeks warm tears to thy deplor'd decease, ‭ Quite daunted, cutting all their curls' increase. ‭ Thy death drave a divine voice through the seas ‭ That started up thy mother from the waves; ‭ And all the márine Godheads left their caves, ‭ Consorting to our fleet her rapt repair. ‭ The Greeks stood frighted to see sea and air ‭ And earth combine so in thy loss's sense, ‭ Had taken ship and fled for ever thence, ‭ If old much-knowing-Nestor had not stay'd ‭ Their rushing off; his counsels having sway'd ‭ In all times former with such cause their courses; ‭ Who bade contain themselves, and trust their forces, ‭ For all they saw was Thetis come from sea, ‭ With others of the wat'ry progeny, ‭ To see and mourn for her deceaséd son. ‭ Which stay'd the fears that all to flight had won; ‭ And round about thee stood th' old sea-God's Seeds ‭ Wretchedly mourning, their immortal weeds ‭ Spreading upon thee. All the sacred Nine ‭ Of deathless Muses paid thee dues divine, ‭ By varied turns their heav'nly voices venting, ‭ All in deep passion for thy death consenting. ‭ And then of all our army not an eye ‭ You could have seen undrown'd in misery, ‭ The moving Muse so rul'd in ev'ry mind. ‭ Full seventeen days and nights our tears confin'd ‭ To celebration of thy mournéd end; ‭ Both men and Gods did in thy moan contend. ‭ The eighteenth day we spent about thy heap ‭ Of dying fire. Black oxen, fattest sheep ‭ We slew past number. Then the precious spoil, ‭ Thy corse, we took up, which with floods of oil ‭ And pleasant honey we embalm'd, and then ‭ Wrapp'd thee in those robes that the Gods did rain. ‭ In which we gave thee to the hallow'd flame; ‭ To which a number of heroical name, ‭ As prest to sacrifice their vital right ‭ To thy dead ruins while so bright they burn'd. ‭ Both foot and horse brake in, and fought and mourn'd ‭ In infinite tumult. But when all the night ‭ The rich flame lasted, and that wasted quite ‭ Thy body was with the enamour'd fire: ‭ We came in early morn, and an entire ‭ Collection made of ev'ry ivory bone; ‭ Which wash'd in wine, and giv'n fit unctión, ‭ A two-ear'd bowl of gold thy mother gave, ‭ By Bacchus giv'n her and did form receive ‭ From Vulcan's famous hand, which, O renown'd ‭ Great Thetis' son, with thy fair bones we crown'd ‭ Mix'd with the bones of Menœtiades ‭ And brave Antilochus; who, in decease ‭ Of thy Patroclus, was thy favour's dear. ‭ About thee then a matchless sepulchre ‭ The sacred host of the Achaians rais'd ‭ Upon the Hellespont, where most it seiz'd, ‭ For height and conspicuity, the eyes ‭ Of living men and their posterities. ‭ Thy mother then obtain'd the Gods' consent ‭ To institute an honour'd game, that spent ‭ The best approvement of our Grecian fames. ‭ In whose praise I must say that many games ‭ About heroës' sepulchres mine eyes ‭ Have seen perform'd, but these bore off the prize ‭ With miracles to me from all before. ‭ In which thy silver-footed mother bore ‭ The institution's name, but thy deserts, ‭ Being great with heav'n, caus'd all the eminent parts. ‭ And thus, through all the worst effects of Fate, ‭ Achilles' fame ev'n Death shall propagate. ‭ While anyone shall lend the light an eye ‭ Divine Æacides shall never die. ‭ But wherein can these comforts be conceiv'd ‭ As rights to me? When, having quite achiev'd ‭ An end with safety, and with conquest, too, ‭ Of so unmatch'd a war, what none could do ‭ Of all our enemies there, at home a friend ‭ And wife have giv'n me inglorious end?" ‭ While these thus spake, the Argus-killing spy ‭ Brought-near Ulysses' noble victory ‭ To their renew'd discourse, in all the ends ‭ The Wooers' suffer'd, and show'd those his friends; ‭ Whom now amaze invaded with the view ‭ And made give back; yet Agamemnon knew ‭ Melanthius' heir, much-fam'd Amphimedon, ‭ Who had in Ithaca guest-favours shown ‭ To great Atrides; who first spake, and said: ‭ "Amphimedon! What suff'rance hath been laid ‭ On your alive parts that hath made you make ‭ This land of darkness the retreat you take, ‭ So all together, all being like in years, ‭ Nor would a man have choos'd, of all the peers ‭ A city honours, men to make a part ‭ More strong for any object? Hath your smart ‭ Been felt from Neptune, being at sea--his wrath ‭ The winds and waves exciting to your scathe? ‭ Or have offensive men impos'd this fate-- ‭ Your oxen driving, or your flock's estate? ‭ Or for your city fighting and your wives, ‭ Have deaths untimely seiz'd your best-tim'd lives? ‭ Inform me truly. I was once your guest, ‭ When I and Menelaus had profest ‭ First arms for Ilion, and were come ashore ‭ On Ithaca, with purpose to implore ‭ Ulysses' aid, that city-racing man, ‭ In wreak of the adult'rous Phrygian. ‭ Retain not you the time? A whole month's date ‭ We spent at sea, in hope to instigate ‭ In our arrival old Laertes' son, ‭ Whom, hardly yet, to our design we won." ‭ The soul made answer: "Worthiest king of men, ‭ I well remember ev'ry passage then ‭ You now reduce to thought, and will relate ‭ The truth in whole form of our timeless fate: ‭ "We woo'd the wife of that long-absent king, ‭ Who (though her second marriage were a thing ‭ Of most hate to her) she would yet deny ‭ At no part our affections, nor comply ‭ With any in performance, but decreed, ‭ In her delays, the cruel Fates we feed. ‭ Her craft was this: She undertook to weave ‭ A funeral garment destin'd to receive ‭ The corse of old Laertes; being a task ‭ Of infinite labour, and which time would ask. ‭ In midst of whose attempt she caus'd our stay ‭ With this attraction: 'Youths, that come in way ‭ Of honour'd nuptials to me, though my lord ‭ Abide amongst the dead, yet cease to board ‭ My choice for present nuptials, and sustain, ‭ Lest what is past me of this web be vain, ‭ Till all receive perfection. 'Tis a weed ‭ Dispos'd to wrap in at his funeral need ‭ The old Laertes; who, possessing much, ‭ Would, in his want of rites as fitting, touch ‭ My honour highly with each vulgar dame.' ‭ Thus spake she, and persuaded; and her frame ‭ All-day she labour'd, her day's work not small, ‭ But ev'ry night-time she unwrought it all. ‭ Three years continuing this imperfect task; ‭ But when the fourth year came her sleights could mask ‭ In no more covert, since her trusted maid ‭ Her whole deceit to our true note betray'd. ‭ With which surpriz'd, she could no more protract ‭ Her work's perfection, but gave end exact ‭ To what remain'd, wash'd-up, and set thereon ‭ A gloss so bright that like the sun and moon ‭ The whole work show'd together. And when now ‭ Of mere necessity her honour'd vow ‭ She must make good to us, ill-fortune brought ‭ Ulysses home, who yet gave none one thought ‭ Of his arrival, but far-off at field ‭ Liv'd with his herdsman, nor his trust would yield ‭ Note of his person, but liv'd there as guest, ‭ Ragg'd as a beggar in that life profest. ‭ At length Telemachus left Pylos' sand, ‭ And with a ship fetch'd soon his native land, ‭ When yet not home he went, but laid his way ‭ Up to his herdsman where his father lay; ‭ And where both laid our deaths. To town then bore ‭ The swine-herd and his King, the swain before, ‭ Telemachus in other ways bestow'd ‭ His course home first, t' associate us that woo'd. ‭ The swain the King led after, who came on ‭ Raggéd and wretched, and still lean'd upon ‭ A borrow'd staff. At length he reach'd his home, ‭ Where (on the sudden and so wretched come) ‭ Nor we nor much our elders once did dream ‭ Of his return there, but did wrongs extreme ‭ Of words and blows to him; all which he bore ‭ With that old patience he had learn'd before. ‭ But when the mind of Jove had rais'd his own, ‭ His son and he fetch'd all their armour down, ‭ Fast-lock'd the doors, and, to prepare their use, ‭ He will'd his wife, for first mean, to produce ‭ His bow to us to draw; of which no one ‭ Could stir the string; himself yet set upon ‭ The deadly strength it held, drew all with ease, ‭ Shot through the steels, and then began to seize ‭ Our armless bosoms; striking first the breast ‭ Of king Antinous, and then the rest ‭ In heaps turn'd over; hopeful of his end ‭ Because some God, he knew, stood firm his friend. ‭ Nor prov'd it worse with him, but all in flood ‭ The pavement straight blush'd with our vital blood. ‭ And thus our souls came here; our bodies laid ‭ Neglected in his roofs, no word convey'd ‭ To any friend to take us home and give ‭ Our wounds fit balming, nor let such as live ‭ Entomb our deaths, and for our fortunes shed ‭ Those tears and dead-rites that renown the dead." ‭ Atrides' ghost gave answer: "O bless'd son ‭ Of old Laertes, thou at length hast won ‭ With mighty virtue thy unmatchéd wife. ‭ How good a knowledge, how untouch'd a life, ‭ Hath wise Penelope! How well she laid ‭ Her husband's rights up, whom she lov'd a maid! ‭ For which her virtues shall extend applause, ‭ Beyond the circles frail mortality draws; ‭ The deathless in this vale of death comprising ‭ Her praise in numbers into infinites rising. ‭ The daughter Tyndarus begat begot ‭ No such chaste thoughts, but cut the virgin knot ‭ That knit her spouse and her with murd'rous swords. ‭ For which posterities shall put hateful words ‭ To notes of her that all her sex defam'd, ‭ And for her ill shall ev'n the good be blam'd." ‭ To this effect these these digressions made ‭ In hell, earth's dark and ever-hiding shade. ‭ Ulysses and his son, now past the town, ‭ Soon reach'd the field elaborately grown ‭ By old Laertes' labour, when, with cares ‭ For his lost son, he left all court affairs, ‭ And took to this rude upland; which with toil ‭ He made a sweet and habitable soil; ‭ Where stood a house to him; about which ran, ‭ In turnings thick and labyrinthian, ‭ Poor hovels, where his necessary men ‭ That did those works (of pleasure to him then) ‭ Might sit, and eat, and sleep. In his own house ‭ An old Sicilian dame liv'd, studious ‭ To serve his sour age with her cheerful pains. ‭ Then said Ulysses to his son and swains: ‭ "Go you to town, and for your dinner kill ‭ The best swine ye can choose; myself will still ‭ Stay with my father, and assay his eye ‭ If my acknowledg'd truth it can descry, ‭ Or that my long time's travel doth so change ‭ My sight to him that I appear as strange." ‭ Thus gave he arms to them, and home they hied. ‭ Ulysses to the fruitful field applied ‭ His present place; nor found he Dolius there, ‭ His sons, or any servant, anywhere ‭ In all that spacious ground; all gone from thence ‭ Were dragging bushes to repair a fence, ‭ Old Dolius leading all. Ulysses found ‭ His father far above in that fair ground, ‭ Employ'd in proining of a plant; his weeds ‭ All torn and tatter'd, fit for homely deeds, ‭ But not for him. Upon his legs he wore ‭ Patch'd boots to guard him from the bramble's gore; ‭ His hands had thorn-proof hedging mittens on; ‭ His head a goat-skin casque; through all which shone ‭ His heart giv'n over to abjectest moan. ‭ Him when Ulysses saw consum'd with age, ‭ And all the ensigns on him that the rage ‭ Of grief presented, he brake out in tears; ‭ And, taking stand then where a tree of pears ‭ Shot high his forehead over him, his mind ‭ Had much contention, if to yield to kind, ‭ Make straight way to his father, kiss, embrace, ‭ Tell his return, and put on all the face ‭ And fashion of his instant-told return; ‭ Or stay th' impulsion, and the long day burn ‭ Of his quite loss giv'n in his father's fear ‭ A little longer, trying first his cheer ‭ With some free dalliance, th' earnest being so near. ‭ This course his choice preferr'd, and forth he went. ‭ His father then his aged shoulders bent ‭ Beneath what years had stoop'd, about a tree ‭ Busily digging: "O, old man," said he, ‭ "You want no skill to dress and deck your ground, ‭ For all your plants doth order'd distance bound. ‭ No apple, pear, or olive, fig; or vine, ‭ Nor any plat or quarter you confine ‭ To grass or flow'rs stands empty of your care, ‭ Which shows exact in each peculiar; ‭ And yet (which let not move you) you bestow ‭ No care upon yourself, though to this show ‭ Of outward irksomeness to what you are ‭ You labour with an inward froward care, ‭ Which is your age, that should wear all without ‭ More neat and cherishing. I make no doubt ‭ That any sloth you use procures your lord ‭ To let an old man go so much abhorr'd ‭ In all his weeds; nor shines there in your look ‭ A fashion and a goodliness so took ‭ With abject qualities to merit this ‭ Nasty entreaty. Your resemblance is ‭ A very king's, and shines through this retreat. ‭ You look like one that having wash'd and eat ‭ Should sleep securely, lying sweet and neat. ‭ _It is the ground of age, when cares abuse it, ‭ To know life's end, and, as 'tis sweet, so use it._ ‭ "But utter truth, and tell what lord is he ‭ That rates your labour and your liberty? ‭ Whose orchard is it that you husband thus? ‭ Or quit me this doubt, for if Ithacus ‭ This kingdom claims for his, the man I found ‭ At first arrival here is hardly sound ‭ Of brain or civil, not enduring stay ‭ To tell nor hear me my inquiry out ‭ Of that my friend, if still he bore about ‭ His life and being, or were <DW37>'d to death, ‭ And in the house of him that harboureth ‭ The souls of men. For once he liv'd my guest; ‭ My land and house retaining interest ‭ In his abode there; where there sojourn'd none ‭ As guest from any foreign region ‭ Of more price with me. He deriv'd his race ‭ From Ithaca, and said his father was ‭ Laertes, surnam'd Arcesiades, ‭ I had him home, and all the offices ‭ Perform'd to him that fitted any friend, ‭ Whose proof I did to wealthy gifts extend: ‭ Seven talents gold; a bowl all-silver, set ‭ With pots of flowers; twelve robes that had no pleat! ‭ Twelve cloaks, or mantles, of delicious dye; ‭ Twelve inner weeds; twelve suits of tapestry. ‭ I gave him likewise women skill'd in use ‭ Of loom and needle, freeing him to choose ‭ Four the most fair." His father, weeping, said: ‭ "Stranger! The earth to which you are convey'd ‭ Is Ithaca; by such rude men possess'd, ‭ Unjust and insolent, as first address'd ‭ To your encounter; but the gifts you gave ‭ Were giv'n, alas! to the ungrateful grave. ‭ If with his people, where you now arrive, ‭ Your fate had been to find your friend alive, ‭ You should have found like guest-rites from his hand, ‭ Like gifts, and kind pass to your wishéd land. ‭ But how long since receiv'd you for your guest ‭ Your friend, my son, who was th' unhappiest ‭ Of all men breathing, if he were at all? ‭ O born when Fates and ill-aspects let fall ‭ A cruel influence for him! Far away ‭ From friends and country destin'd to allay. ‭ The sea-bred appetites, or, left ashore, ‭ To be by fowls and upland monsters tore, ‭ His life's kind authors nor his wealthy wife ‭ Bemoaning, as behov'd, his parted life, ‭ Nor closing, as in honour's course it lies ‭ To all men dead, in bed his dying eyes. ‭ But give me knowledge of your name and race. ‭ What city bred you? Where the anchoring-place ‭ Your ship now rides-at lies that shor'd you here ‭ And where your men? Or, if a passenger ‭ In other keels you came, who (giving land ‭ To your adventures here, some other strand ‭ To fetch in further course) have left to us ‭ Your welcome presence?" His reply was thus: ‭ "I am of Alybandé, where I hold ‭ My name's chief house, to much renown extoll'd. ‭ My father Aphidantes, fam'd to spring ‭ From Polypemon, the Molossian king. ‭ My name Eperitus. My taking land ‭ On this fair Isle was rul'd by the command ‭ Of God or fortune, quite against consent ‭ Of my free purpose, that in course was bent ‭ For th' isle Sicania. My ship is held ‭ Far from the city, near an ample field. ‭ And for Ulysses, since his pass from me ‭ 'Tis now five years. Unbless'd by destiny, ‭ That all this time hath had the fate to err! ‭ Though, at his parting, good birds did augur ‭ His putting-off, and on his right hand flew, ‭ Which to his passage my affection drew, ‭ His spirit joyful; and my hope was now ‭ To guest with him, and see his hand bestow ‭ Rites of our friendship." This a cloud of grief ‭ Cast over all the forces of his life. ‭ With both his hands the burning dust he swept ‭ Up from the earth, which on his head he heapt, ‭ And fetch'd a sigh as in it life were broke. ‭ Which grieved his son, and gave so smart a stroke ‭ Upon his nostrils with the inward stripe, ‭ That up the vein rose there; and weeping ripe ‭ He was to see his sire feel such woe ‭ For his dissembled joy; which now let go, ‭ He sprung from earth, embrac'd and kiss'd his sire, ‭ And said: "O father! He of whom y' enquire ‭ Am I myself, that, from you twenty years, ‭ Is now return'd. But do not break in tears, ‭ For now we must not forms of kind maintain, ‭ But haste and guard the substance. I have slain ‭ All my wife's Wooers, so revenging now ‭ Their wrong so long time suffer'd. Take not you ‭ The comfort of my coming then to heart ‭ At this glad instant, but, in prov'd desert ‭ Of your grave judgment, give moan glad suspense, ‭ And on the sudden put this consequence ‭ In act as absolute, as all time went ‭ To ripening of your resolute assent." ‭ All this haste made not his staid faith so free ‭ To trust his words; who said: "If you are he, ‭ Approve it by some sign." "This scar then see," ‭ Replied Ulysses, "giv'n me by the boar ‭ Slain in Parnassus, I being sent before ‭ By your's and by my honour'd mother's will, ‭ To see your sire Autolycus fulfill ‭ The gifts he vow'd at giving of my name. ‭ I'll tell you, too, the trees, in goodly frame ‭ Of this fair orchard, that I ask'd of you ‭ Being yet a child, and follow'd for your show ‭ And name of ev'ry tree. You gave me then ‭ Of fig-trees forty, apple-bearers ten, ‭ Pear-trees thirteen, and fifty ranks of vine; ‭ Each one of which a season did confine ‭ For his best eating. Not a grape did grow ‭ That grew not there, and had his heavy brow ‭ When Jove's fair daughters, the all ripening Hours, ‭ Gave timely date to it." This charg'd the pow'rs ‭ Both of his knees and heart with such impression ‭ Of sudden comfort, that it gave possession ‭ Of all to Trance, the signs were all so true, ‭ And did the love that gave them so renew. ‭ He cast his arms about his son and sunk, ‭ The circle slipping to his feet; so shrunk ‭ Were all his age's forces with the fire ‭ Of his young love rekindled. The old sire ‭ The son took up quite lifeless. But his breath ‭ Again respiring, and his soul from death ‭ His body's pow'r recov'ring, out he cried, ‭ And said: "O Jupiter! I now have tried ‭ That still there live in heav'n rememb'ring Gods ‭ Of men that serve them; though the periods ‭ They set on their appearances are long ‭ In best men's suff'rings, yet as sure as strong ‭ They are in comforts, be their strange delays ‭ Extended never so from days to days. ‭ Yet see the short joys or the soon-mix'd fears ‭ Of helps withheld by them so many years! ‭ For if the Wooers now have paid the pain ‭ Due to their impious pleasures, now again ‭ Extreme fear takes me, lest we straight shall see ‭ The Ithacensians here in mutiny, ‭ Their messengers dispatch'd to win to friend ‭ The Cephallenian cities." "Do not spend ‭ Your thoughts on these cares," said his suff'ring son, ‭ "But be of comfort, and see that course run ‭ That best may shun the worst. Our house is near, ‭ Telemachus and both his herdsmen there ‭ To dress our supper with their utmost haste; ‭ And thither haste we." This said, forth they past, ‭ Came home, and found Telemachus at feast ‭ With both his swains; while who had done, all drest ‭ With baths and balms and royally array'd ‭ The old king was by his Sicilian maid. ‭ By whose side Pallas stood, his crook'd-age straight'ning, ‭ His flesh more plumping, and his looks enlight'ning. ‭ Who issuing then to view, his son admir'd ‭ The Gods' aspects into his form inspir'd, ‭ And said: "O father, certainly some God ‭ By your addression in this state hath stood, ‭ More great, more rev'rend, rend'ring you by far ‭ At all your parts than of yourself you are!" ‭ "I would to Jove," said he, "the Sun, and She ‭ That bears Jove's shield, the state had stood with me ‭ That help'd me take-in the well-builded tow'rs ‭ Of strong Nericus (the Cephalian pow'rs ‭ To that fair city leading) two days past, ‭ While with the Wooers thy conflict did last, ‭ And I had then been in the Wooers' wreak! ‭ I should have help'd thee so to render weak ‭ Their stubborn knees, that in thy joy's desert ‭ Thy breast had been too little for thy heart." ‭ This said, and supper order'd by their men, ‭ They sat to it; old Dolius ent'ring then, ‭ And with him, tried with labour, his sons came, ‭ Call'd by their mother, the Sicilian dame ‭ That brought them up and dress'd their father's fare, ‭ As whose age grew, with it increas'd her care ‭ To see him serv'd as fitted. When thus set ‭ These men beheld Ulysses there at meat, ‭ They knew him, and astonish'd in the place ‭ Stood at his presence; who, with words of grace, ‭ Call'd to old Dolius, saying: "Come and eat, ‭ And banish all astonishment. Your meat ‭ Hath long been ready, and ourselves made stay, ‭ Expecting ever when your wishéd way ‭ Would reach amongst us." This brought fiercely on ‭ Old Dolius from his stand; who ran upon, ‭ With both his arms abroad, the King, and kiss'd ‭ Of both his rapt up hands the either wrist, ‭ Thus welcoming his presence: "O my love, ‭ Your presence here, for which all wishes strove, ‭ No one expected. Ev'n the Gods have gone ‭ In guide before you to your mansión. ‭ Welcome, and all joys to your heart contend. ‭ Knows yet Penelope? Or shall we send ‭ Some one to tell her this?" "She knows," said he, ‭ "What need these troubles, father, touch at thee?" ‭ Then came the sons of Dolius, and again ‭ Went over with their father's entertain, ‭ Welcom'd, shook hands, and then to feast sat down. ‭ About which while they sat, about the town ‭ Fame flew, and shriek'd about the cruel death ‭ And fate the Wooers had sustain'd beneath ‭ Ulysses' roofs. All heard; together all ‭ From hence and thence met in Ulysses' hall, ‭ Short-breath'd and noiseful, bore out all the dead ‭ To instant burial, while their deaths were spread ‭ To other neighbour cities where they liv'd, ‭ From whence in swiftest fisher-boats arriv'd ‭ Men to transfer them home. In mean space here ‭ The heavy nobles all in council were; ‭ Where, met in much heap, up to all arose ‭ Extremely-griev'd Eupitheus so to lose ‭ His son Antinous, who, first of all, ‭ By great Ulysses' hand had slaught'rous fall. ‭ Whose father, weeping for him, said: "O friends, ‭ This man hath author'd works of dismal ends, ‭ Long since conveying in his guide to Troy ‭ Good men, and many that did ships employ, ‭ All which are lost, and all their soldiers dead; ‭ And now the best men Cephallenia bred ‭ His hand hath slaughter'd. Go we then (before ‭ His 'scape to Pylos, or the Elians' shore, ‭ Where rule the Epeans) 'gainst his horrid hand; ‭ For we shall grieve, and infamy will brand ‭ Our fames for ever, if we see our sons ‭ And brothers end in these confusions, ‭ Revenge left uninflicted. Nor will I ‭ Enjoy one day's life more, but grieve and die ‭ With instant onset. Nor should you survive ‭ To keep a base and beastly name alive. ‭ Haste, then, lest flight prevent us." This with tears ‭ His griefs advis'd, and made all sufferers ‭ In his affliction. But by this was come ‭ Up to the council from Ulysses' home-- ‭ When sleep had left them, which the slaughters there ‭ And their self-dangers from their eyes in fear ‭ Had two nights intercepted--those two men ‭ That just Ulysses sav'd out of the slain, ‭ Which Medon and the sacred singer were. ‭ These stood amidst the council; and the fear ‭ The slaughter had impress'd in either's look ‭ Stuck still so ghastly, that amaze it strook ‭ Through ev'ry there beholder. To whose ears ‭ One thus enforc'd, in his fright, cause of theirs: ‭ "Attend me, Ithacensians! This stern fact ‭ Done by Ulysses was not put in act ‭ Without the Gods' assistance. These self eyes ‭ Saw one of the immortal Deities ‭ Close by Ulysses, Mentor's form put on ‭ At ev'ry part. And this sure Deity shone ‭ Now near Ulysses, setting on his bold ‭ And slaught'rous spirit, now the points controll'd ‭ Of all the Wooers' weapons, round about ‭ The arm'd house whisking, in continual rout ‭ Their party putting, till in heaps they fell." ‭ This news new fears did through their spirits impell, ‭ When Halitherses (honour'd Mastor's son, ‭ Who of them all saw only what was done ‭ Present and future) the much-knowing man ‭ And aged heroë this plain course ran ‭ Amongst their counsels: "Give me likewise ear, ‭ And let me tell ye, friends, that these ills bear ‭ On your malignant spleens their sad effects, ‭ Who not what I persuaded gave respects, ‭ Nor what the people's pastor, Mentor, said,-- ‭ That you should see your issues' follies stay'd ‭ In those foul courses, by their petulant life ‭ The goods devouring, scandalling the wife ‭ Of no mean person, who, they still would say, ‭ Could never more see his returning-day. ‭ Which yet appearing now, now give it trust, ‭ And yield to my free counsels: Do not thrust ‭ Your own safe persons on the acts your sons ‭ So dearly bought, lest their confusions ‭ On your lov'd heads your like addictions draw." ‭ This stood so far from force of any law ‭ To curb their loose attempts, that much the more ‭ They rush'd to wreak, and made rude tumult roar. ‭ The greater part of all the court arose; ‭ Good counsel could not ill designs dispose. ‭ Eupitheus was persuader of the course, ‭ Which, cómplete-arm'd, they put in present force; ‭ The rest sat still in council. These men met ‭ Before the broad town, in a place they set ‭ All girt in arms; Eupitheus choosing chief ‭ To all their follies, who put grief to grief, ‭ And in his slaughter'd son's revenge did burn. ‭ But Fate gave never feet to his return, ‭ Ordaining there his death. Then Pallas spake ‭ To Jove, her Father, with intent to make ‭ His will high arbiter of th' act design'd, ‭ And ask'd of him what his unsearchéd mind ‭ Held undiscover'd? If with arms, and ill, ‭ And grave encounter he, would first fulfill ‭ His sacred purpose, or both parts combine ‭ In peaceful friendship? He ask'd: "Why incline ‭ These doubts thy counsels? Hast not thou decreed ‭ That Ithacus should come and give his deed ‭ The glory of revenge on these and theirs? ‭ Perform thy will; the frame of these affairs ‭ Have this fit issue: When Ulysses' hand ‭ Hath reach'd full wreak, his then renown'd command ‭ Shall reign for ever, faithful truces strook ‭ 'Twixt him and all; for ev'ry man shall brook ‭ His sons' and brothers' slaughters; by our mean ‭ To send Oblivion in, expunging clean ‭ The character of enmity in them all, ‭ As in best leagues before. _Peace, festival, ‭ And riches in abundance, be the state ‭ That crowns the close of wise Ulysses' Fate."_ ‭ This spurr'd the free, who from heav'n's continent ‭ To th' Ithacensian isle made straight descent. ‭ Where, dinner past, Ulysses said: "Some one ‭ Look out to see their nearness." Dolius' son ‭ Made present speed abroad, and saw them nigh, ‭ Ran back, and told, bade arm; and instantly ‭ Were all in arms. Ulysses' part was four, ‭ And six more sons of Dolius; all his pow'r ‭ Two only more, which were his aged sire ‭ And like-year'd Dolius, whose lives'-slak'd fire ‭ All-white had left their heads, yet, driv'n by need, ‭ Made soldiers both of necessary deed. ‭ And now, all-girt in arms, the ports set wide, ‭ They sallied forth, Ulysses being their guide; ‭ And to them in the instant Pallas came, ‭ In form and voice like Mentor, who a flame ‭ Inspir'd of comfort in Ulysses' heart ‭ With her seen presence. To his son, apart, ‭ He thus then spake: "Now, son, your eyes shall see, ‭ Expos'd in slaught'rous fight, the enemy, ‭ Against whom who shall best serve will be seen. ‭ Disgrace not then your race, that yet hath been ‭ For force and fortitude the foremost tried ‭ Of all earth's offsprings." His true son replied: ‭ "Yourself shall see, lov'd father, if you please, ‭ That my deservings shall in nought digress ‭ From best fame of our race's foremost merit." ‭ The old king sprung for joy to hear his spirit, ‭ And said: "O lov'd Immortals, what a day ‭ Do your clear bounties to my life display! ‭ I joy, past measure, to behold my son ‭ And nephew close in such contention ‭ Of virtues martial." Pallas, standing near, ‭ Said: "O my friend! Of all supremely dear, ‭ Seed of Arcesius, pray to Jove and Her ‭ That rules in arms, his daughter, and a dart, ‭ Spritefully brandish'd, hurl at th' adverse part." ‭ This said, he pray'd; and she a mighty force ‭ Inspir'd within him, who gave instant course ‭ To his brave-brandish'd lance, which struck the brass ‭ That cheek'd Eupitheus' casque, and thrust his pass ‭ Quite through his head; who fell, and sounded falling, ‭ His arms the sound again from earth recalling. ‭ Ulysses and his son rush'd on before, ‭ And with their both-way-headed darts did gore ‭ Their enemies' breasts so thick, that all had gone ‭ The way of slaughter, had not Pallas thrown ‭ Her voice betwixt them, charging all to stay ‭ And spare expense of blood. Her voice did fray ‭ The blood so from their faces that it left ‭ A greenish paleness; all their hands it reft ‭ Of all their weapons, falling thence to earth; ‭ And to the common mother of their birth, ‭ The city, all fled, in desire to save ‭ The lives yet left them. Then Ulysses gave ‭ A horrid shout, and like Jove's eagle flew ‭ In fiery pursuit, till Saturnius threw ‭ His smoking lightning 'twixt them, that had fall ‭ Before Minerva, who then out did call ‭ Thus to Ulysses: "Born of Jove! Abstain ‭ From further bloodshed. Jove's hand in the slain ‭ Hath equall'd in their pains their prides to thee. ‭ Abstain, then, lest you move the Deity." ‭ Again then, 'twixt both parts the Seed of Jove, ‭ Athenian Pallas, of all future love ‭ A league compos'd, and for her form took choice ‭ Of Mentor's likeness both in limb and voice. ‭ THE END OF THE TWENTY-FOURTH AND LAST BOOK OF HOMER'S ODYSSEYS. ‭ "SO WROUGHT DIVINE ULYSSES" ‭ _So wrought divine Ulysses through his woes, ‭ So crown'd the light with him his mother's throes, ‭ As through his great Renowner I have wrought, ‭ And my safe sail to sacred anchor brought. ‭ Nor did the Argive ship more burthen feel, ‭ That bore the care of all men in her keel, ‭ That my adventurous bark; the Colchian fleece ‭ Not half so precious as this Soul of Greece, ‭ In whose Songs I have made our shores rejoice, ‭ And Greek itself vail to our English voice. ‭ Yet this inestimable Pearl will all ‭ Our dunghill chanticleers but obvious call; ‭ Each modern scraper this Gem scratching by, ‭ His oat preferring far. Let such let lie. ‭ So scorn the stars the clouds, as true-soul'd men ‭ Despise deceivers. For, as clouds would fain ‭ Obscure the stars, yet (regions left below ‭ With all their envies) bar them but of show, ‭ For they shine ever, and will shine, when they ‭ Dissolve in sinks, make mire, and temper clay; ‭ So puff'd impostors (our muse-vapours) strive, ‭ With their self-blown additions, to deprive ‭ Men solid of their full, though infinite short ‭ They come in their compare, and false report ‭ Of levelling or touching at their light, ‭ That still retain their radiance, and clear right, ‭ And shall shine ever, when, alas! one blast ‭ Of least disgrace tears down th' impostor's mast, ‭ His tops and tacklings, his whole freight, and he ‭ Confiscate to the fishy monarchy, ‭ His trash, by foolish Fame brought now, from hence ‭ Given to serve mackarel forth, and frankincense. ‭ Such then, and any too soft-eyed to see, ‭ Through works so solid, any worth, so free ‭ Of all the learn'd professions, as is fit ‭ To praise at such price, let him think his wit ‭ Too weak to rate it, rather than oppose ‭ With his poor pow'rs Ages and Hosts of Foes._ ‭ _TO THE RUINS OF TROY AND GREECE_ ‭ _Troy rac'd, Greece wrack'd, who mourns? Ye both may boast, ‭ Else th' Iliads and Odysseys had been lost!_ ‭ _AD DEUM_ ‭ _The Only True God (betwixt Whom and me ‭ I only bound my comfort, and agree ‭ With all my actions) only truly knows, ‭ And can judge truly, me, with all that goes ‭ To all my faculties, In Whose free Grace ‭ And Inspiration I only place ‭ All means to know (with my means, study, pray'r, ‭ In and from His Word taken) stair by stair, ‭ In all continual contentation, rising ‭ To knowledge of His Truth, and practising ‭ His Will in it, with my sole Saviour's Aid, ‭ Guide, and Enlight'ning; nothing done, nor said, ‭ Nor thought, that good is, but acknowledg'd by ‭ His Inclination, Skill, and Faculty. ‭ By which, to find the way out to His Love ‭ Past all the worlds, the sphere is where doth move ‭ My studies, pray'rs, and pow'rs; no pleasure taken ‭ But sign'd by His, for which, my blood forsaken, ‭ My soul I cleave to, and what (in His Blood ‭ That hath redeem'd, cleans'd, taught her) fits her good._ ‭ _DEO OPT. MAX. GLORIA_ ‭ BATRACHOMYOMACHIA ‭ THE EPISTLE DEDICATORY ‭ TO MY EVER MOST-WORTHY-TO-BE-MOST HONOURED ‭ LORD, THE EARL OF SOMERSET, ETC. ‭ _Not forc'd by fortune, but since your free mind ‭ (Made by affliction) rests in choice resign'd ‭ To calm retreat, laid quite beneath the wind ‭ Of grace and glory, I well know, my Lord, ‭ You would not be entitled to a word ‭ That might a thought remove from your repose, ‭ To thunder and spit flames, as greatness does, ‭ For all the trumps that still tell where he goes. ‭ Of which trumps Dedication being one, ‭ Methinks I see you start to hear it blown. ‭ But this is no such trump as summons lords ‭ 'Gainst Envy's steel to draw their leaden swords, ‭ Or 'gainst hare-lipp'd Detraction, Contempt, ‭ All which from all resistance stand exempt, ‭ It being as hard to sever wrong from merit, ‭ As meat-indu'd from blood, or blood from spirit. ‭ Nor in the spirit's chariot rides the soul ‭ In bodies chaste, with more divine control, ‭ Nor virtue shines more in a lovely face, ‭ Than true desert is stuck off with disgrace. ‭ And therefore Truth itself, that had to bless ‭ The merit of it all, Almightiness, ‭ Would not protect it from the bane and ban ‭ Of all moods most distraught and Stygian; ‭ As counting it the crown of all desert, ‭ Borne to heaven, to take of earth, no part ‭ Of false joy here, for joys-there-endless troth, ‭ Nor sell his birthright for a mess of broth. ‭ But stay and still sustain, and his bliss bring, ‭ Like to the hatching of the blackthorn's spring, ‭ With bitter frosts, and smarting hailstorms, forth. ‭ Fates love bees' labours; only Pain crown's Worth. ‭ This Dedication calls no greatness, then, ‭ To patron this greatness-creating pen, ‭ Nor you to add to your dead calm a breath, ‭ For those arm'd angels, that in spite of death ‭ Inspir'd those flow'rs that wrought this Poet's wreath, ‭ Shall keep it ever, Poesy's steepest star, ‭ As in Earth's flaming walls, Heaven's sevenfold Car, ‭ From all the wilds of Neptune's wat'ry sphere, ‭ For ever guards the Erymanthian bear. ‭ Since then your Lordship settles in your shade ‭ A life retir'd, and no retreat is made ‭ But to some strength, (for else 'tis no retreat, ‭ But rudely running from your battle's heat) ‭ I give this as your strength; your strength, my Lord, ‭ In counsels and examples, that afford ‭ More guard than whole hosts of corporeal pow'r, ‭ And more deliverance teach the fatal hour. ‭ Turn not your med'cine then to your disease, ‭ By your too set and slight repulse of these, ‭ The adjuncts of your matchless Odysses; ‭ Since on that wisest mind of man relies ‭ Refuge from all life's infelicities. ‭ Nor sing these such division from them, ‭ But that these spin the thread of the same stream ‭ From one self distaff's stuff; for Poesy's pen, ‭ Through all themes, is t' inform the lives of men; ‭ All whose retreats need strengths of all degrees; ‭ Without which, had you even Herculean knees, ‭ Your foes' fresh charges would at length prevail, ‭ To leave your noblest suff'rance no least sail. ‭ Strength then the object is of all retreats; ‭ Strength needs no friends' trust; strength your foes defeats. ‭ Retire to strength, then, if eternal things, ‭ And y'are eternal; for our knowing springs ‭ Flow into those things that we truly know, ‭ Which being eternal, we are render'd so. ‭ And though your high-fix'd light pass infinite far ‭ Th' adviceful guide of my still-trembling star, ‭ Yet hear what my discharg'd piece must foretel, ‭ Standing your poor and perdue sentinel. ‭ Kings may perhaps wish even your beggar's-voice ‭ To their eternities, how scorn'd a choice ‭ Soever now it lies; and (dead) I may ‭ Extend your life to light's extremest ray. ‭ If not, your Homer yet past doubt shall make ‭ Immortal, like himself, your bounty's stake ‭ Put in my hands, to propagate your fame; ‭ Such virtue reigns in such united name. ‭ Retire to him then for advice, and skill, ‭ To know things call'd worst, best; and best, most ill. ‭ Which known, truths best choose, and retire to still. ‭ And as our English general, (whose name [1] ‭ Shall equal interest find in th' house of fame ‭ With all Earth's great'st commanders,) in retreat ‭ To Belgian Gant, stood all Spain's armies' heat ‭ By Parma led, though but one thousand strong; ‭ Three miles together thrusting through the throng ‭ Of th' enemy's horse, still pouring on their fall ‭ 'Twixt him and home, and thunder'd through them all; ‭ The Gallic Monsieur standing on the wall, ‭ And Wond'ring at his dreadful discipline, ‭ Fir'd with a valour that spit spirit divine; ‭ In five battalions ranging all his men, ‭ Bristl'd with pikes, and flank'd with flankers ten; ‭ Gave fire still in his rear; retir'd, and wrought ‭ Down to his fix'd strength still; retir'd and fought; ‭ All the battalions of the enemy's horse ‭ Storming upon him still their fieriest force; ‭ Charge upon charge laid fresh; he, fresh as day, ‭ Repulsing all, and forcing glorious way ‭ Into the gates, that gasp'd, (as swoons for air,) ‭ And took their life in, with untouch'd repair:-- ‭ So fight out, sweet Earl, your retreat in peace; ‭ No ope-war equals that where privy prease ‭ Of never-number'd odds if enemy, ‭ Arm'd all by envy, in blind ambush lie, ‭ To rush out like an opening threat'ning sky, ‭ Broke all in meteors round about your ears. ‭ 'Gainst which, though far from hence, through all your rears, ‭ Have fires prepar'd; wisdom with wisdom flank, ‭ And all your forces range in present rank; ‭ Retiring as you now fought in your strength, ‭ From all the force laid, in time's utmost length, ‭ To charge, and basely come on you behind. ‭ The doctrine of all which you here shall find, ‭ And in the true glass of a human mind. ‭ Your Odysses, the body letting see ‭ All his life past, through infelicity, ‭ And manage of it all. In which to friend, ‭ The full Muse brings you both the prime and end ‭ Of all arts ambient in the orb of man; ‭ Which never darkness most Cimmerian ‭ Can give eclipse, since, blind, he all things saw, ‭ And to all ever since liv'd lord and law. ‭ And through our mere-learn'd men; and modern wise, ‭ Taste not poor Poesy's ingenuities, ‭ Being crusted with their covetous leprosies, ‭ But hold her pains worse than the spiders' work, ‭ And lighter than the shadow of a cork, ‭ Yet th' ancient learn'd, heat with celestial fire, ‭ Affirms her flames so sacred and entire, ‭ That not without God's greatest grace she can ‭ Fall in the wid'st capacity of man._ ‭ _If yet the vile soul of this verminous time ‭ Love more the sale-muse, and the squirrel's chime, ‭ Than this full sphere of poesy's sweetest prime, ‭ Give them unenvied their vain vein and vent, ‭ And rest your wings in his approv'd ascent ‭ That yet was never reach'd, nor ever fell ‭ Into affections bought with things that sell, ‭ Being the sun's flow'r, and wrapt so in his sky ‭ He cannot yield to every candle's eye._ ‭_Whose most worthy discoveries, to your lordship's judicial ‭perspective, in most subdue humility submitteth,_ ‭_GEORGE CHAPMAN._ ‭[1] A simile illustrating the most renowned service of General Norris ‭in his retreat before Gant, never before made sacred to memory. ‭ THE OCCASION OF THIS IMPOSED CROWNE ‭After this not only Prime of Poets, but Philosophers, had written ‭his two great poems of Iliads and Odysses; which (for their first ‭lights born before all learning) were worthily called the Sun and ‭Moon of the Earth; finding no compensation, he writ in contempt ‭of men this ridiculous poem of Vermin, giving them nobility of ‭birth, valorous elocution not inferior to his heroes. At which the ‭Gods themselves, put in amaze, called councils about their ‭assistance of either army, and the justice of their quarrels, even to ‭the mounting of Jove's artillery against them, and discharge of his ‭three-forked flashes; and all for the drowning of a mouse. After ‭which slight and only recreative touch, he betook him seriously to ‭the honour of the Gods, in Hymns resounding all their peculiar ‭titles, jurisdictions, and dignities; which he illustrates at all parts, ‭as he had been continually conversant amongst them; and ‭whatsoever authentic Poesy he omitted in the episodes contained in ‭his Iliads and Odysses, he comprehends and concludes in his ‭Hymns and Epigrams. All his observance and honour of the Gods, ‭rather moved their envies against him, than their rewards, or ‭respects of his endeavours. And so like a man _verecundi ingenii_ ‭(which he witnesseth of himself) he lived unhonoured and needy ‭till his death; and yet notwithstanding all men's servile and ‭manacled miseries, to his most absolute and never-equalled merit, ‭yea even bursten profusion to imposture and impiety, hear our ‭ever-the-same intranced, and never-sleeping, Master of the Muses, ‭to his last accents, incomparably singing. ‭ BATRACHOMYOMACHIA ‭ ‭ Ent'ring the fields, first let my vows call on ‭ The Muses' whole quire out of Helicon ‭ Into my heart, for such a poem's sake, ‭ As lately I did in my tables take, ‭ And put into report upon my knees. ‭ A fight so fierce, as might in all degrees ‭ Fit Mars himself, and his tumultuous hand, ‭ Glorying to dart to th' ears of every land ‭ Of all the voice-divided; [1] and to show ‭ How bravely did both Frogs and Mice bestow ‭ In glorious fight their forces, even the deeds ‭ Daring to imitate of Earth's Giant Seeds. ‭ Thus then men talk'd; this seed the strife begat: ‭ The Mouse once dry, and 'scaped the dangerous cat, ‭ Drench'd in the neighbour lake her tender beard, ‭ To taste the sweetness of the wave it rear'd. ‭ The far-famed Fen-affecter, seeing him, said: ‭ "Ho, stranger! What are you, and whence, that tread ‭ This shore of ours? Who brought you forth? Reply ‭ What truth may witness, lest I find you lie. ‭ If worth fruition of my love and me, ‭ I'll have thee home, and hospitality ‭ Of feast and gift, good and magnificent, ‭ Bestow on thee; for all this confluent ‭ Resounds my royalty; my name, the great ‭ In blown-up-count'nances and looks of threat, ‭ Physignathus, [2] adored of all Frogs here ‭ All their days' durance, and the empire bear ‭ Of all their beings; mine own being begot ‭ By royal Peleus, [3] mix'd in nuptial knot ‭ With fair Hydromedusa, [4] on the bounds ‭ Near which Eridanus [5] his race resounds. ‭ And thee mine eye makes my conceit inclined ‭ To reckon powerful both in form and mind, ‭ A sceptre-bearer, and past others far ‭ Advanc'd in all the fiery fights of war. ‭ Come then, thy race to my renown commend." ‭ The Mouse made answer: "Why inquires my friend? ‭ For what so well know men and Deities, ‭ And all the wing'd affecters of the skies? ‭ Psicharpax [6] I am call'd; Troxartes' [7] seed, ‭ Surnamed the mighty-minded. She that freed ‭ Mine eyes from darkness was Lichomyle, [8] ‭ King Pternotroctes' [9] daughter, showing me, ‭ Within an aged hovel, the young light, ‭ Fed me with figs and nuts, and all the height ‭ Of varied viands. But unfold the cause, ‭ Why, 'gainst similitude's most equal laws ‭ Observed in friendship, thou mak'st me thy friend? ‭ Thy life the waters only help t' extend; ‭ Mine, whatsoever men are used to eat, ‭ Takes part with them at shore; their purest cheat, ‭ Thrice boulted, kneaded, and subdued in paste, ‭ In clean round kymnels, cannot be so fast ‭ From my approaches kept but in I eat; ‭ Nor cheesecakes full of finest Indian wheat, ‭ That crusty-weeds [10] wear, large as ladies' trains; ‭ Liverings, [11] white-skinn'd as ladies; nor the strains, ‭ Of press'd milk, renneted; nor collops cut ‭ Fresh from the flitch; nor junkets, such as put ‭ Palates divine in appetite; nor any ‭ Of all men's delicates, though ne'er so many ‭ Their cooks devise them, who each dish see deckt ‭ With all the dainties all strange soils affect. [12] ‭ Yet am I not so sensual to fly ‭ Of fields embattled the most fiery cry, ‭ But rush out straight, and with the first in fight ‭ Mix in adventure. No man with affright ‭ Can daunt my forces, though his body be ‭ or never so immense a quantity, ‭ But making up, even to his bed, access, ‭ His fingers' ends dare with my teeth compress, ‭ His feet taint likewise, and so soft seize both ‭ They shall not taste th' impression of a tooth. ‭ Sweet sleep shall hold his own in every eye ‭ Where my tooth takes his tartest liberty. ‭ But two there are, that always, far and near, ‭ Extremely still control my force with fear, ‭ The Cat, and Night-hawk, who much scathe confer ‭ On all the outrays where for food I err. ‭ Together with the straits-still-keeping trap, [13] ‭ Where lurks deceitful and set-spleen'd mishap. ‭ But most of all the Cat constrains my fear, ‭ Being ever apt t' assault me everywhere; ‭ For by that hole that hope says I shall 'scape, ‭ At that hole ever she commits my rape. ‭ The best is yet, I eat no pot-herb grass, ‭ Nor radishes, nor coloquintidas, ‭ Nor still-green beets, nor parsley; which you make ‭ Your dainties still, that live upon the lake." ‭ The Frog replied: "Stranger, your boasts creep all ‭ Upon their bellies; though to our lives fall ‭ Much more miraculous meats by lake and land, ‭ Jove tend'ring our lives with a twofold hand, ‭ Enabling us to leap ashore for food, ‭ And hide us straight in our retreatful flood. ‭ Which, if you will serve, you may prove with ease. ‭ I'll take you on my shoulders; which fast seize, ‭ If safe arrival at my house y' intend." ‭ He stoop'd, and thither spritely did ascend, ‭ Clasping his golden neck, that easy seat ‭ Gave to his sally; who was jocund yet, ‭ Seeing the safe harbours of the king so near, ‭ And he a swimmer so exempt from peer. ‭ But when he sunk into the purple wave, ‭ He mourn'd extremely, and did much deprave ‭ Unprofitable penitence; his hair ‭ Tore by the roots up, labour'd for the air ‭ With his feet fetch'd up to his belly close; ‭ His heart within him panted out repose, ‭ For th' insolent plight in which his state did stand; ‭ Sigh'd bitterly, and long'd to greet the land, ‭ Forced by the dire need of his freezing fear. ‭ First, on the waters he his tail did stere, ‭ Like to a stern; then drew it like an oar, ‭ Still praying the Gods to set him safe ashore; ‭ Yet sunk he midst the red waves more and more, ‭ And laid a throat out to his utmost height; ‭ Yet in forced speech he made his peril slight, ‭ And thus his glory with his grievance strove: ‭ "Not in such choice state was the charge of love ‭ Borne by the bull, when to the Cretan shore ‭ He swum Europa through the wavy roar, ‭ As this Frog ferries me, his pallid breast ‭ Bravely advancing, and his verdant crest ‭ (Submitted to my seat) made my support, ‭ Through his white waters, to his royal court." ‭ But on the sudden did apparance make ‭ An horrid spectacle,--a Water-snake ‭ Thrusting his freckled neck above the lake. ‭ Which seen to both, away Physignathus ‭ Dived to his deeps, as no way conscious ‭ Of whom he left to perish in his lake, ‭ But shunn'd black fate himself, and let him take ‭ The blackest of it; who amidst the fen ‭ Swum with his breast up, hands held up in vain, ‭ Cried _Peepe_, and perish'd; sunk the waters oft, ‭ And often with his sprawlings came aloft, ‭ Yet no way kept down death's relentless force, ‭ But, full of water, made an heavy corse. ‭ Before he perish'd yet, he threaten'd thus: ‭ "Thou lurk'st not yet from heaven, Physignathus, ‭ Though yet thou hid'st here, that hast cast from thee, ‭ As from a rock, the shipwrack'd life of me, ‭ Though thou thyself no better was than I, ‭ O worst of things, at any faculty, ‭ Wrastling or race. But, for thy perfidy ‭ In this my wrack, Jove bears a wreakful eye; ‭ And to the host of Mice thou pains shalt pay, ‭ Past all evasion." This his life let say, ‭ And left him to the waters. Him beheld ‭ Lichopinax, [14] placed in the pleasing field, ‭ Who shriek'd extremely, ran and told the Mice; ‭ Who having heard his wat'ry destinies, ‭ Pernicious anger pierced the hearts of all, ‭ And then their heralds forth they sent to call ‭ A council early, at Troxartes' house, ‭ Sad father of this fatal shipwrack'd Mouse; ‭ Whose dead corse upwards swum along the lake, ‭ Nor yet, poor wretch, could be enforced to make ‭ The shore his harbour, but the mid-main Swum. ‭ When now, all haste made, with first morn did come ‭ All to set council; in which first rais'd head ‭ Troxartes, angry for his son, and said: ‭ "O friends, though I alone may seem to bear ‭ All the infortune, yet may all met here ‭ Account it their case. But 'tis true, I am ‭ In chief unhappy, that a triple flame ‭ Of life feel put forth, in three famous sons; ‭ The first, the chief in our confusions, ‭ The Cat, made rape of, caught without his hole: ‭ The second, Man, made with a cruel soul, ‭ Brought to his ruin with a new-found sleight, ‭ And a most wooden engine of deceit, ‭ They term a Trap, mere murth'ress of our Mice. ‭ The last, that in my love held special price, ‭ And his rare mother's, this Physignathus ‭ (With false pretext of wafting to his house) ‭ Strangled in chief deeps of his bloody stream. ‭ Come then, haste all, and issue out on them, ‭ Our bodies deck'd in our Dædalean arms." ‭ This said, his words thrust all up in alarms, ‭ And Mars himself, that serves the cure of war, ‭ Made all in their appropriates circular. ‭ First on each leg the green shales of a bean ‭ They closed for boots, that sat exceeding clean; [15] ‭ The shales they broke ope, boothaling by night, ‭ And ate the beans; their jacks art exquisite ‭ Had shown in them, being cats' skins, everywhere ‭ Quilted with quills; their fenceful bucklers were ‭ The middle rounds of can'sticks; but their spear ‭ A huge long needle was, that could not bear ‭ The brain of any but be Mars his own ‭ Mortal invention; their heads' arming crown ‭ Was vessel to the kernel of a nut. ‭ And thus the Mice their powers in armour put. ‭ This the Frogs hearing, from the water all ‭ Issue to one place, and a council call ‭ Of wicked war; consulting what should be ‭ Cause to this murmur and strange mutiny. ‭ While this was question'd, near them made his stand ‭ An herald with a sceptre in his hand, ‭ Embasichytrus [16] call'd, that fetch'd his kind ‭ From Tyroglyphus [17] with the mighty mind, ‭ Denouncing ill-named war in these high terms: ‭ "O Frogs! the Mice send threats to you of arms, ‭ And bid me bid ye battle and fix'd fight; ‭ Their eyes all wounded with Psicharpax' sight ‭ Floating your waters, whom your king hath kill'd, ‭ And therefore all prepare for force of field, ‭ You that are best born whosoever held." ‭ This said, he sever'd: his speech firing th' ears ‭ Of all the Mice, but freez'd the Frogs with fears, ‭ Themselves conceiting guilty; whom the king ‭ Thus answer'd, rising, "Friends! I did not bring ‭ Psicharpax to his end; he, wantoning ‭ Upon our waters, practising to swim, ‭ Aped us, [18] and drown'd without my sight of him. ‭ And yet these worst of vermin accuse me, ‭ Though no way guilty. Come, consider we ‭ How we may ruin these deceitful Mice. ‭ For my part, I give voice to this advice, ‭ As seeming fittest to direct our deeds: ‭ Our bodies decking with our arming weeds, ‭ Let all our pow'rs stand rais'd in steep'st repose ‭ Of all our shore; that, when they charge us close, ‭ We may the helms snatch off from all so deckt, ‭ Daring our onset, and them all deject ‭ Down to our waters; who, not knowing the sleight. ‭ To dive our soft deeps, may be strangled straight, ‭ And we triumphing may a trophy rear, ‭ Of all the Mice that we have slaughter'd here." ‭ These words put all in arms; and mallow leaves ‭ They drew upon their legs, for arming greaves. [19] ‭ Their curets, broad green beets; their bucklers were ‭ Good thick-leaved cabbage, proof 'gainst any spear; ‭ Their spears sharp bulrushes, of which were all ‭ Fitted with long ones; their parts capital ‭ They hid in subtle cockleshells from blows. ‭ And thus all arm'd, the steepest shores they chose ‭ T' encamp themselves; where lance with lance they lined, ‭ And brandish'd bravely, each Frog full of mind. ‭ Then Jove call'd all Gods in his flaming throne, ‭ And show'd all all this preparation ‭ For resolute war; these able soldiers, ‭ Many, and great, all shaking lengthful spears, ‭ In show like Centaurs, Or the Giants' host. ‭ When, sweetly smiling, he inquired who, most ‭ Of all th' Immortals, pleased to add their aid ‭ To Frogs or Mice; and thus to Pallas said: ‭ "O Daughter! Must not your needs aid these Mice, ‭ That, with the odours and meat sacrifice ‭ Used in your temple, endless triumphs make, ‭ And serve you for your sacred victuals' sake?" ‭ Pallas replied: "O Father, never I ‭ Will aid the Mice in any misery. ‭ So many mischiefs by them I have found, ‭ Eating the cotton that my distaffs crown'd, [20] ‭ My lamps still haunting to devour the oil. ‭ But that which most my mind eats, is their spoil ‭ Made of a veil, that me in much did stand, ‭ On which bestowing an elaborate hand, ‭ A fine woof working of as pure a thread; ‭ Such holes therein their petulancies fed ‭ That, putting it to darning, when 'twas done, ‭ The darner a most dear pay stood upon ‭ For his so dear pains, laid down instantly; ‭ Or, to forbear, exacted usury. [21] ‭ So, borrowing from my fane the weed I wove, ‭ I can by no means th' usurous darner move ‭ To let me have the mantle to restore. ‭ And this is it that rubs the angry sore ‭ Of my offence took at these petulant Mice. ‭ Nor will I yield the Frogs' wants my supplies, ‭ For their infirm minds that no confines keep; ‭ For I from war retir'd, and wanting sleep, ‭ All leap'd ashore in tumult, nor would stay ‭ Till one wink seized mine eyes, and so I lay ‭ Sleepless, and pain'd with headache, till first light ‭ The cock had crow'd up. Therefore, to the fight ‭ Let no God go assistant, lest a lance ‭ Wound whosoever offers to advance, ‭ Or wishes but their aid, that scorn all foes; ‭ Should any God's access their spirits oppose. ‭ Sit we then pleased to see from heaven their fight." ‭ She said, and all Gods join'd in her delight. ‭ And now both hosts to one field drew the jar, ‭ Both heralds bearing the ostents of war. ‭ And then the wine-gnats, [22] that shrill trumpets sound, ‭ Terribly rung out the encounter round; ‭ Jove thund'red; all heaven sad war's sign resounded. ‭ And first Hypsiboas [23] Lichenor [24] wounded, ‭ Standing th' impression of the first in fight. ‭ His lance did in his liver's midst alight, ‭ Along his belly. Down he fell; his face ‭ His fall on that part sway'd, and all the grace ‭ Of his soft hair fil'd with disgraceful dust. ‭ Then Troglodytes [25] his thick javelin thrust ‭ In Pelion's [26] bosom, bearing him to ground, ‭ Whom sad death seiz'd; his soul flew through his wound. ‭ Seutlæus [27] next Embasichytros slew, ‭ His heart through-thrusting. Then Artophagus [28] threw ‭ His lance at Polyphon, [29] and struck him quite ‭ Through his mid-belly; down he fell upright, ‭ And from his fair limbs took his soul her flight. ‭ Limnocharis, [30] beholding Polyphon ‭ Thus done to death, did, with as round a stone ‭ As that the mill turns, Troglodytes wound, ‭ Near his mid-neck, ere he his onset found; ‭ Whose eyes sad darkness seiz'd. Lichenor [31] cast ‭ A flying dart off, and his aim so placed ‭ Upon Limnocharis; that sure he thought [32] ‭ The wound he wish'd him; nor untruly wrought ‭ The dire success, for through his liver flew ‭ The fatal lance; which when Crambophagus [33] knew, ‭ Down the deep waves near shore he, diving, fled; ‭ But fled not fate so; the stern enemy fed ‭ Death with his life in diving; never more ‭ The air he drew in; his vermilion gore ‭ Stain'd all the waters, and along the shore ‭ He laid extended; his fat entrails lay ‭ (By his small guts' impulsion) breaking way ‭ Out at his wound. Limnisius [34] near the shore ‭ Destroy'd Tyroglyphus. Which frighted sore ‭ The soul of Calaminth, [35] seeing coming on, ‭ For wreak, Pternoglyphus; [36] who got him gone ‭ With large leaps to the lake, his target thrown ‭ Into the waters. Hydrocharis [37] slew ‭ King Pternophagus, [38] at whose throat he threw ‭ A huge stone, strook it high, and beat his brain ‭ Out at his nostrils. Earth blush'd with the stain ‭ His blood made on her bosom. For next prise, ‭ Lichopinax to death did sacrifice ‭ Borboroccetes' [39] faultless faculties; ‭ His lance enforced it; darkness closed his eyes. ‭ On which when Prassophagus [40] cast his look, ‭ Cnissodioctes [41] by the heels he took, ‭ Dragg'd him to fen from off his native ground, ‭ Then seized his throat, and soused him till he drown'd ‭ But now Psicharpax wreaks his fellows' deaths, ‭ And in the bosom of Pelusius [42] sheaths, ‭ In centre of his liver, his bright lance. ‭ He fell before the author of the chance; ‭ His soul to hell fled. Which Pelobates [43] ‭ Taking sad note of, wreakfully did seize ‭ His hand's gripe full of mud, and all besmear'd ‭ His forehead with it so, that scarce appear'd ‭ The light to him. Which certainly incensed ‭ His fiery spleen; who with his wreak dispensed ‭ No point of time, but rear'd with his strong hand ‭ A stone so massy it oppress'd the land, ‭ And hurl'd it at him; when below the knee ‭ It strook his right leg so impetuously ‭ It piecemeal brake it; he the dust did seize, ‭ Upwards everted. But Craugasides [44] ‭ Revenged his death, and at his enemy ‭ Discharged a dart that did his point imply ‭ In his mid-belly. All the sharp-pil'd spear ‭ Got after in, and did before it bear ‭ His universal entrails to the earth, ‭ Soon as his swoln hand gave his jav'lin birth. ‭ Sitophagus, [45] beholding the sad sight, ‭ Set on the shore, went halting from the fight, ‭ Vex'd with his wounds extremely; and, to make ‭ Way from extreme fate, leap'd into the lake. ‭ Troxartes strook, in th' instep's upper part, ‭ Physignathus; who (privy to the smart ‭ His wound imparted) with his utmost haste ‭ Leap'd to the lake, and fled. Troxartes cast ‭ His eye upon the foe that fell before, ‭ And, seeing him half-liv'd, long'd again to gore ‭ His gutless bosom; and, to kill him quite, ‭ Ran fiercely at him. Which Prassseus' [46] sight ‭ Took instant note of, and the first in fight ‭ Thrust desp'rate way through, casting his keen lance ‭ Off at Troxartes; whose shield turn'd th' advance ‭ The sharp head made, and check'd the mortal chance. ‭ Amongst the Mice fought an egregious ‭ Young springall, and a close-encount'ring Mouse, ‭ Pure Artepibulus's [47] dear descent; ‭ A prince that Mars himself show'd where he went. ‭ (Call'd Meridarpax, [48]) of so huge a might, ‭ That only he still domineer'd in fight ‭ Of all the Mouse-host. He advancing close ‭ Up to the lake, past all the rest arose ‭ In glorious object, and made vaunt that he ‭ Came to depopulate all the progeny ‭ Of Frogs, affected with the lance of war. ‭ And certainly he had put on as far ‭ As he advanced his vaunt, he was endu'd ‭ With so unmatch'd a force and fortitude, ‭ Had not the Father both of Gods and men ‭ Instantly known it, and the Frogs, even then ‭ Given up to ruin, rescued with remorse. ‭ Who, his head moving, thus began discourse: ‭ "No mean amaze affects me, to behold ‭ Prince Meridarpax rage so uncontroll'd, ‭ In thirst of Frog-blood, all along the lake. ‭ Come therefore still, and all addression make, ‭ Despatching Pallas, with tumultuous Mars, ‭ Down to the field, to make him leave the wars, ‭ How potently soever he be said [49] ‭ Where he attempts once to uphold his head." ‭ Mars answer'd: "O Jove, neither She nor I, ‭ With both our aids, can keep depopulacy ‭ From off the Frogs! And therefore arm we all, ‭ Even thy lance letting brandish to his call ‭ From off the field, that from the field withdrew ‭ The Titanois, the Titanois that slew, ‭ Though most exempt from match of all earth's Seeds, ‭ So great and so inaccessible deeds ‭ It hath proclaim'd to men; bound hand and foot ‭ The vast Enceladus; and rac'd by th' root ‭ The race of upland Giants." This speech past, ‭ Saturnius a smoking lightning cast ‭ Amongst the armies, thund'ring then so sore, ‭ That with a rapting circumflex he bore ‭ All huge heaven over. But the terrible ire ‭ Of his dart, sent abroad, all wrapt in fire, ‭ (Which certainly his very finger was) ‭ Amazed both Mice and Frogs. Yet soon let pass ‭ Was all this by the Mice, who much the more ‭ Burn'd in desire t' exterminate the store ‭ Of all those lance-loved soldiers. Which had been, ‭ If from Olympus Jove's eye had not seen ‭ The Frogs with pity, and with instant speed ‭ Sent them assistants. Who, ere any heed ‭ Was given to their approach, came crawling on ‭ With anvils on their backs, that, beat upon [50] ‭ Never so much, are never wearied yet; ‭ Crook-paw'd, and wrested on with foul cloven feet, ‭ Tongues in their mouths, [51] brick-back'd, all over bone, ‭ Broad shoulder'd, whence a ruddy yellow shone, ‭ Distorted, and small-thigh'd; had eyes that saw ‭ Out at their bosoms; twice four feet did draw ‭ About their bodies; strong-neck'd, whence did rise ‭ Two heads; nor could to any hand be prise; ‭ They call them lobsters; that ate from the Mice ‭ Their tails, their feet, and hands, and wrested all ‭ Their lances from them, so that cold appall ‭ The wretches put in rout, past all return. ‭ And now the Fount of Light forbore to burn ‭ Above the earth; when, which men's laws commend, ‭ Our battle in one day took absolute end. ‭ THE END OF HOMER'S BATTLE OF FROGS AND MICE. ‭[1] Intending _men:_ being divided from all other creatures by the ‭voice; _μέροψ,_ being a periphrasis, signifying _voce divisus,_ of ‭_μείρω (μείρομαι) divido,_ and _ὅψ, ὁπός, vox._ ‭[2] _Φυσίγναθος, Genas et buccas inflans._ ‭[3] _Πηλεύς, qui ex luto nascitur._ ‭[4] _'ϒδρομέδουνα. Aquarum regina._ ‭[5] The river Po, in Italy. ‭[6] _Ψιχάρπαξ._ Gather-crum, or ravish-crum, ‭[7] Shear-crust. ‭[8] Lick-mill. ‭[9] Bacon-flitch-devourer, or gnawer. ‭[10] _Τανύπεπλος. Extenso et prourisso peploamictus._ A metaphor ‭taken from ladies' veils, or trains, and therefore their names are ‭here added. ‭[11] _῞Ηπατα λευκοχίτωνα._ Livering puddings white-skinn'd. ‭[12] _Παντοδαποι̑σιν._ Whose common exposition is only _variis,_ ‭when it properly signifies _ex omni solo._ ‭[13] _Στονόεσσαν,_ of _στενός, angutstus._ ‭[14] Lickdish. ‭[15] _Ευ͒ τ᾽ ἀσκήσαντες, ab ἀσκέω, elaboratè concinno._ ‭[16] Enter-pot, or search-pot. ‭[17] Cheese-miner. _Qui caseum rodendo cavat._ ‭[18] _Μιμούμενος._ Aping, or imitating us. ‭[19] Boots of war. ‭[20] _Στέμματα, Lanas, eo quod colus cingant seu coronent._ Which ‭our learned sect translate eating the crowns that Pallas wore. ‭[21] _Τόκος. Partus, et id quod partu edidit mater. Metap. hic ‭appellatur fænus quod ex usurâ ad nos redit._ ‭[22] _Κώνωψ. Culex vinarius._ ‭[23] Loud-mouth. ‭[24] Kitchen-vessel licker. ‭[25] Hole-dweller. _Qui foramina subit._ ‭[26] Mud-born. ‭[27] Beet-devourer. ‭[28] The great bread eater. ‭[29] _Πολύφωνον._ The great-noise-maker, shrill or big-voiced. ‭[30] The lake-lover. ‭[31] _Qui lambit culinaria vasa._ ‭[32] _Τιτύσκομαι intentissime dirigo ut certum ictum inferam._ ‭[33] The cabbage-eater. ‭[34] _Paludis incola._ Lake-liver. ‭[35] _Qui in calaminthâ, herbâ palustri, habitat._ ‭[36] Bacon-eater. ‭[37] _Qui aquis delectatur._ ‭[38] Collop-devourer. ‭[39] Mud-sleeper. ‭[40] Leek or scallion lover. ‭[41] Kitchen-smell haunter, or hunter. ‭[42] Fenstalk. ‭[43] _Qui per lutum it._ ‭[44] Vociferator. ‭[45] Eat-corn. ‭[46] Scallion-devourer. ‭[47] Bread-betrayer. ‭[48] Scrap, or broken-meat-eater. ‭[49] _Κρατερός, validus seu potens in retineudo._ ‭[50] _Νωτάκμονες. Incudes ferentes,_ or anvil-backed. _῞Ακμων. ‭Incus, dicta per syncopen quasi nullis ictibus fatigetur._ ‭[51] _Ψαλίδοστομος. Forcipem in ore habens._ ‭ HYMNS ‭ A HYMN TO APOLLO ‭ I will remember and express the praise ‭ Of heaven's Far-darter, the fair King of days, ‭ Whom even the Gods themselves fear when he goes ‭ Through Jove's high house; and when his goodly bows ‭ He goes to bend, all from their thrones arise, ‭ And cluster near, t' admire his faculties. ‭ Only Latona stirs not from her seat ‭ Close by the Thund'rer, till her Son's retreat ‭ From his dread archery; but then she goes, ‭ Slackens his string, and shuts his quiver close, ‭ And (having taken to her hand his bow, ‭ From off his able shoulders) doth bestow ‭ Upon a pin of gold the glorious tiller, ‭ The pin of gold fix'd in his father's pillar. ‭ Then doth She to his throne his state uphold, ‭ Where his great Father, in a cup of gold, ‭ Serves him with nectar, and shows all the grace ‭ Of his great son. Then th' other Gods take place; ‭ His gracious mother glorying to bear ‭ So great an archer, and a son so clear. ‭ All hail, O blest Latona! to bring forth ‭ An issue of such all-out-shining worth, ‭ Royal Apollo, and the Queen that loves ‭ The hurls of darts. She in th' Ortygian groves, ‭ And he in cliffy Delos, leaning on ‭ The lofty Oros, and being built upon ‭ By Cynthus' prominent, that his head rears ‭ Close to the palm that Inops' fluent cheers. ‭ How shall I praise thee, far being worthiest praise, ‭ O Phœbus? To whose worth the law of lays ‭ In all kinds is ascrib'd, if feeding flocks ‭ By continent or isle. All eminent'st rocks ‭ Did sing for joy, hill-tops, and floods in song ‭ Did break their billows, as they flow'd along ‭ To serve the sea; the shores, the seas, and all ‭ Did sing as soon as from the lap did fall ‭ Of blest Latona thee the joy of man. ‭ Her child-bed made the mountain Cynthian ‭ In rocky Delos, the sea-circled isle, ‭ On whose all sides the black seas brake their pile, ‭ And overflow'd for joy, so frank a gale ‭ The singing winds did on their waves exhale. ‭ Here born, all mortals live in thy commands, ‭ Whoever Crete holds, Athens, or the strands ‭ Of th' isle Ægina, or the famous land ‭ For ships (Eubœa), or Eresia, ‭ Or Peparethus bord'ring on the sea, ‭ Ægas, or Athos that doth Thrace divide ‭ And Macedon; or Pelion, with the pride ‭ Of his high forehead; or the Samian isle, ‭ That likewise lies near Thrace; or Scyrus' soil; ‭ Ida's steep tops; or all that Phocis fill; ‭ Or Autocanes, with the heaven-high hill; ‭ Or populous Imber; Lemnos without ports; ‭ Or <DW26>s, fit for the divine resorts; ‭ And sacred soil of blest Æolion; ‭ Or Chios that exceeds comparison ‭ For fruitfulness; with all the isles that lie ‭ Embrac'd with seas; Mimas, with rocks so high; ‭ Or lofty-crown'd Corycius; or the bright ‭ Charos; or Æsagæus' dazzling height; ‭ Or watery Samos; Mycale, that bears ‭ Her brows even with the circles of the spheres; ‭ Miletus; Cous, that the city is ‭ Of voice-divided-choice humanities; ‭ High Cnidus; Carpathus, still strook with wind; ‭ Naxos, and Paros; and the rocky-min'd ‭ Rugged Rhenæa. Yet through all these parts ‭ Latona, great-grown with the King of darts, ‭ Travell'd; and tried if any would become ‭ To her dear birth an hospitable home. ‭ All which extremely trembled, shook with fear, ‭ Nor durst endure so high a birth to bear ‭ In their free states, though, for it, they became ‭ Never so fruitful; till the reverend Dame ‭ Ascended Delos, and her soil did seize ‭ With these wing'd words: "O Delos! Wouldst thou please ‭ To be my son Apollo's native seat, ‭ And build a wealthy fane to one so great, ‭ No one shall blame or question thy kind deed. ‭ Nor think I, thou dost sheep or oxen feed ‭ In any such store, or in vines exceed, ‭ Nor bring'st forth such innumerable plants, ‭ Which often make the rich inhabitants ‭ Careless of Deity. If thou then shouldst rear ‭ A fane to Phœbus, all men would confer ‭ Whole hecatombs of beeves for sacrifice, ‭ Still thronging hither; and to thee would rise ‭ Ever unmeasur'd odours, shouldst thou long ‭ Nourish thy King thus; and from foreign wrong ‭ The Gods would guard thee; which thine own address ‭ Can never compass for thy barrenness." ‭ She said, and Delos joy'd, replying thus: ‭ "Most happy sister of Saturnius! ‭ I gladly would with all means entertain ‭ The King your son, being now despised of men, ‭ But should be honour'd with the greatest then. ‭ Yet this I fear, nor will conceal from thee: ‭ Your son, some say, will author misery ‭ In many kinds, as being to sustain ‭ A mighty empire over Gods and men, ‭ Upon the holy-gift-giver the Earth. ‭ And bitterly I fear that, when his birth ‭ Gives him the sight of my so barren soil, ‭ He will contemn, and give me up to spoil, ‭ Enforce the sea to me, that ever will ‭ Oppress my heart with many a wat'ry hill. ‭ And therefore let him choose some other land, ‭ Where he shall please, to build at his command ‭ Temple and grove, set thick with many a tree. ‭ For wretched polypuses breed in me ‭ Retiring chambers, and black sea-calves den ‭ In my poor soil, for penury of men. ‭ And yet, O Goddess, wouldst thou please to swear ‭ The Gods' great oath to me, before thou bear ‭ Thy blessed son here, that thou wilt erect ‭ A fane to him, to render the effect ‭ Of men's demands to them before they fall, ‭ Then will thy son's renown be general, ‭ Men will his name in such variety call, ‭ And I shall then be glad his birth to bear." ‭ This said, the Gods' great oath she thus did swear: ‭ "Know this, O Earth! broad heaven's inferior sphere, ‭ And of black Styx the most infernal lake, ‭ (Which is the gravest oath the Gods can take) ‭ That here shall ever rise to Phœbus' name ‭ An odorous fane and altar; and thy fame ‭ Honour, past all isles else, shall see him employ'd." ‭ Her oath thus took and ended, Delos joy'd ‭ in mighty measure that she should become ‭ To far-shot Phœbus' birth the famous home. ‭ Latona then nine days and nights did fall ‭ In hopeless labour; at whose birth were all ‭ Heaven's most supreme and worthy Goddesses, ‭ Dione, Rhæa, and th' Exploratress ‭ Themis, and Amphitrite that will be ‭ Pursu'd with sighs still; every Deity, ‭ Except the snowy-wristed wife of Jove, ‭ Who held her moods aloft, and would not move; ‭ Only Lucina (to whose virtue vows ‭ Each childbirth patient) heard not of her throes, ‭ But sat, by Juno's counsel, on the brows ‭ Of broad Olympus, wrapp'd in clouds of gold. ‭ Whom Jove's proud wife in envy did withhold, ‭ Because bright-lock'd Latona was to bear ‭ A son so faultless and in force so clear. ‭ The rest Thaumantia sent before, to bring ‭ Lucina to release the envied king, ‭ Assuring her, that they would straight confer ‭ A carcanet, nine cubits long, on her, ‭ All woven with wires of gold. But charg'd her, then, ‭ To call apart from th' ivory-wristed Queen ‭ The childbirth-guiding Goddess, for just fear ‭ Lest, her charge utter'd in Saturnia's ear, ‭ She, after, might dissuade her from descent. ‭ When wind-swift-footed Iris knew th' intent ‭ Of th' other Goddesses, away she went, ‭ And instantly she pass'd the infinite space ‭ 'Twixt earth and heaven; when, coming to the place ‭ Where dwelt th' Immortals, straight without the gate ‭ She gat Lucina, and did all relate ‭ The Goddesses commanded, and inclin'd ‭ To all that they demanded her dear mind. ‭ And on their way they went, like those two doves ‭ That, walking highways, every shadow moves ‭ Up from the earth, forc'd with their natural fear. ‭ When ent'ring Delos, She, that is so dear ‭ To dames in labour, made Latona straight ‭ Prone to delivery, and to wield the weight ‭ Of her dear burthen with a world of ease. ‭ When, with her fair hand, she a palm did seize, ‭ And, staying her by it, stuck her tender knees ‭ Amidst the soft mead, that did smile beneath ‭ Her sacred labour; and the child did breathe ‭ The air in th' instant. All the Goddesses ‭ Brake in kind tears and shrieks for her quick ease, ‭ And thee, O archer Phœbus, with waves clear ‭ Wash'd sweetly over, swaddled with sincere ‭ And spotless swathbands; and made then to flow ‭ About thy breast a mantle, white as snow, ‭ Fine, and new made; and cast a veil of gold ‭ Over thy forehead. Nor yet forth did hold ‭ Thy mother for thy food her golden breast, ‭ But Themis, in supply of it, address'd ‭ Lovely Ambrosia, and drunk off to thee ‭ A bowl of nectar, interchangeably ‭ With her immortal fingers serving thine. ‭ And when, O Phœbus, that eternal wine ‭ Thy taste had relish'd, and that food divine, ‭ No golden swathband longer could contain ‭ Thy panting bosom; all that would constrain ‭ Thy soon-eas'd Godhead, every feeble chain ‭ Of earthy child-rites, flew in sunder all. ‭ And then didst thou thus to the Deities call: ‭ "Let there be given me my lov'd lute and bow, ‭ I'll prophesy to men, and make them know ‭ Jove's perfect counsels." This said, up did fly ‭ From broad-way'd Earth the unshorn Deity, ‭ Far-shot Apollo. All th' Immortals stood ‭ In steep amaze to see Latona's brood. ‭ All Delos, looking on him, all with gold ‭ Was loaden straight, and joy'd to be extoll'd ‭ By great Latona so, that she decreed ‭ Her barrenness should bear the fruitful'st seed ‭ Of all the isles and continents of earth, ‭ And lov'd her from her heart so for her birth. ‭ For so she flourish'd, as a hill that stood ‭ Crown'd with the flow'r of an abundant wood. ‭ And thou, O Phœbus, bearing in thy hand ‭ Thy silver bow, walk'st over every land, ‭ Sometimes ascend'st the rough-hewn rocky hill ‭ Of desolate Cynthus, and sometimes tak'st will ‭ To visit islands, and the plumps of men. ‭ And many a temple, all ways, men ordain ‭ To thy bright Godhead; groves, made dark with trees, ‭ And never shorn, to hide the Deities, ‭ All high-lov'd prospects, all the steepest brows ‭ Of far-seen hills, and every flood that flows ‭ Forth to the sea, are dedicate to thee. ‭ But most of all thy mind's alacrity ‭ Is rais'd with Delos; since, to fill thy fane, ‭ There flocks so many an Ionian, ‭ With ample gowns that flow down to their feet, ‭ With all their children, and the reverend sweet ‭ Of all their pious wives. And these are they ‭ That (mindful of thee) even thy Deity ‭ Render more spritely with their champion fight, ‭ Dances, and songs, perform'd to glorious sight, ‭ Once having publish'd, and proclaim'd their strife. ‭ And these are acted with such exquisite life ‭ That one would say, "Now, the Ionian strains ‭ Are turn'd Immortals, nor know what age means." ‭ His mind would take such pleasure from his eye, ‭ To see them serv'd by all mortality, ‭ Their men so human, women so well grac'd, ‭ Their ships so swift, their riches so increas'd, ‭ Since thy observance, who, being all before ‭ Thy opposites, were all despis'd and poor. ‭ And to all these this absolute wonder add, ‭ Whose praise shall render all posterities glad: ‭ The Delian virgins are thy handmaids all, ‭ And, since they serv'd Apollo, jointly fall ‭ Before Latona, and Diana too, ‭ In sacred service, and do therefore know ‭ How to make mention of the ancient trims ‭ Of men and women, in their well-made hymns, ‭ And soften barbarous nations with their songs, ‭ Being able all to speak the several tongues ‭ Of foreign nations, and to imitate ‭ Their musics there, with art so fortunate ‭ That one would say, there everyone did speak, ‭ And all their tunes in natural accents break, ‭ Their songs so well compos'd are, and their art ‭ To answer all sounds is of such desert. ‭ But come, Latona, and thou King of flames, ‭ With Phœbe, rect'ress of chaste thoughts in dames ‭ Let me salute ye, and your graces call ‭ Hereafter to my just memorial. ‭ And you, O Delian virgins, do me grace, ‭ When any stranger of our earthy race, ‭ Whose restless life affliction hath in chace, ‭ Shall hither come and question you, who is, ‭ To your chaste ears, of choicest faculties ‭ In sacred poesy, and with most right ‭ Is author of your absolut'st delight, ‭ Ye shall yourselves do all the right ye can ‭ To answer for our name:--"The sightless man ‭ Of stony Chios. All whose poems shall ‭ In all last ages stand for capital." ‭ This for your own sakes I desire, for I ‭ Will propagate mine own precedency ‭ As far as earth shall well-built cities bear, ‭ Or human conversation is held dear, ‭ Not with my praise direct, but praises due, ‭ And men shall credit it, because 'tis true. ‭ However, I'll not cease the praise I vow ‭ To far-shot Phœbus with the silver bow, ‭ Whom lovely-hair'd Latona gave the light. ‭ O King! both Lycia is in rule thy right, ‭ Fair Mœony, and the maritimal ‭ Miletus, wish'd to be the seat of all. ‭ But chiefly Delos, girt with billows round, ‭ Thy most respected empire doth resound. ‭ Where thou to Pythus went'st, to answer there, ‭ As soon as thou wert born, the burning ear ‭ Of many a far-come, to hear future deeds, ‭ Clad in divine and odoriferous weeds, ‭ And with thy golden fescue play'dst upon ‭ Thy hollow harp, that sounds to heaven set gone. ‭ Then to Olympus swift as thought he flew, ‭ To Jove's high house, and had a retinue ‭ Of Gods t' attend him; and then straight did fall ‭ To study of the harp, and harpsical, ‭ All th' Immortals. To whom every Muse ‭ With ravishing voices did their answers use, ‭ Singing th' eternal deeds of Deity, ‭ And from their hands what hells of misery ‭ Poor humans suffer, living desperate quite, ‭ And not an art they have, wit, or deceit, ‭ Can make them manage any act aright, ‭ Nor find, with all the soul they can engage, ‭ A salve for death, or remedy for age. ‭ But here the fair-hair'd Graces, the wise Hours, ‭ Harmonia, Hebe, and sweet Venus' pow'rs, ‭ Danc'd, and each other's palm to palm did cling. ‭ And with these danc'd not a deformed thing, ‭ No forespoke dwarf, nor downward witherling, ‭ But all with wond'rous goodly forms were deckt, ‭ And mov'd with beauties of unpriz'd aspect. ‭ Dart-dear Diana, even with Phœbus bred, ‭ Danc'd likewise there; and Mars a march did tread ‭ With that brave bevy. In whose consort fell ‭ Argicides, th' ingenious sentinel. ‭ Phœbus-Apollo touch'd his lute to them ‭ Sweetly and softly, a most glorious beam ‭ Casting about him, as he danc'd and play'd, ‭ And even his feet were all with rays array'd; ‭ His weed and all of a most curious trim ‭ With no less lustre grac'd and circled him. ‭ By these Latona, with a hair that shin'd ‭ Like burnish'd gold, and, with the mighty mind; ‭ Heaven's counsellor, Jove, sat with delightsome eyes; ‭ To see their son new rank'd with Deities. ‭ How shall I praise thee, then, that art all praise? ‭ Amongst the brides shall I thy Deity raise? ‭ Or being in love, when sad thou went'st to woo ‭ The virgin Aza, and didst overthrow ‭ The even-with-Gods, Elation's mighty seed, ‭ That had of goodly horse so brave a breed, ‭ And Phorbas, son of sovereign Triopus, ‭ Valiant Leucippus, and Ereutheus, ‭ And Triopus himself with equal fall, ‭ Thou but on foot, and they on horseback all? ‭ Or shall I sing thee, as thou first didst grace ‭ Earth with thy foot, to find thee forth a place ‭ Fit to pronounce thy oracles to men? ‭ First from Olympus thou alightedst then ‭ Into Pieria, passing all the land ‭ Of fruitless <DW26>s, chok'd with drifts of sand, ‭ The Magnets likewise, and the Perrhæbes; ‭ And to Iolcus variedst thy access, ‭ Cenæus' tops ascending, that their base ‭ Make bright Eubœa, being of ships the grace, ‭ And fix'd thy fair stand in Lelantus' field, ‭ That did not yet thy mind's contentment yield ‭ To raise a fane on, and a sacred grove. ‭ Passing Euripus then, thou mad'st remove ‭ Up to earth's ever-green and holiest hill. ‭ Yet swiftly thence, too, thou transcendedst still ‭ To Mycalessus, and didst touch upon ‭ Teumessus, apt to make green couches on, ‭ And flowery field-beds. Then thy progress found ‭ Thebes out, whose soil with only woods was crown'd, ‭ For yet was sacred Thebes no human seat, ‭ And therefore were no paths nor highways beat ‭ On her free bosom, that flows now with wheat, ‭ But then she only wore on it a wood. ‭ From hence (even loth to part, because it stood ‭ Fit for thy service) thou putt'st on remove ‭ To green Onchestus, Neptune's glorious grove, ‭ Where new-tam'd horse, bred, nourish nerves so rare ‭ That still they frolic, though they travell'd are ‭ Never so sore, and hurry after them ‭ Most heavy coaches, but are so extreme ‭ (In usual travel) fiery and free, ‭ That though their coachman ne'er so masterly ‭ Governs their courages, he sometimes must ‭ Forsake his seat, and give their spirits their lust, ‭ When after them their empty coach they draw, ‭ Foaming, and neighing, quite exempt from awe. ‭ And if their coachman guide through any grove ‭ Unshorn, and vow'd to any Deity's love, ‭ The lords encoach'd leap out, and all their care ‭ Use to allay their fires, with speaking fair ‭ Stroking and trimming them, and in some queach, ‭ Or strength of shade, within their nearest reach, ‭ Reining them up, invoke the deified King ‭ Of that unshorn and everlasting spring, ‭ And leave them then to her preserving hands, ‭ Who is the Fate that there the God commands. ‭ And this was first the sacred fashion there. ‭ From hence thou went'st, O thou in shafts past peer, ‭ And found'st Cephissus with thy all-seeing beams, ‭ Whose flood affects so many silver streams, ‭ And from Lilæus pours so bright a wave. ‭ Yet forth thy foot flew, and thy fair eyes gave ‭ The view of Ocale the rich in tow'rs; ‭ Then to Amartus that abounds in flow'rs, ‭ Then to Delphusa putt'st thy progress on, ‭ Whose blessed soil nought harmful breeds upon; ‭ And there thy pleasure would a fane adorn, ‭ And nourish woods whose shades should ne'er be shorn. ‭ Where this thou told'st her, standing to her close: ‭ "Delphusa, here I entertain suppose ‭ To build a far-fam'd temple, and ordain ‭ An oracle t' inform the minds of men, ‭ Who shall for ever offer to my love ‭ Whole hecatombs; even all the men that move ‭ In rich Peloponnesus, and all those ‭ Of Europe, and the isles the seas enclose, ‭ Whom future search of acts and beings brings. ‭ To whom I'll prophesy the truths of things ‭ In that rich temple where my oracle sings." ‭ This said, the All-bounds-reacher, with his bow, ‭ The fane's divine foundations did foreshow; ‭ Ample they were, and did huge length impart, ‭ With a continuate tenour, full of art. ‭ But when Delphusa look'd into his end, ‭ Her heart grew angry, and did thus extend ‭ Itself to Phœbus: "Phœbus, since thy mind ‭ A far-fam'd fane hath in itself design'd ‭ To bear an oracle to men in me, ‭ That hecatombs may put in fire to thee, ‭ This let me tell thee, and impose for stay ‭ Upon thy purpose: Th' inarticulate neigh ‭ Of fire-hov'd horse will ever disobey ‭ Thy numerous ear, and mules will for their drink ‭ Trouble my sacred springs, and I should think ‭ That any of the human race had rather ‭ See here the hurries of rich coaches gather, ‭ And hear the haughty neighs of swift-hov'd horse, ‭ Than in his pleasure's place convert recourse ‭ T'a mighty temple; and his wealth bestow ‭ On pieties, where his sports may freely flow, ‭ Or see huge wealth that he shall never owe. ‭ And, therefore, wouldst thou hear my free advice,-- ‭ Though mightier far thou art, and much more wise, ‭ O king, than I, thy pow'r being great'st of all ‭ In Crissa, underneath the bosom's fall ‭ Of steep Parnassus,--let thy mind be given ‭ To set thee up a fane, where never driven ‭ Shall glorious coaches be, nor horses' neighs ‭ Storm near thy well-built altars, but thy praise ‭ Let the fair race of pious humans bring ‭ Into thy fane, that Io-pæans sing. ‭ And those gifts only let thy deified mind ‭ Be circularly pleas'd with, being the kind ‭ And fair burnt-offerings that true Deities bind." ‭ With this his mind she altered, though she spake ‭ Not for his good, but her own glory's sake. ‭ From hence, O Phœbus, first thou mad'st retreat, ‭ And of the Phlegians reached the walled seat, ‭ Inhabited with contumelious men, ‭ Who, slighting Jove, took up their dwellings then ‭ Within a large cave, near Cephissus' lake. ‭ Hence, swiftly moving, thou all speed didst make ‭ Up to the tops intended, and the ground ‭ Of Crissa, under the-with-snow-still-crown'd ‭ Parnassus, reach'd, whose face affects the West; ‭ Above which hangs a rock, that still seems prest ‭ To fall upon it, through whose breast doth run ‭ A rocky cave, near which the King the Sun ‭ Cast to contrive a temple to his mind, ‭ And said, "Now here stands my conceit inclin'd ‭ To build a famous fane, where still shall be ‭ An oracle to men, that still to me ‭ Shall offer absolute hecatombs, as well ‭ Those that in rich Peloponnesus dwell ‭ As those of Europe, and the isles that lie ‭ Wall'd with the sea, that all their pains apply ‭ T' employ my counsels. To all which will I ‭ True secrets tell, by way of prophecy, ‭ In my rich temple, that shall ever be ‭ An oracle to all posterity." ‭ This said, the fane's form he did straight present, ‭ Ample, and of a length of great extent; ‭ In which Trophonius and Agamede, ‭ Who of Erginus were the famous seed, ‭ Impos'd the stony entry, and the heart ‭ Of every God had for their excellent art. ‭ About the temple dwelt of human name ‭ Unnumber'd nations, it acquired such fame, ‭ Being all of stone, built for eternal date. ‭ And near it did a fountain propagate ‭ A fair stream far away; when Jove's bright seed, ‭ The King Apollo, with an arrow, freed ‭ From his strong string, destroy'd the Dragoness ‭ That wonder nourish'd, being of such excess ‭ In size, and horridness of monstrous shape, ‭ That on the forc'd earth she wrought many a rape, ‭ Many a spoil made on it, many an ill ‭ On crook-haunch'd herds brought, being impurpled still ‭ With blood of all sorts; having undergone ‭ The charge of Juno, with the golden throne, ‭ To nourish Typhon, the abhorr'd affright ‭ And bane of mortals, whom into the light ‭ Saturnia brought forth, being incensed with Jove, ‭ Because the most renown'd fruit of his love ‭ (Pallas) he got, and shook out of his brain. ‭ For which majestic Juno did complain ‭ In this kind to the Bless'd Court of the skies: ‭ "Know all ye sex-distinguish'd Deities, ‭ That Jove, assembler of the cloudy throng, ‭ Begins with me first, and affects with wrong ‭ My right in him, made by himself his wife, ‭ That knows and does the honour'd marriage life ‭ All honest offices; and yet hath he ‭ Unduly got, without my company, ‭ Blue-eyed Minerva, who of all the sky ‭ Of blest Immortals is the absolute grace; ‭ Where I have brought into the Heavenly Race ‭ A son, both taken in his feet and head, ‭ So ugly, and so far from worth my bed, ‭ That, ravish'd into hand, I took and threw ‭ Down to the vast sea his detested view; ‭ Where Nereus' daughter, Thetis, who her way ‭ With silver feet makes, and the fair array ‭ Of her bright sisters, saved, and took to guard. ‭ But, would to heaven, another yet were spared ‭ The like grace of his godhead! Crafty mate, ‭ What other scape canst thou excogitate? ‭ How could thy heart sustain to get alone ‭ The grey-eyed Goddess? Her conception ‭ Nor bringing forth had any hand of mine, ‭ And yet, know all the Gods, I go for thine ‭ To such kind uses. But I'll now employ ‭ My brain to procreate a masculine joy, ‭ That 'mongst th' Immortals may as eminent shine, ‭ With shame affecting nor my bed nor thine. ‭ Nor will I ever touch at thine again, ‭ But far fly it and thee; and yet will reign ‭ Amongst th' Immortals ever." This spleen spent ‭ (Still yet left angry) far away she went ‭ From all the Deathless, and yet pray'd to all, ‭ Advanced her hand, and, ere she let it fall, ‭ Used these excitements: "Hear me now, O Earth! ‭ Broad Heaven above it, and beneath, your birth, ‭ The deified Titanois, that dwell about ‭ Vast Tartarus, from whence sprung all the rout ‭ Of Men and Deities! Hear me all, I say, ‭ With all your forces, and give instant way ‭ T' a son of mine without Jove, who yet may ‭ Nothing inferior prove in force to him, ‭ But past him spring as far in able limb ‭ As he past Saturn." This pronounced, she strook ‭ Life-bearing Earth so strongly, that she shook ‭ Beneath her numb'd hand. Which when she beheld, ‭ Her bosom with abundant comforts swell'd, ‭ In hope all should to her desire extend. ‭ From hence the year, that all such proofs gives end, ‭ Grew round; yet all that time the bed of Jove ‭ She never touch'd at, never was her love ‭ Enflam'd to sit near his Dædalian throne, ‭ As she accustomed, to consult upon ‭ Counsels kept dark with many a secret skill, ‭ But kept her vow-frequented temple still, ‭ Pleas'd with her sacrifice; till now, the nights ‭ And days accomplish'd, and the year's whole rights ‭ In all her revolutions being expired, ‭ The hours and all run out that were required ‭ To vent a birth-right, she brought forth a son, ‭ Like Gods or men in no condition, ‭ But a most dreadful and pernicious thing, ‭ Call'd Typhon, who on all the human spring ‭ Conferr'd confusion. Which received to hand ‭ By Juno, instantly she gave command ‭ (Ill to ill adding) that the Dragoness ‭ Should bring it up; who took, and did oppress ‭ With many a misery (to maintain th' excess ‭ Of that inhuman monster) all the race ‭ Of men that were of all the world the grace, ‭ Till the far-working Phœbus at her sent ‭ A fiery arrow, that invoked event ‭ Of death gave to her execrable life. ‭ Before which yet she lay in bitter strife, ‭ With dying pains, grovelling on earth, and drew ‭ Extreme short respirations; for which flew ‭ A shout about the air, whence no man knew, ‭ But came by power divine. And then she lay ‭ Tumbling her trunk, and winding every way ‭ About her nasty nest, quite leaving then ‭ Her murderous life, embrued with deaths of men. ‭ Then Phœbus gloried, saying: "Thyself now lie ‭ On men-sustaining earth, and putrefy, ‭ Who first of putrefaction was inform'd. ‭ Now on thy life have death's cold vapours storm'd, ‭ That storm'dst on men the earth-fed so much death, ‭ In envy of the offspring they made breathe ‭ Their lives out on my altars. Now from thee ‭ Not Typhon shall enforce the misery ‭ Of merited death, nor She, whose name implies ‭ Such scathe (Chimæra), but black earth make prise ‭ To putrefaction thy immanities, ‭ And bright Hyperion, that light all eyes shows, ‭ Thine with a night of rottenness shall close." ‭ Thus spake he glorying. And then seiz'd upon ‭ Her horrid heap, with putrefaction, ‭ Hyperion's lovely pow'rs; from whence her name ‭ Took sound of Python, and heaven's Sovereign Flame ‭ Was surnam'd Pythius, since the sharp-eyed Sun ‭ Affected so with putrefaction ‭ The hellish monster. And now Phœbus' mind ‭ Gave him to know that falsehood had strook blind ‭ Even his bright eye, because it could not find ‭ The subtle Fountain's fraud; to whom he flew, ‭ Enflamed with anger, and in th' instant drew ‭ Close to Delphusa, using this short vow: ‭ "Delphusa! You must look no longer now ‭ To vent your frauds on me; for well I know ‭ Your situation to be lovely, worth ‭ A temple's imposition, it pours forth ‭ So delicate a stream. But your renown ‭ Shall now no longer shine here, but mine own." ‭ This said, he thrust her promontory down, ‭ And damm'd her fountain up with mighty stones, ‭ A temple giving consecrations ‭ In woods adjoining. And in this fane all ‭ On him, by surname of Delphusius, call, ‭ Because Delphusa's sacred flood and fame ‭ His wrath affected so, and hid in shame. ‭ And then thought Phœbus what descent of men ‭ To be his ministers he should retain, ‭ To do in stony Pythos sacrifice. ‭ To which his mind contending, his quick eyes ‭ He cast upon the blue sea, and beheld ‭ A ship, on whose masts sails that wing'd it swell'd, ‭ In which were men transferr'd, many and good, ‭ That in Minoian Cnossus ate their food, ‭ And were Cretensians; who now are those ‭ That all the sacrificing dues dispose, ‭ And all the laws deliver to a word ‭ Of Day's great King, that wears the golden sword, ‭ And oracles (out of his Delphian tree ‭ That shrouds her fair arms in the cavity ‭ Beneath Parnassus' mount) pronounce to men. ‭ These now his priests, that lived as merchants then, ‭ In traffics and pecuniary rates, ‭ For sandy Pylos and the Pylian states. ‭ Were under sail. But now encounter'd them ‭ Phœbus-Apollo, who into the stream ‭ Cast himself headlong, and the strange disguise ‭ Took of a dolphin of a goodly size. ‭ Like which he leap'd into their ship, and lay ‭ As an ostent of infinite dismay. ‭ For none with any strife of mind could look ‭ Into the omen, all the ship-masts shook, ‭ And silent all sat with the fear they took, ‭ Arm'd not, nor strook they sail, but as before ‭ Went on with full trim, and a foreright blore, ‭ Stiff, and from forth the south, the ship made fly. ‭ When first they stripp'd the Malean promont'ry, ‭ Touch'd at Laconia's soil, in which a town ‭ Their ship arriv'd at, that the sea doth crown, ‭ Called Tenarus, a place of much delight ‭ To men that serve Heaven's Comforter of sight. ‭ In which are fed the famous flocks that bear ‭ The wealthy fleeces, on a delicate lair ‭ Being fed and seated. Where the merchants fain ‭ Would have put in, that they might out again ‭ To tell the miracle that chanced to them, ‭ And try if it would take the sacred stream, ‭ Rushing far forth, that he again might bear ‭ Those other fishes that abounded there ‭ Delightsome company, or still would stay ‭ Aboard their dry ship. But it fail'd t' obey, ‭ And for the rich Peloponnesian shore ‭ Steer'd her free sail; Apollo made the blore ‭ Directly guide it. That obeying still ‭ Reach'd dry Arena, and (what wish doth fill) ‭ Fair Argyphæa, and the populous height ‭ Of Thryus, whose stream, siding her, doth wait ‭ With safe pass on Alphæus, Pylos' sands, ‭ And Pylian dwellers; keeping by the strands ‭ On which th' inhabitants of Crunius dwell, ‭ And Helida set opposite to hell; ‭ Chalcis and Dymes reach'd, and happily ‭ Made sail by Pheras; all being overjoy'd ‭ With that frank gale that Jove himself employ'd. ‭ And then amongst the clouds they might descry ‭ The hill, that far-seen Ithaca calls her Eye, ‭ Dulichius, Samos, and, with timber graced, ‭ Shady Zacynthus. But when now they past ‭ Peloponnesus all, and then when show'd ‭ The infinite vale of Crissa, that doth shroud ‭ All rich Morea with her liberal breast, ‭ So frank a gale there flew out of the West ‭ As all the sky discover'd; 'twas so great, ‭ And blew so from the very council seat ‭ Of Jove himself, that quickly it might send ‭ The ship through full seas to her journey's end. ‭ From thence they sail'd, quite opposite, to the East, ‭ And to the region where Light leaves his rest, ‭ The Light himself being sacred pilot there, ‭ And made the sea-trod ship arrive them near ‭ The grapeful Crissa, where he rest doth take ‭ Close to her port and sands. And then forth brake ‭ The far-shot King, like to a star that strows ‭ His glorious forehead where the mid-day glows, ‭ That all in sparkles did his state attire, ‭ Whose lustre leap'd up to the sphere of fire. ‭ He trod where no way oped, and pierced the place ‭ That of his sacred tripods held the grace, ‭ In which he lighted such a fluent flame ‭ As gilt all Crissa; in which every dame, ‭ And dame's fair daughter, cast out vehement cries ‭ At those fell fires of Phœbus' prodigies, ‭ That shaking fears through all their fancies threw. ‭ Then, like the mind's swift light, again he flew ‭ Back to the ship, shaped like a youth in height ‭ Of all his graces, shoulders broad and straight, ‭ And all his hair in golden curls enwrapp'd; ‭ And to the merchants thus his speech he shap'd: ‭ "Ho! Strangers! What are you? And from what seat ‭ Sail ye these ways that salt and water sweat? ‭ To traffic justly? Or use vagrant scapes ‭ Void of all rule, conferring wrongs and rapes, ‭ Like pirates, on the men ye never saw, ‭ With minds project exempt from list or law? ‭ Why sit ye here so stupefied, nor take ‭ Land while ye may, nor deposition make ‭ Of naval arms, when this the fashion is ‭ Of men industrious, who (their faculties ‭ Wearied at sea) leave ship, and use the land ‭ For food, that with their healths and stomachs stand?" ‭ This said, with bold minds he their breast supplied, ‭ And thus made answer the Cretensian guide: ‭ "Stranger! Because you seem to us no seed ‭ Of any mortal, but celestial breed ‭ For parts and person, joy your steps ensue, ‭ And Gods make good the bliss we think your due. ‭ Vouchsafe us true relation, on what land ‭ We here arrive, and what men here command. ‭ We were for well-known parts bound, and from Crete ‭ (Our vaunted country) to the Pylian seat ‭ Vow'd our whole voyage; yet arrive we here, ‭ Quite cross to those wills that our motions steer, ‭ Wishing to make return some other way, ‭ Some other course desirous to assay, ‭ To pay our lost pains. But some God hath fill'd ‭ Our frustrate sails, defeating what we will'd." ‭ Apollo answer'd: "Strangers! Though before ‭ Ye dwelt in woody Cnossus, yet no more ‭ Ye must be made your own reciprocals ‭ To your loved city and fair severals ‭ Of wives and houses, but ye shall have here ‭ My wealthy temple, honour'd far and near ‭ Of many a nation; for myself am son ‭ To Jove himself, and of Apollo won ‭ The glorious title, who thus safely through ‭ The sea's vast billows still have held your plough, ‭ No ill intending, that will yet ye make ‭ My temple here your own, and honours take ‭ Upon yourselves, all that to me are given. ‭ And more, the counsels of the King of Heaven ‭ Yourselves shall know, and with his will receive ‭ Ever the honours that all men shall give. ‭ Do as I say then instantly, strike sail, ‭ Take down your tackling, and your vessel hale ‭ Up into land; your goods bring forth, and all ‭ The instruments that into sailing fall; ‭ Make on this shore an altar, fire enflame, ‭ And barley white cakes offer to my name; ‭ And then, environing the altar, pray, ‭ And call me (as ye saw me in the day ‭ When from the windy seas I brake swift way ‭ Into your ship) Delphinius, since I took ‭ A dolphin's form then. And to every look ‭ That there shall seek it, that my altar shall ‭ Be made a Delphian memorial ‭ From thence for ever. After this, ascend ‭ Your swift black ship and sup, and then intend ‭ Ingenuous offerings to the equal Gods ‭ That in celestial seats make blest abodes. ‭ When, having stay'd your healthful hunger's sting, ‭ Come all with me, and Io-pæans sing ‭ All the way's length, till you attain the state ‭ Where I your opulent fane have consecrate." ‭ To this they gave him passing diligent ear, ‭ And vow'd to his obedience all they were. ‭ First, striking sail, their tacklings then they losed, ‭ And (with their gables stoop'd) their mast imposed ‭ Into the mast-room. Forth themselves then went, ‭ And from the sea into the continent ‭ Drew up their ship; which far up from the sand ‭ They rais'd with ample rafters. Then in hand ‭ They took the altar; and inform'd it on ‭ The sea's near shore, imposing thereupon ‭ White cakes of barley, fire made, and did stand ‭ About it round, as Phœbus gave command, ‭ Submitting invocations to his will. ‭ Then sacrific'd to all the heavenly hill ‭ Of pow'rful Godheads. After which they eat ‭ Aboard their ship, till with fit food replete ‭ They rose, nor to their temple used delay. ‭ Whom Phœbus usher'd, and touch'd all the way ‭ His heavenly lute with art above admired, ‭ Gracefully leading them. When all were fired ‭ With zeal to him, and follow'd wond'ring all ‭ To Pythos; and upon his name did call ‭ With Io-pæans, such as Cretans use. ‭ And in their bosoms did the deified Muse ‭ Voices of honey-harmony infuse. ‭ With never-weary feet their way they went, ‭ And made with all alacrity ascent ‭ Up to Parnassus, and that long'd-for place ‭ Where they should live, and be of men the grace. ‭ When, all the way, Apollo show'd them still ‭ Their far-stretch'd valleys, and their two-topp'd hill, ‭ Their famous fane, and all that all could raise ‭ To a supreme height of their joy and praise. ‭ And then the Cretan captain thus inquired ‭ Of King Apollo: "Since you have retired, ‭ O sovereign, our sad lives so far from friends ‭ And native soil (because so far extends ‭ Your dear mind's pleasure) tell us how we shall ‭ Live in your service? To which question call ‭ Our provident minds, because we see not crown'd ‭ This soil with store of vines, nor doth abound ‭ In wealthy meadows, on which we may live, ‭ As well as on men our attendance give." ‭ He smiled, and said: "O men that nothing know, ‭ And so are follow'd with a world of woe, ‭ That needs will succour care and curious moan, ‭ And pour out sighs without cessation, ‭ Were all the riches of the earth your own! ‭ Without much business, I will render known ‭ To your simplicities an easy way ‭ To wealth enough, Let every man purvey ‭ A skeane, or slaught'ring steel, and his right hand, ‭ Bravely bestowing, evermore see mann'd ‭ With killing sheep, that to my fane will flow ‭ From all far nations. On all which bestow ‭ Good observation, and all else they give ‭ To me make you your own all, and so live. ‭ For all which watch before my temple well, ‭ And all my counsels, above all, conceal. ‭ If any give vain language, or to deeds, ‭ Yea or as far as injury, proceeds, ‭ Know that, at losers' hands, for those that gain, ‭ It is the law of mortals to sustain. ‭ Besides, ye shall have princes to obey, ‭ Which still ye must, and (so ye gain) ye may. ‭ All now is said; give all thy memory's stay." ‭ And thus to thee, Jove and Latona's son, ‭ Be given all grace of salutation! ‭ Both thee and others of th' Immortal State ‭ My song shall memorize to endless date. ‭ THE END OF THE HYMN TO APOLLO. ‭ A HYMN TO HERMES ‭ Hermes, the son of Jove and Maia, sing, ‭ O Muse, th' Arcadian and Cyllenian king, ‭ They rich in flocks, he heaven enriching still ‭ In messages return'd with all his will. ‭ Whom glorious Maia, the nymph rich in hair, ‭ Mixing with Jove in amorous affair, ‭ Brought forth to him, sustaining a retreat ‭ From all th' Immortals of the blessed seat, ‭ And living in the same dark cave, where Jove ‭ Inform'd at midnight the effect of love, ‭ Unknown to either man or Deity, ‭ Sweet sleep once having seized the jealous eye ‭ Of Juno deck'd with wrists of ivory. ‭ But when great Jove's high mind was consummate, ‭ The tenth month had in heaven confined the date ‭ Of Maia's labour, and into the sight ‭ She brought in one birth labours infinite; ‭ For then she bore a son, that all tried ways ‭ Could turn and wind to wish'd events assays, ‭ A fair-tongu'd, but false-hearted, counsellor, ‭ Rector of ox-stealers, and for all stealths bore ‭ A varied finger; speeder of night's spies, ‭ And guide of all her dreams' obscurities; ‭ Guard of door-guardians; and was born to be, ‭ Amongst th' Immortals, that wing'd Deity ‭ That in an instant should do acts would ask ‭ The powers of others an eternal task. ‭ Born in the morn, he form'd his lute at noon, ‭ At night stole all the oxen of the Sun; ‭ And all this in his birth's first day was done, ‭ Which was the fourth of the increasing moon. ‭ Because celestial limbs sustain'd his strains, ‭ His sacred swath-bands must not be his chains, ‭ So, starting up, to Phœbus' herd he stept, ‭ Found straight the high-roof'd cave where they were kept, ‭ And th' entry passing, he th' invention found ‭ Of making lutes; and did in wealth abound ‭ By that invention, since he first of all ‭ Was author of that engine musical, ‭ By this means moved to the ingenious work: ‭ Near the cave's inmost overture did lurk ‭ A tortoise, tasting th' odoriferous grass, ‭ Leisurely moving; and this object was ‭ The motive to Jove's son (who could convert ‭ To profitable uses all desert ‭ That nature had in any work convey'd) ‭ To form the lute; when, smiling, thus he said: ‭ "Thou mov'st in me a note of excellent use, ‭ Which thy ill form shall never so seduce ‭ T' avert the good to be inform'd by it, ‭ In pliant force, of my form-forging wit." ‭ Then the slow tortoise, wrought on by his mind, ‭ He thus saluted: "All joy to the kind ‭ Instinct of nature in thee, born to be ‭ The spiriter of dances, company ‭ For feasts, and following banquets, graced and blest ‭ For bearing light to all the interest ‭ Claim'd in this instrument! From whence shall spring ‭ Play fair and sweet, to which may Graces sing. ‭ A pretty painted coat thou putt'st on here, ‭ O Tortoise, while thy ill-bred vital sphere ‭ Confines thy fashion; but, surprised by me, ‭ I'll bear thee home, where thou shalt ever be ‭ A profit to me; and yet nothing more ‭ Will I contemn thee in my merited store. ‭ Goods with good parts got worth and honour gave, ‭ Left goods and honours every fool may have, ‭ And since thou first shall give me means to live, ‭ I'll love thee ever. Virtuous qualities give ‭ To live at home with them enough content, ‭ Where those that want such inward ornament ‭ Fly out for outward, their life made their load. ‭ _Tis best to be at home, harm lurks abroad._ ‭ And certainly thy virtue shall be known, ‭ 'Gainst great-ill-causing incantation ‭ To serve as for a lance or amulet. ‭ And where, in comfort of thy vital heat, ‭ Thou now breath'st but a sound confus'd for song, ‭ Expos'd by nature, after death, more strong ‭ Thou shalt in sounds of art be, and command ‭ Song infinite sweeter." Thus with either hand ‭ He took it up, and instantly took flight ‭ Back to his cave with that his home delight. ‭ Where (giving to the mountain tortoise vents ‭ Of life and motion) with fit instruments ‭ Forged of bright steel he straight inform'd a lute, ‭ Put neck and frets to it, of which a suit ‭ He made of splitted quills, in equal space ‭ Impos'd upon the neck, and did embrace ‭ Both back and bosom. At whose height (as gins ‭ T' extend and ease the string) he put in pins. ‭ Seven strings of several tunes he then applied, ‭ Made of the entrails of a sheep well-dried, ‭ And throughly twisted. Next he did provide ‭ A case for all, made of an ox's hide, ‭ Out of his counsels to preserve as well ‭ As to create. And all this action fell ‭ Into an instant consequence. His word ‭ And work had individual accord, ‭ All being as swiftly to perfection brought ‭ As any worldly man's most ravish'd thought, ‭ Whose mind care cuts in an infinity ‭ Of varied parts or passions instantly, ‭ Or as the frequent twinklings of an eye. ‭ And thus his house-delight given absolute end, ‭ He touch'd it, and did every string extend ‭ (With an exploratory spirit assay'd) ‭ To all the parts that could on it be play'd. ‭ It sounded dreadfully; to which he sung, ‭ As if from thence the first and true force sprung ‭ That fashions virtue. God in him did sing. ‭ His play was likewise an unspeakable thing, ‭ Yet, but as an extemporal assay, ‭ Of what show it would make being the first way, ‭ It tried his hand; or a tumultuous noise, ‭ Such as at feasts the first-flower'd spirits of boys ‭ Pour out in mutual contumelies still, ‭ As little squaring with his curious will, ‭ Or was as wanton and untaught a store. ‭ Of Jove, and Maia that rich shoes still wore, ‭ He sung; who suffer'd ill reports before, ‭ And foul stains under her fair titles bore. ‭ But Hermes sung her nation, and her name ‭ Did iterate ever; all her high-flown fame ‭ Of being Jove's mistress; celebrating all ‭ Her train of servants, and collateral ‭ Sumpture of houses; all her tripods there, ‭ And caldrons huge, increasing every year. ‭ All which she knew, yet felt her knowledge stung ‭ With her fame's loss, which (found) she more wish'd sung. ‭ But now he in his sacred cradle laid ‭ His lute so absolute, and straight convey'd ‭ Himself up to a watch-tow'r forth his house, ‭ Rich, and divinely odoriferous, ‭ A lofty wile at work in his conceit, ‭ Thirsting the practice of his empire's height. ‭ And where impostors rule (since sable night ‭ Must serve their deeds) he did his deeds their right. ‭ For now the never-resting Sun was turn'd ‭ For th' under earth, and in the ocean burn'd ‭ His coach and coursers; when th' ingenious spy ‭ Pieria's shady hill had in his eye, ‭ Where the immortal oxen of the Gods ‭ In air's flood solaced their select abodes, ‭ And earth's sweet green flow'r, that was never shorn, ‭ Fed ever down. And these the witty-born, ‭ Argicides, set serious spy upon, ‭ Severing from all the rest, and setting gone ‭ Full fifty of the violent bellowers. ‭ Which driving through the sands, he did reverse ‭ (His birth's-craft straight rememb'ring) all their hoves, ‭ And them transpos'd in opposite removes, ‭ The fore behind set, the behind before, ‭ T' employ the eyes of such as should explore. ‭ And he himself, as sly-pac'd, cast away ‭ His sandals on the sea sands; past display ‭ And unexcogitable thoughts in act ‭ Putting, to shun of his stol'n steps the tract, ‭ Mixing both tamrisk and like-tamrisk sprays ‭ In a most rare confusion, to raise ‭ His footsteps up from earth. Of which sprays he ‭ (His armful gathering fresh from off the tree) ‭ Made for his sandals ties, both leaves and ties ‭ Holding together; and then fear'd no eyes ‭ That could affect his feet's discoveries. ‭ The tamrisk boughs he gather'd, making way ‭ Back from Pieria, but as to convey ‭ Provision in them for his journey fit, ‭ It being long and, therefore, needing it. ‭ An old man, now at labour near the field ‭ Of green Onchestus, knew the verdant yield ‭ Of his fair armful; whom th' ingenious son ‭ Of Maia, therefore, salutation ‭ Did thus begin to: "Ho, old man! that now ‭ Art crooked grown with making plants to grow, ‭ Thy nerves will far be spent, when these boughs shall ‭ To these their leaves confer me fruit and all. ‭ But see not thou whatever thou dost see, ‭ Nor hear though hear, but all as touching me ‭ Conceal, since nought it can endamage thee." ‭ This, and no more, he said, and on drave still ‭ His broad-brow'd oxen. Many a shady hill, ‭ And many an echoing valley, many a field ‭ Pleasant and wishful, did his passage yield ‭ Their safe transcension. But now the divine ‭ And black-brow'd Night, his mistress, did decline ‭ Exceeding swiftly; Day's most early light ‭ Fast hasting to her first point, to excite ‭ Worldlings to work; and in her watch-tow'r shone ‭ King Pallas-Megamedes' seed (the Moon); ‭ When through th' Alphæan flood Jove's powerful son ‭ Phœbus-Apollo's ample-foreheaded herd ‭ (Whose necks the lab'ring yoke had never sphered) ‭ Drave swiftly on; and then into a stall ‭ (Hilly, yet pass'd to through an humble vale ‭ And hollow dells, in a most lovely mead) ‭ He gather'd all, and them divinely fed ‭ With odorous cypress, and the ravishing tree ‭ That makes his eaters lose the memory ‭ Of name and country. Then he brought withal ‭ Much wood, whose sight into his search let fall ‭ The art of making fire; which thus he tried: ‭ He took a branch of laurel, amplified ‭ Past others both in beauty and in size, ‭ Yet lay next hand, rubb'd it, and straight did rise ‭ A warm fume from it; steel being that did raise ‭ (As agent) the attenuated bays ‭ To that hot vapour. So that Hermes found ‭ Both fire first, and of it the seed close bound ‭ In other substances; and then the seed ‭ He multiplied, of sere-wood making feed ‭ The apt heat of it, in a pile combined ‭ Laid in a low pit, that in flames straight shined, ‭ And cast a sparkling crack up to the sky, ‭ All the dry parts so fervent were, and high ‭ In their combustion. And how long the force ‭ Of glorious Vulcan kept the fire in course, ‭ So long was he in dragging from their stall ‭ Two of the crook-haunch'd herd, that roar'd withal, ‭ And raged for fear, t' approach the sacred fire, ‭ To which did all his dreadful pow'rs aspire. ‭ When, blust'ring forth their breath, he on the soil ‭ Cast both at length, though with a world of toil, ‭ For long he was in getting them to ground ‭ After their through-thrust and most mortal wound. ‭ But work to work he join'd, the flesh and cut, ‭ Cover'd with fat, and, on treen broches put, ‭ In pieces roasted; but in th' intestines ‭ The black blood, and the honorary chines, ‭ Together with the carcases, lay there, ‭ Cast on the cold earth, as no Deities' cheer; ‭ The hides upon a rugged rock he spread. ‭ And thus were these now all in pieces shred, ‭ And undistinguish'd from earth's common herd, ‭ Though born for long date, and to heaven endear'd, ‭ And now must ever live in dead event. ‭ But Hermes, here hence having his content, ‭ Cared for no more, but drew to places even ‭ The fat-works, that, of force, must have for heaven ‭ Their capital ends, though stol'n, and therefore were ‭ In twelve parts cut, for twelve choice Deities' cheer, ‭ By this devotion. To all which he gave ‭ Their several honours, and did wish to have ‭ His equal part thereof, as free and well ‭ As th' other Deities; but the fatty smell ‭ Afflicted him, though he Immortal were, ‭ Playing mortal parts, and being like mortals here ‭ Yet his proud mind nothing the more obey'd ‭ For being a God himself, and his own aid ‭ Having to cause his due, and though in heart ‭ He highly wish'd it; but the weaker part ‭ Subdued the stronger, and went on in ill. ‭ Even heavenly pow'r had rather have his will ‭ Than have his right; and will's the worst of all, ‭ When but in least sort it is criminal, ‭ One taint being author of a number still. ‭ And thus, resolved to leave his hallow'd hill, ‭ First both the fat parts and the fleshy all ‭ Taking away, at the steep-entried stall ‭ He laid all, all the feet and heads entire, ‭ And all the sere-wood, making clear with fire. ‭ And now, he leaving there then all things done, ‭ And finish'd in their fit perfection, ‭ The coals put out, and their black ashes thrown ‭ From all discovery by the lovely light ‭ The cheerful moon cast, shining all the night, ‭ He straight assumed a novel voice's note, ‭ And in the whirl-pit-eating flood afloat ‭ He set his sandals. When now, once again ‭ The that-morn-born Cyllenius did attain ‭ His home's divine height; all the far-stretch'd way ‭ No one bless'd God encount'ring his assay, ‭ Nor mortal man; nor any dog durst spend ‭ His born-to-bark mouth at him; till in th' end ‭ He reach'd his cave, and at the gate went in ‭ Crooked, and wrapt into a fold so thin ‭ That no eye could discover his repair, ‭ But as a darkness of th' autumnal air. ‭ When, going on fore-right, he straight arrived ‭ At his rich fane; his soft feet quite deprived ‭ Of all least noise of one that trod the earth, ‭ They trod so swift to reach his room of birth. ‭ Where, in his swath-bands he his shoulders wrapt, ‭ And (like an infant, newly having scap't ‭ The teeming straits) as in the palms he lay ‭ Of his loved nurse. Yet instantly would play ‭ (Freeing his right hand) with his bearing cloth ‭ About his knees wrapt, and straight (loosing both ‭ His right and left hand) with his left he caught ‭ His much-loved lute. His mother yet was taught ‭ His wanton wiles, nor could a God's wit lie ‭ Hid from a Goddess, who did therefore try ‭ His answer thus: "Why, thou made-all-of-sleight, ‭ And whence arriv'st thou in this rest of night? ‭ Improvident impudent! In my conceit ‭ Thou rather shouldst be getting forth thy gate, ‭ With all flight fit for thy endanger'd state, ‭ (In merit of th' inevitable bands ‭ To be impos'd by vex'd Latona's hands, ‭ Justly incens'd for her Apollo's harms) ‭ Than lie thus wrapt, as ready for her arms, ‭ To take thee up and kiss thee. Would to heaven, ‭ In cross of that high grace, thou hadst been given ‭ Up to perdition, ere poor mortals bear ‭ Those black banes, that thy Father Thunderer ‭ Hath planted thee of purpose to confer ‭ On them and Deities!" He returned reply: ‭ "As master of the feats of policy, ‭ Mother, why aim you thus amiss at me, ‭ As if I were a son that infancy ‭ Could keep from all the skill that age can teach, ‭ Or had in cheating but a childish reach, ‭ And of a mother's mandates fear'd the breach? ‭ I mount that art at first, that will be best ‭ When all times consummate their cunningest, ‭ Able to counsel now myself and thee, ‭ In all things best, to all eternity. ‭ We cannot live like Gods here without gifts, ‭ No, nor without corruption and shifts, ‭ And, much less, without eating; as we must ‭ In keeping thy rules, and in being just, ‭ Of which we cannot undergo the loads. ‭ 'Tis better here to imitate the Gods, ‭ And wine or wench out all time's periods, ‭ To that end growing rich in ready heaps, ‭ Stored with revenues, being in corn-field reaps ‭ Of infinite acres, than to live enclosed ‭ In caves, to all earth's sweetest air exposed. ‭ I as much honour hold as Phœbus does; ‭ And if my Father please not to dispose ‭ Possessions to me, I myself will see ‭ If I can force them in; for I can be ‭ Prince of all thieves. And, if Latona's son ‭ Make after my stealth indignation, ‭ I'll have a scape as well as he a search, ‭ And overtake him with a greater lurch; ‭ For I can post to Pythos, and break through ‭ His huge house there, where harbours wealth enough, ‭ Most precious tripods, caldrons, steel, and gold, ‭ Garments rich wrought, and full of liberal fold. ‭ All which will I at pleasure own, and thou ‭ Shalt see all, wilt thou but thy sight bestow." ‭ Thus changed great words the Goat-hide-wearer's son, ‭ And Maia of majestic fashion. ‭ And now the air-begot Aurora rose ‭ From out the Ocean great-in-ebbs-and-flows, ‭ When, at the never-shorn pure-and-fair grove ‭ (Onchestus) consecrated to the love ‭ Of round-and-long-neck'd Neptune, Phœbus found ‭ A man whom heavy years had press'd half round, ‭ And yet at work in plashing of a fence ‭ About a vineyard, that had residence ‭ Hard by the highway; whom Latona's son ‭ Made it not strange, but first did question, ‭ And first saluted: "Ho you! aged sire, ‭ That here are hewing from the vine the briar, ‭ For certain oxen I come here t' inquire ‭ Out of Pieria; females all, and rear'd ‭ All with horns wreath'd, unlike the common herd; ‭ A coal-black bull fed by them all alone; ‭ And all observ'd, for preservation, ‭ Through all their foody and delicious fen ‭ With four fierce mastiffs, like one-minded men. ‭ These left their dogs and bull (which I admire) ‭ And, when was near set day's eternal fire, ‭ From their fierce guardians, from their delicate fare, ‭ Made clear departure. To me then declare, ‭ O old man, long since born, if thy grave ray ‭ Hath any man seen making steathful way ‭ With all those oxen." Th' old man made reply: ‭ "'Tis hard, O friend, to render readily ‭ Account of all that may invade mine eye, ‭ For many a traveller this highway treads, ‭ Some in much ills search, some in noble threads, ‭ Leading their lives out; but I this young day, ‭ Even from her first point, have made good display ‭ Of all men passing this abundant hill ‭ Planted with vines, and no such stealthful ill ‭ Her light hath shown me; but last evening, late, ‭ I saw a thing that show'd of childish state ‭ To my old lights, and seem'd as he pursued ‭ A herd of oxen with brave heads endued, ‭ Yet but an infant, and retain'd a rod; ‭ Who wearily both this and that way trod, ‭ His head still backwards turn'd." This th' old man spake; ‭ Which he well thought upon, and swiftly brake ‭ Into his pursuit with abundant wing, ‭ That strook but one plain, ere he knew the thing ‭ That was the thief to be th' impostor born; ‭ Whom Jove yet with his son's name did adorn. ‭ In study and with ardour then the King ‭ (Jove's dazzling son) placed his exploring wing ‭ On sacred Pylos, for his forced herd, ‭ His ample shoulders in a cloud enspher'd ‭ Of fiery crimson. Straight the steps he found ‭ Of his stol'n herd, and said: "Strange sights confound ‭ My apprehensive powers, for here I see ‭ The tracks of oxen, but aversively ‭ Converted towards the Pierian hills, ‭ As treading to their mead of daffodils: ‭ But nor mine eye men's feet nor women's draws, ‭ Nor hoary wolves', nor bears', nor lions', paws, ‭ Nor thick-neck'd bulls, they show. But he that does ‭ These monstrous deeds, with never so swift shoes ‭ Hath pass'd from that hour hither, but from hence ‭ His foul course may meet fouler consequence." ‭ With this took Phœbus wing; and Hermes still, ‭ For all his threats, secure lay in his hill ‭ Wall'd with a wood; and more, a rock, beside, ‭ Where a retreat ran, deeply multiplied ‭ In blinding shadows, and where th' endless Bride ‭ Bore to Saturnius his ingenious son; ‭ An odour, worth a heart's desire, being thrown ‭ Along the heaven-sweet hill, on whose herb fed ‭ Rich flocks of sheep, that bow not where they tread ‭ Their horny pasterns. There the Light of men ‭ (Jove's son, Apollo) straight descended then ‭ The marble pavement, in that gloomy den. ‭ On whom when Jove and Maia's son set eye, ‭ Wroth for his oxen, on then, instantly, ‭ His odorous swath-bands flew; in which as close ‭ Th' impostor lay, as in the cool repose ‭ Of cast-on ashes hearths of burning coals ‭ Lie in the woods hid, under the controls ‭ Of skilful colliers; even so close did lie ‭ Inscrutable Hermes in Apollo's eye, ‭ Contracting his great Godhead to a small ‭ And infant likeness, feet, hands, head, and all. ‭ And as a hunter hath been often view'd, ‭ From chase retired, with both his hands embrued ‭ In his game's blood, that doth for water call ‭ To cleanse his hands, and to provoke withal ‭ Delightsome sleep, new-wash'd and laid to rest; ‭ So now lay Hermes in the close-compress'd ‭ Chace of his oxen, his new-found-out lute ‭ Beneath his arm held, as if no pursuit ‭ But that prise, and the virtue of his play, ‭ His heart affected. But to Phœbus lay ‭ His close heart open; and he likewise knew ‭ The brave hill-nymph there, and her dear son, new- ‭ Born, and as well wrapt in his wiles as weeds. ‭ All the close shrouds too, for his rapinous deeds, ‭ In all the cave he knew; and with his key ‭ He open'd three of them, in which there lay ‭ Silver and gold-heaps, nectar infinite store, ‭ And dear ambrosia; and of weeds she wore, ‭ Pure white and purple, a rich wardrobe shined. ‭ Fit for the bless'd states of Pow'rs so divined. ‭ All which discover'd, thus to Mercury ‭ He offer'd conference: "Infant! You that lie ‭ Wrapt so in swath-bands, instantly unfold ‭ In what conceal'd retreats of yours you hold ‭ My oxen stol'n by you; or straight we shall ‭ Jar, as beseems not Pow'rs Celestial. ‭ For I will take and hurl thee to the deeps ‭ Of dismal Tartarus, where ill Death keeps ‭ His gloomy and inextricable fates, ‭ And to no eye that light illuminates ‭ Mother nor Father shall return thee free, ‭ But under earth shall sorrow fetter thee, ‭ And few repute thee their superior." ‭ On him replied craft's subtlest Counsellor: ‭ "What cruel speech hath past Latona's care! ‭ Seeks he his stol'n wild-cows where Deities are? ‭ I have nor seen nor heard, nor can report ‭ From others' mouths one word of their resort ‭ To any stranger. Nor will I, to gain ‭ A base reward, a false relation feign. ‭ Nor would I, could I tell. Resemble I ‭ An ox-thief, or a man? Especially ‭ A man of such a courage, such a force ‭ As to that labour goes, that violent course? ‭ No infant's work is that. My pow'rs aspire ‭ To sleep, and quenching of my hunger's fire ‭ With mother's milk, and, 'gainst cold shades, to arm ‭ With cradle-cloths my shoulders, and baths warm, ‭ That no man may conceive the war you threat ‭ Can spring in cause from my so peaceful heat. ‭ And, even amongst th' Immortals it would bear ‭ Event of absolute miracle, to hear ‭ A new-born infant's forces should transcend ‭ The limits of his doors; much less contend ‭ With untam'd oxen. This speech nothing seems ‭ To savour the decorum of the beams ‭ Cast round about the air Apollo breaks, ‭ Where his divine mind her intention speaks. ‭ I brake but yesterday the blessed womb, ‭ My feet are tender, and the common tomb ‭ Of men (the Earth) lies sharp beneath their tread. ‭ But, if you please, even by my Father's head ‭ I'll take the great oath, that nor I protest ‭ Myself to author on your interest ‭ Any such usurpation, nor have I ‭ Seen any other that feloniously ‭ Hath forced your oxen. Strange thing! What are those ‭ Oxen of yours? Or what are oxen? Knows ‭ My rude mind, think you? My ears only touch ‭ At their renown, and hear that there are such." ‭ This speech he pass'd; and, ever as he spake, ‭ Beams from the hair about his eyelids brake, ‭ His eyebrows up and down cast, and his eye ‭ Every way look'd askance and carelessly, ‭ And he into a lofty whistling fell, ‭ As if he idle thought Apollo's spell. ‭ Apollo, gently smiling, made reply: ‭ "O thou impostor, whose thoughts ever lie ‭ In labour with deceit! For certain, I ‭ Retain opinion, that thou (even thus soon) ‭ Hast ransack'd many a house, and not in one ‭ Night's-work alone, nor in one country neither, ‭ Hast been besieging house and man together, ‭ Rigging and rifling all ways, and no noise ‭ Made with thy soft feet, where it all destroys. ‭ Soft, therefore, well, and tender, thou may'st call ‭ The feet that thy stealths go and fly withal, ‭ For many a field-bred herdsman (unheard still) ‭ Hast thou made drown the caverns of the hill, ‭ Where his retreats lie, with his helpless tears, ‭ When any flesh-stealth thy desire endears, ‭ And thou encount'rest either flocks of sheep, ‭ Or herds of oxen! Up then! Do not sleep ‭ Thy last nap in thy cradle, but come down, ‭ Companion of black night, and, for this crown ‭ Of thy young rapines, bear from all the state ‭ And style of Prince Thief, into endless date." ‭ This said, he took the infant in his arms, ‭ And with him the remembrance of his harms, ‭ This presage utt'ring, lifting him aloft: ‭ "Be evermore the miserably-soft ‭ Slave of the belly, pursuivant of all, ‭ And author of all mischiefs capital." ‭ He scorn'd his prophecy so he sneezed in's face ‭ Most forcibly; which hearing, his embrace ‭ He loathed and hurl'd him 'gainst the ground; yet still ‭ Took seat before him, though, with all the ill ‭ He bore by him, he would have left full fain ‭ That hewer of his heart so into twain. ‭ Yet salv'd all thus: "Come, you so-swaddled thing! ‭ Issue of Maia, and the Thunder's King! ‭ Be confident, I shall hereafter find ‭ My broad-brow'd oxen, my prophetic mind ‭ So far from blaming this thy course, that I ‭ Foresee thee in it to posterity ‭ The guide of all men, always, to their ends." ‭ This spoken, Hermes from the earth ascends, ‭ Starting aloft, and as in study went, ‭ Wrapping himself in his integument, ‭ And thus ask'd Phœbus: "Whither force you me, ‭ Far-shot, and far most powerful Deity? ‭ I know, for all your feigning, you're still wroth ‭ About your oxen, and suspect my troth. ‭ O Jupiter! I wish the general race ‭ Of all earth's oxen rooted from her face. ‭ I steal your oxen! I again profess ‭ That neither I have stol'n them, nor can guess ‭ Who else should steal them. What strange beasts are these ‭ Your so-loved oxen? I must say, to please ‭ Your humour thus far, that even my few hours ‭ Have heard their fame. But be the sentence yours ‭ Of the debate betwixt us, or to Jove ‭ (For more indifferency) the cause remove." ‭ Thus when the solitude-affecting God, ‭ And the Latonian seed, had laid abroad ‭ All things betwixt them; though not yet agreed, ‭ Yet, might I speak, Apollo did proceed ‭ Nothing unjustly, to charge Mercury ‭ With stealing of the cows he does deny. ‭ But his profession was, with filed speech, ‭ And craft's fair compliments, to overreach ‭ All, and even Phœbus. Who because he knew ‭ His trade of subtlety, he still at view ‭ Hunted his foe through all the sandy way ‭ Up to Olympus. Nor would let him stray ‭ From out his sight, but kept behind him still. ‭ And now they reach'd the odorif'rous hill ‭ Of high Olympus, to their Father Jove, ‭ To arbitrate the cause in which they strove. ‭ Where, before both, talents of justice were ‭ Propos'd for him whom Jove should sentence clear, ‭ In cause of their contention. And now ‭ About Olympus, ever crown'd with snow, ‭ The rumour of their controversy flew. ‭ All the Incorruptible, to their view, ‭ On Heaven's steep mountain made return'd repair. ‭ Hermes, and He that light hurls through the air, ‭ Before the Thund'rer's knees stood; who begun ‭ To question thus far his illustrious Son: ‭ "Phœbus! To what end bring'st thou captive here ‭ Him in whom my mind puts delights so dear? ‭ This new-born infant, that the place supplies ‭ Of Herald yet to all the Deities? ‭ This serious business, you may witness, draws ‭ The Deities' whole Court to discuss the cause." ‭ Phœbus replied: "And not unworthy is ‭ The cause of all the Court of Deities, ‭ For, you shall hear, it comprehends the weight ‭ Of devastation, and the very height ‭ Of spoil and rapine, even of Deities' rights. ‭ Yet you, as if myself loved such delights, ‭ Use words that wound my heart. I bring you here ‭ An infant, that, even now, admits no peer ‭ In rapes and robb'ries. Finding out his place, ‭ After my measure of an infinite space, ‭ In the Cyllenian mountain, such a one ‭ In all the art of opprobration, ‭ As not in all the Deities I have seen, ‭ Nor in th' oblivion-mark'd whole race of men. ‭ In night he drave my oxen from their leas, ‭ Along the lofty roar-resounding seas, ‭ From out the road-way quite; the steps of them ‭ So quite transpos'd, as would amaze the beam ‭ Of any mind's eye, being so infinite much ‭ Involv'd in doubt, as show'd a deified touch ‭ Went to the work's performance; all the way, ‭ Through which my cross-hoved cows he did convey, ‭ Had dust so darkly-hard to search, and he ‭ So past all measure wrapt in subtilty. ‭ For, nor with feet, nor hands, he form'd his steps, ‭ In passing through the dry way's sandy heaps, ‭ But used another counsel to keep hid ‭ His monstrous tracts, that show'd as one had slid ‭ On oak or other boughs, that swept out still ‭ The footsteps of his oxen, and did fill ‭ Their prints up ever, to the daffodill ‭ (Or dainty-feeding meadow) as they trod, ‭ Driven by this cautelous and infant God. ‭ A mortal man, yet, saw him driving on ‭ His prey to Pylos. Which when he had done, ‭ And got his pass sign'd, with a sacred fire, ‭ In peace, and freely (though to his desire, ‭ Not to the Gods, he offer'd part of these ‭ My ravish'd oxen) he retires, and lies, ‭ Like to the gloomy night, in his dim den, ‭ All hid in darkness; and in clouts again ‭ Wrapp'd him so closely, that the sharp-seen eye ‭ Of your own eagle could not see him lie. ‭ For with his hands the air he rarified ‭ (This way, and that moved) till bright gleams did glide ‭ About his being, that, if any eye ‭ Should dare the darkness, light appos'd so nigh ‭ Might blind it quite with her antipathy. ‭ Which wile he wove, in curious care t' illude ‭ Th' extreme of any eye that could intrude. ‭ On which relying, he outrageously ‭ (When I accus'd him) trebled his reply: ‭ 'I did not see, I did not hear, nor I ‭ Will tell at all, that any other stole ‭ Your broad-brow'd beeves. Which an impostor's soul ‭ Would soon have done, and any author fain ‭ Of purpose only a reward to gain.' ‭ And thus he colour'd truth in every lie." ‭ This said, Apollo sat; and Mercury ‭ The Gods' Commander pleased with this reply: ‭ "Father! I'll tell thee truth (for I am true, ‭ And far from art to lie): He did pursue ‭ Even to my cave his oxen this self day, ‭ The sun new-raising his illustrious ray; ‭ But brought with him none of the Bliss-endued, ‭ Nor any ocular witness, to conclude ‭ His bare assertion; but his own command ‭ Laid on with strong and necessary hand, ‭ To show his oxen; using threats to cast ‭ My poor and infant powers into the vast ‭ Of ghastly Tartarus; because he bears ‭ Of strength-sustaining youth the flaming years, ‭ And I but yesterday produced to light. ‭ By which it fell into his own free sight, ‭ That I in no similitude appear'd ‭ Of power to be the forcer of a herd. ‭ And credit me, O Father, since the grace ‭ Of that name, in your style, you please to place, ‭ I drave not home his oxen, no, nor prest ‭ Past mine own threshold; for 'tis manifest, ‭ I reverence with my soul the Sun, and all ‭ The knowing dwellers in this heavenly Hall, ‭ Love you, observe the least; and 'tis most clear ‭ In your own knowledge, that my merits bear ‭ No least guilt of his blame. To all which I ‭ Dare add heaven's great oath, boldly swearing by ‭ All these so well-built entries of the Blest. ‭ And therefore when I saw myself so prest ‭ With his reproaches, I confess I burn'd ‭ In my pure gall, and harsh reply return'd. ‭ Add your aid to your younger then, and free ‭ The scruple fixt in Phœbus' jealousy." ‭ This said he wink'd upon his Sire; and still ‭ His swathbands held beneath his arm; no will ‭ Discern'd in him to hide, but have them shown. ‭ Jove laugh'd aloud at his ingenious Son, ‭ Quitting himself with art, so likely wrought, ‭ As show'd in his heart not a rapinous thought; ‭ Commanding both to bear atoned minds ‭ And seek out th' oxen; in which search he binds ‭ Hermes to play the guide, and show the Sun ‭ (All grudge exil'd) the shrowd to which he won ‭ His fair-eyed oxen; then his forehead bow'd ‭ For sign it must be so; and Hermes show'd ‭ His free obedience; so soon he inclined ‭ To his persuasion and command his mind. ‭ Now, then, Jove's jarring Sons no longer stood, ‭ But sandy Pylos and th' Alphæan flood ‭ Reach'd instantly, and made as quick a fall ‭ On those rich-feeding fields and lofty stall ‭ Where Phœbus' oxen Hermes safely kept, ‭ Driven in by night. When suddenly he stept ‭ Up to the stony cave, and into light ‭ Drave forth the oxen. Phœbus at first sight ‭ Knew them the same, and saw apart dispread ‭ Upon a high-rais'd rock the hides new flead ‭ Of th' oxen sacrific'd. Then Phœbus said: ‭ "O thou in crafty counsels undisplaid! ‭ How couldst thou cut the throats, and cast to earth, ‭ Two such huge oxen, being so young a birth, ‭ And a mere infant? I admire thy force, ‭ And will, behind thy back. But this swift course ‭ Of growing into strength thou hadst not need ‭ Continue any long date, O thou Seed ‭ Of honour'd Maia!" Hermes (to show how ‭ He did those deeds) did forthwith cut and bow ‭ Strong osiers in soft folds, and strappled straight ‭ One of his hugest oxen, all his weight ‭ Lay'ng prostrate on the earth at Phœbus' feet, ‭ All his four cloven hoves eas'ly made to greet ‭ Each other upwards, all together brought. ‭ In all which bands yet all the beast's powers wrought, ‭ To rise, and stand; when all the herd about ‭ The mighty Hermes rush'd in, to help out ‭ Their fellow from his fetters. Phœbus' view ‭ Of all this up to admiration drew ‭ Even his high forces; and stern looks he threw ‭ At Hermes for his herd's wrong, and the place ‭ To which he had retir'd them, being in grace ‭ And fruitful riches of it so entire; ‭ All which set all his force on envious fire. ‭ All whose heat flew out of his eyes in flames, ‭ Which fain he would have hid, to hide the shames, ‭ Of his ill-govern'd passions. But with ease ‭ Hermes could calm them, and his humours please. ‭ Still at his pleasure, were he ne'er so great ‭ In force and fortitude, and high in heat, ‭ In all which he his lute took, and assay'd ‭ A song upon him, and so strangely play'd, ‭ That from his hand a ravishing horror flew. ‭ Which Phœbus into laughter turn'd, and grew ‭ Pleasant past measure; tunes so artful clear ‭ Strook even his heart-strings, and his mind made hear. ‭ His lute so powerful was in forcing love, ‭ As his hand rul'd it, that from him it drove ‭ All fear of Phœbus; yet he gave him still ‭ The upper hand; and, to advance his skill ‭ To utmost miracle, he play'd sometimes ‭ Single awhile; in which, when all the climes ‭ Of rapture he had reach'd, to make the Sun ‭ Admire enough, O then his voice would run ‭ Such points upon his play, and did so move, ‭ They took Apollo prisoner to his love. ‭ And now the deathless Gods and deathful Earth ‭ He sung, beginning at their either's birth ‭ To full extent of all their empery. ‭ And, first, the honour to Mnemosyne, ‭ The Muses' mother, of all Goddess states ‭ He gave; even forced to't by the equal fates. ‭ And then (as it did in priority fall ‭ Of age and birth) he celebrated all. ‭ And with such elegance and order sung ‭ (His lute still touch'd, to stick more off his tongue) ‭ That Phœbus' heart with infinite love he eat. ‭ Who, therefore, thus did his deserts entreat: ‭ "Master of sacrifice! Chief soul of feast! ‭ Patient of all pains! Artizan so blest, ‭ That all things thou canst do in anyone! ‭ Worth fifty oxen is th' invention ‭ Of this one lute. We both shall now, I hope, ‭ In firm peace work to all our wishes' scope. ‭ Inform me (thou that every way canst wind, ‭ And turn to act, all wishes of thy mind) ‭ Together with thy birth came all thy skill? ‭ Or did some God, or God-like man, instill ‭ This heavenly song to thee? Methink I hear ‭ A new voice, such as never yet came near ‭ The breast of any, either man or God, ‭ Till in thee it had prime and period. ‭ What art, what Muse that med'cine can produce ‭ For cares most cureless, what inveterate use ‭ Or practice of a virtue so profuse ‭ (Which three do all the contribution keep ‭ That Joy or Love confers, or pleasing Sleep.) ‭ Taught thee the sovereign facture of them all? ‭ I of the Muses am the capital ‭ Consort, or follower; and to these belong ‭ The grace of dance, all worthy ways of song, ‭ And ever-flourishing verse, the delicate set ‭ And sound of instruments. But never yet ‭ Did anything so much affect my mind ‭ With joy and care to compass, as this kind ‭ Of song and play, that for the spritely feast ‭ Of flourishing assemblies are the best ‭ And aptest works that ever worth gave act. ‭ My powers with admiration stand distract, ‭ To hear with what a hand to make in love ‭ Thou rul'st thy lute. And (though thy yong'st hours move ‭ At full art in old councils) here I vow ‭ (Even by this cornel dart I use to throw) ‭ To thee, and to thy mother, I'll make thee ‭ Amongst the Gods of glorious degree, ‭ Guide of men's ways and theirs; and will impart ‭ To thee the mighty imperatory art, ‭ Bestow rich gifts on thee, and in the end ‭ Never deceive thee." Hermes (as a friend ‭ That wrought on all advantage, and made gain ‭ His capital object) thus did entertain ‭ Phœbus Apollo: "Do thy dignities, ‭ Far-working God and circularly wise, ‭ Demand my virtues? Without envy I ‭ Will teach thee to ascend my faculty. ‭ And this day thou shalt reach it; finding me, ‭ In acts and counsels, all ways kind to thee, ‭ As one that all things knows, and first tak'st seat ‭ Amongst th' Immortals, being good and great, ‭ And therefore to Jove's love mak'st free access, ‭ Even out of his accomplisht holiness. ‭ Great gifts he likewise gives thee; who, fame says, ‭ Hast won thy greatness by his will, his ways, ‭ By him know'st all the powers prophetical, ‭ O thou far-worker, and the fates of all! ‭ Yea, and I know thee rich, yet apt to learn, ‭ And even thy wish dost but discern and earn. ‭ And since thy soul so burns to know the way ‭ So play and sing as I do, sing, and play; ‭ Play, and perfection in thy play employ; ‭ And be thy care, to learn things good, thy joy. ‭ Take thou my lute (my love) and give thou me ‭ The glory of so great a faculty. ‭ This sweet-tuned consort, held but in thy hand, ‭ Sing, and perfection in thy song command. ‭ For thou already hast the way to speak ‭ Fairly and elegantly, and to break ‭ All eloquence into thy utter'd mind. ‭ One gift from heaven found may another find. ‭ Use then securely this thy gift, and go ‭ To feasts and dances that enamour so, ‭ And to that covetous sport of getting glory, ‭ That day nor night will suffer to be sory. ‭ Whoever does but say in verse, sings still; ‭ Which he that can of any other skill ‭ Is capable, so he be taught by art ‭ And wisdom, and can speak at every part ‭ Things pleasing to an understanding mind; ‭ And such a one that seeks this lute shall find. ‭ Him still it teaches eas'ly, though he plays ‭ Soft voluntaries only, and assays ‭ As wanton as the sports of children are, ‭ And (even when he aspires to singular ‭ In all the mast'ries he shall play or sing) ‭ Finds the whole work but an unhappy thing, ‭ He, I say, sure shall of this lute be king. ‭ But he, whoever rudely sets upon ‭ Of this lute's skill th' inquest or question ‭ Never so ardently and angrily, ‭ Without the aptness and ability ‭ Of art, and nature fitting, never shall ‭ Aspire to this, but utter trivial ‭ And idle accents, though sung ne'er so loud, ‭ And never so commended of the crowd. ‭ But thee I know, O eminent Son of Jove, ‭ The fiery learner of whatever Love ‭ Hath sharpen'd thy affections to achieve, ‭ And thee I give this lute. Let us now live ‭ Feeding upon the hill and horse-fed earth ‭ Our never-handled oxen; whose dear birth ‭ Their females, fellow'd with their males, let flow ‭ In store enough hereafter; nor must you ‭ (However cunning-hearted your wits are) ‭ Boil in your gall a grudge too circular." ‭ Thus gave he him his lute, which he embrac'd, ‭ And gave again a goad, whose bright head cast ‭ Beams like the light forth; leaving to his care ‭ His oxen's keeping. Which, with joyful fare, ‭ He took on him. The lute Apollo took ‭ Into his left hand, and aloft he shook ‭ Delightsome sounds up, to which God did sing. ‭ Then were the oxen to their endless spring ‭ Turn'd; and Jove's two illustrous Offsprings flew ‭ Up to Olympus where it ever snew, ‭ Delighted with their lute's sound all the way. ‭ Whom Jove much joy'd to see, and endless stay ‭ Gave to their knot of friendship. From which date ‭ Hermes gave Phœbus an eternal state ‭ In his affection, whose sure pledge and sign ‭ His lute was, and the doctrine so divine ‭ Jointly conferr'd on him; which well might be ‭ True symbol of his love's simplicity. ‭ On th' other part, Apollo in his friend ‭ Form'd th' art of wisdom, to the binding end ‭ Of his vow'd friendship; and (for further meed) ‭ Gave him the far-heard fistulary reed. ‭ For all these forms of friendship, Phœbus yet ‭ Fear'd that both form and substance were not met ‭ In Mercury's intentions; and, in plain, ‭ Said (since he saw him born to craft and gain, ‭ And that Jove's will had him the honour done ‭ To change at his will the possession ‭ Of others' goods) he fear'd his breach of vows ‭ In stealing both his lute and cunning bows, ‭ And therefore wish'd that what the Gods affect ‭ Himself would witness, and to his request ‭ His head bow, swearing by th' impetuous flood ‭ Of Styx that of his whole possessions not a good ‭ He would diminish, but therein maintain ‭ The full content in which his mind did reign. ‭ And then did Maia's son his forehead bow, ‭ Making, by all that he desired, his vow ‭ Never to prey more upon anything ‭ In just possession of the far-shot King, ‭ Nor ever to come near a house of his. ‭ Latonian Phœbus bow'd his brow to this, ‭ With his like promise, saying: "Not anyone ‭ Of all the Gods, nor any man, that son ‭ Is to Saturnius, is more dear to me, ‭ More trusted, nor more honour'd is than thee. ‭ Which yet with greater gifts of Deity ‭ In future I'll confirm, and give thy state ‭ A rod that riches shall accumulate, ‭ Nor leave the bearer thrall to death, or fate, ‭ Or any sickness. All of gold it is, ‭ Three-leaved, and full of all felicities. ‭ And, this shall be thy guardian, this shall give ‭ The Gods to thee in all the truth they live, ‭ And, finally, shall this the tut'ress be ‭ Of all the words and works informing me ‭ From Jove's high counsels, making known to thee ‭ All my instructions. But to prophesy, ‭ Of best of Jove's beloved, and that high skill ‭ Which to obtain lies burning in thy will, ‭ Nor thee, nor any God, will Fate let learn. ‭ Only Jove's mind hath insight to discern ‭ What that importeth; yet am I allow'd ‭ (My known faith trusted, and my forehead bow'd, ‭ Our great oath taken, to resolve to none ‭ Of all th' Immortals the restriction ‭ Of that deep knowledge) of it all the mind. ‭ Since then it sits in such fast bounds confin'd, ‭ O brother, when the golden rod is held ‭ In thy strong hand, seek not to have reveal'd ‭ Any sure fate that Jove will have conceal'd. ‭ For no man shall, by know'ng, prevent his fate; ‭ And therefore will I hold in my free state ‭ The pow'r to hurt and help what man I will, ‭ Of all the greatest, or least touch'd with ill, ‭ That walk within the circle of mine eye, ‭ In all the tribes and sexes it shall try. ‭ Yet, truly, any man shall have his will ‭ To reap the fruits of my prophetic skill, ‭ Whoever seeks it by the voice or wing ‭ Of birds, born truly such events to sing. ‭ Nor will I falsely, nor with fallacies, ‭ Infringe the truth on which his faith relies, ‭ But he that truths in chattering plumes would find, ‭ Quite opposite to them that prompt my mind, ‭ And learn by natural forgers of vain lies ‭ The more-than-ever-certain Deities, ‭ That man shall sea-ways tread that leave no tracts, ‭ And false or no guide find for all his facts. ‭ And yet will I his gifts accept as well ‭ As his to whom the simple truth I tell. ‭ One other thing to thee I'll yet make known, ‭ Maia's exceedingly renowned son, ‭ And Jove's, and of the Gods' whole session ‭ The most ingenious genius: There dwell ‭ Within a crooked cranny, in a dell ‭ Beneath Parnassus, certain Sisters born, ‭ Call'd Parcæ, whom extreme swift wings adorn, ‭ Their number three, that have upon their heads ‭ White barley-flour still sprinkled, and are maids; ‭ And these are schoolmistresses of things to come, ‭ Without the gift of prophecy. Of whom ‭ (Being but a boy, and keeping oxen near) ‭ I learn'd their skill, though my great Father were ‭ Careless of it, or them. These flying from home ‭ To others' roofs, and fed with honeycomb, ‭ Command all skill, and (being enraged then) ‭ Will freely tell the truths of things to men. ‭ But if they give them not that Gods' sweet meat, ‭ They then are apt to utter their deceit, ‭ And lead men from their way. And these will I ‭ Give thee hereafter, when their scrutiny ‭ And truth thou hast both made and learn'd; and then ‭ Please thyself with them, and the race of men ‭ (Wilt thou know any) with thy skill endear, ‭ Who will, be sure, afford it greedy ear, ‭ And hear it often if it prove sincere. ‭ Take these, O Maia's son, and in thy care ‭ Be horse and oxen, all such men as are ‭ Patient of labour, lions, white-tooth'd boars, ‭ Mastiffs, and flocks that feed the flow'ry shores, ‭ And every four-foot beast; all which shall stand ‭ In awe of thy high imperatory hand. ‭ Be thou to Dis, too, sole Ambassador, ‭ Who, though all gifts and bounties he abhor, ‭ On thee he will bestow a wealthy one." ‭ Thus king Apollo honour'd Maia's son ‭ With all the rites of friendship; all whose love ‭ Had imposition from the will of Jove. ‭ And thus with Gods and mortals Hermes lived, ‭ Who truly help'd but few, but all deceived ‭ With an undifferencing respect, and made ‭ Vain words and false persuasions his trade. ‭ His deeds were all associates of the night, ‭ In which his close wrongs cared for no man's right. ‭ So all salutes to Hermes that are due, ‭ Of whom, and all Gods, shall my Muse sing true. ‭ THE END OF THE HYMN TO HERMES. ‭ A HYMN TO VENUS ‭ The force, O Muse, and functions now unfold ‭ Of Cyprian Venus, grac'd with mines of gold; ‭ Who even in Deities lights love's sweet desire, ‭ And all Death's kinds of men makes kiss her fire, ‭ All air's wing'd nation, all the belluine, ‭ That or the earth feeds, or the seas confine. ‭ To all which appertain the love and care ‭ Of well-crown'd Venus' works. Yet three there are ‭ Whose minds She neither can deceive nor move; ‭ Pallas, the Seed of Ægis-bearing Jove, ‭ Who still lives indevirginate, her eyes ‭ Being blue, and sparkling like the freezing skies, ‭ Whom all the gold of Venus never can ‭ Tempt to affect her facts with God or man. ‭ She, loving strife, and Mars's working banes, ‭ Pitch'd fields and fights, and famous artizans, ‭ Taught earthy men first all the arts that are, ‭ Chariots, and all the frames vehicular, ‭ Chiefly with brass arm'd, and adorn'd for war. ‭ Where Venus only soft-skinn'd wenches fills ‭ With wanton house-works, and suggests those skills ‭ Still to their studies. Whom Diana neither, ‭ That bears the golden distaff, and together ‭ Calls horns, and hollows, and the cries of hounds, ‭ And owns the epithet of loving sounds ‭ For their sakes, springing from such spritely sports, ‭ Can catch with her kind lures; but hill resorts ‭ To wild-beasts, slaughters, accents far-off heard ‭ Of harps and dances, and of woods unshear'd ‭ The sacred shades she loves, yet likes as well ‭ Cities where good men and their offspring dwell. ‭ The third, whom her kind passions nothing please, ‭ Is virgin Vesta; whom Saturnides ‭ Made reverend with his counsels, when his Sire, ‭ That adverse counsels agitates, life's fire ‭ Had kindled in her, being his last-begot. ‭ Whom Neptune woo'd to knit with him the knot ‭ Of honour'd nuptials, and Apollo too; ‭ Which with much vehemence she refused to do, ‭ And stern repulses put upon them both, ‭ Adding to all her vows the Gods' great oath, ‭ And touching Jove's chin, which must consummate ‭ All vows so bound, that she would hold her state, ‭ And be th' invincible Maid of Deities ‭ Through all her days' dates. For Saturnides ‭ Gave her a fair gift in her nuptials' stead, ‭ To sit in midst of his house, and be fed ‭ With all the free and richest feast of heaven, ‭ In all the temples of the Gods being given ‭ The prize of honour. Not a mortal man, ‭ (That either, of the Pow'rs Olympian ‭ His half-birth having, may be said to be ‭ A mortal of the Gods, or else that he, ‭ Deities' wills doing, is of Deity) ‭ But gives her honour of the amplest kind. ‭ Of all these three can Venus not a mind ‭ Deceive, or set on forces to reflect. ‭ Of all Pow'rs else yet, not a sex, nor sect, ‭ Flies Venus; either of the blessed Gods, ‭ Or men confin'd in mortal periods. ‭ But even the mind of Jove she doth seduce, ‭ That chides with thunder so her lawless use ‭ In human creatures, and by lot is given ‭ Of all most honour, both in earth and heaven. ‭ And yet even his all-wise and mighty mind ‭ She, when she lists, can forge affects to blind, ‭ And mix with mortal dames his Deity, ‭ Conceal'd at all parts from the jealous eye ‭ Of Juno, who was both his sister born, ‭ And made his wife; whom beauty did adorn ‭ Past all the bevy of Immortal Dames, ‭ And whose so chiefly-glorified flames ‭ Cross-counsell'd Saturn got, and Rhæa bore, ‭ And Jove's pure counsels (being conqueror) ‭ His wife made of his sister. Ay, and more, ‭ Cast such an amorous fire into her mind ‭ As made her (like him) with the mortal kind ‭ Meet in unmeet bed; using utmost haste, ‭ Lest she should know that he lived so unchaste, ‭ Before herself felt that fault in her heart, ‭ And gave her tongue too just edge of desert ‭ To tax his lightness. With this end, beside, ‭ Lest laughter-studying Venus should deride ‭ The Gods more than the Goddesses, and say ‭ That she the Gods commix'd in amorous play ‭ With mortal dames, begetting mortal seed ‭ T' immortal sires, and not make Goddesses breed ‭ The like with mortal fathers. But, t' acquite ‭ Both Gods and Goddesses of her despite, ‭ Jove took (even in herself) on him her pow'r, ‭ And made her with a mortal paramour ‭ Use as deform'd a mixture as the rest; ‭ Kindling a kind affection in her breast ‭ To God-like-limb'd Anchises, as he kept, ‭ On Ida's top-on-top-to-heaven's-pole-heapt, [1] ‭ Amongst the many fountains there, his herd. ‭ For, after his brave person had appear'd ‭ To her bright eye, her heart flew all on fire, ‭ And to amaze she burn'd in his desire, ‭ Flew straight to Cyprus, to her odorous fane ‭ And altars, that the people Paphian ‭ Advanced to her. Where, soon as enter'd, she ‭ The shining gates shut; and the Graces three ‭ Wash'd, and with oils of everlasting scent ‭ Bathed, as became, her deathless lineament. ‭ Then her ambrosian mantle she assum'd, ‭ With rich and odoriferous airs perfum'd. ‭ Which being put on, and all her trims beside ‭ Fair, and with all allurements amplified, ‭ The all-of-gold-made laughter-loving Dame ‭ Left odorous Cyprus, and for Troy became ‭ A swift contendress, her pass cutting all ‭ Along the clouds, and made her instant fall ‭ On fountful Ida, that her mother-breasts ‭ Gives to the preyful brood of savage beasts. ‭ And through the hill she went the ready way ‭ T' Anchises' oxstall, where did fawn and play ‭ About her blessed feet wolves grisly-gray, ‭ Terrible lions, many a mankind bear, ‭ And lybberds swift, insatiate of red deer. ‭ Whose sight so pleas'd, that, ever as she past, ‭ Through every beast a kindly love she cast, ‭ That, in their dens obscured with shadows deep, ‭ Made all, distinguish'd in kind couples, sleep. ‭ And now she reach'd the rich pavilion ‭ Of the heroë, in whom heavens had shown ‭ A fair and goodly composition, ‭ And whom she in his oxstall found, alone, ‭ His oxen feeding in fat pastures by, ‭ He walking up and down, sounds clear and high ‭ From his harp striking. Then before him she ‭ Stood like a virgin, that invincibly ‭ Had borne her beauties; yet alluringly ‭ Bearing her person, lest his ravish'd eye ‭ Should chance t' affect him with a stupid fear. ‭ Anchises seeing her, all his senses were ‭ With wonder stricken, and high-taken heeds ‭ Both of her form, brave stature, and rich weeds. ‭ For, for a veil, she shin'd in an attire ‭ That cast a radiance past the ray of fire. ‭ Beneath which wore she, girt to her, a gown ‭ Wrought all with growing-rose-buds, reaching down ‭ T' her slender smalls, which buskins did divine, ‭ Such as taught Thetis' silver feet to shine. ‭ Her soft white neck rich carquenets embraced, ‭ Bright, and with gold in all variety graced, ‭ That to her breasts let down lay there and shone, ‭ As, at her joyful full, the rising Moon. ‭ Her sight show'd miracles. Anchises' heart ‭ Love took into his hand, and made him part ‭ With these high salutations; "Joy, O Queen! ‭ Whoever of the Blest thy beauties been ‭ That light these entries; or the Deity ‭ That darts affecteth; or that gave the Eye ‭ Of heaven his heat and lustre; or that moves ‭ The hearts of all with all-commanding loves; ‭ Or generous Themis; or the blue-eyed Maid; ‭ Or of the Graces any that are laid ‭ With all the Gods in comparable scales, ‭ And whom fame up to immortality calls; ‭ Or any of the Nymphs, that unshorn groves, ‭ Or that this fair hill-habitation, loves, ‭ Or valleys flowing with earth's fattest goods, ‭ Or fountains pouring forth eternal floods! ‭ Say, which of all thou art, that in some place ‭ Of circular prospect, for thine eyes' dear grace, ‭ I may an altar build, and to thy pow'rs ‭ Make sacred all the year's devoted hours, ‭ With consecrations sweet and opulent. ‭ Assur'd whereof, be thy benign mind bent ‭ To these wish'd blessings of me: Give me parts ‭ Of chief attraction in Trojan hearts; ‭ And, after, give me the refulgency ‭ Of most renown'd and rich posterity; ‭ Long, and free life, and heaven's sweet light as long; ‭ The people's blessings, and a health so strong ‭ That no disease it let my life engage, ‭ Till th' utmost limit of a human age." ‭ To this Jove's Seed this answer gave again; ‭ "Anchises! Happiest of the human strain! ‭ I am no Goddess! Why, a thrall to death ‭ Think'st thou like those that immortality breathe? ‭ A woman brought me forth; my father's name ‭ Was Otreüs, if ever his high fame ‭ Thine ears have witness'd, for he govern'd all ‭ The Phrygian state, whose every town a wall ‭ Impregnable embrac'd. Your tongue, you hear, ‭ I speak so well, that in my natural sphere ‭ (As I pretend) it must have taken prime. ‭ A woman, likewise, of the Trojan clime ‭ Took of me, in her house, the nurse's care ‭ From my dear mother's bosom; and thus are ‭ My words of equal accent with your own. ‭ How here I come, to make the reason known, ‭ Argicides, that bears the golden rod, ‭ Transferr'd me forcibly from my abode ‭ Made with the maiden train of Her that joys ‭ In golden shafts, and loves so well the noise ‭ Of hounds and hunters (heaven's pure-living Pow'r) ‭ Where many a nymph and maid of mighty dow'r ‭ Chaste sports employ'd, all circled with a crown ‭ Of infinite multitude, to see so shown ‭ Our maiden pastimes. Yet, from all the fair ‭ Of this so forceful concourse, up in air ‭ The golden-rod-sustaining Argus'-Guide ‭ Rapt me in sight of all, and made me ride ‭ Along the clouds with him, enforcing me ‭ Through many a labour of mortality, ‭ Through many an unbuilt region, and a rude, ‭ Where savage beasts devour'd preys warm and crude, ‭ And would not let my fears take one foot's tread ‭ On Her by whom are all lives comforted, ‭ But said my maiden state must grace the bed ‭ Of king Anchises, and bring forth to thee ‭ Issue as fair as of divine degree. ‭ Which said, and showing me thy moving grace, ‭ Away flew he up to th' Immortal Race, ‭ And thus came I to thee; Necessity, ‭ With her steel stings, compelling me t' apply ‭ To her high pow'r my will. But you must I ‭ Implore by Jove, and all the reverence due ‭ To your dear parents, who, in bearing you, ‭ Can bear no mean sail, lead me home to them ‭ An untouch'd maid, being brought up in th' extreme ‭ Of much too cold simplicity to know ‭ The fiery cunnings that in Venus glow. ‭ Show me to them then, and thy brothers born, ‭ I shall appear none that parts disadorn, ‭ But such as well may serve a brother's wife, ‭ And show them now, even to my future life, ‭ If such or no my present will extend. ‭ To horse-breed-vary'ng Phrygia likewise send, ‭ T' inform my sire and mother of my state, ‭ That live for me extreme disconsolate; ‭ Who gold enough, and well-woven weeds, will give. ‭ All whose rich gifts in my amends receive. ‭ All this perform'd, and celebration then ‭ Of honour'd nuptials, that by God and men ‭ Are held in reverence." All this while she said, ‭ Into his bosom jointly she convey'd ‭ The fires of love; when, all-enamour'd, he ‭ In these terms answer'd: "If mortality ‭ Confine thy fortunes, and a woman were ‭ Mother to those attractions that appear ‭ In thy admir'd form, thy great father given ‭ High name of Otreüs; and the Spy of heaven ‭ (Immortal Mercury) th' enforceful cause ‭ That made thee lose the prize of that applause ‭ That modesty immaculate virgins gives, ‭ My wife thou shalt be call'd through both our lives. ‭ Nor shall the pow'rs of men nor Gods withhold ‭ My fiery resolution to enfold ‭ Thy bosom in mine arms; which here I vow ‭ To firm performance, past delay, and now. ‭ Nor, should Apollo with his silver bow ‭ Shoot me to instant death, would I forbear ‭ To do a deed so full of cause so dear. ‭ For with a heaven-sweet woman I will lie, ‭ Though straight I stoop the house of Dis, and die." ‭ This said, he took her hand, and she took way ‭ With him, her bright eyes casting round; whose stay ‭ She stuck upon a bed, that was before ‭ Made for the king, and wealthy coverings wore. ‭ On which bears' hides and big-voic'd lions' lay, ‭ Whose preyful lives the king had made his prey, ‭ Hunting th' Idalian hills. This bed when they ‭ Had both ascended, first he took from her ‭ The fiery weed, that was her utmost wear; ‭ Unbutton'd her next rosy robe; and loos'd ‭ The girdle that her slender waist enclos'd; ‭ Unlac'd her buskins; all her jewelry ‭ Took from her neck and breasts, and all laid by ‭ Upon a golden-studded chair of state. ‭ Th' amaze of all which being remov'd, even Fate ‭ And council of the equal Gods gave way ‭ To this, that with a deathless Goddess lay ‭ A deathful man; since, what his love assum'd, ‭ Not with his conscious knowledge was presum'd. ‭ Now when the shepherds and the herdsmen, all, ‭ Turn'd from their flow'ry pasture to their stall, ‭ With all their oxen, fat and frolic sheep, ‭ Venus into Anchises cast a sleep, ‭ Sweet and profound; while with her own hands now ‭ With her rich weeds she did herself endow; ‭ But so distinguish'd, that he clear might know ‭ His happy glories; then (to her desire ‭ Her heavenly person put in trims entire) ‭ She by the bed stood of the well-built stall, ‭ Advanc'd her head to state celestial, ‭ And in her cheeks arose the radiant hue ‭ Of rich-crown'd Venus to apparent view. ‭ And then she rous'd him from his rest, and said: ‭ "Up, my Dardanides, forsake thy bed. ‭ What pleasure, late employ'd, lets humour steep ‭ Thy lids in this inexcitable sleep? ‭ Wake, and now say, if I appear to thee ‭ Like her that first thine eyes conceited me." ‭ This started him from sleep, though deep and dear, ‭ And passing promptly he enjoy'd his ear. ‭ But when his eye saw Venus' neck and eyes, ‭ Whose beauties could not bear the counterprise ‭ Of any other, down his own eyes fell, ‭ Which pallid fear did from her view repell, ‭ And made him, with a main respect beside, ‭ Turn his whole person from her state, and hide ‭ (With his rich weed appos'd) his royal face, ‭ These wing'd words using: "When, at first, thy grace ‭ Mine eyes gave entertainment, well I knew ‭ Thy state was deified; but thou told'st not true; ‭ And therefore let me pray thee (by thy love ‭ Borne to thy father, Ægis-bearing Jove) ‭ That thou wilt never let me live to be ‭ An abject, after so divine degree ‭ Taken in fortune, but take ruth on me, ‭ For any man that with a Goddess lies, ‭ Of interest in immortalities, ‭ Is never long-liv'd." She replied: "Forbear, ‭ O happiest of mortal men, this fear, ‭ And rest assured, that (not for me, at least) ‭ Thy least ills fear fits; no, nor for the rest ‭ Of all the Blessed, for thou art their friend; ‭ And so far from sustaining instant end, ‭ That to thy long-enlarg'd life there shall spring ‭ Amongst the Trojans a dear son, and king, ‭ To whom shall many a son, and son's son, rise ‭ In everlasting great posterities; ‭ His name Æneas; therein keeping life, ‭ For ever, in my much-conceited grief, ‭ That I, immortal, fell into the bed ‭ Of one whose blood mortality must shed. ‭ But rest thou comforted, and all the race ‭ That Troy shall propagate, in this high grace: ‭ That, past all races else, the Gods stand near ‭ Your glorious nation, for the forms ye bear, ‭ And natures so ingenuous and sincere. ‭ For which, the great-in-counsels (Jupiter) ‭ Your gold-lock'd Ganymedes did transfer ‭ (In rapture far from men's depressed fates) ‭ To make him consort with our Deified States, ‭ And scale the tops of the Saturnian skies, ‭ He was so mere a marvel in their eyes. ‭ And therefore from a bowl of gold he fills ‭ Red nectar, that the rude distension kills ‭ Of winds that in your human stomachs breed. ‭ But then did languor on the liver feed ‭ Of Tros, his father, that was king of Troy, ‭ And ever did his memory employ [2] ‭ With loss of his dear beauty so bereaven, ‭ Though with a sacred whirlwind rapt to heaven. ‭ But Jove, in pity of him, saw him given ‭ Good compensation, sending by Heaven's Spy ‭ White-swift-hov'd horse, that Immortality ‭ Had made firm-spirited; and had, beside, ‭ Hermes to see his ambassy supplied ‭ With this vow'd bounty (using all at large ‭ That his unalter'd counsels gave in charge) ‭ That he himself should immortality breathe, ‭ Expert of age and woe as well as death. ‭ "This ambassy express'd, he mourn'd no more, ‭ But up with all his inmost mind he bore, ‭ Joying that he, upon his swift-hov'd horse, ‭ Should be sustain'd in an eternal course." ‭ "So did the golden-throned Aurora raise, ‭ Into her lap, another that the praise ‭ Of an immortal fashion had in fame, ‭ And of your nation bore the noble name, ‭ (His title Tithon) who, not pleased with her, ‭ As she his lovely person did transfer, ‭ To satisfy him, she bade ask of Jove ‭ The gift of an Immortal for her love. ‭ Jove gave, and bound it with his bowed brow, ‭ Performing to the utmost point his vow. ‭ Fool that she was, that would her love engage, ‭ And not as long ask from the bane of age ‭ The sweet exemption, and youth's endless flow'r! ‭ Of which as long as both the grace and pow'r ‭ His person entertain'd, she loved the man, ‭ And (at the fluents of the ocean ‭ Near Earth's extreme bounds) dwelt with him; but when ‭ According to the course of aged men) ‭ On his fair head, and honourable beard, ‭ His first grey hairs to her light eyes appear'd, ‭ She left his bed, yet gave him still for food ‭ The Gods' ambrosia, and attire as good. ‭ Till even the hate of age came on so fast ‭ That not a lineament of his was grac'd ‭ With pow'r of motion, nor did still sustain, ‭ Much less, the vigour had t' advance a vein, ‭ The virtue lost in each exhausted limb, ‭ That at his wish before would answer him; ‭ All pow'rs so quite decay'd, that when he spake ‭ His voice no perceptible accent brake. ‭ Her counsel then thought best to strive no more, ‭ But lay him in his bed and lock his door. ‭ Such an Immortal would not I wish thee, ‭ T' extend all days so to eternity. ‭ But if, as now, thou couldst perform thy course ‭ In grace of form, and all corporeal force, ‭ To an eternal date, thou then shouldst bear ‭ My husband's worthy name, and not a tear ‭ Should I need rain, for thy deserts declin'd, ‭ From my all-clouded bitterness of mind. ‭ But now the stern storm of relentless age ‭ Will quickly circle thee, that waits t' engage ‭ All men alike, even loathsomeness, and bane ‭ Attending with it, every human wane, ‭ Which even the Gods hate. Such a penance lies ‭ Impos'd on flesh and blood's infirmities! ‭ Which I myself must taste in great degree, ‭ And date as endless, for consorting thee. ‭ All the Immortals with my opprobry ‭ Are full by this time; on their hearts so lie, ‭ (Even to the sting of fear) my cunnings us'd, ‭ And wiving conversations infus'd ‭ Into the bosoms of the best of them ‭ With women, that the frail and mortal stream ‭ Doth daily ravish. All this long since done. ‭ Which now no more, but with effusion ‭ Of tears, I must in heaven so much as name, ‭ I have so forfeited in this my fame, ‭ And am impos'd pain of so great a kind ‭ For so much erring from a Goddess' mind. ‭ For I have put beneath my girdle here ‭ A son, whose sire the human mortal sphere ‭ Gives circumscription. But, when first the light ‭ His eyes shall comfort, Nymphs that haunt the height ‭ Of hills, and breasts have of most deep receipt; ‭ Shall be his nurses; who inhabit now ‭ A hill of so vast and divine a brow, ‭ As man nor God can come at their retreats; ‭ Who live long lives, and eat immortal meats, ‭ And with Immortals in the exercise ‭ Of comely dances dare contend, and rise ‭ Into high question which deserves the prize. ‭ The light Sileni mix in love with these, ‭ And, of all Spies the Prince, Argicides; ‭ In well-trimm'd caves their secret meetings made. ‭ And with the lives of these doth life invade ‭ Or odorous fir-trees, or high-foreheaded oaks, ‭ Together taking their begetting strokes, ‭ And have their lives and deaths of equal dates, ‭ Trees bearing lovely and delightsome states, ‭ Whom Earth first feeds, that men initiates. ‭ On her high hills she doth their states sustain, ‭ And they their own heights raise as high again. ‭ Their growths together made, Nymphs call their groves ‭ Vow'd to th' Immortals services and loves; ‭ Which men's steels therefore touch not, but let grow. ‭ But when wise Fates times for their fadings know, ‭ The fair trees still before the fair Nymphs die, ‭ The bark about them grown corrupt and dry, ‭ And all their boughs fall'n yield to Earth her right; ‭ And then the Nymphs' lives leave the lovely night, ‭ "And these Nymphs in their caves shall nurse my son, ‭ Whom (when in him youth's first grace is begun) ‭ The Nymphs, his nurses, shall present to thee; ‭ And show thee what a birth thou hast by me. ‭ And, sure as now I tell thee all these things, ‭ When Earth hath cloth'd her plants in five fair springs, ‭ Myself will make return to this retreat, ‭ And bring that flow'r of thy enamour'd heat; ‭ Whom when thou then seest, joy shall fire thine eyes; ‭ He shall so well present the Deities. ‭ And then into thine own care take thy son ‭ From his calm seat to windy Ilion, ‭ Where, if strict question be upon the past, ‭ Asking what mother bore beneath her waist ‭ So dear a son, answer, as I afford ‭ Fit admonition, nor forget a word: ‭ They say a Nymph, call'd Calucopides, ‭ That is with others an inhabitress ‭ On this thy wood-crown'd hill, acknowledges ‭ That she his life gave. But, if thou declare ‭ The secret's truth, and art so mad to dare ‭ (In glory of thy fortunes) to approve ‭ That rich-crown'd Venus mix'd with thee in love, ‭ Jove, fired with my aspersion so dispread, ‭ Will with a wreakful lightning dart thee dead. ‭ "All now is told thee, comprehend it all. ‭ Be master of thyself, and do not call ‭ My name in question; but with reverence vow ‭ To Deities' angers all the awe ye owe." ‭ This said, She reach'd heaven, where airs ever flow. ‭ And so, O Goddess, ever honour'd be, ‭ In thy so odorous Cyprian empery! ‭ My Muse, affecting first thy fame to raise, ‭ Shall make transcension now to others' praise. ‭ THE END OF THE FIRST HYMN TO VENUS ‭[1] _᾿Ακροπόλος. Altissimum habens verticem, cujus summitas ‭ipsum polum attingit._ ‭[2] _ἄληστος. Cujus memoria erit perpetua._ ‭ TO THE SAME ‭ The reverend, rich-crown'd, and fair Queen I sing, ‭ Venus, that owes ill fate the fortressing ‭ Of all maritimal Cyprus; where the force ‭ Of gentle-breathing Zephyr steer'd her course ‭ Along the waves of the resounding sea, ‭ While, yet unborn, in that soft foam she lay ‭ That brought her forth; whom those fair Hours that bear ‭ The golden bridles joyfully stood near, ‭ Took up into their arms, and put on her ‭ Weeds of a never-corruptible wear. ‭ On her immortal head a crown they plac'd, ‭ Elaborate, and with all the beauties grac'd ‭ That gold could give it; of a weight so great, ‭ That, to impose and take off, it had set ‭ Three handles on it, made, for endless hold, ‭ Of shining brass, and all adorn'd with gold. ‭ Her soft neck all with carquenets was grac'd, ‭ That stoop'd, and both her silver breasts embrac'd, ‭ Which even the Hours themselves wear in resort ‭ To Deities' dances, and her Father's court. ‭ Grac'd at all parts, they brought to heaven her graces; ‭ Whose first sight seen, all fell into embraces, ‭ Hugg'd her white hands, saluted, wishing all ‭ To wear her maiden flow'r in festival ‭ Of sacred Hymen, and to lead her home; ‭ All, to all admiration, overcome ‭ With Cytherea with the violet crown. ‭ So to the Black-brow'd Sweet-spoke all renown! ‭ Prepare my song, and give me, in the end, ‭ The victory to whose palm all contend! ‭ So shall my Muse for ever honour thee, ‭ And, for thy sake, thy fair posterity. ‭ BACCHUS, OR THE PIRATES ‭ Of Dionysus, noble Semele's Son, ‭ I now intend to render mention, ‭ As on a prominent shore his person shone, ‭ Like to a youth whose flow'r was newly blown, ‭ Bright azure tresses play'd about his head, ‭ And on his bright broad shoulders was dispread ‭ A purple mantle. Strait he was descried ‭ By certain manly pirates, that applied ‭ Their utmost speed to prise him, being aboard ‭ A well-built bark, about whose broad sides roar'd ‭ The wine-black Tyrrhene billows; death as black ‭ Brought them upon him in their future wrack. ‭ For, soon as they had purchas'd but his view, ‭ Mutual signs past them, and ashore they flew, ‭ Took him, and brought him instantly aboard, ‭ Soothing their hopes to have obtain'd a hoard ‭ Of riches with him; and a Jove-kept king ‭ To such a flow'r must needs be natural spring. ‭ And therefore straight strong fetters they must fetch, ‭ To make him sure. But no such strength would stretch ‭ To his constrain'd pow'rs. Far flew all their bands ‭ From any least force done his feet or hands. ‭ But he sat casting smiles from his black eyes ‭ At all their worst. At which discoveries ‭ Made by the master, he did thus dehort ‭ All his associates: "Wretches! Of what sort ‭ Hold ye the person ye assay to bind? ‭ Nay, which of all the Pow'r fully-divin'd ‭ Esteem ye him, whose worth yields so much weight ‭ That not our well-built bark will bear his freight? ‭ Or Jove himself he is, or He that bears ‭ The silver bow, or Neptune. Nor appears ‭ In him the least resemblance of a man, ‭ But of a strain at least Olympian. ‭ Come! Make we quick dismission of his state, ‭ And on the black-soil'd earth exonerate ‭ Our sinking vessel of his deified load, ‭ Nor dare the touch of an intangible God, ‭ Lest winds outrageous, and of wrackful scathe, ‭ And smoking tempests, blow his fiery wrath." ‭ This well-spoke master the tall captain gave ‭ Hateful and horrible language; call'd him slave, ‭ And bade him mark the prosp'rous gale that blew, ‭ And how their vessel with her mainsail flew; ‭ Bade all take arms, and said, their works requir'd ‭ The cares of men, and not of an inspir'd ‭ Pure zealous master; his firm hopes being fir'd ‭ With this opinion, that they should arrive ‭ In Ægypt straight, or Cyprus, or where live ‭ Men whose brave breaths above the north wind blow; ‭ Yea, and perhaps beyond their region too. ‭ And that he made no doubt but in the end ‭ To make his prisoner tell him every friend ‭ Of all his offspring, brothers, wealth, and all; ‭ Since that prise, certain, must some God let fall. ‭ This said, the mast and mainsail up he drew, ‭ And in the mainsail's midst a frank gale blew; ‭ When all his ship took arms to brave their prise. ‭ But straight strange works appear'd to all their eyes: ‭ First, sweet wine through their swift-black bark did flow, ‭ Of which the odours did a little blow ‭ Their fiery spirits, making th' air so fine ‭ That they in flood were there as well as wine. ‭ A mere immortal-making savour rose, ‭ Which on the air the Deity did impose. ‭ The seamen see'ng all, admiration seiz'd; ‭ Yet instantly their wonders were increas'd, ‭ For on the topsail there ran, here and there, ‭ A vine that grapes did in abundance bear, ‭ And in an instant was the ship's mainmast ‭ With an obscure-green ivy's arms embrac'd, ‭ That flourish'd straight, and were with berries grac'd; ‭ Of which did garlands circle every brow ‭ Of all the pirates, and no one knew how. ‭ Which when they saw, they made the master steer ‭ Out to the shore; whom Bacchus made forbear, ‭ With showing more wonders. On the hatches He ‭ Appear'd a terrible lion, horribly ‭ Roaring; and in the mid-deck a male bear, ‭ Made with a huge mane; making all, for fear, ‭ Crowd to the stern, about the master there, ‭ Whose mind he still kept dauntless and sincere, ‭ But on the captain rush'd and ramp'd, with force ‭ So rude and sudden, that his main recourse ‭ Was to the main-sea straight: and after him ‭ Leapt all his mates, as trusting to their swim ‭ To fly foul death; but so found what they fled, ‭ Being all to dolphins metamorphosed. ‭ The master he took ruth of, sav'd, and made ‭ The blessed'st man that ever tried his trade, ‭ These few words giving him: "Be confident, ‭ Thou God-inspired pilot, in the bent ‭ Of my affection, ready to requite ‭ Thy late-to-me-intended benefit. ‭ I am the roaring God of spritely wine, ‭ Whom Semele (that did even Jove incline ‭ To amorous mixture, and was Cadmus' care) ‭ Made issue to the mighty Thunderer." ‭ And thus, all excellence of grace to thee, ‭ Son of sweet-count'nance-carry'ng Semele. ‭ I must not thee forget in least degree, ‭ But pray thy spirit to render so my song ‭ Sweet, and all ways in order'd fury strong. ‭ TO MARS ‭ Mars, most-strong, gold-helm'd, making chariots crack; ‭ Never without a shield cast on thy back; ‭ Mind-master, town-guard, with darts never driven; ‭ Strong-handed, all arms, fort, and fence of heaven; ‭ Father of victory with fair strokes given; ‭ Joint surrogate of justice, lest she fall ‭ In unjust strifes a tyrant; general ‭ Only of just men justly; that dost bear ‭ Fortitude's sceptre, to heaven's fiery sphere ‭ Giver of circular motion, between ‭ That and the Pleiads that still wand'ring been, ‭ Where thy still-vehemently-flaming horse ‭ About the third heaven make their fiery course; ‭ Helper of mortals; hear!--As thy fires give ‭ The fair and present boldnesses that strive ‭ In youth for honour, being the sweet-beam'd light ‭ That darts into their lives, from all their height, ‭ The fortitudes and fortunes found in fight; ‭ So would I likewise wish to have the pow'r ‭ To keep off from my head thy bitter hour, ‭ And that false fire, cast from my soul's low kind, ‭ Stoop to the fit rule of my highest mind, ‭ Controlling that so eager sting of wrath ‭ That stirs me on still to that horrid scathe ‭ Of war, that God still sends to wreak his spleen ‭ (Even by whole tribes) of proud injurious men. ‭ But O thou Ever-Blessed! give me still ‭ Presence of mind to put in act my will, ‭ Varied, as fits, to all occasion; ‭ And to live free, unforc'd, unwrought upon, ‭ Beneath those laws of peace that never are ‭ Affected with pollutions popular ‭ Of unjust hurt, or loss to anyone; ‭ And to bear safe the burthen undergone ‭ Of foes inflexive, and inhuman hates, ‭ Secure from violent and harmful fates. ‭ TO DIANA ‭ Diana praise, Muse, that in darts delights, ‭ Lives still a maid, and had nutritial rights ‭ With her born-brother, the far-shooting Sun. ‭ That doth her all-of-gold-made chariot run ‭ In chase of game, from Meles that abounds ‭ In black-brow'd bulrushes, and, where her hounds ‭ She first uncouples, joining there her horse, ‭ Through Smyrna carried in most fiery course ‭ To grape-rich Claros; where (ill his rich home, ‭ And constant expectation She will come) ‭ Sits Phœbus, that the silver bow doth bear, ‭ To meet with Phœbe, that doth darts transfer ‭ As far as He his shafts. As far then be ‭ Thy chaste fame shot, O Queen of archery! ‭ Sacring my song to every Deity. ‭ TO VENUS ‭ To Cyprian Venus still my verses vow, ‭ Who gifts as sweet as honey doth bestow ‭ On all mortality; that ever smiles, ‭ And rules a face that all foes reconciles; ‭ Ever sustaining in her hand a flow'r ‭ That all desire keeps ever in her pow'r. ‭ Hail, then, O Queen of well-built Salamine, ‭ And all the state that Cyprus doth confine, ‭ Inform my song with that celestial fire ‭ That in thy beauties kindles all desire. ‭ So shall my Muse for ever honour thee, ‭ And any other thou commend'st to me. ‭ TO PALLAS ‭ Pallas Minerva only I begin ‭ To give my song; that makes war's terrible din, ‭ Is patroness of cities, and with Mars ‭ Marshall'd in all the care and cure of wars, ‭ And in everted cities, fights, and cries. ‭ But never doth herself set down or rise ‭ Before a city, but at both times She ‭ All injur'd people sets on foot and free. ‭ Give, with thy war's force, fortune then to me, ‭ And, with thy wisdom's force, felicity. ‭ TO JUNO ‭ Saturnia, and her throne of gold, I sing, ‭ That was of Rhea the eternal spring, ‭ And empress of a beauty never yet ‭ Equall'd in height of tincture. Of the great ‭ Saturnius (breaking air in awful noise) ‭ The far-fam'd wife and sister; whom in joys ‭ Of high Olympus all the Blessed love, ‭ And honour equal with unequall'd Jove. ‭ TO CERES ‭ The rich-hair'd Ceres I assay to sing; ‭ A Goddess, in whose grace the natural spring ‭ Of serious majesty itself is seen; ‭ And of the wedded, yet in grace still green, ‭ Proserpina, her daughter, that displays ‭ A beauty casting every way her rays. ‭ All honour to thee, Goddess! Keep this town; ‭ And take thou chief charge of my song's renown! ‭ TO THE MOTHER OF THE GODS ‭ Mother of all, both Gods and men, commend, ‭ O Muse, whose fair form did from Jove descend; ‭ That doth with cymbal sounds delight her life, ‭ And tremulous divisions of the fife; ‭ Love's dreadful lions' roars, and wolves' hoarse howls, ‭ Sylvan retreats, and hills, whose hollow knolls ‭ Raise repercussive sounds about her ears. ‭ And so may honour ever crown thy years ‭ With all-else Goddesses, and ever be ‭ Exalted in the Muses' harmony! ‭ TO LION-HEARTED HERCULES ‭ Alcides, forcefullest of all the brood ‭ Of men enforc'd with need of earthy food, ‭ My Muse shall memorise; the son of Jove, ‭ Whom, in fair-seated Thebes (commix'd in love ‭ With great heaven's sable-cloud-assembling State) ‭ Alcmena bore to him; and who, in date ‭ Of days forepast, through all the sea was sent, ‭ And Earth's inenarrable continent, ‭ To acts that king Eurystheus had decreed; ‭ Did many a petulant and imperious deed ‭ Himself, and therefore suffer'd many a toil; ‭ Yet now inhabits the illustrious soil ‭ Of white Olympus, and delights his life ‭ With still-young Hebe, his well-ankled wife. ‭ Hail, King, and Son of Jove! Vouchsafe me ‭ Virtue, and, her effect, felicity! ‭ TO ÆSCULAPIUS ‭ With Æsculapius, the physician, ‭ That cur'd all sickness, and was Phœbus' son, ‭ My Muse makes entry; to whose life gave yield ‭ Divine Coronis in the Dotian field, ‭ (King Phlegius' daughter) who much joy on men ‭ Conferr'd, in dear ease of their irksome pain. ‭ For which, my salutation, worthy king, ‭ And vows to thee paid, ever when I sing! ‭ TO CASTOR AND POLLUX ‭ Castor and Pollux, the Tyndarides, ‭ Sweet Muse illustrate; that their essences ‭ Fetch from the high forms of Olympian Jove, ‭ And were the fair fruits of bright Leda's love, ‭ Which she produc'd beneath the sacred shade ‭ Of steep Taygetus, being subdu'd, and made ‭ To serve th' affections of the Thunderer. ‭ And so all grace to you, whom all aver ‭ (For skill in horses, and their manage given) ‭ To be the bravest horsemen under heaven! ‭ TO MERCURY ‭ Hermes I honour, the Cyllenian Spy, ‭ King of Cyllenia, and of Arcady ‭ With flocks abounding; and the Messenger ‭ Of all th' Immortals, that doth still infer ‭ Profits of infinite value to their store; ‭ Whom to Saturnius bashful Maia bore, ‭ Daughter of Atlas, and did therefore fly ‭ Of all th' Immortals the society, ‭ To that dark cave, where, in the dead of night, ‭ Jove join'd with her in love's divine delight, ‭ When golden sleep shut Juno's jealous eye, ‭ Whose arms had wrists as white as ivory, ‭ From whom, and all, both men and Gods beside, ‭ The fair-hair'd nymph had scape kept undescried. ‭ Joy to the Jove-got then, and Maia's care, ‭ 'Twixt men and Gods the general Messenger, ‭ Giver of good grace, gladness, and the flood ‭ Of all that men or Gods account their good! ‭ TO PAN ‭ Sing, Muse, this chief of Hermes' love-got joys, ‭ Goat-footed, two-horn'd, amorous of noise, ‭ That through the fair greens, all adorn'd with trees, ‭ Together goes with Nymphs, whose nimble knees ‭ Can every dance foot, that affect to scale ‭ The most inaccessible tops of all ‭ Uprightest rocks, and ever use to call ‭ On Pan, the bright-hair'd God of pastoral; ‭ Who yet is lean and loveless, and doth owe ‭ By lot all loftiest mountains crown'd with snow; ‭ All tops of hills, and cliffy highnesses, ‭ All sylvan copses, and the fortresses ‭ Of thorniest queaches, here and there doth rove, ‭ And sometimes, by allurement of his love, ‭ Will wade the wat'ry softnesses. Sometimes ‭ (In quite oppos'd _capriccios_) he climbs ‭ The hardest rocks, and highest, every way ‭ Running their ridges. Often will convey ‭ Himself up to a watch-tow'r's top, where sheep ‭ Have their observance. Oft through hills as steep ‭ His goats he runs upon, and never rests. ‭ Then turns he head, and flies on savage beasts, ‭ Mad of their slaughters; so most sharp an eye ‭ Setting upon them, as his beams let fly ‭ Through all their thickest tapistries. And then ‭ (When Hesp'rus calls to fold the flocks of men) ‭ From the green clossets of his loftiest reeds ‭ He rushes forth, and joy with song he feeds. ‭ When, under shadow of their motions set, ‭ He plays a verse forth so profoundly sweet, ‭ As not the bird that in the flow'ry spring, ‭ Amidst the leaves set, makes the thickets ring ‭ Of her sour sorrows, sweeten'd with her song, ‭ Runs her divisions varied so and strong. ‭ And then the sweet-voic'd Nymphs that crown his mountains ‭ (Flock'd round about the deep-black-water'd fountains) ‭ Fall in with their contention of song. ‭ To which the echoes all the hills along ‭ Their repercussions add. Then here and there ‭ (Plac'd in the midst) the God the guide doth bear ‭ Of all their dances, winding in and out, ‭ A lynce's hide, besprinkled round about ‭ With blood, cast on his shoulders. And thus He, ‭ With well-made songs, maintains th' alacrity ‭ Of his free mind, in silken meadows crown'd ‭ With hyacinths and saffrons, that abound ‭ In sweet-breath'd odours, that th' unnumber'd grass ‭ (Besides their scents) give as through all they pass. ‭ And these, in all their pleasures, ever raise ‭ The blessed Gods' and long Olympus' praise: ‭ Like zealous Hermes, who of all I said ‭ Most profits up to all the Gods convey'd. ‭ Who, likewise, came into th' Arcadian state, ‭ (That's rich in fountains, and all celebrate ‭ For nurse of flocks,) where He had vow'd a grove ‭ (Surnam'd Cyllenius) to his Godhead's love. ‭ Yet even himself (although a God he were) ‭ Clad in a squalid sheepskin, govern'd there ‭ A mortal's sheep. For soft love ent'ring him ‭ Conform'd his state to his conceited trim, ‭ And made him long, in an extreme degree, ‭ T' enjoy the fair-hair'd virgin Dryope. ‭ Which ere he could, she made consummate ‭ The flourishing rite of Hymen's honour'd state; ‭ And brought him such a piece of progeny ‭ As show'd, at first sight, monstrous to the eye, ‭ Goat-footed, two-horn'd, full of noise even then, ‭ And (opposite quite to other childeren) ‭ Told, in sweet laughter, he ought death no tear. ‭ Yet straight his mother start, and fled, in fear, ‭ The sight of so unsatisfying a thing, ‭ In whose face put forth such a bristled spring. ‭ Yet the most useful Mercury embrac'd, ‭ And took into his arms, his homely-fac'd, ‭ Beyond all measure joyful with his sight; ‭ And up to heaven with him made instant flight, ‭ Wrapp'd in the warm skin of a mountain hare, ‭ Set him by Jove, and made most merry fare ‭ To all the Deities else with his son's sight; ‭ Which most of all fill'd Bacchus with delight; ‭ And Pan they call'd him, since he brought to all ‭ Of mirth so rare and full a festival. ‭ And thus all honour to the shepherds' King, ‭ For sacrifice to thee my Muse shall sing! ‭ TO VULCAN ‭ Praise Vulcan, now Muse; whom fame gives the prize ‭ For depth and fracture of all forge-devise; ‭ Who, with the sky-ey'd Pallas, first did give ‭ Men rules of buildings, that before did live ‭ In caves and dens, and hills, like savage beasts; ‭ But now, by art-fam'd Vulcan's interests ‭ In all their civil industries, ways clear ‭ Through th' all-things-bringing-to-their-ends (the year) ‭ They work out to their ages' ends, at ease ‭ Lodg'd in safe roofs from Winter's utmost prease. ‭ But, Vulcan, stand propitious to me, ‭ Virtue safe granting, and felicity! ‭ TO PHŒBUS ‭ O Phœbus! Even the swan from forth her wings, ‭ Jumping her proyning-bank, thee sweetly sings, ‭ By bright Peneus' whirl-pit-making streams. ‭ Thee, that thy lute mak'st sound so to thy beams, ‭ Thee, first and last, the sweet-voic'd singer still ‭ Sings, for thy song's all-songs-transcending skill. ‭ Thy pleasure, then, shall my song still supply, ‭ And so salutes thee King of Poesy. ‭ TO NEPTUNE ‭ Neptune, the mighty marine God, I sing, ‭ Earth's mover, and the fruitless ocean's King, ‭ That Helicon and th' Ægean deeps dost hold. ‭ O thou Earth-shaker! Thy command two-fold ‭ The Gods have sorted; making thee of horses ‭ The awful tamer, and of naval forces ‭ The Sure preserver. Hail, O Saturn's birth! ‭ Whose graceful green hair circles all the earth. ‭ Bear a benign mind; and thy helpful hand ‭ Lend all submitted to thy dread command. ‭ TO JOVE ‭ Jove now I sing, the greatest and the best ‭ Of all these Pow'rs that are with Deity blest, ‭ That far-off doth his dreadful voice diffuse, ‭ And, being King of all, doth all conduce ‭ To all their ends. Who (shut from all Gods else ‭ With Themis, that the laws of all things tells) ‭ Their fit composures to their times doth call, ‭ Weds them together, and preserves this all. ‭ Grace then, O far-heard Jove, the grace thou'st given, ‭ Most Glorious, and most Great of Earth and Heaven! ‭ TO VESTA ‭ Vesta, that as a servant oversees ‭ King Phœbus' hallow'd house, in all degrees ‭ Of guide about it, on the sacred shore ‭ Of heavenly Pythos, and hast evermore ‭ Rich balms distilling from thy odorous hair, ‭ Grace this house with thy housewifely repair! ‭ Enter, and bring a mind that most may move, ‭ Conferring even, the great in counsels, Jove; ‭ And let my verse taste of your either's love. ‭ TO THE MUSES AND APOLLO ‭ The Muses, Jove, and Phœbus, now I sing; ‭ For from the far-off-shooting Phœbus spring ‭ All poets and musicians, and from Jove ‭ Th' ascents of kings. The man the Muses love, ‭ Felicity blesses; elocution's choice ‭ In syrup lay'ng of sweetest breath his voice. ‭ Hail, Seed of Jove, my song your honours give, ‭ And so in mine shall yours and others' live. ‭ TO BACCHUS ‭ Ivy-crown'd Bacchus iterate in thy praises, ‭ O Muse; whose voice all loftiest echoes raises, ‭ And he with all th' illustrious Seed of Jove ‭ Is join'd in honour, being the fruit of love ‭ To him, and Semele the-great-in-graces; ‭ And from the King his father's kind embraces ‭ By fair-hair'd Nymphs was taken to the dales ‭ Of Nyssa, and with curious festivals. ‭ Given his fair grought, far from his father's view, ‭ In caves from whence eternal odours flew, ‭ And in high number of the Deities plac'd. ‭ Yet when the many-hymn-given God had past ‭ His Nurses' cares, in ivies and in bays ‭ All over thicketed, his varied ways ‭ To sylvan coverts evermore He took, ‭ With all his Nurses, whose shrill voices shook ‭ Thickets, in which could no foot's entry fall, ‭ And he himself made captain of them all. ‭ And so, O grape-abounding Bacchus, be ‭ Ever saluted by my Muse and me! ‭ Give us to spend with spirit our hours out here, ‭ And every hour extend to many a year. ‭ TO DIANA ‭ Diana, that the golden spindle moves, ‭ And lofty sounds as well as Bacchus loves, ‭ A bashful virgin, and of fearful hearts ‭ The death-affecter with delighted darts, ‭ By sire and mother Phœbus' sister born, ‭ Whose thigh the golden falchion doth adorn, ‭ I sing; who likewise over hills of shade ‭ And promontories that vast winds invade, ‭ Amorous of hunting, bends her all-gold bow, ‭ And sigh-begetting arrows doth bestow ‭ In fates so dreadful that the hill-tops quake, ‭ And bristled woods their leafy foreheads shake, ‭ Horrors invade earth, and [the] fishy seas ‭ Impassion'd furies; nothing can appease ‭ The dying brays of beasts. And her delight ‭ In so much death affects so with affright ‭ Even all inanimate natures; for, while she ‭ Her sports applies, their general progeny ‭ She all ways turns upon to all their banes. ‭ Yet when her fiery pleasures find their wanes, ‭ Her yielding bow unbent, to th' ample house, ‭ Seated in Delphos, rich and populous, ‭ Of her dear brother, her retreats advance. ‭ Where th' instauration of delightsome dance ‭ Amongst the Muses and the Graces she ‭ Gives form; in which herself the regency ‭ (Her unbent bow hung up, and casting on ‭ A gracious robe) assumes, and first sets gone ‭ The dances' entry; to which all send forth ‭ Their heavenly voices, and advance the worth ‭ Of her fair-ankled mother, since to light ‭ She children brought the far most exquisite ‭ In counsels and performances of all ‭ The Goddesses that grace the heavenly hall. ‭ Hail then, Latona's fair-hair'd Seed, and Jove's! ‭ My song shall ever call to mind your loves. ‭ TO PALLAS ‭ Pallas-Minerva's deity, the renown'd, ‭ My Muse in her variety must resound; ‭ Mighty in councils; whose illustrous eyes ‭ In all resemblance represent the skies. ‭ A reverend maid of an inflexible mind; ‭ In spirit and person strong; of triple kind; ‭ Fautress of cities that just laws maintain; ‭ Of Jove, the-great-in-councils, very brain ‭ Took prime existence, his unbounded brows ‭ Could not contain her, such impetuous throes ‭ Her birth gave way to, that abroad she flew, ‭ And stood, in gold arm'd, in her Father's view, ‭ Shaking her sharp lance. All Olympus shook ‭ So terribly beneath her, that it took ‭ Up in amazes all the Deities there. ‭ All earth resounded with vociferous fear. ‭ The sea was put up all in purple waves, ‭ And settled suddenly her rudest raves. ‭ Hyperion's radiant son his swift-hov'd steeds ‭ A mighty time stay'd, till her arming weeds, ‭ As glorious as the Gods', the blue-ey'd Maid ‭ Took from her deathless shoulders; but then stay'd ‭ All these distempers, and heaven's counsellor, Jove, ‭ Rejoic'd that all things else his stay could move. ‭ So I salute thee still; and still in praise ‭ Thy fame, and others', shall my memory raise. ‭ TO VESTA AND MERCURY ‭ Vesta I sing, who, in bequest of fate, ‭ Art sorted out an everlasting state ‭ In all th' Immortals' high-built roofs, and all ‭ Those of earth-dwelling men, as general ‭ And ancient honours given thee for thy gift ‭ Of free-liv'd chastity, and precious thrift. ‭ Nor can there amongst mortals banquets be, ‭ In which, both first and last, they give not thee ‭ Their endless gratitudes in pour'd-out wine, ‭ As gracious sacrifice to thy divine ‭ And useful virtues; being invok'd by all, ‭ Before the least taste of their festival ‭ In wine or food affect their appetites. ‭ And Thou, that of th' adorn'd-with-all-delights ‭ Art the most useful angel, born a God ‭ Of Jove and Maia, of heaven's golden rod ‭ The sole sustainer, and hast pow'r to bless ‭ With all good all men, great Argicides, ‭ Inhabit all good houses, see'ng no wants ‭ Of mutual minds' love in th' inhabitants, ‭ Join in kind blessing with the bashful maid ‭ And all-lov'd virgin, Vesta; either's aid ‭ Combin'd in every hospitable house; ‭ Both being best seen in all the gracious ‭ House-works of mortals. Jointly follow then, ‭ Even from their youths, the minds of dames and men. ‭ Hail then, old Daughter of the oldest God, ‭ And thou Great Bearer of Heaven's golden rod! ‭ Yet not to you alone my vows belong, ‭ Others as well claim th' homage of my song. ‭ TO EARTH, THE MOTHER OF ALL ‭ Mother of all things, the well-founded Earth, ‭ My Muse shall memorize; who all the birth ‭ Gives food that all her upper regions breed, ‭ All that in her divine diffusions feed ‭ In under continents, all those that live ‭ In all the seas, and all the air doth give ‭ Wing'd expeditions, of thy bounties eat; ‭ Fair children, and fair fruits, thy labour's sweat, ‭ O great in reverence; and referr'd to thee, ‭ For life and death is all the pedigree ‭ Of mortal humans. Happy then is he ‭ Whom the innate propensions of thy mind ‭ Stand bent to honour. He shall all things find ‭ In all abundance; all his pastures yield ‭ Herds in all plenties; all his roofs are fill'd ‭ With rich possessions; he, in all the sway ‭ Of laws best order'd, cuts out his own way ‭ In cities shining with delicious dames, ‭ And takes his choice of all those striving flames; ‭ High happiness and riches, like his train, ‭ Follow his fortunes, with delights that reign ‭ In all their princes; glory invests his sons; ‭ His daughters, with their crown'd selections ‭ Of all the city, frolic through the meads, ‭ And everyone her call'd-for dances treads ‭ Along the soft-flow'r of the claver-grass. ‭ All this, with all those, ever comes to pass, ‭ That thy love blesses, Goddess full of grace, ‭ And treasurous Angel t' all the human race. ‭ Hail, then, Great Mother of the Deified Kind, ‭ Wife to the cope of stars! Sustain a mind ‭ Propitious to me for my praise, and give ‭ (Answering my mind) my vows fit means to live. ‭ TO THE SUN ‭ The radiant Sun's divine renown diffuse, ‭ Jove's daughter, great Calliope, my Muse; ‭ Whom ox-ey'd Euryphaëssa gave birth ‭ To the bright Seed of starry Heaven and Earth. ‭ For the far-fam'd Hyperion took to wife ‭ His sister Euryphaëssa, that life ‭ Of his high race gave to these lovely three: ‭ Aurora, with the rosy-wrists; and She ‭ That owns th' enamouring tresses, the bright Moon; ‭ Together with the never-wearied Sun, ‭ Who (his horse mounting) gives both mortals light ‭ And all th' Immortals. Even to horror, bright ‭ A blaze burns from his golden burgonet, ‭ Which to behold exceeds the sharpest set ‭ Of any eye's intention, beams so clear ‭ It all ways pours abroad. The glorious cheer ‭ Of his far-shining face up to his crown ‭ Casts circular radiance, that comes streaming down ‭ About his temples, his bright cheeks, and all, ‭ Retaining the refulgence of their fall. ‭ About his bosom flows so fine a weed ‭ As doth the thinness of the wind exceed ‭ In rich context; beneath whose deep folds fly ‭ His masculine horses round about the sky, ‭ Till in this hemisphere he renders stay ‭ T' his gold-yok'd coach and coursers; and his way, ‭ Let down by heaven, the heavenly coachman makes ‭ Down to the ocean, where his rest he takes. ‭ My salutations then, fair King, receive, ‭ And in propitious returns relieve ‭ My life with mind-fit means; and then from thee, ‭ And all the race of complete Deity, ‭ My song shall celebrate those half-god States, ‭ That yet sad death's condition circulates, ‭ And whose brave acts the Gods show men that they ‭ As brave may aim at, since they can but die. ‭ TO THE MOON ‭ The Moon, now, Muses, teach me to resound, ‭ Whose wide wings measure such a world of ground; ‭ Jove's daughter, deck'd with the mellifluous tongue, ‭ And seen in all the sacred art of song. ‭ Whose deathless brows when she from heaven displays, ‭ All earth she wraps up in her orient rays. ‭ A heaven of ornament in earth is rais'd ‭ When her beams rise. The subtle air is sais'd ‭ Of delicate splendour from her crown of gold. ‭ And when her silver bosom is extoll'd, ‭ Wash'd in the ocean, in day's equall'd noon ‭ Is midnight seated; but when she puts on ‭ Her far-off-sprinkling-lustre evening weeds, ‭ (The month is two cut; her high-breasted steeds ‭ Man'd all with curl'd flames, put in coach and all, ‭ Her huge orb fill'd,) her whole trims then exhale ‭ Unspeakable splendours from the glorious sky. ‭ And out of that state mortal men imply ‭ Many predictions. And with her then, ‭ In love mix'd, lay the King of Gods and men; ‭ By whom made fruitful, she Pandea bore, ‭ And added her state to th' Immortal Store. ‭ Hail, Queen, and Goddess, th' ivory-wristed Moon ‭ Divine, prompt, fair-hair'd! With thy grace begun, ‭ My Muse shall forth, and celebrate the praise ‭ Of men whose states the Deities did raise ‭ To semi-deities; whose deeds t' endless date ‭ Muse-lov'd and sweet-sung poets celebrate. ‭ TO CASTOR AND POLLUX ‭ Jove's fair Sons, father'd by th' Oebalian king, ‭ Muses well-worth-all men's beholdings, sing! ‭ The dear birth that bright-ankl'd Leda bore; ‭ Horse-taming Castor, and, the conqueror ‭ Of tooth-tongu'd Momus, Pollux; whom beneath ‭ Steep-brow'd Taygetus she gave half-god breath, ‭ In love mix'd with the black-clouds King of Heaven; ‭ Who, both of men and ships, being tempest driven, ‭ When Winter's wrathful empire is in force ‭ Upon th' implacable seas, preserve the course. ‭ For when the gusts begin, if near the shore, ‭ The seamen leave their ship, and, evermore ‭ Bearing two milk-white lambs aboard, they now ‭ Kill them ashore, and to Jove's issue vow, ‭ When though their ship, in height of all the roar ‭ The winds and waves confound, can live no more ‭ In all their hopes, then suddenly appear ‭ Jove's saving Sons, who both their bodies bear ‭ 'Twixt yellow wings down from the sparkling pole, ‭ Who straight the rage of those rude winds control, ‭ And all the high-waves couch into the breast ‭ Of th' hoary seas. All which sweet signs of rest ‭ To seamen's labours their glad souls conceive, ‭ And end to all their irksome grievance give. ‭ So, once more, to the swift-horse-riding race ‭ Of royal Tyndarus, eternal grace! ‭ TO MEN OF HOSPITALITY ‭ Reverence a man with use propitious ‭ That hospitable rites wants; and a house ‭ (You of this city with the seat of state ‭ To ox-ey'd Juno vow'd) yet situate ‭ Near Pluto's region. At the extreme base ‭ Of whose so high-hair'd city, from the race ‭ Of blue-wav'd Hebrus lovely fluent, grac'd ‭ With Jove's begetting, you divine cups taste. ‭ EPIGRAMS ‭ TO CUMA ‭ Lend hospitable rites and house-respect, ‭ You that the virgin with the fair eyes deckt ‭ Make fautress of your stately-seated town, ‭ At foot of Sardes, with the high-hair'd crown, ‭ Inhabiting rich Cuma; where ye taste ‭ Of Hermus' heavenly fluent, all embrac'd ‭ By curl'd-head whirl pits; and whose waters move ‭ From the divine seed of immortal Jove. ‭ IN HIS RETURN TO CUMA ‭ Swiftly my feet sustain me to the town, ‭ Where men inhabit whom due honours crown, ‭ Whose minds with free-given faculties are mov'd, ‭ And whose grave counsels best of best approv'd. ‭ UPON THE SEPULCHRE OF MIDUS ‭ CUT IN BRASS, IN THE FIGURE OF A VIRGIN ‭ A maid of brass I am, infixed here ‭ T' eternize honest Midus' sepulchre; ‭ And while the stream her fluent seed receives, ‭ And steep trees curl their verdant brows with leaves, ‭ While Phœbus rais'd above the earth gives sight, ‭ And th' humorous Moon takes lustre from his light, ‭ While floods bear waves, and seas shall wash the shore, ‭ At this his sepulchre, whom all deplore, ‭ I'll constantly abide; all passers by ‭ Informing, "Here doth honest Midus lie." ‭ CUMA ‭ REFUSING HIS OFFER TO ETERNIZE THEIR STATE, ‭ THOUGH BROUGHT THITHER BY THE MUSES ‭ O to what fate hath Father Jove given o'er ‭ My friendless life, born ever to be poor! ‭ While in my infant state he pleas'd to save me, ‭ Milk on my reverend mother's knees he gave me, ‭ In delicate and curious nursery; ‭ Æolian Smyrna, seated near the sea, ‭ (Of glorious empire, and whose bright sides ‭ Sacred Meletus' silver current glides,) ‭ Being native seat to me. Which, in the force ‭ Of far-past time, the breakers of wild horse, ‭ Phriconia's noble nation, girt with tow'rs; ‭ Whose youth in fight put on with fiery pow'rs, ‭ From hence, the Muse-maids, Jove's illustrous Seed, ‭ Impelling me, I made impetuous speed, ‭ And went with them to Cuma, with intent ‭ T' eternize all the sacred continent ‭ And state of Cuma. They, in proud ascent ‭ From off their bench, refus'd with usage fierce ‭ The sacred voice which I aver is verse. ‭ Their follies, yet, and madness borne by me, ‭ Shall by some pow'r be thought on futurely, ‭ To wreak of him whoever, whose tongue sought ‭ With false impair my fall. What fate God brought ‭ Upon my birth I'll bear with any pain, ‭ But undeserv'd defame unfelt sustain. ‭ Nor feels my person (dear to me though poor) ‭ Any great lust to linger any more ‭ In Cuma's holy highways; but my mind ‭ (No thought impair'd, for cares of any kind ‭ Borne in my body) rather vows to try ‭ The influence of any other sky, ‭ And spirits of people bred in any land ‭ Of ne'er so slender and obscure command. ‭ AN ASSAY OF HIS BEGUN ILIADS ‭ Ilion, and all the brave-horse-breeding soil, ‭ Dardania, I sing; that many a toil ‭ Impos'd upon the mighty Grecian pow'rs, ‭ Who were of Mars the manly servitours. ‭ TO THESTOR'S SON [1] ‭ INQUISITIVE OF HOMER ABOUT THE CAUSES OF THINGS ‭ Thestorides! of all the skills unknown ‭ To errant mortals, there remains not one ‭ Of more inscrutable affair to find ‭ Than is the true state of a human mind. ‭[1] Homer intimated, in this his answer to Thestorides, a will to have ‭him learn the knowledge of himself, before he inquired so ‭curiously the causes of other things. And from hence had the great ‭peripatetic, Themistius, his most grave epiphoneme, _Anima quæ ‭seipsam ignorat, quid sciret ipsa de aliis?_ And, therefore, ‭according to Aristotle, advises all philosophical students to begin ‭with that study. ‭ TO NEPTUNE ‭ Hear, pow'rful Neptune, that shak'st earth in ire, ‭ King of the great green, where dance all the quire ‭ Of fair-hair'd Helicon; give prosperous gales; ‭ And good pass, to these guiders of our sails, ‭ Their voyage rend'ring happily directed, ‭ And their return with no ill fate affected. ‭ Grant likewise at rough Mimas' lowest roots, ‭ Whose strength up to her tops prærupt rocks shoots, ‭ My passage safe arrival; and that I ‭ My bashful disposition may apply ‭ To pious men, and wreak myself upon ‭ The man whose verbal circumvention ‭ In me did wrong t' hospitious Jove's whole state, ‭ And th' hospitable table violate. ‭ TO THE CITY ERYTHRÆA ‭ Worshipful Earth, Giver of all things good! ‭ Giver of even felicity; whose flood ‭ The mind all-over steeps in honeydew; ‭ That to some men dost infinite kindness shew, ‭ To others that despise thee art a shrew, ‭ And giv'st them gamester's galls; who, once their main ‭ Lost with an ill chance, fare like abjects slain. ‭ TO MARINERS ‭ Ye wave-trod watermen, as ill as she ‭ That all the earth in infelicity ‭ Of rapine plunges; who upon your fare ‭ As sterv'd-like-ravenous as cormorants are; ‭ The lives ye lead, but in the worst degree, ‭ Not to be envied more than misery; ‭ Take shame, and fear the indignation ‭ Of Him that thunders from the highest throne, ‭ Hospitious Jove, who, at the back, prepares ‭ Pains of abhorr'd effect of him that dares ‭ The pieties break of his hospitious squares. ‭ THE PINE ‭ Any tree else bears better fruit than thee, ‭ That Ida's tops sustain, where every tree ‭ Bears up in air such perspirable heights, ‭ And in which caves and sinuous receipts ‭ Creep in such great abundance. For about ‭ Thy foots, that ever all thy fruits put out, ‭ As nourish'd by them, equal with thy fruits, ‭ Pour Mars's iron-mines their accurs'd pursuits. ‭ So that when any earth-encroaching man, ‭ Of all the martial brood Cebrenian, ‭ Plead need of iron, they are certain still ‭ About thy roots to satiate every will. ‭ TO GLAUCUS ‭ WHO WAS SO MISERABLY SPARING THAT HE FEARED ‭ ALL MEN'S ACCESS TO HIM ‭ Glaucus! though wise enough, yet one word more ‭ Let my advice add to thy wisdom's store, ‭ For 'twill be better so: Before thy door ‭ Give still thy mastiffs meat, that will be sure ‭ To lie there, therefore, still, and not endure ‭ (With waylaid ears) the softest foot can fall, ‭ But men and beasts make fly thee and thy stall. ‭ AGAINST THE SAMIAN MINISTRESS, OR NUN ‭ ‭ Hear me, O Goddess, that invoke thine ear, ‭ Thou that dost feed and form the youthful year, ‭ And grant that this dame may the loves refuse, ‭ And beds, of young men, and affect to use ‭ Humans whose temples hoary hairs distain, ‭ Whose pow'rs are passing coy, whose wills would fain. ‭ WRITTEN ON THE COUNCIL CHAMBER ‭ Of men, sons are the crowns of cities' tow'rs; ‭ Of pastures, horse are the most beauteous flow'rs; ‭ Of seas, ships are the grace; and money still ‭ With trains and titles doth the family fill. ‭ But royal counsellors, in council set, ‭ Are ornaments past all, as clearly great ‭ As houses are that shining fires enfold, ‭ Superior far to houses nak'd and cold. ‭ THE FURNACE CALLED IN TO SING BY POTTERS ‭ If ye deal freely, O my fiery friends, ‭ As ye assure, I'll sing, and serve your ends. ‭ Pallas, vouchsafe thou here invok'd access, I ‭ Impose thy hand upon this Forge, and bless ‭ All cups these artists earn so, that they may ‭ Look black still with their depth, and every way ‭ Give all their vessels a most sacred sale. ‭ Make all well-burn'd; and estimation call ‭ Up to their prices. Let them market well, ‭ And in all highways in abundance sell, ‭ Till riches to their utmost wish arise, ‭ And, as thou mak'st them rich, so make me wise. ‭ But if ye now turn all to impudence, ‭ And think to pay with lies my patience, ‭ Then will I summon 'gainst your Furnace all ‭ Hell's harmfull'st spirits; Maragus I'll call, ‭ Sabactes, Asbett, and Omadamus, ‭ Who ills against your art innumerous ‭ Excogitates, supplies, and multiplies. ‭ Come, Pallas, then, and all command to rise, ‭ Infesting forge and house with fire, till all ‭ Tumble together, and to ashes fall, ‭ These potters selves dissolv'd in tears as small. ‭ And as a horse-cheek chides his foaming bit, ‭ So let this Forge murmur in fire and flit, ‭ And all this stuff to ashy ruins run. ‭ And thou, O Circe, daughter of the Sun, ‭ Great-many-poison-mixer, come, and pour ‭ Thy cruell'st poisons on this Potters' floor, ‭ Shivering their vessels; and themselves affect ‭ With all the mischiefs possible to direct ‭ 'Gainst all their beings, urg'd by all thy fiends. ‭ Let Chiron likewise come; and all those friends ‭ (The Centaurs) that Alcides' fingers fled, ‭ And all the rest too that his hand strook dead, ‭ (Their ghosts excited) come, and macerate ‭ These earthen men; and yet with further fate ‭ Affect their Furnace; all their tear-burst eyes ‭ Seeing and mourning for their miseries, ‭ While I look on, and laugh their blasted art ‭ And them to ruin. Lastly, if apart ‭ Any lies lurking, and sees yet, his face ‭ Into a coal let th' angry fire embrace, ‭ That all may learn by them, in all their lust, ‭ To dare deeds great, to see them great and just. ‭ EIRESIONE, OR, THE OLIVE BRANCH ‭ The turrets of a man of infinite might, ‭ Of infinite action, substance infinite, ‭ We make access to; whose whole being rebounds ‭ From earth to heaven, and nought but bliss resounds. ‭ Give entry then, ye doors; more riches yet ‭ Shall enter with me; all the Graces met ‭ In joy of their fruition, perfect peace ‭ Confirming all; all crown'd with such increase, ‭ That every empty vessel in your house ‭ May stand replete with all things precious; ‭ Elaborate Ceres may your larders fill ‭ With all dear delicates, and serve in still; ‭ May for your son a wife make wish'd approach ‭ Into your tow'rs, and rapt in in her coach ‭ With strong-kneed mules; may yet her state prove staid, ‭ With honour'd housewiferies; her fair hand laid ‭ To artful loomworks; and her nak'd feet tread ‭ The gum of amber to a golden bead. ‭ But I'll return; return, and yet not press ‭ Your bounties now assay'd with oft access, ‭ Once a year only, as the swallow prates ‭ Before the wealthy Spring's wide open gates. ‭ Meantime I stand at yours, nor purpose stay ‭ More time t' entreat. Give, or not give, away ‭ My feet shall bear me, that did never come ‭ With any thought to make your house my home. ‭ TO CERTAIN FISHER BOYS ‭ PLEASING HIM WITH INGENIOUS RIDDLES ‭ Yet from the bloods even of your self-like sires ‭ Are you descended, that could make ye heirs ‭ To no huge hoards of coin, nor leave ye able ‭ To feed flocks of innumerable rabble. ‭ THE END OF ALL THE ENDLESS WORKS OF HOMER. ‭ THE TRANSLATOR'S EPILOGUE ‭ _The work that I was born to do is done! ‭ Glory to Him that the conclusion ‭ Makes the beginning of my life; and never ‭ Let me be said to live, till I live ever. ‭ Where's the outliving of my fortunes then, ‭ Ye errant vapours of Fame's Lernean fen, ‭ That, like possess'd storms, blast all not in herd ‭ With your abhorr'd heads; who, because cashier'd ‭ By men for monsters, think men monsters all, ‭ That are not of your pied Hood and your Hall, ‭ When you are nothing but the scum of things, ‭ And must be cast off; drones, that have no stings; ‭ Nor any more soul than a stone hath wings? ‭ Avaunt, ye hags! Your hates and scandals are ‭ The crowns and comforts of a good man's care; ‭ By whose impartial perpendicular, ‭ All is extuberance, and excretion all, ‭ That you your ornaments and glories call. ‭ Your wry mouths censure right! Your blister'd tongues, ‭ That lick but itches! And whose ulcerous lungs ‭ Come up at all things permanent and sound! ‭ O you, like flies in dregs, in humours drown'd! ‭ Your loves, like atoms, lost in gloomy air, ‭ I would not retrieve with a wither'd hair. ‭ Hate, and cast still your stings then, for your kisses ‭ Betray but truth, and your applauds are hisses. ‭ To see our supercilious wizards frown, ‭ Their faces fall'n like fogs, and coming down, ‭ Stinking the sun out, makes me shine the more; ‭ And like a check'd flood bear above the shore, ‭ That their profane opinions fain would set ‭ To what they see not, know not, nor can let. ‭ Yet then our learn'd men with their torrents come, ‭ Roaring from their forc'd hills, all crown'd with foam, ‭ That one not taught like them, should learn to know ‭ Their Greek roots, and from thence the groves that grow, ‭ Casting such rich shades from great Homer's wings, ‭ That first and last command the Muses' springs. ‭ Though he's best scholar, that, through pains and vows ‭ Made his own master only, all things knows. ‭ Nor pleads my poor skill form, or learned place, ‭ But dauntless labour, constant prayer, and grace. ‭ And what's all their skill, but vast varied reading? ‭ As if broad-beaten highways had the leading ‭ To Truth's abstract, and narrow path, and pit; ‭ Found in no walk of airy worldly wit. ‭ And without Truth, all's only sleight of hand, ‭ Or our law-learning in a foreign land, ‭ Embroidery spent on cobwebs, braggart show ‭ Of men that all things learn, and nothing know. ‭ For ostentation humble Truth still flies, ‭ And all confederate fashionists defies. ‭ And as some sharp-brow'd doctor, English born, ‭ In much learn'd Latin idioms can adorn ‭ A verse with rare attractions, yet become ‭ His English Muse like an Arachnean loom, ‭ Wrought spite of Pallas, and therein bewrays ‭ More tongue than truth, begs, and adopts his bays; ‭ So Ostentation, be he never so ‭ Larded with labour to suborn his show, ‭ Shall sooth within him but a bastard soul, ‭ No more heaven heiring than, Earth's son, the mole, ‭ But as in dead calms emptiest smokes arise, ‭ Uncheck'd and free, up straight into the skies; ‭ So drowsy Peace, that in her humour steeps ‭ All she affects, lets such rise while she sleeps. ‭ Many, and most men, have of wealth least store, ‭ But none the gracious shame that fits the poor. ‭ So most learn'd men enough are ignorant, ‭ But few the grace have to confess their want, ‭ Till lives and learnings come concomitant. ‭ Far from men's knowledges their lives'-acts flow; ‭ Vainglorious acts then vain prove all they know. ‭ As night the life-inclining stars best shows, ‭ So lives obscure the starriest souls disclose. ‭ For me, let just men judge by what I show ‭ In acts expos'd how much I err or know; ‭ And let not envy make all worse than nought, ‭ With her mere headstrong and quite brainless thought, ‭ Others, for doing nothing, giving all, ‭ And bounding all worth in her bursten gall. ‭ God and my dear_ Redeemer _rescue me ‭ From men's immane and mad impiety, ‭ And by my life and soul (sole known to Them) ‭ Make me of palm, or yew, an anadem. ‭ And so my sole_ God, _the_ Thrice-Sacred-Trine, ‭ _Bear all th' ascription of all me and mine._ ‭Supplico tibi, Domine, Pater, et Dux rationis nostræ, ut nostræ ‭nobilitatis recordemur quâ Tu nos ornasti; et ut Tu nobis præstó sis, ‭ut iis qui per sese moventur; ut et à corporis contagio, ‭brutorumque affectuum, repurgemur, eosque superemus, atque ‭regamus, et, sicut decet, pro instrumentis iis utamur. Deinde, ut ‭nobis adjumento sis, ad accuratam rationis nostræ correctionem, et ‭conjunctionem cum iis qui verè sunt per lucem veritatis. Et ‭tertiùm, Salvatori supplex oro, ut ab oculis animorum nostrorum, ‭caliginem prorsus abstergas, ut norimus bene qui Deus, aut ‭mortalis, habendus. _Amen._ ‭ _Sine honore vivam, nulloque numera ero._ ‭ FINIS End of the Project Gutenberg EBook of The Odysseys of Homer, by Homer ***	{ "redpajama_set_name": "RedPajamaBook" }	9,598
\section{Introduction} \label{sec: Introduction} \textbf{Subject-verb agreement (SVA)} is a phenomenon where the \emph{main subject} agrees in grammatical number with its \emph{associated verb}, oblivious to the presence of any other noun phrase in the sentence. An example is: \begin{enumerate} \item \label{incorr} The \textbf{keys} to the \underline{cabinet} \textbf{is} on the table. \item \label{corr} The \textbf{keys} to the \underline{cabinet} \textbf{are} on the table. \end{enumerate} The main noun and the associated verb are in bold. Intervening nouns are underlined, and denotes a grammatically incorrect sentence. In the above example, the number of the main verb \emph{are} (plural) has to agree with the number of the main subject \emph{keys} (plural). Here, the intervening noun \emph{cabinet} has the opposite number (singular) to that of the main subject. Such intervening nouns are referred to as \textbf{agreement attractors} \cite{bock1991broken}. In natural language sentences, there can be any number of intervening nouns behaving as either agreement attractors or non-attractors (nouns with the same number as the main noun). Previous work \cite{linzen2016assessing, marvin2018targeted, mccoy2018revisiting, kuncoro2019scalable, noji-takamura-2020-analysis, hao2020attribution} assessing the ability of RNN Language Models (LMs) to capture syntax-sensitive dependencies via SVA tasks has found that they often do quite well, despite lacking explicit tree structure. However, it is still not clear if good performance on such tasks is necessarily a result of the RNN's ability to capture the underlying syntax, and this is the question we seek to further investigate here. For a given learning task, there may be multiple hypotheses predictive of the training set labels; the learning model's \emph{inductive bias} can play a key role in selecting one hypothesis over another. To account for the varying inductive biases that different RNN models might encode, we look at multiple architectures -- LSTM, GRU, ONLSTM, and Decay RNN (\S \ref{sec: Architectures}). \citet{mccoy2020does,mccoy2018revisiting} showed that hierarchical bias in the models, as well as the inputs, helps to generalize to unseen sentences. On the other hand, \citet{chaves-2020-dont} and \citet{sennhauser2018evaluating} provide evidence that LSTM models are more likely to learn surface-level heuristics, such as agreeing with the most recent noun, than the underlying grammar. Following \citet{mccoy2018revisiting} who show that training on syntactically rich sentences with agreement information increases the probability of good syntactic generalization, we experiment with training RNN models on sentences with at least one attractor -- \emph{Selective Sampling} (Figure \ref{fig:dataset}). Thus, the sentences in the selectively chosen dataset are syntactically richer than naturally sampled sentences, and can hopefully impart additional hierarchical cues which prevent models from relying on simple linear heuristics. We test the hypothesis that if these models were to capture the correct grammatical structure from syntactically rich input, then they would generalize well out-of-distribution (OOD), {\em i.e.}, when tested on sentences without attractors having been trained solely on sentences with at least one attractor. Since human learners are known to have frequent access to simple structures, our learning setup itself is not realistic for human language acquisition; but the aim is to see whether it can push RNN models towards more human-like syntactic generalisation. In addition to the examining the accuracies of these models on natural language sentences, we perform a Representation Similarity Analysis (RSA) in \S \ref{Analysis of representations}, and find that their inductive biases appear to be overridden by the training distribution, extending the findings of \citet{mccoy2020does}. To evaluate the effect of the choice of training data on the ability to capture SVA on a variety of syntactic constructions, we perform Targeted Syntactic Evaluation (TSE) as proposed by \citet{marvin2018targeted}, along with surprisal analysis (\S \ref{Targeted Syntactic Evaluation},\ref{Surprisal}). We find that training on selectively sampled `hard' instances improves the model's performance on difficult constructions (sentences with clauses between the main noun and the main verb), but degrades their performance on simpler constructions. Our analysis indicates that even when RNNs are able to capture non-trivial dependency patterns, they fail to perform well on easier dependency relations (instances without agreement attractors). This suggests that RNNs tend to efficiently learn surface-level heuristics from the training distribution rather than gleaning the actual syntactic rules. Our major outcomes are the following: \begin{itemize} \item We show that despite providing strong hierarchical cues via a selectively sampled training set (Figure \ref{fig:dataset}), RNNs, including the ONLSTM (which has a soft hierarchical inductive bias), do not generalize to an unseen configuration of intervening nouns. \item We observe that training data effectively override the model's structural bias, as our model representations clearly cluster by the type of training distribution. (Figure \ref{fig:RSA}). \item We verify that our findings are consistent across multiple learning paradigms, self-supervised language modeling and supervised grammaticality judgment, as well as varied test sets, natural and constructed (Tables \ref{tab:nat}, \ref{att}). \end{itemize} \begin{figure}[h!] \centering \includegraphics[scale=0.5]{dataset_description.png} \caption{Dataset description. As structure-insensitive RNN models suffer from agreement attraction errors, our \textit{selectively sampled} dataset is syntactically challenging for such sequential models, for whom surface-level heuristics such as `agree with recent noun' are efficiently available. Hence, training RNNs on such datasets might induce them to capture hierarchical relations rather than learning shallower heuristics.} \label{fig:dataset} \end{figure} \section{Related Work} \label{sec: Related Work} Prior work by \citet{linzen2016assessing, gulordava2018colorless, marvin2018targeted, tran-etal-2018-importance} have shown that language models RNNs can capture hierarchical information from natural language to solve SVA tasks. However, it is still not clear if the models are necessarily capturing underlying syntactic rules to make a good prediction. \citet{mccoy2018revisiting} conclude that GRU with attention generalizes hierarchically despite the absence of hierarchical inductive bias on question formation task. Additionally, they find that training on agreement language helps in inducing syntactic bias. However, they could not conclude what these RNNs capture which gives rise to non-trivial performance. A subsequent study by \citet{mccoy2020does} shows that hierarchical generalization is only plausible by providing explicit hierarchical inputs (annotated parse information) to the model having an explicit hierarchical inductive bias (tree-based models). Similar observations have been made by \citet{kuncoro-etal-2018-lstms} and \citet{wilcox2020structural}, suggesting that structural supervision improves syntactic generalization in neural language models. In this work, we analyze if exposure to `hard' agreement instances, which cannot be modelled by inferring readily-available heuristics, can help RNNs to improve their syntactic abilities. \citet{van-schijndel-etal-2019-quantity} showed that neural LMs lag far behind humans on Targeted Syntactic Evaluation (TSE), even when trained with a large corpus and increased model capacity. However, by virtue of high variance in the performance of LMs on TSE across different random seeds and hyperparameter tuning, \citet{kuncoro2019scalable} achieved better accuracy in the same setting. \citet{noji-takamura-2020-analysis} and \citet{kuncoro2019scalable} came up with methodologies to improve performance on TSE, via contrastive learning and knowledge distillation from models with explicit grammar induction \cite{dyer2016recurrent} respectively. It has been observed that these models have trouble capturing agreement in sentences with center embeddings, especially agreement across object relative clauses (RCs) \cite{noji-takamura-2020-analysis, mueller-etal-2020-cross}. In our work, we show that syntactically rich training sentences can also improve performance on such instances substantially (Table \ref{TSE table}, Appendix Table 5). Studies on linguistic phenomena such as filler-gap dependencies \cite{chaves-2020-dont} and assessing the ability of LSTMs to capture the rules of context-free grammars \cite{sennhauser2018evaluating} argue that LSTMs learn shallower heuristics from the dataset rather than acquiring the underlying linguistic rules. In this work, we show that even a model with implicit hierarchical inductive bias (the ONLSTM) is behaviourally close to a vanilla LSTM in terms of the learned representations, for both supervised and self-supervised learning settings. \section{Architectures} \label{sec: Architectures} In this work, we conduct our experiments on four recurrent schemes -- LSTM \cite{hochreiter1997long}, GRU \cite{cho-etal-2014-learning}, Decay RNN (DRNN) \cite{bhatt-etal-2020-much}, and ONLSTM \cite{shen2018ordered}. The governing equations of these architectures are mentioned in Appendix \S A.1. The ONLSTM, unlike the other models under consideration, is a recurrent network with soft hierarchical inductive bias. The DRNN is a recurrent network without any gating mechanism that imposes biologically-inspired constraints on the neurons. Amongst all these RNN types, the DRNN is the least complex, and has been shown to outperform vanilla RNNs and perform on par with other gated networks on grammaticality judgment tasks \cite{bhatt-etal-2020-much}. \begin{table}[ht] \centering \resizebox{\linewidth}{!}{% \begin{tabular}{l \| r \| r} \textbf{Property} & Natural & Selective \\ \hline Training sentences~ & 97842 & 97842 \\ Ratio of Singular to Plural main nouns & 67\% & 45\% \\ Ratio of Singular to Plural nouns (total) & 79\% & 71\% \\ Fraction of 0 attractors & 93\% & - \\ Fraction of 1 attractors & 5.6\% & 79\% \\ Fraction of 2 attractors & 1.1\% & 15\% \\ Fraction of 3 attractors & 0.3\% & 3.7\% \\ \hline \hline Testing Sentences & 157k & 157k \end{tabular}} \caption{Data statistics.} \label{appen table: data analysis} \end{table} \section{Dataset} \label{sec: Dataset} We use sentences from the Wikipedia corpus made available by \citet{linzen2016assessing}. For training, we further choose two subsets from the main dataset, based on the number of attractors in each sentence (Figure \ref{fig:dataset}). The sentences without any attractor are grammatically simple and allow for out-of-distribution testing as they are not seen while training on the selectively sampled dataset. We train our models for two objectives: language modeling and binary classification for grammaticality judgment (\S \ref{Experiments}). For uniform comparison, we keep the testing set identical across the subsets of the training data. The testing set contains $157$k sentences for both the binary classifier and the LM. Table \ref{appen table: data analysis} contains a quantitative description of the datasets. To perform well on the selectively sampled dataset, models cannot resort to learning simple linear heuristics such as associating the main verb with the preceding noun rather than the main noun. However, such heuristics are encouraged by a naturally sampled dataset due to a heavy skew towards sentences without attractors (Table \ref{appen table: data analysis}). The tendency to capture these shallow patterns would allow models to correctly predict the verb number in most instances, but for the wrong reasons. For the binary classifier, we augment each sentence with its corresponding counterfactual example. Augmenting with counterfactual examples has been shown to be effective in reducing the tendency of the models to capture spurious correlations (for sentiment analysis) by \citet{Kaushik2020Learning}. Consider the example from \S \ref{sec: Introduction}: \begin{enumerate} \item \label{corr} The \textbf{keys} to the \underline{cabinet} \textbf{are} on the table. \item \label{incorr} The \textbf{keys} to the \underline{cabinet} \textbf{is} on the table. \end{enumerate} Sentence \ref{incorr} is the counterfactual example for the sentence \ref{corr}. Thus our dataset will consist of pairs of a sentence and its corresponding counterfactual sentence. Additionally, we test our models on an artificially constructed corpus with a different distribution of sentence types than the training set. As proposed by \citet{marvin2018targeted}, this helps in evaluating if the models have mastered syntax across different syntactic constructions (\S \ref{Targeted Syntactic Evaluation}). \section{Experiments} \label{Experiments} We focus on evaluating the models' ability to make number agreement judgments when trained for classification (supervised) and language modeling (self-supervised). For each task, we train models (with 5 different random seeds) on both training subsets from the corpus.\footnote{Code will be made available as part of the camera-ready version.} Training settings for our experiments are mentioned in Appendix \S A.2. Consider the sentences from the introduction. A classifier is expected to label sentence \ref{incorr} as ungrammatical and sentence \ref{corr} as grammatical. For grammaticality judgment via a language model (LM), we train on a standard LM objective and during inference, check if our model gives a higher probability to the grammatically correct verb form conditioned on previous tokens in the sentence. \begin{table}[ht] \centering \resizebox{\linewidth}{!}{% \begin{tabular}{l \| c c c c\| c c c c} Training set & \multicolumn{4}{c\|}{Natural Sampling} & \multicolumn{4}{c}{Selective Sampling} \\ \hline Test attractors & 0 & 1 & 2 & 3 & 0 & 1 & 2 & 3 \\ \hline & \multicolumn{8}{c}{LANGUAGE MODEL} \\ \hline LSTM & \textbf{0.98} & 0.91 & 0.84 & 0.78 & 0.89 & \textbf{0.98} & \textbf{0.98} & 0.95 \\ ONLSTM &\textbf{ 0.98} & 0.92 & 0.86& 0.82& 0.90 & \textbf{0.98} & \textbf{0.98} & 0.95 \\ GRU & \textbf{0.97} & 0.88& 0.78 & 0.73& 0.87 & \textbf{0.98} & 0.97 & 0.94 \\ DRNN & \textbf{0.96} & 0.69 & 0.47 & 0.36 & 0.83 & \textbf{0.97} & 0.94 & 0.91 \\ \hline & \multicolumn{8}{c}{BINARY CLASSIFIER} \\ \hline LSTM &\textbf{ 0.97} & 0.93 & 0.87& 0.82& 0.60& \textbf{0.98} & 0.96 & 0.97 \\ ONLSTM &\textbf{ 0.97} & 0.91 & 0.84 & 0.81 & 0.64 & \textbf{0.98} & 0.97 & \textbf{0.98} \\ GRU &\textbf{ 0.97} & 0.88 & 0.76 & 0.69 & 0.62 & 0.95 & 0.94& \textbf{0.96} \\ DRNN & \textbf{0.97 }& 0.90& 0.81 & 0.77& 0.70 &\textbf{ 0.97 }& 0.96 & 0.96 \\ \hline \end{tabular}} \caption{Accuracy of RNN architectures trained as LMs and classifiers, for test instances with an increasing number of attractors between main subject and verb; variances mentioned in Appendix Table 3. The maximum accuracy for each model and training setup across attractor counts is in bold. Note that the models trained on the selectively sampled dataset are not able to generalize well OOD (sentences without attractors).} \label{tab:nat} \end{table} \subsection{Performance on Natural Sentences} \label{Performance on Natural Sentences} Table \ref{tab:nat} shows the main results for the described experiments. For the models trained on a naturally sampled dataset, the performance degrades quite quickly with an increasing number of attractors between the subject and the corresponding verb, for both the LM and the classifier versions. However, the reduction in the accuracy with increasing attractor count for the models trained on the selectively sampled dataset is much less than with the natural sampling training. For the selectively sampled dataset, the sentences without attractors serve as OOD sentences, and the performance boost on \emph{in-distribution} complex sentences comes at the cost of a reduction in the accuracy of the OOD yet relatively simple sentences. The error rate for the ONLSTM, a model with inherent tree bias, also increases when tested on the OOD sentences, and when trained for a classification objective it performs worse than the architecturally simpler Decay RNN. This fall-off on grammatically simpler OOD samples seems counter-intuitive. We note that the increase in error rates is much greater when training the models as classifiers rather than LMs. This shows that models with supervised training for grammaticality on syntactically rich and counterfactually augmented data are still unable to capture the actual syntactic rules and appear to be learning shallower heuristics, but ones that capture more nuanced patterns than simply going by linear distance. We can infer this because while our selectively sampled subset contains sentences with at least one attractor, many (over 30\%) of the intervening nouns in these sentences are non-attractors. Hence there are sentences in which a non-attractor noun (same number as the main subject) immediately precedes the verb rather than an attractor noun. Therefore, the agreement performance (on sentences with attractors) of the models trained on this dataset cannot arise from an overly simple heuristic like disagreeing with the most recent noun, and the observed decline in OOD performance implies that less trivial heuristics are being learned which nevertheless fail to capture the actual syntax. \subsection{Analysis of representations} \label{Analysis of representations} To analyze the differences in the learned internal representations among the models trained on the two subsets of the data, we perform a representation similarity analysis (RSA) \cite{laakso2000content}. We take 2000 sentences selected randomly from the test set. As we had trained each model on five different random seeds, we compare 40 models (20 for each subset) across different learning objectives. Our major observation from Figure \ref{fig:RSA} is that the representations of models trained on different subsets are easily linearly separable in this space, for both the LM and the classifier objectives. This implies that the representation clustering is not so much based on model architecture or inductive bias, but is overridden by the training data. Additionally, we observe that the learned representations of the ONLSTM and LSTM are not well separable, neither for the LM nor for the classifier across training configurations. This shows that despite having a soft hierarchical inductive bias, the ONLSTM appears similar to the regular LSTM in terms of patterns captured at the representational level. Moreover, the learned representations for GRU and LSTM are well separable This differentiates the two architectures, which are often used interchangeably on the representation level, and such differences may be arising due to the squashing phenomena in GRUs pointed out by \citet{mccoy2020does}. For the binary classifier (Figure \ref{BC RSA}), although we observe a little variance in the accuracy on the test set across the different seeds, the variance (spread of the points) in the projected space is substantial when compared to that of the LM. Quantitative analysis of the variance is available in Appendix \S A.5. This might be due to the existence of multiple valleys in the loss landscape for the binary classification objective, and we posit that an LM objective is more reliable when comparing the ability to capture the syntax sensitive dependencies in RNNs. In the following sections, we shall further analyze the performance of models trained with LM objective in greater detail. \begin{figure}[h!] \centering \centering \begin{subfigure}[b]{\linewidth} \includegraphics[width=\textwidth]{RSA_BC_1.png} \caption{Binary classifier} \label{BC RSA} \end{subfigure} \hfill \begin{subfigure}[b]{\linewidth} \includegraphics[width=\textwidth]{RSA_LM_1.png} \caption{Language Model} \label{LM RSA} \end{subfigure} \caption{Representation similarity analysis of the hidden units of different RNN models (5 different seeds for each model). We observe that for both the learning objectives, one can partition the 2D space using a line that separates models trained on the two subsets of the data, natural and selective sampling.} \label{fig:RSA} \end{figure} \begin{table}[ht] \centering \resizebox{1\textwidth}{!}{% \begin{tabular}{l\|l\|c c\|c c\|c c\|c c} Subject Verb Agreement & \#sentences & \multicolumn{2}{c\|}{LSTM} & \multicolumn{2}{c\|}{ONLSTM} & \multicolumn{2}{c\|}{GRU} & \multicolumn{2}{c}{DRNN} \\ \hline Condition & & \multicolumn{1}{c\|}{Natural} & \multicolumn{1}{c\|}{Selective} & \multicolumn{1}{c\|}{Natural} & \multicolumn{1}{c\|}{Selective} & \multicolumn{1}{c\|}{Natural} & \multicolumn{1}{c\|}{Selective} & \multicolumn{1}{c\|}{Natural} & \multicolumn{1}{c}{Selective} \\ \hline Simple & 312 & \textbf{0.99} ($\pm$0.01) & 0.86 ($\pm$0.01) & \textbf{0.98} ($\pm$0.02) & 0.86 ($\pm$0.01) & \textbf{0.98} ($\pm$0.01) & 0.84 ($\pm$0.04) & \textbf{0.97} ($\pm$0.02) & 0.79 ($\pm$0.05) \\ Short VP & 3432 & \textbf{0.85} ($\pm$0.02) & 0.71 ($\pm$0.06) & \textbf{0.88} ($\pm$0.02) & 0.73 ($\pm$0.08) & \textbf{0.81} ($\pm$0.03) & 0.69 ($\pm$0.04) & \textbf{0.70} ($\pm$0.05) & 0.66 ($\pm$0.04) \\ Within ORC (A) & 9984 & \textbf{0.79} ($\pm$0.06) & 0.63 ($\pm$0.05) & \textbf{0.78} ($\pm$0.10) & 0.59 ($\pm$0.06) & \textbf{0.75} ($\pm$0.02) & 0.50 ($\pm$0.02) & \textbf{0.7} ($\pm$0.08) & 0.46 ($\pm$0.04) \\ Within ORC (IA) & 4032 & \textbf{0.77} ($\pm$0.06) & 0.64 ($\pm$0.06) & \textbf{0.75} ($\pm$0.08) & 0.59 ($\pm$0.04) & \textbf{0.73} ($\pm$0.02) & 0.50 ($\pm$0.03) & \textbf{0.69} ($\pm$0.06) & 0.46 ($\pm$0.05) \\ Within no that ORC (A) & 9984 & \textbf{0.73} ($\pm$0.06) & 0.61 ($\pm$0.05) & \textbf{0.72} ($\pm$0.08) & 0.57 ($\pm$0.07) & \textbf{0.72} ($\pm$0.03) & 0.47 ($\pm$0.04) & \textbf{0.63} ($\pm$0.04) & 0.45 ($\pm$0.06) \\ Within no that ORC (IA) & 4032 & \textbf{0.66} ($\pm$0.04) & 0.61 ($\pm$0.05) & \textbf{0.66} ($\pm$0.06) & 0.56 ($\pm$0.06) & \textbf{0.62} ($\pm$0.04) & 0.47 ($\pm$0.04) & \textbf{0.68} ($\pm$0.06) & 0.45 ($\pm$0.06) \\ Long VP & 520 & 0.65 ($\pm$0.03) & \textbf{0.69} ($\pm$0.07) & \textbf{0.67} ($\pm$0.04) & \textbf{0.67} ($\pm$0.06) & 0.63 ($\pm$0.04) & \textbf{0.65} ($\pm$0.04) & 0.56 ($\pm$0.05) & \textbf{0.65} ($\pm$0.03) \\ Across Prep Phrase (A) & 29952 & 0.86 ($\pm$0.04) & \textbf{0.89} ($\pm$0.03) & \textbf{0.88} ($\pm$0.03) & \textbf{0.88} ($\pm$0.01) & 0.81 ($\pm$0.02) & \textbf{0.88} ($\pm$0.02) & 0.68 ($\pm$0.04) & \textbf{0.83} ($\pm$0.01) \\ Across Prep Phrase (IA) & 4032 & 0.87 ($\pm$0.03) & \textbf{0.94} ($\pm$0.02) & 0.88 ($\pm$0.02) & \textbf{0.95} ($\pm$0.01) & 0.86 ($\pm$0.02) & \textbf{0.94} ($\pm$0.01) & 0.69 ($\pm$0.06) & \textbf{0.91} ($\pm$0.02) \\ Across SRC & 9984 & 0.81 ($\pm$0.03) & \textbf{0.89} ($\pm$0.05) & 0.81 ($\pm$0.05) & \textbf{0.87} ($\pm$0.02) & 0.77 ($\pm$0.05) & \textbf{0.86} ($\pm$0.05) & 0.58 ($\pm$0.04) & \textbf{0.80} ($\pm$0.05) \\ Across ORC (A) & 9984 & 0.73 ($\pm$0.10) & \textbf{0.82} ($\pm$0.07) & 0.78 ($\pm$0.07) & \textbf{0.84} ($\pm$0.02) & 0.72 ($\pm$0.06) & \textbf{0.79} ($\pm$0.05) & 0.63 ($\pm$0.04) & \textbf{0.78} ($\pm$0.05) \\ Across ORC (IA) & 4032 & 0.74 ($\pm$0.09) & \textbf{0.84} ($\pm$0.10) & 0.81 ($\pm$0.07) & \textbf{0.87} ($\pm$0.02) & 0.74 ($\pm$0.08) & \textbf{0.85} ($\pm$0.05) & 0.65 ($\pm$0.07) & \textbf{0.86} ($\pm$0.02) \\ Across no that ORC (A) & 9984 & 0.61 ($\pm$0.04) & \textbf{0.72} ($\pm$0.08) & 0.62 ($\pm$0.05) & \textbf{0.78} ($\pm$0.02) & 0.60 ($\pm$0.02) & \textbf{0.68} ($\pm$0.06) & 0.64 ($\pm$0.03) & \textbf{0.73} ($\pm$0.02) \\ Across no that ORC (IA) & 4032 & 0.66 ($\pm$0.04) & \textbf{0.77} ($\pm$0.11) & 0.66 ($\pm$0.06) & \textbf{0.84} ($\pm$0.03) & 0.62 ($\pm$0.04) & \textbf{0.72} ($\pm$0.07) & 0.68 ($\pm$0.06) & \textbf{0.83} ($\pm$0.02) \\ \hline Average Performance & 104296 & 0.78 ($\pm$0.03) & 0.78 ($\pm$0.02) & 0.79 ($\pm$0.03) & 0.78 ($\pm$0.01) & 0.75 ($\pm$0.01) & 0.73 ($\pm$0.02) & 0.66 ($\pm$0.02) & 0.71 ($\pm$0.02) \\ \hline \end{tabular}} \caption{Accuracy of models on targeted syntactic evaluation. Quantities in bold marks the maximum accuracy for each model across the configuration. ORC: Objective Relative Clause, SRC: Subject Relative Clause, Prep Phrase: Prepositional Phrase, VP: Verb Phrase. A/IA in the parenthesis represents an animate/inanimate main subject. Models trained on selectively sampled subset perform well on the difficult sentences, but not on the simpler ones.} \label{TSE table} \end{table} \subsection{Targeted Syntactic Evaluation (TSE)} \label{Targeted Syntactic Evaluation} We test how training the language models on the strategically chosen inputs impacts generalisation to different syntactic constructions. Testing on such examples lets us evaluate if our models are capturing what we intend them to capture. As the subjects can be separated from their verb by long clauses, SVA requires models to capture robust hierarchical representations. The models capturing surface level regularities of the data would not be able to perform well on these constructed examples. Sentence \ref{ORC} corresponds to the agreement across an object relative clause, while the sentence \ref{SRC} corresponds to the agreement across a subject relative clause. \begin{enumerate} \item \label{ORC} The \textbf{authors} that the \underline{chef} likes \textbf{laugh}. \item \label{SRC} The \textbf{authors} that like the \underline{chef} \textbf{laugh}. \end{enumerate} Table \ref{TSE table} mentions the results of TSE on the LM. For each model, we observe that as the difficulty of the sentences increases, models trained on the selectively sampled dataset starts surpassing those trained on the natural dataset. Difficult sentences involve number agreement across the prepositional phrase and subject/object relative clauses. However, this improvement in the performance came at a cost where their performance on simple sentences, having agreement across short verb phrases and agreement within object relative clauses, decreases. Such sentences do not have any intervening noun between the subject and the corresponding verb. Table \ref{att} presents the performance of the LMs on the synthetic data, for sentences with 0 or 1 agreement attractors. These findings corroborate our observations on natural language sentences -- the models trained on the selectively sampled dataset performed worse on sentences without attractors which are syntactically simpler. As supplementary results, we present a comparison of the LSTM LM trained on the selectively sampled subset with the techniques presented by \citet{kuncoro2019scalable} in Appendix Table 5. \begin{table}[ht] \resizebox{\linewidth}{!}{% \begin{tabular}{l\|c\|c\|c\|c} Training set & \multicolumn{2}{c\|}{ Natural} & \multicolumn{2}{c}{ Selective} \\ \hline Test attractors & 0 & 1 & 0 & 1 \\ \hline LSTM & \textbf{0.77} {($\pm$ 0.05)} & 0.66 ($\pm$ 0.04) & 0.63 ($\pm$ 0.04) & \textbf{0.83} {($\pm$ 0.06)} \\ ONLSTM & \textbf{0.76} {($\pm$ 0.07)} & 0.70 ($\pm$ 0.06) & 0.60 ($\pm$ 0.05) & \textbf{0.85} {($\pm$ 0.01)} \\ GRU & \textbf{0.74} {($\pm$ 0.02)} & 0.64 ($\pm$ 0.02) & 0.51 ($\pm$ 0.02) & \textbf{0.81} {($\pm$ 0.04)} \\ DRNN & \textbf{0.67} {($\pm$ 0.04)} & 0.44 ($\pm$ 0.04) & 0.48 ($\pm$ 0.04) & \textbf{0.79} {($\pm$ 0.03)} \\ \bottomrule \end{tabular}} \caption{Accuracy of LMs on test instances with 0 or 1 attractors from the artificial corpus. Models trained on the selectively sampled subset do not generalize well on OOD sentences without attractors.} \label{att} \end{table} \subsubsection{Fine-Grained Analysis} \label{Fine-Grained Analysis} To assess the performance of the models trained on the selectively sampled dataset, we take a closer look at constructed sentences that are structurally similar to in-distribution sentences but contain non-attractor intervening nouns rather than agreement attractors. Figure \ref{fig:FGA} depicts the performance of the LSTM LM on three agreement conditions -- across Object RC, Preposition Phrase, and Subject RC, each with an animate main noun. For sentences with two nouns, we have four possibilities corresponding to their combination of grammatical numbers. Consider the following examples for the sentences with object relative clause across the main noun and its verb ($\ast$ marks the incorrect verb). \begin{enumerate} \item \label{SS} (SS) The \textbf{author} that the \underline{minister} likes laughs/laugh. \item \label{SP} (SP) The \textbf{author} that the \underline{ministers} like laughs/laugh. \item \label{PS} (PS) The \textbf{authors} that the \underline{minister} likes laugh/laughs. \item \label{PP} (PP) The \textbf{authors} that the \underline{ministers} like laugh/laughs. \end{enumerate} Here SS denotes sentences having singular main noun and a singular embedded subject, and likewise for other cases. We observe that with our selective training, the performance on sentences with non-attractor intervening nouns (the SS/PP configurations, which are unobserved in the selectively sampled dataset) worsens for 2 out of 3 syntactic constructions -- across Preposition Phrase and Subject RC. This pattern highlights that the reduction in the performance on simple sentences may not be completely attributed to their difference in syntactic structure from training distribution. \begin{figure}[h!] \centering \begin{subfigure}[b]{\linewidth} \includegraphics[width=\textwidth]{K=-1.png} \caption{Accuracy: LSTM trained on naturally sampled subset} \label{FGA_a} \end{subfigure} \hfill \begin{subfigure}[b]{\linewidth} \includegraphics[width=\textwidth]{K=0.png} \caption{Accuracy: LSTM trained on selectively sampled subset} \label{FGA_b} \end{subfigure} \caption{Fine-grained analysis of the LSTM LM on Obj/Subj Relative Clauses and Preposition Phrases, demarcated by the inflections of the main subject and the embedded subject. P: Plural, S: Singular; thus SS denotes sentences with a singular main noun and a singular embedded subject, and likewise for the other cases.} \label{fig:FGA} \end{figure} For all the cases under consideration presented in Figure \ref{FGA_a}, the performance of the LSTM LM is worst when the main noun is singular with the plural embedded subject (SP case). This indicates that plural attractors have a stronger attraction effect than singular attractors. Note that the naturally sampled dataset has more plural attractors while the selectively sampled one has an almost equal balance of plural and singular attractors (Table \ref{appen table: data analysis}). Thus, our findings are not due to a lack of plural attractors seen during the training phase. For completeness, we report the fine-grained analysis accuracies for all the models under consideration in the supplementary material (Tables 6, 7, and 8). \subsection{How confident are RNN language models?} \label{Surprisal} From the previous experiments, it is not clear how confident neural LMs are while making predictions about the number of the upcoming verb given the context till that verb. Surprisal at a given word is defined as $-\log p(x_n \ \| \ x_{[1:n-1]})$, where $x_n$ represents the $n^{th}$ token in the sentence and $x_{[1:n-1]}$ represents the sequence of preceding tokens. We define \emph{prediction confidence} as the difference in surprisal values at the verb location between the incorrect verb and the correct verb; higher values correspond to more confident correct predictions. In this section we compare the performance of models trained on the two subsets in terms of their average prediction confidence at the verb position, evaluated on 16k simple sentences from the natural corpus (testing set) of the following form: \begin{center} The $<$Subject$>$ $<$Verb$>...$ \end{center} Note that this amounts to evaluation on sentences involving agreement without attractors. Table \ref{surp} shows the average prediction confidence and the average ratio of predicted probabilities for the grammatical verb and the ungrammatical verb. We can see that the average probability ratio of the grammatically correct verb to the incorrect verb is much lower for the models trained on the selectively sampled subset than those trained on the naturally sampled subset. Thus, in addition to the difference between the accuracies of LMs trained on the two subsets being close to 10\% on sentences with no attractors (Table \ref{tab:nat}), models trained with selective sampling are also less confident, even when they predict correctly. Moreover, we see that the ONLSTM suffers as big a drop in prediction confidence as the regular LSTM when trained on this selectively sampled dataset, despite the former having a hierarchical inductive bias which we might have hoped would help it capture the correct syntax. \begin{table}[ht] \centering \resizebox{0.8\linewidth}{!}{% \begin{tabular}{l\|c \|c\|c\| c} \multicolumn{1}{c\|}{Training set} & \multicolumn{1}{c\|}{Natural} & \multicolumn{1}{c\|}{Selective} & \multicolumn{1}{c\|}{Natural} & \multicolumn{1}{c}{Selective} \\ \hline Test metric & \multicolumn{2}{c\|}{Prediction Confidence} & \multicolumn{2}{c}{ $\frac{P(grammatical)}{P(ungrammatical)}$} \\ \hline LSTM & \textbf{5.72} & 2.56 & \textbf{303.91} & 12.90 \\ ONLSTM & \textbf{5.80} & 2.64 & \textbf{331.83} & 14.08 \\ GRU & \textbf{5.13} & 2.40 & \textbf{169.28} & 11.02 \\ DRNN & \textbf{5.15} & 2.38 & \textbf{172.78} & 10.77 \\ \end{tabular}} \caption{Average prediction confidence and correct-to-incorrect probability ratio for agreement without attractors. Models trained on the selectively sampled dataset have lower confidence on non-attractor sentences than those trained on the natural dataset.} \label{surp} \end{table} \subsection{Can fine-tuning help?} \label{Can finetuning help?} Fine-tuning has been shown to be an effective strategy to improve the syntactic robustness of RNNs. \citet{lepori-etal-2020-representations} fine-tuned their model on a small number of synthetic sentences which could not solved using word co-occurrence statistics. This eventually helped in decreasing their model's error on the number agreement task. We assess if a similar technique could improve the syntactic generalization ability of the models trained on the selectively sampled dataset. We fine-tune our LMs with artificially generated sentences following the rules of context-free grammar. We notice that our model's error rates did not decrease on sentences without attractor with fine-tuning. This observation may be the result of catastrophic forgetting during the fine-tuning phase \cite{jiang-etal-2020-smart, aghajanyan2020better, McCloskey1989}. Another possibility is that the RNNs have not been able to learn underlying syntactic rules from the given training distribution. Recent information-theoretic analysis by \citet{lovering2021informationtheoretic} points out that fine-tuning might not uncover new features that are not already captured during the pre-training phase. This suggests that training on `hard' instances might not have led the RNNs to capture dependency patterns at the level of syntax. See Appendix \S A.6 for fine-tuning results. \section{Discussion and Conclusion} \label{Discussion} In this work, we analyzed the effects of a strategically chosen training set with exclusively `hard' agreement instances, on neural language models and binary classifiers for grammaticality judgment. We observed that the models' inability to perform well on out of distribution (OOD) sentences, even those which would seem to be `easy' agreement instances, is consistent across variation in learning mechanism (supervised or self-supervised), innate architectural bias, and testing set -- natural or artificial sentences. Our analysis showed that the error rates of models trained on sentences with at least one agreement attractor are higher on sentences with no attractors than on sentences with attractors, for both corpus sentences (Table \ref{tab:nat}) and artificial sentences (Table \ref{att}). This observation is counter-intuitive because the models were trained on syntactically rich sentences and yet failed to perform well on simpler sentences. Had our RNN models picked up the correct grammatical rules, we would not expect this behavior. We obtained a similar counter-intuitive result for targeted syntactic evaluation (Table \ref{TSE table}), where models trained on the selectively sampled dataset performed much better on difficult constructed sentences involving agreement across nested dependencies than on simpler sentences involving agreement within nested dependencies. Our analysis of representations suggested that training set bias dominates over the model's architectural features or inductive bias in shaping representation learning; {\em e.g.}, there was no discernible difference between the learned representations of the ONLSTM and LSTM models. The reasons for this merit further exploration. Moreover, for the binary classifiers (Figure \ref{BC RSA}), although we observe little variance in test accuracy across different training seeds, the variance in the projected representation space is substantially greater than for LMs. Thus, we posit that an LM objective is more reliable when comparing the ability of different RNN models to capture syntax-sensitive dependencies. Additionally, multi-task learning may improve language modeling by predicting the CCG supertags of each word \cite{marvin2018targeted}, or by incorporating a contrastive loss term in the objective \cite{noji-takamura-2020-analysis}. We observed that the hierarchical inductive bias in the ONLSTM is not sufficient to perform well on OOD sentences. \citet{mccoy2020does} argued that an architecture with explicit tree bias, plus syntactically annotated inputs, are needed to capture syntax for sequence-to-sequence tasks. Here we show that the ONLSTM (soft tree bias) trained on a syntactically rich dataset (soft structural information) turns out to be insufficient to generalize well to OOD sentences and capture the underlying grammar. Our targeted syntactic evaluation pinpoints the cases which our models fail to capture, and improving performance on such cases is a key future direction. Our observations suggest that RNNs, being fundamentally statistical models, can efficiently capture the correlation of the output variable with the input as observed during training (even for relatively `hard' or non-linear linguistic dependencies) without necessarily learning the underlying hierarchical structure. This is consistent with the conclusions of \citet{sennhauser2018evaluating} and \citet{chaves-2020-dont}. Thus, we need to be cautious in inferring the ability of such models to capture syntax-sensitive dependencies. Performance on any particular kind of construction might always reflect some overfitting to it, even if it is syntactically rich or complex. Although we have here focused on training solely on hard instances as a means of hierarchical cueing, identifying the best mix of simpler and more complex sentences that a model should be exposed to for optimal generalisation performance across a variety of syntactic constructions remains a direction for future work. Broad-based testing on instances of diverse types and complexity levels is essential to the development of models that better capture the structure of human language in all its richness and variety. \bibliographystyle{acl_natbib}	{ "redpajama_set_name": "RedPajamaArXiv" }	316

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